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ADS astronomy entries on 2022-09-14
=author:"Low, B.C." OR =author:"Low, Boon Chye"
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Title: Chapter 6 - Coronal Magnetism as a Universal Phenomenon
Authors: Low, B. C.
2019sgsp.book..207L Altcode:
In the 60 years after E. N. Parker's prediction of the existence
of the solar wind and the magnetic origin of coronal heating,
space-borne and ground-based observations have built a conceptually
complete phenomenology of the corona as a fully ionized hydromagnetic
atmosphere responding in step to the global magnetic reversals of
the Sun in 11-year cycles. This phenomenology is reviewed with the
theoretical ideas it motivated, describing the photospheric emergence
of new-cycle magnetic fluxes of a reversed polarity into the corona,
ubiquitous coronal heating, hydromagnetic self-organization, explosive
energy release, and the breaking of self-confinement into flows of
expansion winds and episodic ejections of magnetic structures. High
electrical and thermal conductivities at coronal million-degree
temperatures have central roles. The corona obeys a hemispherical rule
independent of magnetic cycle, that self-organized structures have a
statistical preference for left- and right-handed magnetic twists,
respectively, in the northern and southern hemispheres relative to
the rotational axis. It is pointed out, perhaps for the first time,
that this hemispherical rule is a hydromagnetic implication of the
Parker (1955a,b) dynamo, straightforward to deduce graphically from
his book Cosmical Magnetic Fields (1979). Solar physics has reached
a broad-brush physical understanding of the corona solar-wind system
as the prototype of a universal astrophysical phenomenon.
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Title: Field topologies in ideal and near-ideal magnetohydrodynamics
and vortex dynamics
Authors: Low, B. C.
2015SCPMA..58.5626L Altcode: 2015SCPMA..58a5626L; 2014arXiv1412.6158L
Magnetic field topology frozen in ideal magnetohydrodynamics (MHD)
and its breakage in near-ideal MHD are reviewed in two parts,
clarifying and expanding basic concepts. The first part gives a
physically complete description of the frozen field topology derived
from magnetic flux conservation as the fundamental property, treating
four conceptually related topics: Eulerian and Lagrangian descriptions
of three dimensional (3D) MHD, Chandrasekhar-Kendall and Euler-potential
field representations, magnetic helicity, and inviscid vortex dynamics
as a fluid system in physical contrast to ideal MHD. A corollary of
these developments clarifies the challenge of achieving a high degree
of the frozen-in condition in numerical MHD. The second part treats
field-topology breakage centered around the Parker Magnetostatic Theorem
on a general incompatibility of a continuous magnetic field with the
dual demand of force-free equilibrium and an arbitrarily prescribed,
3D field topology. Preserving field topology as a global constraint
readily results in formation of tangential magnetic discontinuities,
or, equivalently, electric current-sheets of zero thickness. A similar
incompatibility is present in the steady force-thermal balance of a
heated radiating fluid subject to an anisotropic thermal flux conducted
strictly along its frozen-in magnetic field in the low- β limit. In a
weakly resistive fluid the thinning of current sheets by these general
incompatibilities inevitably results in sheet dissipation, resistive
heating and topological changes in the field notwithstanding the small
resistivity. Strong Faraday induction drives but also macroscopically
limits this mode of energy dissipation, trapping or storing free
energy in self-organized ideal-MHD structures. This property of MHD
turbulence captured by the Taylor hypothesis is reviewed in relation
to the Sun's corona, calling for a basic quantitative description of
the breakdown of flux conservation in the low-resistivity limit. A
cylindrical initial-boundary value problem provides specificity in
the general MHD ideas presented.
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Title: The Rayleigh-Taylor Instability and the role of Prominences
in the Chromosphere-Corona Mass Cycle
Authors: Berger, Thomas; Liu, Wei; Hillier, Andrew; Scullion, Eamon;
Low, Boon Chye
2014AAS...22421201B Altcode:
We review recent results in the study of so-called "prominence
bubbles", a buoyant instability discovered in quiescent solar
prominences by the Hinode/SOT instrument in 2007. Analysis of the
plasma flows along the boundary of the bubbles indicates that shear
flows leading to Kelvin-Helmholtz instability waves can develop into
the seed perturbations triggering the Rayleigh-Taylor instability. The
non-linear phase of the RT instability leads to the formation of large
turbulent plumes that transport the bubble plasma (and presumably
magnetic flux) into the overlying coronal flux rope. We propose that
the upward turbulent transport of hot bubble plasma and the downflows
of cooler chromospheric plasma in the prominence are related aspects
of a large-scale "chromosphere-corona mass cycle" in which hot plasma
and magnetic flux and helicity from the chromosphere are transported
upwards while the cooler prominence plasma downflows, which decouple
from the magnetic field they are originally frozen-into, represent
the condensation return flows of the cycle. This cycling enables a
mechanism by which magnetic flux and helicity build up in the coronal
flux rope while mass drains out of the flux rope, eventually triggering
a "loss of confinement" eruption in the form of a CME.
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Title: A solar tornado caused by flares
Authors: Panesar, N. K.; Innes, D. E.; Tiwari, S. K.; Low, B. C.
2014IAUS..300..235P Altcode:
An enormous solar tornado was observed by SDO/AIA on 25 September
2011. It was mainly associated with a quiescent prominence with an
overlying coronal cavity. We investigate the triggering mechanism
of the solar tornado by using the data from two instruments: SDO/AIA
and STEREO-A/EUVI, covering the Sun from two directions. The tornado
appeared near to the active region NOAA 11303 that produced three
flares. The flares directly influenced the prominence-cavity system. The
release of free magnetic energy from the active region by flares
resulted in the contraction of the active region field. The cavity,
owing to its superior magnetic pressure, expanded to fill this vacated
space in the corona. We propose that the tornado developed on the top
of the prominence due to the expansion of the prominence-cavity system.
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Title: Coronal Condensation in Funnel Prominences as Return Flows
of the Chromosphere-Corona Mass Cycle
Authors: Liu, Wei; Berger, Thomas E.; Low, B. C.
2014IAUS..300..441L Altcode:
We present SDO/AIA observations of a potentially novel type of
prominence, called “funnel prominence”, that forms out of coronal
condensation at magnetic dips. <P />They can drain a large amount
of mass (up to ~10<SUP>15</SUP> g day<SUP>-1</SUP>) and may play an
important role as return flows of the chromosphere-corona mass cycle.
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Title: Funnel Prominences as Return Flows of the Chromosphere-Corona
Mass Cycle: SDO/AIA Observations of Coronal Condensation
Authors: Liu, Wei; Berger, T.; Low, B. C.
2013SPD....44...42L Altcode:
It has recently been proposed that prominences play an important role
as return flows of the chromosphere-corona mass cycle, in which hot
plasma is transported upward in forms of spicules and prominence bubbles
(likely due to flux emergence), while cool plasma drains downward in
forms of vertical prominence threads (Berger et al. 2011 Nature). A
critical step in this cycle is the condensation of the million-degree
coronal plasma into T<10,000 K prominence material by a radiative
cooling instability (i.e., thermal non-equilibrium), as numerically
simulated (Karpen & Antiochos 2008; Xia et al. 2012) and first
evidenced in recent SDO/AIA observations (Liu et al. 2012; Berger et
al. 2012 ApJL). Such a runaway cooling process occurs in coronal loops
of various sizes and generally leads to condensation at magnetic dips
and formation of funnel-shaped prominences. A moderate-sized prominence
can drain a significant mass of typically 10^15 gram/day, which is
comparable to the mass of a CME or a fraction of the entire corona. Here
we present a survey of funnel prominences that appear to be common
in AIA observations at various locations and times. We find longer
cooling times in longer/taller coronal loops whose densities are lower,
consistent with the expected quadratic dependence on density of the
optically-thin radiative loss. We propose that such funnel prominences,
usually small in size, can constitute a new type of prominences, and
similar processes can produce elementary building blocks of large-scale
quiescent prominences in filament channels. This picture is supported
by the recent theoretical development on spontaneous formation of
current sheets and condensations manifested as prominence threads
(Low et al. 2012a, b, ApJ).Abstract (2,250 Maximum Characters): It
has recently been proposed that prominences play an important role
as return flows of the chromosphere-corona mass cycle, in which hot
plasma is transported upward in forms of spicules and prominence bubbles
(likely due to flux emergence), while cool plasma drains downward in
forms of vertical prominence threads (Berger et al. 2011 Nature). A
critical step in this cycle is the condensation of the million-degree
coronal plasma into T<10,000 K prominence material by a radiative
cooling instability (i.e., thermal non-equilibrium), as numerically
simulated (Karpen & Antiochos 2008; Xia et al. 2012) and first
evidenced in recent SDO/AIA observations (Liu et al. 2012; Berger et
al. 2012 ApJL). Such a runaway cooling process occurs in coronal loops
of various sizes and generally leads to condensation at magnetic dips
and formation of funnel-shaped prominences. A moderate-sized prominence
can drain a significant mass of typically 10^15 gram/day, which is
comparable to the mass of a CME or a fraction of the entire corona. Here
we present a survey of funnel prominences that appear to be common
in AIA observations at various locations and times. We find longer
cooling times in longer/taller coronal loops whose densities are lower,
consistent with the expected quadratic dependence on density of the
optically-thin radiative loss. We propose that such funnel prominences,
usually small in size, can constitute a new type of prominences, and
similar processes can produce elementary building blocks of large-scale
quiescent prominences in filament channels. This picture is supported
by the recent theoretical development on spontaneous formation of
current sheets and condensations manifested as prominence threads
(Low et al. 2012a, b, ApJ).
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Title: Newtonian and Non-Newtonian Magnetic-field Relaxations in
Solar-coronal MHD
Authors: Low, B. C.
2013ApJ...768....7L Altcode:
This paper treats the relaxation of a magnetic field into
a minimum-energy force-free state in a cold (pressure-less) viscous
fluid, under the frozen-in condition of perfect electrical conductivity
and letting the viscosity-dissipated energy be completely lost. A
non-Newtonian fluid in popular use is studied in relation to the
Newtonian viscous fluid, as two alternative numerical means to (1)
construct force-free fields representing solar coronal structures in
realistic geometry and (2) investigate the Parker theory of spontaneous
formation of electric current sheets as a basic MHD process. Faraday's
induction equation imposes an independent condition on the fluid
velocity at rigid, perfectly conducting boundaries. This boundary
condition is quite compatible with Newtonian mechanics but not with the
non-Newtonian fluid model where velocity is equated to the Lorentz force
with a free, positive multiplicative-factor. This defining property
gives rise to unphysical or artificial singularities not previously
known that are completely distinct from the physically admissible
singularities representing the current sheets of the Parker theory. In
particular, the non-Newtonian fluid takes a magnetic field with neutral
points from any one of a continuum of initial states into an unphysical
state instead of the proper force-free end-state accessible by Newtonian
relaxation. The validity of previously published MHD results based on
this non-Newtonian fluid, including some counterclaims against the
Parker theory, is dubious. Investigating the Parker theory requires
numerical relaxation models capable of anticipating and accurately
describing inevitable current-sheet singularities. By including a
weak resistivity to dissipate the inevitable current sheets as they
form, the field can change topology intermittently to seek a terminal
force-free state free of singularities. The minimum-energy state of this
more complete model corresponds to the long-lived relaxed structures
in the corona.
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Title: A solar tornado triggered by flares?
Authors: Panesar, N. K.; Innes, D. E.; Tiwari, S. K.; Low, B. C.
2013A&A...549A.105P Altcode: 2012arXiv1211.6569P
Context. Solar tornados are dynamical, conspicuously helical magnetic
structures that are mainly observed as a prominence activity. <BR />
Aims: We investigate and propose a triggering mechanism for the solar
tornado observed in a prominence cavity by SDO/AIA on September 25,
2011. <BR /> Methods: High-cadence EUV images from the SDO/AIA and
the Ahead spacecraft of STEREO/EUVI are used to correlate three
flares in the neighbouring active-region (NOAA 11303) and their EUV
waves with the dynamical developments of the tornado. The timings
of the flares and EUV waves observed on-disk in 195 Å are analysed
in relation to the tornado activities observed at the limb in 171
Å. <BR /> Results: Each of the three flares and its related EUV wave
occurred within ten hours of the onset of the tornado. They have an
observed causal relationship with the commencement of activity in
the prominence where the tornado develops. Tornado-like rotations
along the side of the prominence start after the second flare. The
prominence cavity expands with the accelerating tornado motion after
the third flare. <BR /> Conclusions: Flares in the neighbouring active
region may have affected the cavity prominence system and triggered
the solar tornado. A plausible mechanism is that the active-region
coronal field contracted by the "Hudson effect" through the loss of
magnetic energy as flares. Subsequently, the cavity expanded by its
magnetic pressure to fill the surrounding low corona. We suggest that
the tornado is the dynamical response of the helical prominence field
to the cavity expansion. <P />Movies are available in electronic form
at <A href="http://www.aanda.org">http://www.aanda.org</A>
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Title: SDO/AIA Detection of Solar Prominence Formation within a
Coronal Cavity
Authors: Berger, Thomas E.; Liu, Wei; Low, B. C.
2012ApJ...758L..37B Altcode: 2012arXiv1208.3431B
We report the first analyses of SDO/AIA observations of the formation of
a quiescent polar crown prominence in a coronal cavity. The He II 304 Å
(log T <SUB>max </SUB> ~ 4.8 K) data show both the gradual disappearance
of the prominence due to vertical drainage and lateral transport of
plasma followed by the formation of a new prominence 12 hr later. The
formation is preceded by the appearance of a bright emission "cloud"
in the central region of the coronal cavity. The peak brightness of
the cloud progressively shifts in time from the Fe XIV 211 Å channel,
through the Fe XII 193 Å channel, to the Fe IX 171 Å channel (log T
<SUB>max </SUB> ~ 6.2, 6.1, 5.8 K, respectively) while simultaneously
decreasing in altitude. Filter ratio analysis estimates the initial
temperature of the cloud to be approximately log T ~ 6.25 K with
evidence of cooling over time. The subsequent growth of the prominence
is accompanied by darkening of the cavity in the 211 Å channel. The
observations imply prominence formation via in situ condensation of hot
plasma from the coronal cavity, in support of our previously proposed
process of magnetothermal convection in coronal magnetic flux ropes.
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Title: The Hydromagnetic Interior of a Solar Quiescent
Prominence. II. Magnetic Discontinuities and Cross-field Mass
Transport
Authors: Low, B. C.; Liu, W.; Berger, T.; Casini, R.
2012ApJ...757...21L Altcode:
This second paper of the series investigates the transverse response
of a magnetic field to the independent relaxation of its flux tubes
of fluid seeking hydrostatic and energy balance, under the frozen-in
condition and suppression of cross-field thermal conduction. The
temperature, density, and pressure naturally develop discontinuities
across the magnetic flux surfaces separating the tubes, requiring the
finite pressure jumps to be compensated by magnetic-pressure jumps in
cross-field force balance. The tangentially discontinuous fields are
due to discrete currents in these surfaces, δ-function singularities
in the current density that are fully admissible under the rigorous
frozen-in condition but must dissipate resistively if the electrical
conductivity is high but finite. The magnetic field and fluid must
thus endlessly evolve by this spontaneous formation and resistive
dissipation of discrete currents taking place intermittently in
spacetime, even in a low-β environment. This is a multi-dimensional
effect in which the field plays a central role suppressed in the
one-dimensional (1D) slab model of the first paper. The study begins
with an order-of-magnitude demonstration that of the weak resistive
and cross-field thermal diffusivities in the corona, the latter is
significantly weaker for small β. This case for spontaneous discrete
currents, as an important example of the general theory of Parker, is
illustrated with an analysis of singularity formation in three families
of two-dimensional generalizations of the 1D slab model. The physical
picture emerging completes the hypothesis formulated in Paper I that
this intermittent process is the origin of the dynamic interiors of
a class of quiescent prominences revealed by recent Hinode/SOT and
SDO/AIA high-resolution observations.
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Title: Granular-Scale Magnetic Flux Cancellations in the Photosphere
Authors: Kubo, M.; Low, B. C.; Lites, B. W.
2012ASPC..454...41K Altcode:
We find the unresolved flux removal process at the polarity inversion
line formed by canceling opposite-polarity magnetic elements. Further
details and results of this work can be seen in Kubo et al. (2010).
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Title: The Hydromagnetic Interior of a Solar Quiescent
Prominence. I. Coupling between Force Balance and Steady Energy
Transport
Authors: Low, B. C.; Berger, T.; Casini, R.; Liu, W.
2012ApJ...755...34L Altcode: 2012arXiv1203.1056L
This series of papers investigates the dynamic interiors of quiescent
prominences revealed by recent Hinode and SDO/AIA high-resolution
observations. This first paper is a study of the static equilibrium
of the Kippenhahn-Schlüter diffuse plasma slab, suspended vertically
in a bowed magnetic field, under the frozen-in condition and subject
to a theoretical thermal balance among an optically thin radiation,
heating, and field-aligned thermal conduction. The everywhere-analytical
solutions to this nonlinear problem are an extremely restricted subset
of the physically admissible states of the system. For most values
of the total mass frozen into a given bowed field, force balance
and steady energy transport cannot both be met without a finite
fraction of the total mass having collapsed into a cold sheet of zero
thickness, within which the frozen-in condition must break down. An
exact, resistive hydromagnetic extension of the Kippenhahn-Schlüter
slab is also presented, resolving the mass-sheet singularity into
a finite-thickness layer of steadily falling dense fluid. Our
hydromagnetic result suggests that the narrow, vertical prominence
H<SUB>α</SUB> threads may be falling across magnetic fields, with
optically thick cores much denser and ionized to much lower degrees than
conventionally considered. This implication is discussed in relation
to (1) the recent SDO/AIA observations of quiescent prominences that
are massive and yet draining mass everywhere in their interiors, (2)
the canonical range of 5-60 G determined from spectral polarimetric
observations of prominence magnetic fields over the years, and (3)
the need for a more realistic multi-fluid treatment.
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Title: SDO/AIA Observations of Sustained Coronal Condensation in
Prominences as Return Flows of the Chromosphere-Corona Mass Cycle
Authors: Liu, Wei; Berger, T.; Low, B. C.
2012AAS...22020708L Altcode:
It has recently been proposed that prominences are manifestations
of a magneto-thermal convection process that involves ever-present
dynamic descents of cool material threads and upflows of hot bubbles
(Berger et al. 2011 Nature). On global scales, prominences may play
an important role as the return flows of the chromosphere-corona
mass cycle, in which hot mass is originally transported upward
through spicules. A critical step in this cycle is the condensation of
million-degree coronal plasma into T<10,000 K prominence material by
radiative cooling instability. However, direct observation of coronal
condensation has been difficult in the past, a situation recently
changed. We present here the first example observed with SDO/AIA,
in which hours of gradual cooling through multiple EUV channels (from
2 MK to 80,000 K) in large-scale loops leads to eventual condensation
at magnetic dips, where we find evidence of magnetic reconnection and
subsequent outflows. A moderate-size prominence of 10^14 gram is then
formed. Its mass is not static but maintained by a continual supply
through condensation at a high rate of 10^10 gram/s against a comparable
drainage through numerous vertical threads at less than free-fall
speeds. Most of the total condensation of 10^15 gram, comparable
to a CME mass and an order of magnitude more than the instantaneous
mass of the prominence itself, is drained in merely one day. These
new observations show that a macroscopically quiescent prominence is
microscopically dynamic (Liu, Berger, Low 2012 ApJL), involving the
passage of a significant mass that bears important implications for
the chromosphere-corona mass cycle. This interpretation is further
supported by the recent theoretical development on spontaneous formation
of current sheets and cool condensations (Low, Berger, Casini, &
Liu, 2012 submitted to ApJ).
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Title: The Hydromagnetic Nature of Quiescent Prominences
Authors: Low, B. C.; Berger, T.; Casini, R.; Liu, W.
2012decs.confE..84L Altcode:
High-resolution observations of quiescent prominences with Hinode
and SDO have revealed within their interiors the ever-¬present
descent at less than free-fall speeds of cool, vertical dense
filaments interspersed among upward, narrow streams at comparable
speeds of heated, low-density plasma. We address the physical nature
of this dynamical state. Despite the high magnetic Reynolds numbers
characterizing this hydromagnetic environment, magnetic reconnection
takes place via spontaneous formation and dissipation of current sheets
by the coupled effects of highly-anisotropic thermal conduction,
gravity, optically-thin radiation, heating, and high electrical
conductivity. In this interesting new version of the theory of Parker
(1994, Spontaneous current sheets in magnetic fields, Cambridge U
Press), pervasive reconnections produce a perennial local descent of
dense condensations under gravity along newly reconnected magnetic field
lines and a concurrent turbulent rise of buoyant pockets of heated
magnetized plasma through the large-scale magnetic structure. This
mechanism may explain the massive downward drainage through a quiescent
prominence observed recently (Liu et al. 2012 ApJ 745, L21) and, in
the broader context, relate the quiescent prominence to the surrounding
chromosphere/corona as a novel, large-scale, magneto-thermal convective
phenomenon (Berger et al. 2011, Nature 472, 197).
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Title: SDO/AIA Observations of Sustained Coronal Condensation and Mass
Drainage in Prominences as Return Flows of the Chromosphere-Corona
Mass Cycle
Authors: Liu, Wei; Berger, Thomas; Low, B. C.
2012decs.confE..90L Altcode:
It has recently been proposed that prominences are manifestations
of a magneto-thermal convection process that involves ever-present
dynamic descents of cool material threads and upflows of hot bubbles
(Berger et al. 2011 Nature). On global scales, prominences may play
an important role as the return flows of the chromosphere-corona mass
cycle, in which hot mass is originally transported upward through
spicules. A critical step in this cycle is the condensation of
million-degree coronal plasma into T<10,000 K prominence material
by radiative cooling instability. However, direct observation of
coronal condensation has been difficult in the past, a situation
recently changed with the launch of the Hinode/SOT and SDO/AIA. We
present here the first example observed with SDO/AIA, in which hours of
gradual cooling through multiple EUV channels (from 2 MK to 80,000 K)
in large-scale loops leads to eventual condensation at magnetic dips,
forming a moderate-size prominence of 10^14 gram. The prominence
mass is not static but maintained by a continual supply through
condensation at a high rate of 10^10 gram/s against a comparable
drainage through numerous vertical threads at less than free-fall
speeds. Most of the total condensation of 10^15 gram, comparable
to a CME mass and an order of magnitude more than the instantaneous
mass of the prominence itself, is drained in merely one day. These
new observations show that a macroscopically quiescent prominence
is microscopically dynamic, involving the passage of a significant
mass that bears important implications for the chromosphere-corona
mass cycle. This interpretation is further supported by the recent
theoretical development on spontaneous formation of current sheets
and cool condensations (Low, Berger, Casini, & Liu, this meeting).
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Title: First SDO/AIA Observation of Solar Prominence Formation
Following an Eruption: Magnetic Dips and Sustained Condensation
and Drainage
Authors: Liu, Wei; Berger, Thomas E.; Low, B. C.
2012ApJ...745L..21L Altcode:
Imaging solar coronal condensation forming prominences was difficult
in the past, a situation recently changed by Hinode and the Solar
Dynamics Observatory (SDO). We present the first example observed with
the SDO/Atmospheric Imaging Assembly, in which material gradually cools
through multiple EUV channels in a transequatorial loop system that
confines an earlier eruption. Nine hours later, this leads to eventual
condensation at the dips of these loops, forming a moderate-size
prominence of ~10<SUP>14</SUP> g, to be compared to the characteristic
10<SUP>15</SUP> g mass of a coronal mass ejection (CME). The prominence
mass is not static but maintained by condensation at a high estimated
rate of 10<SUP>10</SUP> g s<SUP>-1</SUP> against a comparable, sustained
drainage through numerous vertical downflow threads, such that 96% of
the total condensation (~10<SUP>15</SUP> g) is drained in approximately
one day. The mass condensation and drainage rates temporally correlate
with the total prominence mass. The downflow velocity has a narrow
Gaussian distribution with a mean of 30 km s<SUP>-1</SUP>, while the
downward acceleration distribution has an exponential drop with a
mean of ~1/6 g <SUB>⊙</SUB>, indicating a significant canceling of
gravity, possibly by the Lorentz force. Our observations show that
a macroscopically quiescent prominence is microscopically dynamic,
involving the passage of a significant mass through it, maintained
by a continual mass supply against a comparable mass drainage, which
bears important implications for CME initiation mechanisms in which
mass unloading is important.
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Title: SDO/AIA Observations of Coronal Condensation Leading to
Prominence Formation
Authors: Liu, Wei; Berger, T.; Low, B. C.; Casini, R.
2011SPD....42.2119L Altcode: 2011BAAS..43S.2119L
Coronal condensation takes place when million degree coronal plasma
undergoes radiative cooling instability. Direct observation of coronal
condensation in prominences has been difficult in the past, but with the
launch of the Hinode/SOT and SDO/AIA instruments, numerous observations
of plasma condensing "out of nowhere" high up in quiescent prominences
have been captured. We present here one such event seen with SDO/AIA. On
25-Nov-2010, a prominence above the southwest limb is swept away by
a nearby eruption, and for next a few hours there is no visible 304
A material in the local corona. Then, a portion of the coronal loops
at the same location progressively sags and forms a local dip, where
the first sign of new, cool material appears, 7.5 hours after the
eruption. This is a clear indication of coronal condensation, and the
gradual sag of the loops is likely a result of increasing weight of
the condensed material that has been accumulated at the dip. Similar
condensation occurs nearby at a larger rate and leads to the formation
of a moderate-size prominence. The estimated prominence mass increases
linearly for about 7 hours at a rate of 2.6e10 grams/sec and reaches
approximately 6e14 grams. Simultaneously, the prominence drains through
vertical flows of approximately 32 km/s, bringing the mass back to the
chromosphere. We estimate the mass drain rate to be 2.7e10 grams/sec,
which, together with the estimated mass accumulation rate, implies a
coronal condensation rate of approximately 5.3e10 grams/sec. This study
can provide critical information about the coupling between condensation
energetics and MHD, prominence mass cycles, and coronal mass ejections
initiated by loss of anchoring prominence mass (e.g., Low 2001).
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Title: Magneto-thermal convection in solar prominences
Authors: Berger, Thomas; Testa, Paola; Hillier, Andrew; Boerner, Paul;
Low, Boon Chye; Shibata, Kazunari; Schrijver, Carolus; Tarbell, Ted;
Title, Alan
2011Natur.472..197B Altcode:
Coronal cavities are large low-density regions formed by
hemispheric-scale magnetic flux ropes suspended in the Sun's outer
atmosphere. They evolve over time, eventually erupting as the dark
cores of coronal mass ejections. Although coronal mass ejections are
common and can significantly affect planetary magnetospheres, the
mechanisms by which cavities evolve to an eruptive state remain poorly
understood. Recent optical observations of high-latitude `polar crown'
prominences within coronal cavities reveal dark, low-density `bubbles'
that undergo Rayleigh-Taylor instabilities to form dark plumes rising
into overlying coronal cavities. These observations offered a possible
mechanism for coronal cavity evolution, although the nature of the
bubbles, particularly their buoyancy, was hitherto unclear. Here we
report simultaneous optical and extreme-ultraviolet observations of
polar crown prominences that show that these bubbles contain plasma at
temperatures in the range (2.5-12)×10<SUP>5</SUP> kelvin, which is
25-120 times hotter than the overlying prominence. This identifies a
source of the buoyancy, and suggests that the coronal cavity-prominence
system supports a novel form of magneto-thermal convection in the solar
atmosphere, challenging current hydromagnetic concepts of prominences
and their relation to coronal cavities.
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Title: Chromospheric Jet and Growing "Loop" Observed by Hinode: New
Evidence of Fan-spine Magnetic Topology Resulting from Flux Emergence
Authors: Liu, Wei; Berger, Thomas E.; Title, Alan M.; Tarbell,
Theodore D.; Low, B. C.
2011ApJ...728..103L Altcode: 2010arXiv1012.1897L
We present observations of a chromospheric jet and growing "loop" system
that show new evidence of a fan-spine topology resulting from magnetic
flux emergence. This event, occurring in an equatorial coronal hole on
2007 February 9, was observed by the Hinode Solar Optical Telescope in
the Ca II H line in unprecedented detail. The predecessor of the jet is
a bundle of fine material threads that extend above the chromosphere and
appear to rotate about the bundle axis at ~50 km s<SUP>-1</SUP> (period
lsim200 s). These rotations or transverse oscillations propagate upward
at velocities up to 786 km s<SUP>-1</SUP>. The bundle first slowly and
then rapidly swings up, with the transition occurring at the onset of an
A4.9 flare. A loop expands simultaneously in these two phases (velocity:
16-135 km s<SUP>-1</SUP>). Near the peak of the flare, the loop appears
to rupture; simultaneous upward ejecta and mass downflows faster than
free-fall appear in one of the loop legs. The material bundle then
swings back in a whip-like manner and develops into a collimated jet,
which is orientated along the inferred open-field lines with transverse
oscillations continuing at slower rates. Some material falls back along
smooth streamlines, showing no more oscillations. At low altitudes, the
streamlines bifurcate at presumably a magnetic null point and bypass
an inferred dome, depicting an inverted-Y geometry. These streamlines
closely match in space the late Ca II H loop and X-ray flare loop. These
observations are consistent with the model that flux emergence in an
open-field region leads to magnetic reconnection, forming a jet and
fan-spine topology. We propose that the material bundle and collimated
jet represent the outer spine in quasi-static and eruptive stages,
respectively, and the growing loop is a two-dimensional projection of
the three-dimensional fan surface.
---------------------------------------------------------
Title: The Craig - Sneyd Analytic Solutions to the Parker Problem
Authors: Low, B. C.
2010SoPh..266..277L Altcode: 2010SoPh..tmp..159L
This paper follows up on the conclusion by Craig and Sneyd (2005) that
the solutions to a linearized magnetostatic problem are counterexamples
to the magnetostatic model of Parker (1972), demonstrating a general
absence of continuous equilibrium for a magnetic field with an
arbitrarily prescribed topology. The analysis presented here shows
that Craig and Sneyd had incorrectly rejected an important subset
of those solutions in a misunderstanding of the Parker model. The
complete set of solutions when correctly interpreted is, in fact,
physically consistent with the Parker model. A general discussion of
the Parker theory of spontaneous current sheets is given.
---------------------------------------------------------
Title: The Topological Changes of Solar Coronal Magnetic
Fields. III. Reconnected Field Topology Produced by Current-sheet
Dissipation
Authors: Janse, Å. M.; Low, B. C.
2010ApJ...722.1844J Altcode:
In this paper, the third in a series of papers on topological changes
of magnetic fields, we study how the dissipation of an initial current
sheet (CS) in a closed three-dimensional (3D) field affects the
field topology. The initial field is everywhere potential except at
the location of the CS which is in macroscopic equilibrium under the
condition of perfect conductivity. In the physical world of extremely
high, but finite, conductivity, the CS dissipates and the field seeks
a new equilibrium state in the form of an everywhere potential field
since the initial field is everywhere untwisted. Our semi-analytical
study indicates that the dissipation of the single initial CS must
induce formation of additional CSs in extensive parts of the magnetic
volume. The subsequent dissipation of these other sheets brings about
topological changes by magnetic reconnection in order for the global
field to become potential. In 2D fields, the magnetic reconnection due
to the dissipation of a CS is limited to the magnetic vicinity of the
dissipating sheet. Thus, the consequence of CS dissipation is physically
and topologically quite different in 2D and 3D fields. A discussion
of this result is given in general relation to the Parker theory of
spontaneous CSs and heating in the solar corona and solar flares.
---------------------------------------------------------
Title: The Parker Magnetostatic Theorem
Authors: Low, B. C.
2010ApJ...718..717L Altcode: 2010arXiv1002.4399L
We demonstrate the Parker Magnetostatic Theorem in terms of a small
neighborhood in solution space containing continuous force-free magnetic
fields in small deviations from the uniform field. These fields are
embedded in a perfectly conducting fluid bounded by a pair of rigid
plates where each field is anchored, taking the plates perpendicular
to the uniform field. Those force-free fields obtainable from the
uniform field by continuous magnetic footpoint displacements at the
plates have field topologies that are shown to be a restricted subset of
the field topologies similarly created without imposing the force-free
equilibrium condition. The theorem then follows from the deduction that
a continuous nonequilibrium field with a topology not in that subset
must find a force-free state containing tangential discontinuities.
---------------------------------------------------------
Title: Granular-scale Magnetic Flux Cancellations in the Photosphere
Authors: Kubo, M.; Low, B. C.; Lites, B. W.
2010ApJ...712.1321K Altcode: 2010arXiv1003.2863K
We investigate the evolution of five granular-scale magnetic flux
cancellations just outside the moat region of a sunspot by using
accurate spectropolarimetric measurements and G-band images with the
Solar Optical Telescope (SOT) aboard Hinode. The opposite-polarity
magnetic elements approach a junction of the intergranular lanes and
then collide with each other there. The intergranular junction has
strong redshifts, darker intensities than the regular intergranular
lanes, and surface converging flows. This clearly confirms that
the converging and downward convective motions are essential for the
approaching process of the opposite-polarity magnetic elements. However,
the motion of the approaching magnetic elements does not always match
with their surrounding surface flow patterns in our observations. This
suggests that, in addition to the surface flows, subsurface downward
convective motions and subsurface magnetic connectivities are important
for understanding the approach and collision of the opposite-polarity
elements observed in the photosphere. We find that the horizontal
magnetic field appears between the canceling opposite-polarity
elements in only one event. The horizontal fields are observed along
the intergranular lanes with Doppler redshifts. This cancellation is
most probably a result of the submergence (retraction) of low-lying
photospheric magnetic flux. In the other four events, the horizontal
field is not observed between the opposite-polarity elements at any time
when they approach and cancel each other. These approaching magnetic
elements are more concentrated rather than gradually diffused, and
they have nearly vertical fields even while they are in contact each
other. We thus infer that the actual flux cancellations are highly
time-dependent events at scales less than a pixel of Hinode SOT (about
200 km) near the solar surface.
---------------------------------------------------------
Title: Granular scale magnetic flux cancellations .
Authors: Kubo, M.; Low, B. C.; Lites, B. W.
2010MmSAI..81..790K Altcode:
We summarize the evolution of granular-scale “magnetic-flux
cancellation” as observed with Hinode/SOT. Further details and results
of this work are given in \citet{Kubo2009}.
---------------------------------------------------------
Title: Observations of Large-Scale Dynamic Bubbles in Prominences
Authors: de Toma, G.; Casini, R.; Berger, T. E.; Low, B. C.; de Wijn,
A. G.; Burkepile, J. T.; Balasubramaniam, K. S.
2009ASPC..415..163D Altcode:
Solar prominences are very dynamic objects, showing continuous motions
down to their smallest resolvable spatial and temporal scales. However,
as macroscopic magnetic structures, they are remarkably stable during
their quiescent phase. We present recent ground-based and Hinode
observations of large-scale bubble-like, dynamic sub-structures that
form within and rise through quiescent prominences without disrupting
them. We investigate the similarities and differences of the Hinode
and ground-based observations and discuss their implications for models
of prominences.
---------------------------------------------------------
Title: Spontaneous Current Sheet Formation and Break-Up of Magnetic
Flux Surfaces
Authors: Bhattacharyya, R.; Low, B. C.; Smolarkiewicz, P. K.
2009ASPC..415..451B Altcode:
The dynamics of spontaneous current sheet formation is demonstrated in
a viscous, perfectly conducting, incompressible magnetofluid through
numerical simulations. The magnetic field is represented in terms of
evolving flux surfaces which are the possible sites of current sheet
formation. The computation follows global magnetic flux surfaces of
simple initial geometry as they deform into more complex forms creating
current sheets in the process. Ultimately, the flux surfaces break their
initial topology, as the spatial scale of surface folds decreases below
the model resolution. This breaking is used to identify the sites of
the current sheets formation.
---------------------------------------------------------
Title: Polarimetric Diagnostics of Unresolved Chromospheric Magnetic
Fields
Authors: Casini, R.; Manso Sainz, R.; Low, B. C.
2009ApJ...701L..43C Altcode: 2008arXiv0811.0512C
For about a decade, spectropolarimetry of He I λ10830 has been applied
to the magnetic diagnostics of the solar chromosphere. This resonance
line is very versatile as it is visible both on disk and in off-limb
structures, and it has a good sensitivity to both the weak-field
Hanle effect and the strong-field Zeeman effect. Recent observations
of an active-region filament showed that the linear polarization was
dominated by the transverse Zeeman effect, with very little or no
hint of scattering polarization. This is surprising, since the He I
levels should be significantly polarized in a conventional scattering
scenario. To explain the observed level of atomic depolarization by
collisional or radiative processes, one must invoke plasma densities
larger by several orders of magnitude than currently known values
for prominences. We show that such depolarization can be explained
quite naturally by the presence of an unresolved, highly entangled
magnetic field, which averages to give the ordered field inferred
from spectropolarimetric data, over the typical temporal and spatial
scales of the observations. We present a modeling of the polarized He I
λ10830 in this scenario, and discuss its implications for the magnetic
diagnostics of prominences and spicules, and for the general study of
unresolved magnetic field distributions in the solar atmosphere.
---------------------------------------------------------
Title: The Topological Changes of Solar Coronal Magnetic
Fields. II. The Reclosing of an Opened Field
Authors: Low, B. C.; Janse, Å. M.
2009ApJ...696..821L Altcode:
This is a study of the spontaneous formation of current sheets
responding to the closing of an opened magnetic field by resistive
reconnection in an electrically, highly conducting atmosphere
outside a unit sphere. Pairs of initial-final equilibrium states
are calculated explicitly, taking the field to be composed of three
systems of untwisted flux in both states. In the initial state, two of
the three flux systems are closed potential fields whereas the third
system contains an equilibrium current sheet that keeps the potential
fields on its two sides globally open. The final state is an everywhere
potential field, with all three flux systems closed, produced by the
resistive dissipation of the current sheet in the initial state. The
unit sphere is taken to be a rigid, perfectly conducting wall during
reconnection, so that the normal flux distribution is unchanged
on the unit sphere. Field solutions subject to this unchanging
boundary condition are obtained with and without the assumption of
axisymmetry. The mathematical model has been designed to show that
the topological changes produced by the current-sheet dissipation are
simple under axisymmetry but radically different in the absence of
axisymmetry, a fundamental point established in the first paper of this
series. In the general case, the topological changes imply that other
current sheets must have formed. Some of these current sheets form
on the separatrix flux surfaces of the multipolar field. Others form
throughout the closed-flux systems induced by volumetric changes. The
opening and reclosing of magnetic fields during a solar coronal mass
ejection may produce a multitude of current sheets not previously
anticipated in the current understanding of this phenomenon. Basic to
this study is a general topological property of magnetic flux tubes
treated separately in the Appendix.
---------------------------------------------------------
Title: The Topological Changes of Solar Coronal Magnetic
Fields. I. Spontaneous Current Sheets in Three-Dimensional Fields
Authors: Janse, Å. M.; Low, B. C.
2009ApJ...690.1089J Altcode:
We present mathematical models to demonstrate the inevitability of
current-sheet formation in a cylindrical magnetic field governed by
the ideal hydromagnetic induction equation, as described by the Parker
theory. This process, central to the heating of the solar corona,
is radically different in fully three-dimensional fields as compared
with two-dimensional fields. Magnetic neutral points or separatrix
flux surfaces are necessary for sheet formation in two-dimensional
fields. In fully three-dimensional fields, current sheets form readily
even in the complete absence of neutral points and separatrix surfaces,
and these sheets can form densely throughout the field in response to
changes in the magnetic volume. This general result is established for
cylindrical fields that are topologically untwisted, including the
first direct demonstration of sheet formation in the absence of any
magnetic neutral point. We discuss simple implications of this basic
result for solar flares and coronal heating. In subsequent papers,
we apply our result to coronal mass ejections and solar flares.
---------------------------------------------------------
Title: Magnetic Relaxation in the Solar Corona
Authors: Miller, Kenneth; Fornberg, Bengt; Flyer, Natasha; Low, B. C.
2009ApJ...690..720M Altcode:
This is a mathematical study of the long-lived hydromagnetic structures
produced in the tenuous solar corona by the turbulent, resistive
relaxation of a magnetic field under the condition of extremely high
electrical conductivity. The relaxation theory of Taylor, originally
developed for a laboratory device, is extended to treat the open
atmosphere where the relaxing field must interact with its surrounding
fields. A boundary-value problem is posed for a two-dimensional model
that idealizes the corona as the half Cartesian plane filled with a
potential field (1) that is anchored to a rigid, perfectly conducting
base and (2) that embeds a force-free magnetic field in the form of
a flux-rope oriented horizontally and perpendicular to the Cartesian
plane. The flux-rope has a free boundary, which is an unknown in the
construction of a solution for this atmosphere. Pairs of magnetostatic
solutions are constructed to represent the initial and final states of a
flux-rope relaxation that conserve both the total magnetic helicity and
total axial magnetic flux, using a numerical iterative method specially
developed for this study. The collection of numerical solutions found
provides an insight into the interplay among several hydromagnetic
properties in the formation of long-lived coronal structures. In
particular, the study shows (1) that the outward spread of reconnection
between a relaxing flux-rope and its external field may be arrested at
some outer magnetic flux surface within which a constant-α force-free
field emerges as the minimum-energy state and (2) that this outward
spread is complicated by an inward, partial collapse of the relaxing
flux-rope produced by a loss of internal magnetic pressure.
---------------------------------------------------------
Title: Magnetically driven activity in the solar corona: a path to
understanding the energetics of astrophysical plasmas
Authors: Gibson, Sarah; Bastian, Tim; Lin, Haoscheng; Low, B. C.;
Tomczyk
2009astro2010S..94G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Rise of a Dark Bubble through a Quiescent Prominence
Authors: de Toma, G.; Casini, R.; Burkepile, J. T.; Low, B. C.
2008ApJ...687L.123D Altcode:
We report on a dynamical event observed in a quiescent prominence on
2007 November 8: a well-formed dark "bubble" with a bright core rose
vertically through the prominence without causing it to erupt. This
event was observed in Hα and He I 1083 nm with the instruments of
the Mauna Loa Solar Observatory. The dark bubble had a size of over
40” and rose from the prominence base, at an average speed of ~12 km
s<SUP>-1</SUP>, forming a bright compression front as it traversed the
prominence. It finally assumed a "keyhole" shape before fading. The
bright core embedded in the dark bubble was observed to rise from the
solar limb, accelerating from ~12 to ~20 km s<SUP>-1</SUP>, leaving a
thin trail of material behind. Subsequent observations indicate that
this was not an exceptional event, but rather that similar disturbances
do occur occasionally in prominences without disrupting them. In this
Letter we present the November 8 observations, and propose a possible
interpretation of the physical mechanism behind these dynamic events.
---------------------------------------------------------
Title: Parker spontaneous current-sheets in topologically untwisted
magnetic fields
Authors: Low, B. C.
2008iac..talk..202L Altcode: 2008iac..talk....5L
No abstract at ADS
---------------------------------------------------------
Title: The Solar Interior-Atmospheric System
Authors: Athay, R. G.; Low, B. C.; White, O. R.
2008ASPC..383..315A Altcode:
This article discusses an unpublished paradigm by Athay that relates
the general properties of the solar photosphere, chromosphere, and
corona to the stream of photons, kinetic energy, and magnetic fields
flowing from the solar interior. Using the Athay paradigm, we discuss
the physics of the solar atmosphere and its coupling to the solar
dynamo to clarify the connection of observed structures and variations
in the three layers to their hydromagnetic interpretation. The details
of the eleven-year cycles of solar activity are quite different, but
each cycle exhibits two invariant features. First, the chromosphere and
corona are always present above the photosphere in its turbulent state
maintained by the radiative flux escaping at the surface as the solar
luminosity. Second, the solar magnetic field is globally reversed early
in each cycle, accompanied by systematic drifts in magnetic activity
shown in the sunspot butterfly diagram of each cycle. We describe a
scenario for the corresponding systematic changes in the upper solar
atmosphere that recover the minimum-activity corona from one cycle
to the next. We discuss in some detail the mechanisms that heat the
atmosphere and process the magnetic flux continually emerging from the
interior, providing a unified view of the interior-atmospheric system.
---------------------------------------------------------
Title: The Topological Nature of Boundary Value Problems for
Force-Free Magnetic Fields
Authors: Low, B. C.; Flyer, N.
2007ApJ...668..557L Altcode:
The difficulties of constructing a three-dimensional, continuous
force-free magnetic field in the solar corona are investigated
through a boundary value problem posed for the unbounded domain
external to a unit sphere. The normal field component B<SUB>n</SUB>
and the boundary value α<SUB>b</SUB> of the twist function α on
the unit sphere, combined with the demand for a vanishing field
at infinity, do constitute sufficient conditions for determining a
solution if it exists, but B<SUB>n</SUB> and α<SUB>b</SUB> cannot
be prescribed independently. An exhaustive classification of the
admissible (B<SUB>n</SUB>,α<SUB>b</SUB>)-pairs is developed, using
the topological properties of the α flux surfaces implied by their
footprints described by the constant-α<SUB>b</SUB> curves on the
unit sphere. The incompatibilities arising from boundary conditions
contradicting the field equations are distinguished from the interesting
one of (B<SUB>n</SUB>,α<SUB>b</SUB>) being, in principle, admissible
but requiring a weak solution describing a force-free field containing
inevitable magnetic tangential discontinuities. This particular
incompatibility relates the boundary value problem to the Parker
theory of spontaneous current sheets in magnetic fields embedded
in electrically perfectly conducting fluids. Our investigation
strategically skirts around some important but formidable mathematical
problems to arrive at physically definite conclusions and insights
on the construction of force-free fields, both in the practical task
of modeling coronal magnetic fields with magnetopolarimetric data
and in the basic understanding of the Parker theory. Two specific
demonstrations of (B<SUB>n</SUB>,α<SUB>b</SUB>) are given to illustrate
circumstances under which a continuous solution to the boundary value
may or may not exist.
---------------------------------------------------------
Title: Coronal hydromagnetic implosions
Authors: Janse, Å. M.; Low, B. C.
2007A&A...472..957J Altcode:
Aims:The released magnetic energy in coronal events, i.e. in flares
and coronal mass ejections (CMEs), is believed to have been stored
locally in the coronal magnetic field. The energy in a magnetic
field B is distributed in space with density {B<SUP>2</SUP> over 8
π} that is also the isotropic magnetic pressure at each point in
space. A localized release of magnetic energy would therefore imply a
localized reduction of magnetic pressure. Hence, such a release could
lead to an implosion of the magnetic structure as its atmospheric
surrounding pushes inward. Whether an implosion would take place
immediately depends on how fast the released energy can escape,
through optically-thin radiation, thermal conduction, hydromagnetic
waves, and, the magnetic channeling of high-energy particles. <BR
/>Methods: We determined whether an expansion or an implosion would
occur when cylindrical tubes of twisted flux relaxed to lower energy
states. Depending on the dynamical nature of the relaxation we assumed,
relevant dynamical invariants were invoked to relate a particular end
state to the given initial state. <BR />Results: Comparing the initial
and the end state, we found that when most of the liberated energy
escaped the cylinder imploded. The results suggest that implosions
may take place simultaneously with flares and CMEs.
---------------------------------------------------------
Title: Spectral Lines for Polarization Measurements of the Coronal
Magnetic Field. IV. Stokes Signals in Current-carrying Fields
Authors: Judge, P. G.; Low, B. C.; Casini, R.
2006ApJ...651.1229J Altcode:
We present the first theoretical, forward calculations of the Stokes
profiles of several magnetic dipole (“M1”) coronal emission lines
produced in current-carrying magnetic structures. An idealized coronal
model of Low, Fong, and Fan is used, which describes a spherically
symmetric, hydrostatic background atmosphere, isothermal at a
coronal temperature of 1.6×10<SUP>6</SUP> K. Embedded is a global,
axisymmetric magnetic field that is everywhere potential except
at a quiescent prominence, consisting of an infinitesimally thin,
equatorial current sheet whose weight is supported by the outward
discrete Lorentz force in the sheet. This model contains a physically
nontrivial, localized magnetic structure, although the atmospheric
plasma is thermally of the simplest stratification possible. The
calculated M1 coronal lines show clear and distinct signatures of
the presence and magnitude of this localized magnetic structure,
in both linear and circular polarizations, even though the thermal
structure is almost homogeneous. The morphology of maps of linear
polarization is particularly sensitive to the existence and strength
of the current sheets, as field lines wrap around them according to
the Biot-Savart law, and the linear polarization responds to different
projections of field line directions onto local radius vectors. Of the
M1 lines studied, those of Fe XIII (1074.7 nm) and Si X (1430.1 nm)
are especially promising because of their relatively strong linear
polarization. These forward calculations provide a basis for optimism
that emission-line measurements may reveal the presence and nature of
current systems in the corona, and provide motivation for developing
instruments capable of routinely measuring polarized light in forbidden
coronal lines.
---------------------------------------------------------
Title: Spontaneous Current Sheets in an Ideal Hydromagnetic Fluid
Authors: Low, B. C.
2006ApJ...649.1064L Altcode:
Parker's theory of spontaneous current sheets, or magnetic
tangential discontinuities, in electrically perfectly conducting
fluids is demonstrated for globally untwisted magnetic fields in
the Chandrasekhar-Kendall representation. All the three-dimensional,
globally untwisted fields sharing the same flux distribution, fixed at
the rigid boundary of the domain, span an infinity of different field
topologies, each preserved in a field under the frozen-in condition. The
general result is obtained and illustrated that only one of these
topologies allows a field to relax into an everywhere continuous
force-free state, namely, the potential field uniquely determined by
the boundary flux distribution. All other topologies require the field
to find a force-free state containing inevitable tangential magnetic
discontinuities. This result extends a class of two-dimensional
demonstrations of the Parker theory to three dimensions. A field of a
fixed topology and boundary flux distribution can be in a continuous
state in one equilibrium but may have to contain inevitable tangential
discontinuities on transition to another equilibrium. This property,
demonstrated here with untwisted fields, is probably the hydromagnetic
origin of flares occurring in the course of slow evolution in the
solar corona.
---------------------------------------------------------
Title: Magnetic Helicity in a Two-Flux Partitioning of an Ideal
Hydromagnetic Fluid
Authors: Low, B. C.
2006ApJ...646.1288L Altcode:
A primitive form of magnetic helicity is constructed that (1) recovers
the classical helicity of a wholly contained magnetic field, as well as
the Berger-Field relative helicity of a partially contained magnetic
field, and (2) generalizes the infinity of global, helicity-like
invariants derived by Bhattacharjee & Dewar for a plasma approaching
toroidal magnetostatic equilibrium. This construction is based on a
general partitioning of an ideal hydromagnetic fluid into disjoint,
infinitesimally thin, toroidal subvolumes using a two-flux description
of the embedded magnetic field. Each of these toroidal subvolumes
of fluid is endowed with a gauge-independent magnetic helicity
conserved during its ideal Lagrangian evolution. This conservation law
constitutes an equivalent statement of the frozen-in condition. The
Chandrasekhar-Kendall solenoidal representation of a magnetic field is
conceptually related to the two-flux description in the basic theory
developed. Magnetic helicity-related phenomena in the solar corona are
briefly discussed to provide an astrophysical context for this basic
development, postponing proper applications to the papers to follow.
---------------------------------------------------------
Title: Magnetic Field Confinement in the Corona: The Role of Magnetic
Helicity Accumulation
Authors: Zhang, Mei; Flyer, Natasha; Low, Boon Chye
2006ApJ...644..575Z Altcode: 2006astro.ph..3011Z
A loss of magnetic field confinement is believed to be the cause of
coronal mass ejections (CMEs), a major form of solar activity in the
corona. The mechanisms for magnetic energy storage are crucial in
understanding how a field may possess enough free energy to overcome
the Aly limit and open up. Previously, we have pointed out that the
accumulation of magnetic helicity in the corona plays a significant
role in storing magnetic energy. In this paper, we investigate another
hydromagnetic consequence of magnetic-helicity accumulation. We propose
a conjecture that there is an upper bound on the total magnetic helicity
that a force-free field can contain. This is directly related to the
hydromagnetic property that force-free fields in unbounded space have
to be self-confining. Although a mathematical proof of this conjecture
for any field configuration is formidable, its plausibility can be
demonstrated with the properties of several families of power-law,
axisymmetric force-free fields. We put forth mathematical evidence,
as well as numerical, indicating that an upper bound on the magnetic
helicity may exist for such fields. Thus, the accumulation of magnetic
helicity in excess of this upper bound would initiate a nonequilibrium
situation, resulting in a CME expulsion as a natural product of
coronal evolution.
---------------------------------------------------------
Title: The Internal Structures and Dynamics of Solar Quiescent
Prominences
Authors: Petrie, G. J. D.; Low, B. C.
2005ASPC..346..211P Altcode:
We present generalized Kippenhahn-Schlüter (KS) equilibrium solutions
of the magnetohydrodynamic (MHD) equations, constructed of arrays
of laminated isothermal (KS) prominence sheets whose temperatures,
sag angles and dip positions may vary arbitrarily from sheet to
sheet. This great versatility allows us to model the filamentary
structure of prominences and illustrate why their observed dimensions
differ from their characteristic hydrostatic scale lengths. We also
apply these equilibria to investigate the role of internal prominence
motions in solar magnetism. The solar corona is continually being
injected with magnetic flux from the solar interior, flux that
cannot be annihilated in bulk by the electrically highly conducting
corona. Ascending small-scale structures as well as large-scale
eruptions of prominences may both serve to carry excess magnetic flux
out of the corona. This process is investigated with an interest in
the dissipation of tangential discontinuities forming spontaneously
in the supporting magnetic field of a prominence. The net effect of
the magnetic reconnection is a downflow of mass accompanied by an
upward transport of magnetic flux. This effect may play an important,
direct and indirect, role in ejecting magnetic flux from the corona
into interplanetary space. Thin counter-streaming layers of prominence
plasma predicted by this work have already been observed.
---------------------------------------------------------
Title: Magnetic Field Confinement in the Solar
Corona. II. Field-Plasma Interaction
Authors: Flyer, N.; Fornberg, B.; Thomas, S.; Low, B. C.
2005ApJ...631.1239F Altcode:
The numerical study of axisymmetric force-free magnetic fields in the
unbounded space outside a unit sphere, presented in the first paper of
this series, is extended to treat twisted fields in static equilibrium
with plasma pressure and weight in a polytropic atmosphere. The study
considers dipolar magnetic fields all sharing the same boundary
flux distribution on the unit sphere and characterized with (1) a
nonlinear distribution of its azimuthal field component expressed as
a power of the poloidal flux function and (2) a plasma distribution
varying linearly with the poloidal flux function. Nonlinear boundary
value problems are solved numerically to generate a continuum of
solutions with two parameters to control the total azimuthal flux
and the strength of field-plasma interaction. The study includes the
force-free fields of the first paper as a special case. Models with
polytropic indices Γ=7/6, 14/11 are treated to show the interplay
between the degree of magnetic twist and hydrostatic stratification
in determining atmospheric structures, with particular interests in
magnetic flux ropes and their storage of magnetic energy and azimuthal
flux at levels above those bounds applicable to force-free fields. The
concluding discussion relates physical insights from the study to the
solar corona and the energetics of coronal mass ejections and flares.
---------------------------------------------------------
Title: The Hydromagnetic Nature of Solar Coronal Mass Ejections
Authors: Zhang, Mei; Low, Boon Chye
2005ARA&A..43..103Z Altcode:
Solar coronal mass ejections (CMEs) are a major form of activity
on the Sun. A CME takes 10<SUP>15-16</SUP> g of plasma from the low
corona into the solar wind, to disturb the near-Earth space if the CME
direction is favorable. We summarize current observations and ideas of
CME physics to provide a hydromagnetic view of the CMEs as the products
of continual magnetic flux emergence and an interplay between magnetic
reconnection and approximate magnetic-helicity conservation in the
corona. Each flux emergence brings helicity to accumulate additively
in a coronal structure while excess magnetic energy is flared away by
reconnection. Self-confinement eventually fails with a CME shedding
the accumulated helicity out of the low corona to enable the field
to reach the minimum-energy state. Similar evolutionary processes may
occur in other magnetic stars and galaxies.
---------------------------------------------------------
Title: The Dynamical Consequences of Spontaneous Current Sheets in
Quiescent Prominences
Authors: Petrie, G. J. D.; Low, B. C.
2005ApJS..159..288P Altcode:
The solar corona is continually being injected with magnetic flux from
the solar interior, flux that cannot be annihilated in bulk by the
electrically highly conducting corona. Observations have shown that
mass loss through downflows within solar prominences may be responsible
for the ascent and eventual eruption of these prominences. Ascending
small-scale structures as well as large-scale eruptions of prominences
may both serve to carry excess magnetic flux out of the corona. We
investigate the dissipation and field reconnection across the tangential
discontinuities that form spontaneously in the supporting magnetic
field of a prominence. Our analysis of a variety of postdissipation,
nonequilibrium states provides instructive insights into the observable
motions in prominences. The net effect of the magnetic reconnection
is a downflow of mass accompanied by an upward transport of magnetic
flux. This effect may play an important, direct and indirect, role in
ejecting magnetic flux from the corona into interplanetary space. Shock
waves are a natural consequence of this dissipative process, and
their detection may serve as a diagnostic observational tool. Thin
counterstreaming layers of prominence plasma predicted by this work
have already been observed.
---------------------------------------------------------
Title: The Internal Structures and Dynamics of Solar Quiescent
Prominences
Authors: Low, B. C.; Petrie, G. J. D.
2005ApJ...626..551L Altcode:
We present generalized Kippenhahn-Schlüter (KS) equilibrium and
steady-flow solutions of the magnetohydrodynamic (MHD) equations. These
solutions are constructed of arrays of laminated isothermal KS
prominence sheets whose temperatures, sag angles, and dip positions
may vary arbitrarily from sheet to sheet. Moreover, the sheets can move
at arbitrary constant uniform velocities relative to each other within
their planes. This great versatility allows us to model the filamentary
structure of prominences and illustrate why their observed dimensions
differ from their characteristic hydrostatic scale lengths. We are
also able to explain observed vertical and horizontal velocities as
naturally arising steady rigid motions of plasma sheets in local force
equilibrium but global nonequilibrium.
---------------------------------------------------------
Title: Three-dimensional Structures of Magnetostatic
Atmospheres. VII. Magnetic Flux Surfaces and Boundary Conditions
Authors: Low, B. C.
2005ApJ...625..451L Altcode:
We treat a long-standing difficulty with the boundary conditions for
the governing equations derived in the third paper of this series
describing magnetic fields in equilibrium in a three-dimensional
atmosphere. The force-free magnetic fields are special cases of this
magnetostatic model. Among the flux surfaces of these magnetic fields,
those of constant twist parameter, the so-called α-surfaces, have a
basic topological property previously pointed out by Aly for force-free
fields. This property dictates a natural set of boundary conditions
for the field equations and can be used to reduce the vector field
equations to a novel form, illustrated here with analytical examples of
three-dimensional force-free fields. The physical implications of this
theoretical development for solar coronal magnetic fields are discussed.
---------------------------------------------------------
Title: Magnetostatic Structures of the Solar Corona. III. Normal
and Inverse Quiescent Prominences
Authors: Low, B. C.; Zhang, M.
2004ApJ...609.1098L Altcode:
Analytical solutions describing equilibrium magnetic fields in the
solar corona, deformed by prominence-like plasma condensations in the
Cartesian plane, are treated in this paper. The equilibrium equations
for this class of problems usually take different forms in distinct
subdomains, separated by free boundaries to be solved as one of the
unknowns, across which solutions on the two sides are matched by
suitable jump conditions. By idealizing the plasma condensations as a
horizontal, circular cylinder whose weight in a uniform gravitational
field is supported by an external magnetic field, we avoid solving
free-boundary problems and present a method to directly construct
solutions presenting prominence magnetic fields in the so-called
normal and inverse configurations. The solutions illustrate the
morphologies of plasma and vector magnetic field distributions in the
cylindrical condensations in relation to the magnetic fields beneath
the condensations. These solutions provide theoretical magnetic field
properties that may be relevant to the current renewed interest in
observing solar prominence magnetic fields by polarimetric spectroscopy.
---------------------------------------------------------
Title: Magnetic Field Confinement in the Solar Corona. I. Force-free
Magnetic Fields
Authors: Flyer, N.; Fornberg, B.; Thomas, S.; Low, B. C.
2004ApJ...606.1210F Altcode:
Axisymmetric force-free magnetic fields external to a unit sphere
are studied as solutions to boundary value problems in an unbounded
domain posed by the equilibrium equations. It is well known from
virial considerations that stringent global constraints apply for a
force-free field to be confined in equilibrium against expansion into
the unbounded space. This property as a basic mechanism for solar
coronal mass ejections is explored by examining several sequences of
axisymmetric force-free fields of an increasing total azimuthal flux
with a power-law distribution over the poloidal field. Particular
attention is paid to the formation of an azimuthal rope of twisted
magnetic field embedded within the global field, and to the energy
storage properties associated with such a structure. These sequences
of solutions demonstrate (1) the formation of self-similar regions in
the far global field where details of the inner boundary conditions
are mathematically irrelevant, and (2) the possibility that there is a
maximum to the amount of azimuthal magnetic flux confined by a poloidal
field of a fixed flux anchored rigidly to the inner boundary. The
nonlinear elliptic boundary value problems we treat are mathematically
interesting and challenging, requiring a specially designed solver,
which is described in the Appendix.
---------------------------------------------------------
Title: The Filamentary Structures of Quiescent Prominences
Authors: Low, B. C.; Petrie, G. J. D.
2004AAS...204.5503L Altcode: 2004BAAS...36Q.761L
We present examples from a rich family of magnetostatic solutions
describing sheets of vertical filamentary plasmas suspended in a
bow-shaped magnetic field. These solutions are characterized with the
realism of uneven loadings of mass on the field lines which produces
a sheared field topology associated with a coupling between the
field-aligned and cross-field current densities. These analytical
models are useful for forward calculations of prominence emission
and absorption, as well as the polarimetric signatures of prominence
magnetic fields. <P />The National Center for Atmospheric Research is
sponsored by the National Science Foundation.
---------------------------------------------------------
Title: Magnetic Energy Storage in the Two Hydromagnetic Types of
Solar Prominences
Authors: Zhang, M.; Low, B. C.
2004ApJ...600.1043Z Altcode:
We present analytical solutions that describe the hydromagnetic support
of solar prominences in two characteristic configurations, called normal
and inverse. We model the corona as axisymmetric outside a unit sphere
and treat the prominence as a distributed cold plasma inside a purely
azimuthal magnetic flux rope, held in equilibrium by the prominence
weight and by an external poloidal magnetic field rigidly anchored to
the base of the modeled corona. We focus on the storage of magnetic
energy, in particular its potential for driving solar coronal mass
ejections (CMEs). Our calculations indicate that both characteristic
magnetic configurations are capable of storing enough magnetic energy
to overcome the Aly limit for opening up an initially closed magnetic
field. These calculations also indicate that magnetic topology is an
important influence in magnetic energy storage. Fields with a normal
configuration are more likely to attain energetic states leading to
CME-type expulsions than those with an inverse configuration, a property
we use to explain Leroy's observations of the height distributions of
the two types of solar prominences.
---------------------------------------------------------
Title: Coronal mass ejections and solar magnetism
Authors: Low, B. C.
2004cosp...35..496L Altcode: 2004cosp.meet..496L
The ultimate cause of activity in the solar corona is magnetic-flux
emergence culminating in the reversal of the solar global magnetic
field in the early part of each eleven-year cycle. The million-degree
corona is effectively a perfect electrical conductor and yet is
resistively dissipative through the Parker process of spontaneous
current sheets. It is in such a hydromagnetic atmosphere where the
magnetic flux of a new cycle must mix with the opposite flux of the
old cycle. Although the corona is structurally complex and rapidly
evolving during a field reversal, its characteristic activity-minimum
form is faithfully recovered in each cycle. Coronal mass ejections
play a central role in this remarkable phenomenon. I will describe
this view of the corona to point out its implication that magnetic
flux systems may be bodily transported from the solar interior first
into the corona and then out as coronal mass ejections into the solar
wind. This global process couples the corona to the solar dynamo.
---------------------------------------------------------
Title: The Mass of a Solar Quiescent Prominence
Authors: Low, B. C.; Fong, B.; Fan, Y.
2003ApJ...594.1060L Altcode:
This paper follows up on our recent paper on the role of prominence mass
in the storage of magnetic energy for driving a coronal mass ejection
(CME). The previous paper erroneously rejected a set of sheet-prominence
solutions, the recovery of which allows for a simple theoretical
estimate of the mass of a quiescent prominence. For coronal fields
of 5-10 G, these hydromagnetic solutions suggest that a prominence
mass of (1-26)×10<SUP>16</SUP> g is needed to hold detached magnetic
fields of intensity comparable to the coronal fields in an unbounded
atmosphere such that the global magnetic field is energetically able to
spontaneously open up and still have enough energy to account for the
kinetic and gravitational potential energies carried away in a CME. This
simple result is discussed in relation to observed prominence magnetic
field intensities, densities, and masses, pointing to the relevance
of such observations to the question of magnetic energy storage in
the solar corona.
---------------------------------------------------------
Title: A Morphological Study of Helical Coronal Magnetic Structures
Authors: Low, B. C.; Berger, M. A.
2003ApJ...589..644L Altcode:
Magnetostatic solutions describing magnetic flux ropes in realistic
geometry are used to study solar coronal structures observed to have
sigmoidal forms in soft X-rays. These solutions are constructed by
embedding a rope of helically symmetric force-free magnetic fields in
an external field such that force balance is assured everywhere. The
two observed sigmoidal shapes, the S shapes and the mirror-reflected
S shapes referred to as Z shapes in this paper, are found in both
hemispheres of the solar corona, but observations made over the last two
solar cycles suggest that the Z and S shapes occur preferentially in the
northern and southern solar hemispheres, respectively. Our study makes
an identification of the sigmoidal high-temperature coronal plasmas
with heating by the spontaneous formation of current sheets described by
the theory of Parker. This process involves a tangential discontinuity
developing across a ribbon-like, twisted flux surface through an
interaction between a magnetic flux rope and the photosphere, under
conditions of high electrical conductivity. In this identification,
Z- and S-shaped sigmoids are associated with flux ropes with negative
and positive magnetic helicities, respectively. This association is
physically consistent with the conclusion, based independently on
measurements of prominence magnetic fields, that magnetic flux ropes
occur preferentially with negative and positive helicities in the
northern and southern solar hemispheres, respectively.
---------------------------------------------------------
Title: Magnetic Flux Emergence into the Solar Corona. III. The Role
of Magnetic Helicity Conservation
Authors: Zhang, M.; Low, B. C.
2003ApJ...584..479Z Altcode:
This paper treats the reconfiguration of a twisted magnetic field,
from an initial two-flux system containing a current sheet to a
minimum-energy state, under the conservation of total relative
magnetic helicity. In the specific model presented, we assume that
a fresh magnetic field of the opposite polarity has emerged into a
corona containing a preexisting magnetic field, both represented by
constant-α force-free fields with the same constant α. The magnetic
reconnection that takes place between the two twisted magnetic
flux systems during a relaxation is assumed to take the field to a
minimum-energy state that keeps the total relative magnetic helicity
conserved. Our calculations suggest that this kind of relaxation may
result in the formation of magnetic flux ropes and may change the
twist directions in flux ropes in situations where flux ropes exist
in the emerging or preexisting fields. These effects are all due to
the interplays between the internal magnetic helicities of the two
flux systems and their mutual magnetic helicity, with redistribution
of these helicities through magnetic reconnection. In the absence
of an interior current sheet, the lowest α force-free field always
has the minimum magnetic energy for a given magnetic helicity, as
Berger has shown. When an interior current sheet is present, this
result breaks down. The lowest α force-free magnetic field with an
interior equilibrium current sheet does not always have the minimum
magnetic energy for a given total magnetic helicity. Implications of
our results for flux emergence in the solar corona are also addressed.
---------------------------------------------------------
Title: Magnetic Reconnection and the Solar Corona (Invited review)
Authors: Low, B. C.
2003ASPC..286..335L Altcode: 2003ctmf.conf..335L
No abstract at ADS
---------------------------------------------------------
Title: Dynamics of CME Driven by a Buoyant Prominence Flux Tube
Authors: Fan, Y.; Low, B. C.
2003ASPC..286..347F Altcode: 2003ctmf.conf..347F
No abstract at ADS
---------------------------------------------------------
Title: Magnetic flux ropes: Would we know one if we saw one?
Authors: Gibson, S. E.; Low, B. C.; Leka, K. D.; Fan, Y.; Fletcher, L.
2002ESASP.505..265G Altcode: 2002IAUCo.188..265G; 2002solm.conf..265G
There has been much debate lately about whether twisted magnetic flux
ropes exist in the corona. When asked for observational evidence
of them, the temptation is to show images of apparently twisted
structures. However, we must be very careful of projection effects in
interpreting these observations. Two critical aspects of understanding
how we might observe flux ropes are 1) the 3D nature of the flux rope,
and 2) physically, which bits are visible and for what reasons? In
this paper we will use a simple but physically reasonable 3D analytic
model to address these two issues, and develop techniques that can in
future be used on more general models, both analytic and numerical.
---------------------------------------------------------
Title: Magnetic coupling between the corona and the solar dynamo
Authors: Low, B. C.
2002ESASP.505...35L Altcode: 2002solm.conf...35L; 2002IAUCo.188...35L
We summarize published works describing the behavior of the large-scale
solar corona over an 11-year solar cycle. This hydromagnetic description
goes beyond magnetic flux emergence, flares, coronal mass ejections,
prominences and their related structures as individual events to see
their collective role in the coronal reversal of the global magnetic
field in response to the solar dynamo. Central to this process is
an implied transport of systems of twisted magnetic flux from the
solar dynamo, first into the corona and then out as coronal mass
ejections into the heliosphere. This transport combined with the
observed hemispherical distribution of magnetic twists in the solar
atmosphere suggests an active coupling in which the corona serves as
a magnetic sink for the dynamo.
---------------------------------------------------------
Title: Magnetic Flux Emergence into the Solar Corona. II. Global
Magnetic Fields with Current Sheets
Authors: Zhang, M.; Low, B. C.
2002ApJ...576.1005Z Altcode:
Hydromagnetic structural and stability properties of global magnetic
fields with current sheets are discussed in this paper. These fields
describe solar coronal magnetic structures that form when a fresh
magnetic field of opposite polarity has emerged into the corona
containing a preexisting magnetic field. Three classes of axisymmetric
fields are treated. The first is characterized by a continuous normal
field distribution at the boundary and an infinitesimally thin current
sheet in the field. As ideal hydromagnetic equilibria, these fields are
globally stable, but they are resistively unstable within the current
sheet. Magnetic reconnection is unavoidable no matter how large the
electrical conductivity is. The other two classes of fields may be
stable without this kind of resistive nonequilibrium. Of particular
interest among them are equilibrium fields with finite-thickness current
sheets in force balance with pressure gradients and gravity. These
fields are shown to have enough free magnetic energy to let some parts
of its field to become open during magnetic reconnection, an effect
important for the dynamics of coronal mass ejections.
---------------------------------------------------------
Title: Quiescent Solar Prominences and Magnetic-Energy Storage
Authors: Fong, B.; Low, B. C.; Fan, Y.
2002ApJ...571..987F Altcode:
Analytical solutions are presented to describe the hydromagnetic support
of quiescent solar prominences treated as cold plasma sheets in the
characteristic normal and inverse configurations. The solar corona is
modeled to be axisymmetric outside a unit sphere, with the prominence
sheet lying in the equatorial plane extending from the sphere out
to a finite radial distance subject to an inverse-square Newtonian
gravity. The relationship between prominence support and the global
topology of the surrounding poloidal magnetic field is discussed, with
a particular interest in the role of magnetic flux ropes in the support
of inverse prominences. A novel solution is also studied describing
a rope of purely azimuthal magnetic flux held in equilibrium by the
weight of an internal distribution of cold mass and by an external
poloidal magnetic field rigidly anchored to the base of the model
corona. This solution illustrates the role that prominence weight may
play in storing magnetic energy for driving coronal mass ejections.
---------------------------------------------------------
Title: Emergence of twisted magnetic flux into the corona
Authors: Gibson, S.; Low, B. C.; Fan, Y.; Fletcher, L.
2002AAS...200.3603G Altcode: 2002BAAS...34..693G
The interaction between emerging magnetic structures and preexisting
overlying coronal structures will be addressed using a combination of
observations and physical models that incorporate a range of twisted
magnetic topologies. Solar explosive events such as coronal mass
ejections (CMEs) and flares are commonly considered to be driven by
the free magnetic energy stored in twisted (current carrying) coronal
magnetic fields. Understanding the origin and the three-dimensional
nature of these twisted coronal magnetic structures is a crucial step
towards explaining and predicting CMEs and flares. One possible and
appealing picture is that the twisted coronal magnetic structures
form as a result of the emergence of twisted magnetic flux tubes
from the solar interior. We might imagine a scenario where a flux
rope forms sub-photospherically, emerges through the photosphere,
exists in the corona until it loses its stability and erupts in a
CME which moves out through interplanetary space until ultimately
impacting on the Earth's magnetosphere. Attractively simple as this
picture is, reality is likely to be more complicated since the various
regimes are physically very different and pre-existing structures
would get in the way of our traveling flux rope. We will concentrate
on joining up two of these regimes, by considering how a flux rope
could rise from beneath the photosphere and emerge into the corona,
interacting with pre-existing coronal structures. We will approach this
problem by using a combination of numerical models of the flux rope
emergence from beneath the photosphere, analytic models of coronal
dynamic and equilibrium magnetic structures, and photospheric and
coronal observations of the 3-d structure and evolution of a so-called
"sigmoidal", or S-shaped active region. In so doing we hope to gain
essential insight into how twisted magnetic fields are formed and how
they could be ultimately removed from the solar corona.
---------------------------------------------------------
Title: Towards an Operational Sun-to-Earth Model for Space Weather
Forecasting
Authors: Gombosi, T. I.; Clauer, C. R.; De Zeeuw, D. L.; Hansen,
K. C.; Manchester, W. B.; Powell, K. G.; Ridley, A. J.; Roussev, I.;
Sokolov, I. V.; Toth, G.; Wolf, R. A.; Sazykin, S.; Holzer, T. E.;
Low, B. C.; Richmond, A. D.; Roble, R. G.
2002AGUSMSH51B..06G Altcode:
We are presently developing a physics based, modular, large-scale
model of the solar-terrestrial environment simulating space weather
phenomena and providing a framework to test theories and explore the
possibility of operational use in space weather forecasting. This talk
will describe the main components of the model (a global MHD code,
an upper atmosphere and ionosphere model, and the inner magnetosphere
drift physics model). We will also discuss the testing and transitioning
the model through CCMC to operational use by NOAA SEC and the Air
Force. Particular attention will be paid to the need of validation
and metrics studies.
---------------------------------------------------------
Title: The Hydromagnetic Origin of the Two Dynamical Types of Solar
Coronal Mass Ejections
Authors: Low, B. C.; Zhang, M.
2002ApJ...564L..53L Altcode:
We propose a qualitative theory relating flux rope coronal mass
ejections (CMEs) to initial states, represented by inverse or normal
quiescent prominences corresponding to whether the flux rope magnetic
field circulates in the same or opposite sense relative to the
surrounding coronal magnetic field. Our theory explains the observed
dual character of CME speed-height profiles in terms of the interplays
between flux rope expulsion and magnetic reconnection in topologically
different magnetic environments and relates CMEs, prominences, and
flares to coronal magnetic field reversal during activity maximum.
---------------------------------------------------------
Title: Magnetic Flux Emergence into the Solar Corona. I. Its Role
for the Reversal of Global Coronal Magnetic Fields
Authors: Zhang, M.; Low, B. C.
2001ApJ...561..406Z Altcode:
Some physical insights into how the corona reverses its global
magnetic field are described in this paper based on a set of elementary
hydromagnetic calculations. We assume that a fresh magnetic field of
opposite polarity has emerged into a corona containing a preexisting
magnetic field. The inevitable magnetic reconnection that takes place
between the two magnetic flux systems may result in an expulsion of
magnetic flux to infinity. Our calculations suggest the following
physical story of the coronal reversal process: When the emerged
flux exceeds the preexisting flux by a critical amount, the corona
will reverse its polarity. Before this critical ratio is attained,
the field with the emerged flux may have enough energy to let only one
or two bipolar parts of the multipolar field open up. This opening-up
process, taking place as a coronal mass ejection (CME), may take
some of the preexisting flux out of the corona and thus increase the
emerged-to-preexisting flux ratio and bring the corona closer to the
critical value for its global magnetic reversal. Our calculations also
indicate that it is possible that the position where the field opens
up may be different from that where the new flux emerges. This may
help explain the difference in the latitude distribution of active
regions and CMEs during a solar cycle as observed by Hundhausen.
---------------------------------------------------------
Title: Coronal mass ejections, magnetic flux ropes, and solar
magnetism
Authors: Low, B. C.
2001JGR...10625141L Altcode:
This review on coronal mass ejections (CMEs) treats hydromagnetic issues
posed by observations, in order to relate CMEs to flares and prominence
eruptions and to consider the roles these processes play in the
evolution of the solar corona in the course of an 11-year cycle. This
global view of the corona, proposed in varying degrees of completeness
by the author, physically connects the corona to the photosphere and
the dynamo in the solar interior. This view is synthesized afresh
starting with CME phenomenology, in order to include some new insights
and to arrive at definite statements on the hydromagnetic nature of
CMEs. The synthesis shows that each CME culminates a long, coherent
physical process involving magnetic-flux emergence; flares and magnetic
reconnection; creation of long-lived, large-scale coronal structures;
conservation of magnetic helicity; and failure of confinement of
magnetic flux ropes in the open atmosphere. Each CME contributes a
systematic permanent change to the coronal magnetic field. In this
view the cumulative changes brought by all the CMEs in the course
of a solar cycle have fundamental implications for the magnetic-flux
budgets of the photosphere and the corona.
---------------------------------------------------------
Title: Three-dimensional and twisted: An MHD interpretation of
on-disk observational characteristics of coronal mass ejections
Authors: Gibson, S. E.; Low, B. C.
2000JGR...10518187G Altcode:
A physical interpretation of observed coronal “on-disk” manifestations
of an Earth-directed coronal mass ejection (CME) is presented. The
fundamental question of how the CME's magnetic field and its plasma
distribution are related is largely unanswered, because a crucial piece
of the puzzle, that is the three-dimensional (3-D) morphology of the
CME, remains difficult to ascertain so long as coronal observations
are limited to projections onto a single plane of the sky. In order
to understand the relationship between observations of CMEs projected
at the solar limb and those projected on the solar disk, some sort of
model of the 3-D CME is required. In this paper we address both the
question of the 3-D morphology of the CME and the more fundamental
question of the nature of the plasma-magnetic field relationship,
by comparing the limb and on-disk CME representations of an analytic
3-D MHD model based on a spheromak-type flux rope magnetic field
configuration. In particular, we show that the morphology of twin
dimmings (also referred to as transient coronal holes) observed
in X ray and EUV can be reproduced by the CME model as the on-disk
projection of the prominence cavity modeled for limb CMEs. Moreover,
the bright core of a limb CME, generally corresponding to the material
in an erupting prominence, may be interpreted to be the S-shaped
central core of the modeled on-disk CME, splitting the cavity into
twin dimmings when observed head-on without obstruction. The magnetic
field structure of this central core exhibits many of a filament's
magnetic field features required to match observations. Finally,
we consider the nature of S-shaped filaments and X-ray “sigmoids”
in the context of the model, in terms of localized heating and cooling
acting on the modeled CME magnetic field structure.
---------------------------------------------------------
Title: Magnetostatic atmospheres possessing identical invariants of
ideal magnetohydrodynamics
Authors: Manchester, Ward; Low, B. C.
2000PhPl....7.1263M Altcode:
A physical analysis is presented of two distinct families of
two-dimensional (2D) analytical solutions for isothermal periodic
magnetostatic atmospheres in uniform gravity, one arrived at by Dungey
and the other arrived at by Low and Manchester. It is demonstrated
that particular members of the two families of 2D equilibria may be
generated from the same planar state by plasma displacements which move
the system through continuous sequences of equilibria while ensuring
flux freezing. The two families of solutions both possess undulating
magnetic field lines but geometrically different flux surfaces. The
Dungey solutions can be created from a planar state by an undulating
deformation whose spatial variation is along the field lines. By
contrast, the 2D plane of variation of the Low-Manchester solutions lies
at an angle to the field lines of the planar state. As a result, a mixed
mode of undulating, interchange and shearing displacements must be made
to the planar state to produce the more complex 2D state. Finally,
the physical properties of these topologically equivalent states,
including the magnetic and electrical helicities and the hydromagnetic
potential energy, as introduced by Mouschovias, are discussed in terms
of the variational principles of Kruskal and Kulsrud.
---------------------------------------------------------
Title: Equilibrium and Stability of Magnetostatic
Atmospheres. I. Dungey-Type Isothermal States
Authors: Low, B. C.; Manchester, Ward, IV
2000ApJ...528.1026L Altcode:
Two families of analytical solutions are presented that describe
isothermal magnetostatic atmospheres in uniform gravity and varying
in two Cartesian dimensions. The solutions in each family share a
common set of magnetic flux surfaces but have different profiles of
field intensity, magnetic shear, and plasma distribution across
these flux surfaces such that force balance is satisfied. A
family of solutions with this mathematical degree of freedom had
previously been found by Dungey. The construction and properties
of the new solutions are described. The hydromagnetic stability of
these solutions is discussed by using the sufficiency criteria of
Hu to determine those profiles of magnetic field and plasma that
assure stability for the whole system. Among the stable equilibria
found are examples of sheared magnetic structures intruding into a
uniformly magnetized, isothermal atmosphere. One of the two families
of solutions is extended to equilibrium states that vary fully with
all three Cartesian coordinates. These extended solutions allow the
possibility of constructing complex structures by juxtapositioning
discrete three-dimensional magnetic structures built separately. These
two-dimensional and three-dimensional magnetostatic states may be
useful as initial states for numerical simulation of time-dependent
magnetohydrodynamic processes in the solar atmosphere.
---------------------------------------------------------
Title: Coronal Mass Ejections, flares and prominences
Authors: Low, B. C.
1999AIPC..471..109L Altcode: 1999sowi.conf..109L
This article describes the hydromagnetic relationships among Coronal
Mass Ejections, flares and prominences to put these phenomena in the
context of the solar corona evolving in response to the solar dynamo.
---------------------------------------------------------
Title: Topologically Equivalent Magnetostatic Atmospheres and
Numerical MHD Simulations of Buoyancy Instabilities
Authors: Manchester, W.; Low, B. C.
1999AAS...194.5508M Altcode: 1999BAAS...31..911M
We present a physical application of two distinct families of
two-dimensional analytical solutions which describe isothermal periodic
magnetostatic atmospheres in uniform gravity. We demonstrate that
members of both families of 2D solutions can be arrived at from the
same planar atmosphere by finite plasma displacements which ensures the
conservation of mass and magnetic flux. The fist family of solutions is
characterized by undulating field lines which are confined to the plane
of variation. By contrast, the second family of solutions has the plane
of variation rotated away from the field lines. As a result, this family
possesses a sheared field geometry with a field component out of the
plane of variation. A striking feature of this 2D configuration is the
way in which the field lines becomes highly sheared as the undulations
increase in height. Both families of solutions are used as initial
states for two-dimensional, time-dependent magnetohydrodynamic numerical
simulations of buoyancy instabilities. The simulations demonstrate how
the magnetic field component out of the plane of variation propagates
into rising loops by the action of shear Alfven waves. We show that
this has a profound effect on the buoyancy instability and that the
resulting velocity field resembles the photospheric shear flow observed
across the polarity inversion line of flux emerging regions.
---------------------------------------------------------
Title: Partially Open Solar Coronal Magnetic Field in 3D Magnetostatic
Atmosphere
Authors: Low, B. C.; Dikpati, M.
1999AAS...194.9408L Altcode: 1999BAAS...31..992L
We present a family of analytic solutions describing the quiescent solar
corona as magnetostatic equilibrium states in the presence of a 1/r(2)
gravity. These solutions assume no symmetry so that large-scale coronal
magnetic structures may be modeled in realistic geometry. In particular,
these solutions are capable of modeling multiple helmet-streamer
belts associated with several magnetic polarity inversion lines at
the base of the corona, with each streamer-belt sandwiched between
coronal regions of open magnetic fields. The neglect of the solar wind
limits the applicability of such models to the low solar corona. These
solutions are useful as illustrative examples of the global magnetic
field topologies expected in the solar corona, and, as initial states
for three-dimensional, time-dependent magnetohydrodynamic numerical
simulations as a means of developing coronal models that include the
effect of the solar wind. *The National Center for Atmospheric Research
is sponsored by the National Science Foundation.
---------------------------------------------------------
Title: Complex magnetohydrodynamic bow shock topology in field-aligned
low-β flow around a perfectly conducting cylinder
Authors: de Sterck, H.; Low, B. C.; Poedts, S.
1998PhPl....5.4015D Altcode:
Two-dimensional ideal magnetohydrodynamic (MHD) simulations are
presented that demonstrate several novel phenomena in MHD shock
formation. The stationary symmetrical flow of a uniform, planar,
field-aligned, low-β and superfast magnetized plasma around a
perfectly conducting cylinder is calculated. The velocity of the
incoming flow is chosen such that the formation of fast switch-on
shocks is possible. Using a time marching procedure, a stationary
bow shock is obtained, composed of two consecutive interacting shock
fronts. The leading shock front has a dimpled shape and is composed
of fast, intermediate and hydrodynamic shock parts. A second shock
front follows the leading front. Additional intermediate shocks and
tangential discontinuities are present in the downstream part of the
flow. The intermediate shocks are of the 1-3, 1-4, 2-4 and 1=2-3=4
types. This is a confirmation in two dimensions of recent results
on the admissibility of these types of shocks. Recently it has also
been shown that the 1=2-3=4 shock, embedded in a double compound wave,
is present in the analytical solution of some planar one-dimensional
MHD Riemann problems. This MHD flow with interacting shocks may have
applications for some observed features of fast solar Coronal Mass
Ejections and other phenomena in low-β space plasmas.
---------------------------------------------------------
Title: A Time-Dependent Three-Dimensional Magnetohydrodynamic Model
of the Coronal Mass Ejection
Authors: Gibson, S. E.; Low, B. C.
1998ApJ...493..460G Altcode:
We present a theoretical magnetohydrodynamic (MHD) model describing the
time-dependent expulsion of a three-dimensional coronal mass ejection
(CME) out of the solar corona. The model relates the white-light
appearance of the CME to its internal magnetic field, which takes the
form of a closed bubble, filled with a partly anchored, twisted magnetic
flux rope, and embedded in an otherwise open background field. The model
is constructed by solving in closed form the time-dependent ideal MHD
equations for a γ = 4/3 polytrope making use of a similarity assumption
and the application of a mathematical stretching transformation in order
to treat a complex field geometry with three-dimensional variations. The
density distribution frozen into the expanding CME magnetic field
is obtained. The scattered white light integrated along the line of
sight shows the conspicuous three features often associated with CMEs
as observed with white-light coronagraphs: a surrounding high-density
region, an internal low-density cavity, and a high-density core. We
also show how the orientation of this three-dimensional structure
relative to the line of sight can give rise to a variety of different
geometric appearances in white light. These images generated from a CME
model in a realistic geometry offer an opportunity to directly compare
theoretical predictions on CME shapes with observations of CMEs in
white light. The mathematical methods used in the model construction
have general application and are described in the Appendices.
---------------------------------------------------------
Title: Self-similar Time-dependent MHD in Three-dimensional Space
Authors: Low, B. C.; Gibson, S. E.
1997AAS...19112006L Altcode: 1997BAAS...29.1403L
A general class of self-similar exact solutions to the time-dependent
ideal MHD equations was discovered in the early eighties (Low 1982 ApJ
254, 796; Low 1984 ApJ 281, 392). These solutions describe exploding or
imploding atmospheres in the polytropic approximation with a 4/3 index
and in the presence of Newtonian gravity. A full range of accelerating,
decelerating, or inertial explosions or implosions are possible. A novel
feature of these solutions is that they allow for full variation in
three dimensional space unstricted by any spatial symmetry, presenting
an opportunity for generating models of exploding or imploding
atmospheres in realistic geometry. The reduction of the problem from
four dimensional space-time to the three-dimensional similarity space
leads to governing equations which are still highly non-trivial to
solve. This paper presents the results of a method of solution which
yields a three-dimensional, analytic model of a coronal mass ejection
carrying a ball of twisted magnetic fields pushing its way through
surrounding open magnetic fields in a time-dependent expulsion out of
the solar corona (Gibson and Low 1998 ApJ, in press). This method may
be useful in other astrophysical applications. The National Center for
Atmospheric Research is sponsored by the National Science Foundation.
---------------------------------------------------------
Title: Flux Emergence and Prominences: a New Scenario for
3-DIMENSIONAL Field Geometry Based on Observations with the Advanced
Stokes Polarimeter
Authors: Lites, B. W.; Low, B. C.
1997SoPh..174...91L Altcode:
This paper presents an interpretation of the evolution of the vector
magnetic field at the photosphere based on measurements of the advanced
Stokes polarimeter, along with chromospheric Hα from the Lockheed
instrument operating on La Palma and X-ray images of the corona from
Yohkoh. These measurements are consistent with the emergence of a nearly
closed magnetic structure from the solar interior into the corona. The
highly non-potential field topology inferred from the data suggests
that strong field-aligned currents exist in the emergent magnetic
structure as it buoyantly rises through the photosphere. Material
trapped in this closed structure is pulled upward to later condense
into a prominence. By analogy of this small active region evolution
with the observed properties of large quiescent prominences, we
speculate that this process might also be operative on a much larger
scale. A 3-dimensional magnetostatic model is presented which has many
topological features in common with the observations.
---------------------------------------------------------
Title: Solar activity from the coronal perspective.
Authors: Low, B. C.
1997smf..conf....1L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solar Activity and the Corona
Authors: Low, B. C.
1996SoPh..167..217L Altcode:
This review puts together what we have learned about coronal
structures and phenomenology to synthesize a physical picture of the
corona as a voluminous, thermally and electrically highly-conducting
atmosphere responding dynamically to the injection of magnetic flux
from below. The synthesis describes complementary roles played by
the magnetic heating of the corona, the different types of flares,
and the coronal mass ejections as physical processes by which magnetic
flux and helicity make their way from below the photosphere into the
corona, and, ultimately, into interplanetary space. In these processes,
a physically meaningful interplay among dissipative magnetohydrodynamic
turbulence, ideal ordered flows, and magnetic helicity determines how
and when the rich variety of relatively long-lived coronal structures,
spawned by the emerged magnetic flux, will evolve quasi-steadily
or erupt with the impressive energies characteristic of flares and
coronal mass ejections. Central to this picture is the suggestion,
based on recent theoretical and observational works, that the the
emerged flux may take the form of a twisted flux rope residing
principally in the corona. Such a flux rope is identified with the
low-density cavity at the base of a coronal helmet, often but not always
encasing a quiescent prominence. The flux rope may either be bodily
transported into the corona from below the photosphere, or reform out
of a state of flaring turbulence under some suitable constraint of
magnetic-helicity conservation. The appeal of this synthesis is its
physical simplicity and the manner it relates a large set of diverse
phenomena into a self-consistent whole. The implications of this view
point are discussed.
---------------------------------------------------------
Title: Current sheets in the solar minimum corona
Authors: Gibson, S. E.; Bagenal, F.; Low, B. C.
1996JGR...101.4813G Altcode:
We analytically combine stress-free current sheets with a coronal
magnetostatic bulk current model. We begin by imposing a current sheet
at the equator as an upper boundary condition on the modeled coronal
field. We find that in order to reproduce the sharp gradients across
the boundaries of helmet streamers, we also have to add current sheets
along the interface between open and closed field lines. We find a
description of coronal magnetic field and density in the presence
of both bulk and sheet currents that matches both white light and
photospheric magnetic flux observations.
---------------------------------------------------------
Title: The Role of Coronal Mass Ejections in Solar Activity
Authors: Low, B. C.
1996ASPC...95..148L Altcode: 1996sdit.conf..148L
No abstract at ADS
---------------------------------------------------------
Title: Magnetohydrodynamic processes in the solar corona: flares,
coronal mass ejections and magnetic helicity.
Authors: Low, B. C.
1996ASIC..481..133L Altcode:
The magnetized, million-degree solar corona evolves in cycles of
about eleven years, in dynamical response to newly generated magnetic
fluxes emerging from below to eventually reverse the global magnetic
polarity. Over the larger scales, the corona does not erupt violently
all the time. Violent events like the flares and episodic ejections
of material into interplanetary space occur frequently, several times
a day, but they often originate in long-lived magnetic structures
which form continually throughout the solar cycle. In this paper,
the creation, stability, and eventual eruption of these structures
are discussed from basic principles, drawing on recent advances in
observation and theory. A global view is offered in which different
pieces of observation relate physically, with distinct roles for the
conservation of magnetic helicity and the releases of magnetic energy
in dissipated and ordered forms.
---------------------------------------------------------
Title: The spontaneous formation of current-sheets in astrophysical
magnetic fields.
Authors: Low, B. C.
1996ASIC..481..109L Altcode:
This article is an introduction to Parker's idea that electric current
sheets form spontaneously in astrophysical magnetic fields under the
condition of high electrical conductivity. Upon formation, the current
sheets will collapse to such small widths as to result in resistive
reconnection of magnetic fields and heating, despite the very large
but finite electrical conductivity. This mechanism is an attractive
explanation of the ubiquitous association between magnetic fields and
heated plasmas in many astrophysical situations. The hydromagnetic
process of this mechanism is illustrated, using a well-studied
two-dimensional Cartesian model involving a quadrupolar magnetic field
with or without a magnetic null point.
---------------------------------------------------------
Title: The Possible Ascent of a Closed Magnetic System through
the Photosphere
Authors: Lites, B. W.; Low, B. C.; Martinez Pillet, V.; Seagraves,
P.; Skumanich, A.; Frank, Z. A.; Shine, R. A.; Tsuneta, S.
1995ApJ...446..877L Altcode:
We present a comprehensive interpretation of the evolution of a small
magnetic region observed during its entire disk passage. The vector
magnetic field measurements from the Advanced Stokes Polarimeter,
along with Hα and magnetogram measurements from the Lockheed SOUP
instrument operating at the Swedish Solar Observatory on La Palma,
and soft X-ray images from the Yohkoh satellite support the hypothesis
that we have observed the passage of a nearly closed magnetic system
through the photosphere into the corona. The observations suggest that
as the magnetic flux begins to emerge into the photosphere it shows a
rather simple geometry, but it subsequently develops a small δ-sunspot
configuration with a highly sheared vector field along the polarity
inversion line running through it. At that stage, the vector field is
consistent with a concave upward magnetic topology, indicative of strong
electric currents above the photosphere. An Hα prominence is found
above this inversion line when the δ-sunspot is fully formed. These
observed features and the sequence of events are interpreted in terms
of a nearly closed magnetic system that rises through the photosphere
into the corona as a result of magnetic buoyancy. The magnetic system
persists in the corona well after the dark δ-sunspot has disappeared
in the photosphere We suggest that this coronal structure is in
quasi-static equilibrium with its buoyancy partially countered by
the weight of the plasma trapped at the bottom of closed magnetic
loops. The plausibility of such a scenario is demonstrated by a
three-dimensional magnetostatic model of the emergence of a closed,
spheroidal magnetic system in the corona, in which the Lorentz force
arising from cross-field currents is balanced by the gravitational
and pressure forces. This theoretical model carries many features in
common with the observed morphology of our active region.
---------------------------------------------------------
Title: Magnetostatic Structures of the Solar Corona. II. The Magnetic
Topology of Quiescent Prominences
Authors: Low, B. C.; Hundhausen, J. R.
1995ApJ...443..818L Altcode:
This paper treats the magnetic properties of the quiescent prominence
as a part of the larger coronal structure made up of the prominence,
cavity, and helmet dome. A rigorous analysis of the mechanical support
of a vertical prominence sheet suspended in equilibrium by magnetic
fields in uniform gravity shows that the finite vertical extension
of the prominence sheet has an important dynamic constraint. For the
inverse topology with the prominence magnetic field pointing opposite
to the field implied by the bipolar photospheric region below,
this constraint requries the prominence sheet to be embedded in a
horizontal, nearly force-free, magnetic flux rope which crucially
supports a part of the prominence weight by current attraction from
above. A similar analysis of the support problem is carried out for
the prominence in the normal topology in which both prominence and
photospheric magnetic fields point in the same sense. Starting with
the observation that most prominences are of the inverse topology,
a recent model is extended to show that this topology implies that the
prominence sits in a two-flux magnetic system, one flux connecting the
bipolar magnetic sources in the photosphere below and the other forming
a rope which embeds the prominence and runs above and parallel to the
photospheric polarity-inversion line. This model physically relates
several pieces of well-known but hitherto disjoint observations. The
prominence flux rope manifests itself as the cavity in the corona and
as the filament channel in the chromosphere. The chromospheric fibril
patterns associated with prominences and filament channels can, for
the first time, be modeled faithfully. Several physical implications
on the origin of the prominence and questions deriving from the results
are discussed.
---------------------------------------------------------
Title: Coronal mass ejections and magnetic helicity
Authors: Low, B. C.
1994ESASP.373..123L Altcode: 1994soho....3..123L
No abstract at ADS
---------------------------------------------------------
Title: A Class of Force-Free Magnetic Fields for Modeling Pre-Flare
Coronal Magnetic Configurations
Authors: Chou, Y. P.; Low, B. C.
1994SoPh..153..255C Altcode:
Three-dimensional, quasi-static evolutions of coronal magnetic
fields driven by photospheric flux emergence are modeled by a class
of analytic force-free magnetic fields. Our models relate commonly
observed photospheric magnetic phenomena, such as the formation and
growth of sunspots, the emergence of an X-type separator, and the
collision and merging of sunspots, to the three-dimensional magnetic
fields in the corona above. By tracking the evolution in terms of a
continuous sequence of force-free states, we show that flux emergence
and submergence along magnetic neutral lines in the photosphere
are essential processes in all these photospheric phenomena. The
analytic solutions we present have a parametric regime within which
the magnetic energy attained by an evolving force-free field may be
of the order of 10<SUP>30</SUP> ergs to several 10<SUP>31</SUP> ergs,
depending on the magnetic environment into which an emerging flux
intrudes. The commonly used indicators of magnetic shear in magnetogram
interpretation are discussed in terms of field connectivity in our
models. It is demonstrated that the crossing angle of the photospheric
transverse magnetic field with the neutral line may not be a reliable
indicator of the magnetic shear in the coronal field above, due to the
complexity of three-dimensionality. The poorly understood constraint
of magnetic-helicity conservation on the availability of magnetic free
energy for a flare is briefly discussed.
---------------------------------------------------------
Title: Magnetostatic Structures of the Solar Corona. I. A Model
Based on the Cauchy Boundary Value Problem
Authors: Hundhausen, J. R.; Low, B. C.
1994ApJ...429..876H Altcode:
A model is presented for the static equilibrium of a magnetized,
polytropic atmosphere stratified by uniform gravity and invariant in
a Cartesian direction. The profiles of plasma pressure and magnetic
shear as functions of the magnetic stream function, which render the
governing equation linear, lead to unphysical features if these profiles
are applied to the infinite half-space bounded below by a plane. These
undesirable features are shown to be removed when these special profiles
are localized to a region bounded by a magnetic flux surface, outside of
which is an atmosphere in plane-parallel hydrostatic equilibrium with
a potential magnetic field. Two families of solutions are constructed
by direct solution of the Cauchy boundary value problem for the Laplace
equation, one with continuous and the other with discontinuous pressures
across this magnetic boundary. Illustrative solutions are analyzed,
with applications to long-lived density enhancements and depletions
in the solar corona. In particular, the hydromagnetic stability of
pressure discontinuities is studied as an example of a general result
due to Hu (1988). It is pointed out that the stability of the sharp
interface between the prominence cavity and the high-density coronal
helmet may be understood in terms of competing effects arising from
density stratification and magnetic curvature. The model presented
lays the mathematical groundwork for the other papers of the series.
---------------------------------------------------------
Title: Magnetohydrodynamic processes in the solar corona: Flares,
coronal mass ejections, and magnetic helicity
Authors: Low, B. C.
1994PhPl....1.1684L Altcode:
The magnetized, million-degree solar corona evolves in cycles of
about 11 years, in dynamical response to newly generated magnetic
fluxes emerging from below to eventually reverse the global magnetic
polarity. Over the larger scales, the corona does not erupt violently
all the time. Violent events like the flares and episodic ejections
of material into interplanetary space occur frequently, several times
a day, but they often originate in long-lived magnetic structures
that form continually throughout the solar cycle. In this paper,
the creation, stability, and eventual eruption of these structures
are discussed from basic principles, drawing on recent advances in
observation and theory. A global view is offered in which different
pieces of observation relate physically, with distinct roles for the
conservation of magnetic helicity and the release of magnetic energy
in dissipated and ordered forms.
---------------------------------------------------------
Title: The Free Energies of Partially Open Magnetic Fields and
Coronal Mass Ejections
Authors: Smith, D. F.; Low, B. C.
1994scs..conf...97S Altcode: 1994IAUCo.144...97S
The results of Low and Smith (1993) on how to circumvent Aly's
limitation on the energy of force-free magnetic fields are briefly
reviewed. Two non-force-free configurations with energies in excess of
the energy of the corresponding completely open field are discussed:
1. A magnetic bubble configuration with completely detached field
lines. 2. A combined configuration consisting of closed field lines
with plasma compressed against the star and a superimposed helmet
streamer with all field lines tied to the surface. It is shown that
the bubble configuration is unstable.
---------------------------------------------------------
Title: A Class of Three-dimensional Isothermal Laminated Equilibria
and Their Stability
Authors: Chou, Y. P.; Low, B. C.; Bhattacharjee, A.
1993ApJ...416..379C Altcode:
Three-dimensional ideal magnetostatic equilibria with laminated
magnetic field in which one component of the magnetic field vanishes,
are constructed for isothermal coronal plasmas in the presence of
uniform gravity. Three subsets of the general solution are found to
be absolutely stable, when subject to rigid anchoring of the magnetic
field lines at the base of the atmosphere. The magnetic fields in these
cases carry currents. For equilibria with general magnetic strength
variations, the criteria for stability are obtained by minimizing the
energy integral. Numerical solutions for the Euler-Lagrange equations
that result from the minimization procedure are given, and are used
to determine critical equilibrium parameters that give a bound for the
marginal stability. For low values of plasma β(≡ 8πp/B<SUP>2</SUP>),
the scale length of the plasma density variation can be small and the
magnetic shear can be large, suggestive of the observed fine plasma
loops and the rapid fluctuation of the inclination angle of the field
lines in the sunspot penumbra.
---------------------------------------------------------
Title: Mass acceleration processes: The case of the coronal mass
ejection
Authors: Low, B. C.
1993AdSpR..13i..63L Altcode: 1993AdSpR..13...63L
A theoretical review is given on what drives the coronal mass ejection,
centering on the question of the origin of its total energy, typically
of the order of a few 10<SUP>31</SUP> erg. This energy accounts for
the work of lifting and accelerating the ejected mass as well as a
significant amount left in the open magnetic field created by the
ejection. It is pointed out that the total energy cannot be stored in
the pre-eruption corona entirely in the form of force-free electric
currents, based on a plausible magnetohydrodynamic conjecture of
Aly. Storage in the form of cross-field electric currents held in
equilibrium by pressure and gravitational forces seems possible,
in particular if these currents are associated with closed magnetic
fluxes entirely detached from the atmospheric base. The implications and
physical issues of these results for the mass ejection are discussed,
leading to several suggestions for future study. <P />The National
Center for Atmospheric Research is sponsored by the National Science
Foundation of the United States
---------------------------------------------------------
Title: The Free Energies of Partially Open Coronal Magnetic Fields
Authors: Low, B. C.; Smith, D. F.
1993ApJ...410..412L Altcode:
A simple model of the low corona is examined in terms of a static
polytropic atmosphere in equilibrium with a global magnetic field. The
question posed is whether magnetostatic states with partially open
magnetic fields may contain magnetic energies in excess of those in
fully open magnetic fields. Based on the analysis presented here, it is
concluded that the cross-field electric currents in the pre-eruption
corona are a viable source of the bulk of the energies in a mass
ejection and its associated flare.
---------------------------------------------------------
Title: The Nature of the Quiescent Prominence Cavity
Authors: Low, B. C.
1993BAAS...25.1218L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A Class of Three-Dimensional Isothermal Laminated Equilibria
and Their Stability
Authors: Chou, Y. P.; Low, B. C.; Bhattacharjee, A.
1993BAAS...25Q1208C Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Force-free Magnetic Fields with Singular Current-Density
Surfaces
Authors: Low, B. C.
1993ApJ...409..798L Altcode:
This paper is a study of a family of nonlinear force-free magnetic
fields, in Cartesian geometry and invariant in a given direction,
as simple models of the magnetic fields in the solar corona. Posed
as a problem in the infinite half-space bounded below by the
photosphere taken as a rigid plane, the solution is constructed
with the field-aligned currents confined within a cylindrical plasma
surface outside of which the magnetic field is potential. An infinity
of solutions are shown to be tractable by the method of images of
potential theory. Among the results presented is the demonstration of a
magnetic flux surface in the plasma interior, which is ideally stable,
where the electric current density becomes an integrable infinity,
created quasi-statically by continuous boundary displacement of the
magnetic footpoints. This result is discussed in connection with
Parker's theory of coronal heating by the dissipation of electric
current sheets. Simple modifications of the force-free solutions are
also carried out to demonstrate (1) the formation of a magnetic cusp
point in a bipolar magnetic field in equilibrium with an isotropic
pressure, and (2) the possibility of a Kuperus-Raadu type prominence
embedded in a horizontal, helical magnetic flux rope.
---------------------------------------------------------
Title: Three-dimensional Structures of Magnetostatic
Atmospheres. V. Coupled Electric Current Systems
Authors: Low, B. C.
1993ApJ...408..689L Altcode:
The magnetostatic equations describing equilibrium among the Lorentz,
pressure, and gravitational forces are transformed to a statement of
Ampere's law incorporating the condition of equilibrium. The pressure
as a function of space is expressed in terms of the gravitational
potential, a component of the magnetic field, and an arbitrary third
variable to complete a set of local curvilinear coordinates. The
coupling of the two current systems is shown to be manifest in the
need for the third variable to describe the pressure structure. A
discussion relating the derived equations to other known forms of the
magnetostatic equations is presented.
---------------------------------------------------------
Title: Three-dimensional Structures of Magnetostatic
Atmospheres. VI. Examples of Coupled Electric Current Systems
Authors: Low, B. C.
1993ApJ...408..693L Altcode:
Attention is given to exact solutions which describe the static
equilibrium of atmospheres stratified by a uniform gravity, in the
presence of magnetic fields lying in parallel vertical planes. These
equilibrium states consist of different, highly varied structures
in these planes stacked together in global equilibrium. A subset of
the solutions presented describe a magnetostatic system closed by a
simple equation of state, namely, an atmosphere which conducts heat
perfectly along the magnetic field but no heat across it. It is found
that periodic structures in adjacent magnetic flux planes can march
out of step as a result of an irrational ratio between their periods,
leading to extreme electric current densities despite the boundedness
of the magnetic intensity and plasma pressure.
---------------------------------------------------------
Title: Three-dimensional Structures of Magnetostatic
Atmospheres. IV. Magnetic Structures over a Solar Active Region
Authors: Low, B. C.
1992ApJ...399..300L Altcode:
A static model is presented for the long-lived structures over a solar
active region dominated by a pair of sunspots of opposite magnetic
polarities. The magnetic field is approximately force-free high in
the atmosphere but interacts strongly with the plasma and gravity
in the lower region through cross-field electric currents. Basic
atmospheric features long discussed in the literature can be reproduced
in realistic geometry, such as the density depletion over a sunspot,
magnetic shear, and levitated magnetic flux ropes interpretable as
chromospheric filaments. Explicit solutions showing these features
are described and compared, with a discussion of the implications for
the interpretation of vector-magnetograph data. These solutions are
illustrative examples taken from a large set obtainable by transforming
the magnetostatic equations to solvable, linear differential equations
given in the preceding paper in this series.
---------------------------------------------------------
Title: Self-similar Magnetohydrodynamics. V. Gravitating Spheres
and Spheroids
Authors: Low, B. C.
1992ApJ...390..567L Altcode:
This paper presents a family of explicit, time-dependent
magnetohydrodynamic solutions describing gravitating, magnetized,
gamma = 4/3 polytropes in the shape of a spheroid undergoing
self-similar expansion or contraction in vacuum. Included in this
family are the solutions for a gravitating, magnetized sphere, which
are mathematically akin to Prendergast's (1956) equilibrium solutions
for a static magnetic star. The solutions presented here are of basic
physical interest and may be useful for the testing of multidimensional,
numerical magnetohydrodynamic codes which include self-gravity as an
important effect.
---------------------------------------------------------
Title: A Numerical Scheme for the Modeling of Electric Current Sheet
Formation in the Solar Atmosphere
Authors: Charbonneau, P.; Low, B. C.
1992ASPC...26..531C Altcode: 1992csss....7..531C
No abstract at ADS
---------------------------------------------------------
Title: Formation of electric-current sheets in the magnetostatic
atmosphere
Authors: Low, B. C.
1992A&A...253..311L Altcode:
An analytical illustration is presented of the theorem by Parker (1989,
1990), which states that a magnetic field with an arbitrarily prescribed
topology in an electrically perfectly conducting medium tends toward
equilibrium states with either embedded electric current sheets or
magnetic tangential discontinuities. The illustration concerns an
isothermal atmosphere in which the Lorentz force does not vanish,
but rather balances pressure and gravitational forces in static
equilibrium. It is shown that the quasi-static evolution of the
atmosphere in response to a continuously changing plasma pressure
distribution at the atmospheric base can bring an initially smooth
state to one in which an electric current sheet forms.
---------------------------------------------------------
Title: On the Spontaneous Formation of Electric Current Sheets above
a Flexible Solar Photosphere
Authors: Low, B. C.
1991ApJ...381..295L Altcode:
This paper treats the general tendency for a magnetic field in an
electrically perfectly conducting plasma to seek an equilibrium
state with embedded electric current sheets or magnetic tangential
discontinuities. This property is simplest to demonstrate theoretically
with two-dimensional force-free magnetic fields in the infinite
half-space above a plane boundary where magnetic footpoints are
rigidly anchored. The principal results of recent treatments of
this simple model are summarized and extended to clarify their basic
physics in order to answer the criticism of this model by Karpen et
al. (1990). These authors have concluded that the formation of current
sheets in this model depended on the use of rigid boundary conditions
to the extent that current sheets would not form if the boundary is not
rigid but is replaced by a gravitationally stratified photosphere of
finite thickness. It is shown that the conclusion of these authors is
not valid, based on a physical analysis and an explicit magnetostatic
construction of a possible equilibrium state in which a current sheet
has formed in the presence of a flexible photosphere.
---------------------------------------------------------
Title: Three-Dimensional Magnetostatic Equilibrium
Authors: Low, B. C.
1991BAAS...23..967L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Three-dimensional Structures of Magnetostatic
Atmospheres. III. A General Formulation
Authors: Low, B. C.
1991ApJ...370..427L Altcode:
This paper presents a mathematical description of the three-dimensional
structures of static, magnetized atmospheres in terms of the
electric-current flux surfaces. In the first paper of this series,
a class of three-dimensional magnetostatic states was presented. These
states are characterized by electric currents flowing perpendicular to
gravity which was taken to be either uniform in space or spherically
symmetric about a point mass. A limitation of these solutions is
that the magnetic field in general cannot have a net twist. The new
formulation generalizes these solutions in two significant ways,
namely, to allow for other general potential body forces than the
special gravitational forces assumed in the first paper and to include
the presence of a net magnetic twist. This theoretical development
opens up opportunities in modeling realistic solar magnetic fields as
well as other astrophysical magnetic fields. The obliquely rotating
magnetosphere and self-gravitating magnetized plasma clouds are
two astrophysical examples for which the governing equations are
derived. The complete analytic solution to a specific problem is
presented, which illustrates the anchoring of a fully three-dimensional
force-free magnetic field in the solar atmosphere to the base of the
atmosphere through a non-force-free boundary layer where the magnetic
field interacts strongly with the plasma. This and a rich variety
of other three-dimensional magnetic fields will be studied in the
subsequent papers of this series.
---------------------------------------------------------
Title: Modeling Solar Force-free Magnetic Fields
Authors: Low, B. C.; Lou, Y. Q.
1990ApJ...352..343L Altcode:
A class of nonlinear force-free magnetic fields is presented, described
in terms of the solutions to a second-order, nonlinear ordinary
differential equation. These magnetic fields are three-dimensional,
filling the infinite half-space above a plane where the lines of force
are anchored. They model the magnetic fields of the sun over active
regions with a striking geometric realism. The total energy and the
free energy associated with the electric current are finite and can
be calculated directly from the magnetic field at the plane boundary
using the virial theorem. In the study of solar magnetic fields with
data from vector magnetographs, there is a long-standing interest in
devising algorithms to extrapolate for the force-free magnetic field
in a given domain from prescribed field values at the boundary. The
closed-form magnetic fields of this paper open up an opportunity
for testing the reliability and accuracy of algorithms that claim
the capability of performing this extrapolation. The extrapolation
procedure as an ill-posed mathematical problem is discussed.
---------------------------------------------------------
Title: Slow shocks in an open magnetic field near the sun
Authors: Hu, You-Qiu; Zhu, Zhong-Wei; Hundhausen, A. J.; Holzer,
T. E.; Low, B. C.
1990SCSMP..33..332H Altcode:
A numerical study on the formation of the slow shock in an open
magnetic field due to the motion of a coronal mass ejection driven by
a magnetic flux eruption from below the corona is presented. The slow
shock obtained in the numerical model is characterized by a limited
latitudinal extent and a slightly flattened shape. It is determined
that a fast-mode wave always coexists and interacts with the medium
ahead of the slow shock and deflects the background magnetic field
to create a rarefaction ahead of the slow shock and a compression in
the flank. Thus, these effects have a significant influence on the
geometry and features of the slow shock.
---------------------------------------------------------
Title: Solar Coronal Mass Ejections
Authors: Hundhausen, A. J.; Sime, D. G.; Low, B. C.
1990IAUS..140...16H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Equilibrium and dynamics of coronal magnetic fields.
Authors: Low, B. C.
1990ARA&A..28..491L Altcode:
The paper surveys various hydromagnetic processes whose study has
been stimulated by the observed behavior of the magnetic field in the
solar corona. Attention is given to the equilibrium and stability
of magnetic fields, the onset mechanics of the eruption, and the
large-scale organization and time-dependent ordered dynamics of the
corona. The aim of this survey is to achieve a qualitative physical
understanding of the basic behavior of the coronal plasma.
---------------------------------------------------------
Title: The Dynamics of Solar Coronal Magnetic Fields
Authors: Low, B. C.
1990IAUS..140...13L Altcode:
Coronal mass ejection is discussed in terms of its observable
hydromagnetic processes to define the dynamics of the coronal magnetic
field and thereby extrapolate the findings to other hydromagnetic
phenomena. The three important observations in terms of hydromagnetism
include the broad range of speeds of the mass ejections, the timing of
the eruption of the prominence filaments, and the possibility of slow
shocks based on the slow mass ejections. The observation of coronal
mass ejection suggests that other hydromagnetic phenomena can be
observed and studied using similar techniques.
---------------------------------------------------------
Title: Steady Hydromagnetic Flows in Open Magnetic Fields. II. Global
Flows with Static Zones
Authors: Tsinganos, K.; Low, B. C.
1989ApJ...342.1028T Altcode:
A theoretical study of an axisymmetric steady stellar wind with a
static zone is presented, with emphasis on the situation where the
global magnetic field is symmetrical about the stellar equator and is
partially open. In this scenario, the wind escapes in open magnetic
fluxes originating from a region at the star pole and a region at an
equatorial belt of closed magnetic field in static equilibrium. The
two-dimensional balance of the pressure gradient and the inertial,
gravitational, and Lorentz forces in different parts of the flow are
studied, along with the static interplay between external sources
of energy (heating and/or cooling) distributed in the flow and the
pressure distribution.
---------------------------------------------------------
Title: Astrophysics of the Sun
Authors: Zirin, Harold; Low, Boon Chye
1989PhT....42g..74Z Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Steady Hydromagnetic Flows in Open Magnetic
Fields. III. Allowing for Variations of Density with Latitude and
Nonalignment of Velocity with Magnetic Field
Authors: Hu, Y. Q.; Low, B. C.
1989ApJ...342.1049H Altcode:
A steady hydromagnetic stellar wind flowing in a rotating axisymmetric
partially open magnetic field is modeled under the assumptions that
the density is a function of radial distance only and that the flow is
everywhere aligned to the local magnetic field. The model illustrates
that monotonic acceleration of the wind speed in the polar region
requires a decrease of density toward the stellar pole at fixed radial
distance. In the presence of rotation, a nonalignment between the
flow velocity and the magnetic field is found to be necessary for the
acceleration of the poloidal flow speed from below to above the Alfven
speed defined in terms of the poloidal part of the magnetic field.
---------------------------------------------------------
Title: Spontaneous Formation of Electric Current Sheets by the
Expulsion of Magnetic Flux
Authors: Low, B. C.
1989ApJ...340..558L Altcode:
Two theoretical examples are given to demonstrate the spontaneous
formation of electric current sheets in force-free magnetic fields
frozen into a medium with an infinite electrical conductivity, as a
result of the continuous displacement of the magnetic footpoints at the
boundary. An initial three-lobe axisymmetric magnetic field without
neutral points in the infinite medium outside a unit sphere is found
to adjust to footpoint displacements by a slipping of the central lobe
relative to the other two lobes. Also, a three-dimensional force-free
magnetic field is studied, showing that conditions for the expulsion of
flux from a local region to bring spatially separate fluxes together to
form rotational discontinuities are readily obtained between ordinary
magnetic surfaces.
---------------------------------------------------------
Title: Coronal mass ejections and coronal structures.
Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.;
Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing,
R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos,
P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Stewart,
R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T.
1989epos.conf..493H Altcode:
The work of this team was concerned with modelling of post-flare arches,
the reconnection theory of flares, the slow variation of coronal
structure, and the coronal and interplanetary detection, evolution,
and consequences of mass ejections.
---------------------------------------------------------
Title: On the relationship between the topology of magnetic field
lines and flux surfaces
Authors: Rosner, R.; Low, B. C.; Tsinganos, K.; Berger, M. A.
1989GApFD..48..251R Altcode:
We consider the topological relationship between magnetic field
lines and magnetic flux surfaces. Magnetic helicity provides the
most elementary description of the topology of magnetic field lines
in terms of their linkage. In a simply-connected volume, a sufficient
but not necessary condition for the total magnetic helicity to vanish
is that there exist two independent families of globally-extendable
flux surfaces (given by the level surfaces of Euler potentials). In
contrast, the existence of two distinct global Euler potentials for
multiply-connected volumes is insufficient to guarantee that the total
magnetic helicity vanishes. These well-known results are discussed
in the context of Frobenius' theorem as applied to the differential
equations describing magnetic lines of force; and the notion of Euler
potentials is extended by introducing an analogy to the Hopf map
between the three-sphere and the two-sphere.
---------------------------------------------------------
Title: Magnetic free-energy in the solar atmosphere.
Authors: Low, B. C.
1989GMS....54...21L Altcode: 1989sspp.conf...21L
A program for extrapolating magnetic field in the force-free
approximation has much to teach us about solar magnetic fields and
this review surveys what can be done and the kind of pitfalls that
beset the program.
---------------------------------------------------------
Title: Magnetic Field Configurations Associated with Polarity
Intrusion in a Solar Active Region - Part Two
Authors: Low, B. C.
1988SoPh..115..269L Altcode:
The theoretical force-free magnetic fields in the first paper of this
series, modeling magnetic configurations associated with polarity
intrusion in active regions, are established to be all stable to linear
ideal hydromagnetic perturbations under the boundary condition that
anchors the lines of force rigidly to the photosphere. It is shown first
that these force-free fields belong to an even larger class found by
Chang and Carovillano (1981). A proof by the energy principle is then
given to establish that all force-free magnetic fields in the larger
class are absolutely stable. The physical implications of this result
are discussed.
---------------------------------------------------------
Title: On the Hydromagnetic Stability of a Class of Laminated
Force-Free Magnetic Fields
Authors: Low, B. C.
1988ApJ...330..992L Altcode:
Chang and Carovillano (1981) pointed out the existence of two classes
of nonlinear force-free magnetic fields varying with three spatial
dimensions which can be described analytically. In this paper, it is
established by a general proof using the energy principle that one
of these two classes of fields, in which all lines of force lie on
parallel planes with the field pattern varying from plane to plane,
are all stable to linear perturbations in the ideal hydromagnetic
approximation. Laminated fields are derived which provide an excellent
opportunity to study the propagation of small-amplitude hydromagnetic
waves in a three-dimensional inhomogeneous magnetized medium.
---------------------------------------------------------
Title: Structure and Dynamics of Magnetic Fields in the Solar
Atmosphere
Authors: Low, B. C.
1988BAAS...20..723L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Spontaneous Formation of Electric Current Sheets and the
Origin of Solar Flares
Authors: Low, B. C.; Wolfson, R.
1988ApJ...324..574L Altcode:
It is demonstrated that the continuous boundary motion of a sheared
magnetic field in a tenuous plasma with an infinite electrical
conductivity can induce the formation of multiple electric current
sheets in the interior plasma. In response to specific footpoint
displacements, the quadrupolar magnetic field considered is shown
to require the formation of multiple electric current sheets as it
achieves a force-free state. Some of the current sheets are found to
be of finite length, running along separatrix lines of force which
separate lobes of magnetic flux. It is suggested that current sheets
in the form of infinitely thin magnetic shear layers may be unstable to
resistive tearing, a process which may have application to solar flares.
---------------------------------------------------------
Title: Electric Current Sheet Formation in a Magnetic Field Induced
by Continuous Magnetic Footpoint Displacements
Authors: Low, B. C.
1987ApJ...323..358L Altcode:
Attention is given to two analytical examples illustrating the
formation of an electric current sheet in a magnetic field without
neutral points, as a result of a continuous boundary displacement of
the magnetic footpoints. This effect can be demonstrated by resort
to potential magnetic fields that are treated as special cases of
the general force-free magnetic field. The problem of the force-free
magnetic field is cast in terms of Euler potentials.
---------------------------------------------------------
Title: Do slow shocks precede some coronal mass ejections?
Authors: Hundhausen, A. J.; Holzer, T. E.; Low, B. C.
1987JGR....9211173H Altcode:
The observed speeds of coronal mass ejections are often below the
estimated Alfvén speed but above the sound speed for the background
solar corona. This suggets that slow magnetohydrodynamic shocks may form
as mass ejections sweep through the corona. We argue on the basis of
the Rankine-Hugoniot relations and the propagation of small-amplitude
slow mode waves that the shape of a slow shock front would be flattened
(with respect to a sun-centered sphere) or perhaps even concave outward
(from the sun) and thus present a very different appearance from the
fast coronal shock waves that have been commonly modeled as wrapping
around a mass ejection. The region behind a slow shock front standing
just off the top of a coronal mass ejection would extend well out
beyond the visible flanks of the ejection. The deflections of coronal
structures that are commonly observed well outside of these flanks
(and which are inconsistent with a fast shock wrapped around the mass
ejection) are consistent with the presence of the slow shock, whether
they lie in the enlarged postshock region or in a region still further
beyond. Although the flattering of the tops of some mass ejections
suggests our proposed slow shock configuration, a true test of its
existence awaits formulation of quantitative models and detailed
comparison with observations.
---------------------------------------------------------
Title: Characteristics of the Expansion Associated with Eruptive
Prominences
Authors: Athay, R. G.; Low, B. C.; Rompolt, B.
1987SoPh..110..359A Altcode:
Gradients of Hα and electron scattering intensities derived from
instantaneous radial distributions of erupting prominence material
observed at several solar radii by Illing and Athay (1986) are often
markedly smaller than those inferred by comparing the intensities
observed near several radii to average prominence intensities
observed near the limb. In this paper, we show that gradients derived
by following individual features in their outward progression with
time yield values that are consistent with limb observations and that
usually exceed the values obtained from instantaneous distributions. We
conclude from the diversity of observed gradients that the prominence
eruption cannot be described by a self-similar expansion in which the
expansion velocity is a function of radius and time only. However,
we cannot rule out possible self-similar solutions that allow the
expansion velocity to be a function of angular direction.
---------------------------------------------------------
Title: Electric Current-Sheet Formation in a Magnetic Field Induced
by Continuous Magnetic Footpoint Displacements
Authors: Low, B. C.
1987BAAS...19..922L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The velocity field of a coronal mass ejection: The event of
September 1, 1980
Authors: Low, B. C.; Hundhausen, A. J.
1987JGR....92.2221L Altcode:
A coronal mass ejection with the appearance of two sets of overlapping
loops occurred at about 0600 UT on September 1, 1980, over the
northwest limb of the sun. It was one of the fastest events observed
by the Solar Maximum Mission coronagraph during the 1980 epoch, with
apparent radial velocity components or several features approaching
1000 km s<SUP>-1</SUP>. A study of the slow evolution of H<SUB>α</SUB>
prominence filaments and coronal structures in the northwest solar
sector suggests that the mass ejection resulted from the disruption of
a helmet streamer in association with, possibly, two filaments to give
rise to the double-loop structure. This event is well covered by 10
coronagraph images of good quality so that the complex velocity field,
defined by the apparent motions of many different parts of the mass
ejection, can be mapped out as a function of space and time. The results
of such an analysis are presented and related to current concerns
in the theoretical understanding of mass ejections. In particular,
it is concluded that a self-similar description of the velocity field
is a gross oversimplification and that although some evidence of wave
propagation can be found, the bright features in this mass ejection are
plasma structures moving (presumably) with frozen-in magnetic fields,
rather than waves propagating through plasmas and magnetic fields.
---------------------------------------------------------
Title: Static Current-Sheet Models of Quiescent Prominences
Authors: Wu, F.; Low, B. C.
1987ApJ...312..431W Altcode:
A two-dimensional solar prominence model is extended to
three-dimensional variations and curved current sheets. The model treats
prominences as infinitely thin electric current sheets forming vertical
planes supported by a magnetic potential. Equilibrium states are derived
by solving Ampere's equation for a discrete current density of a surface
where the Lorentz force is everywhere upward. The mass distribution
is calculated to balance the Lorentz force. Linear superpositions of
potential fields are employed to define three-dimensional models for
periodic prominences in a given direction and for a prominence mass
sheet with a finite length.
---------------------------------------------------------
Title: Modeling Two-Dimensional Solar Wind Flows (R)
Authors: Low, B. C.
1987sowi.conf..113L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Interplanetary Effects of Coronal Mass Ejections
Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.;
Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing,
R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos,
P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Steward,
R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T.
1986epos.conf.6.52H Altcode: 1986epos.confF..52H
No abstract at ADS
---------------------------------------------------------
Title: Initiations of Coronal Mass Ejections
Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.;
Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing,
R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos,
P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Steward,
R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T.
1986epos.conf.6.27H Altcode: 1986epos.confF..27H
No abstract at ADS
---------------------------------------------------------
Title: Static current-sheet models of quiescent prominences.
Authors: Wu, F.; Low, B. C.
1986NASCP2442...69W Altcode: 1986copp.nasa...69W
A particular class of theoretical models idealize the prominence to
be a discrete flat electric-current sheet suspended vertically in a
potential magnetic field. The weight of the prominence is supported by
the Lorentz force in the current sheet. These models can be extended to
have curved electric-current sheets and to vary three-dimensionally. The
equation for force balance is 1 over 4 pi (del times B) times Bdel p- p9
z=zero. Using Cartesian coordinates we take, for simplicity, a uniform
gravity with constant acceleration g in the direction -z. If we are
interested not in the detailed internal structure of the prominence,
but in the global magnetic configuration around the prominence, we may
take prominence plasma to be cold. Consideration is given to how such
equilibrium states can be constructed. To simplify the mathematical
problem, suppose there is no electric current in the atmosphere
except for the discrete currents in the cold prominence sheet. Let us
take the plane z =0 to be the base of the atmosphere and restrict our
attention to the domain z greater than 0. The task we have is to solve
for a magnetic field which is everywhere potential except on some free
surface S, subject to suit able to boundary conditions. The surface S is
determined by requiring that it possesses a discrete electric current
density such that the Lorentz force on it is everywhere vertically
upward to balance the weight of the material m(S). Since the magnetic
field is potential in the external atmosphere, the latter is decoupled
from the magnetic field and its plane parallel hydrostatic pressure
and density can be prescribed.
---------------------------------------------------------
Title: The Slowly Varying Corona Near Solar Activity Maximum
Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.;
Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing,
R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos,
P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Steward,
R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T.
1986epos.conf.6.57H Altcode: 1986epos.confF..57H
No abstract at ADS
---------------------------------------------------------
Title: Three-dimensional magnetostatic models of the large-scale
corona.
Authors: Bogdan, T. J.; Low, B. C.
1986NASCP2442..275B Altcode: 1986copp.nasa..275B
A special class of magnetostatic equilibria is described, which are
mathematically simple and yet sufficiently versatile so as to fit any
arbitrary normal magnetic flux prescribed at the photosphere. With
these solutions, the corona can be modeled with precisely the same
mathematically simple procedure as has previously been done with
potential fields. The magnetostatic model predicts, in addition to the
coronal magnetic field, the three dimensional coronal density which
can be compared with coronagraph observations.
---------------------------------------------------------
Title: Modelling of Coronal Mass Ejections and POST Flare Arches
Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.;
Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing,
R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos,
P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Steward,
R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T.
1986epos.conf6.366H Altcode: 1986epos.confF.366H
No abstract at ADS
---------------------------------------------------------
Title: Models of Partially Open Magnetospheres with and without
Magnetodisks
Authors: Low, B. C.
1986ApJ...310..953L Altcode:
This paper presents a large class of analytic solutions describing
partially open magnetic fields in static equilibrium outside a central
object, which may be taken to be a planet or a star. The problem
for a potential magnetic field is first treated in axisymmetric
geometry, with an equatorial, stress-free electric current sheet
whose presence results in part of the magnetic flux opening to
infinity. The solutions can be linearly superposed to construct
idealized models of the solar coronal magnetic field in a partially
open configuration. These solutions are further developed to allow for
stresses in the current sheet and three-dimensionality, in that order of
complexity. The stresses can be balanced in equilibrium by introducing
gravitational and centrifugal forces acting on dense matter confined
in the electric current sheet. Explicit solutions are presented to
illustrate magnetic topologies of magnetospheres having rotating and
nonrotating magnetodisks. A simple physical illustration is given to
estimate the total mass in the Jovian magnetodisk from the observed
macroscopic parameters of the disk electric current.
---------------------------------------------------------
Title: Blowup of Force-free Magnetic Fields in the Infinite Region
of Space
Authors: Low, B. C.
1986ApJ...307..205L Altcode:
The model for the quasi-static evolution of a magnetic field through
force-free states in response to slow motions of its footpoints at
the boundary is considered using an axisymmetric model for a bipolar
magnetic field in the infinite space outside a unit sphere. It is
shown that, as has been suggested, footpoint displacements exist
which can take a magnetic field in further evolution beyond a critical
point, through force-free states with a suitably modified form of the
alpha scalar function. However, not all footpoint displacements have
this property. By direct example, it is shown that other footpoint
displacements exist, in response to which quasi-static evolution breaks
down and the magnetic field undergoes a catastrophic opening of part
of its flux.
---------------------------------------------------------
Title: The Three-dimensional Structure of Magnetostatic
Atmospheres. II. Modeling the Large-Scale Corona
Authors: Bogdan, T. J.; Low, B. C.
1986ApJ...306..271B Altcode:
Employing the formalism developed in the first paper in this series,
a class of magnetostatic atmospheres is constructed in a 1/r-squared
gravity. These solutions possess electric current densities distributed
continuously in space and directed perpendicular to the gravitational
force. A self-consistent treatment of the energy balance equation is
omitted, but the problem is treated in fully three-dimensional geometry,
allowing for an arbitrary prescription of the normal magnetic flux at
some fixed spherical surface. The prospects of modeling real coronal
structures in approximate magnetostatic equilibrium with observational
inputs from magnetographs and coronographs will be evident from the
illustrative examples presented.
---------------------------------------------------------
Title: A Three-Dimensional Model of the Solar Coronal Helmut-Streamer
Authors: Low, B. C.
1986BAAS...18..709L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Steady Hydromagnetic Flows in Open Magnetic Fields. I. A
Class of Analytic Solutions
Authors: Low, B. C.; Tsinganos, K.
1986ApJ...302..163L Altcode:
This paper introduces a class of axisymmetric steady hydromagnetic
flows along open stellar magnetic fields. The full set of hydromagnetic
equations that describes these flows in spherical coordinates is reduced
to a set of ordinary differential equations in the radial distance
from the origin. A judicious choice of free functions admits solutions
for a spherically symmetric density in an otherwise nonspherically
symmetric flow. In general, the flow requires a formal, steady
energy addition whose amount and spatial distribution are calculated
self-consistently to conserve energy everywhere. These solutions provide
a rare opportunity to study the basic physics of hydromagnetic stellar
winds in terms of exact relationships. The rich variety of solutions
presented include flows along dipolar magnetic fields that are purely
radial and those that, in addition, have θ-components.
---------------------------------------------------------
Title: Coronal mass ejections and coronal structures.
Authors: Hildner, E.; Bassi, J.; Bougeret, J. L.; Duncan, R. A.;
Gary, D. E.; Gergely, T. E.; Harrison, R. A.; Howard, R. A.; Illing,
R. M. E.; Jackson, B. V.; Kahler, S. W.; Kopp, K.; Low, B. C.; Lantos,
P.; Phillips, K. J. H.; Poletto, G.; Sheeley, N. R., Jr.; Stewart,
R. T.; Svestka, Z.; Waggett, P. W.; Wu, S. T.
1986NASCP2439....6H Altcode:
Contents: 1. Introduction. 2. Observations. 3. Initiation of
coronal mass ejections - observations. 4. Modelling of coronal mass
ejections and post-flare arches. 5. Interplanetary effects of coronal
mass ejections. 6. The slowly varying corona near solar activity
maximum. 7. Summary.
---------------------------------------------------------
Title: Physical processes in the solar corona.
Authors: Rosner, R.; Low, B. C.; Holzer, T. E.
1986psun....2..135R Altcode:
Contents: Transport theory (fundamental parameter regimes, the "ideal"
problem, viscosity, parallel thermal energy transport, perpendicular
transport, some comments on model building). Magnetohydrodynamic
processes in the corona (equilibrium magnetic fields, linear stability
and nonequilibrium, time-dependent phenomena). Energy and momentum
balance of open and closed coronal structures (coronal holes and
high-speed streams, Alfvén waves in the lower solar atmosphere,
energy supply to magnetically closed coronal regions).
---------------------------------------------------------
Title: Coronal mass ejections.
Authors: Low, B. C.
1986HiA.....7..743L Altcode:
The ejection of coronal mass by the sun is characterized, reviewing the
results of recent observational and theoretical investigations. Topics
discussed include the structure of loop-type ejections, the relatively
low ejection speeds (less than the Alfven and gravitational speeds
except near the solar maximum), the variation of occurrence rate with
the solar cycle, and the association of ejections with prominence
events, with or without flares. Consideration is given to numerical MHD
simulations of ejection-initiation mechanisms (both impulsive-energy
and coronal-structure-instability models), helmet structures, and the
three-dimensional nature of the ejection loop. The value of coronal
mass ejections as easily observable members of a larger class of
astrophysical events (magnetized-plasma expulsion from gravitational
wells) is indicated.
---------------------------------------------------------
Title: Some Recent Developments in the Theoretical Dynamics of
Magnetic Fields
Authors: Low, B. C.
1985SoPh..100..309L Altcode:
This article describes recent developments in the theoretical
investigation of magnetostatic equilibrium in the presence of
gravity, nonequilibrium in hydromagnetics, and classical problems
in hydromagnetic stability. The construction of magnetostatic
equilibria has progressed beyond geometrically idealized systems,
such as the axisymmetric system, to fully three-dimensional systems
capable of modelling realistic solar structures. Nonequilibrium in
a magnetic field with an arbitrary interweaving of lines of force
due to random footpoint motion is a novel and subtle property
with important implications for the solar atmosphere. Work begun
by Parker and subsequent developments are described. To the extent
quasi-static solar structures are approximated by stable equilibrium,
ideal hydromagnetic stability theory provides a first insight into how
stability is achieved in the solar environment. A qualitative physical
picture based on recent stability analyses is given. The article
places emphasis on understanding basic principles and issues rather
than detailed results which can be found in the published literature.
---------------------------------------------------------
Title: Axisymmetric expansion of a rotating adiabatic gas
Authors: Low, B. C.
1985ApJ...293...44L Altcode:
A differentially rotating adiabatic gas can exhibit axisymmetric,
time-dependent, self-similar expansion. Analytic hydrodynamic solutions
describing such an expansion are derived. These solutions are the
generalization of well known spherically symmetric self-similar
solutions for which rotation is not included. Basic properties are
discussed and illustrated with explicit solutions for rotating gaseous
bodies expanding freely in vacuum. The existence of these self-similar
solutions is due to a compatibility in the transport of the pressure,
density, and angular momentum of a gamma = 5/3 adiabatic gas undergoing
expansion. The distribution of pressure gradient and centrifugal
force can be maintained in an invariant form so that acceleration is
everywhere radial at all time. A rotating, ejected stellar envelope
may evolve asymptotically into such a state of motion. The discussion
relates these self-similar solutions to others found recently for
time-dependent magnetohydrodynamic flows in the presence of gravity.
---------------------------------------------------------
Title: Three-dimensional structures of magnetostatic atmospheres. I
- Theory
Authors: Low, B. C.
1985ApJ...293...31L Altcode:
This paper presents two families of magnetostatic equilibrium states
for two atmospheres, one with a uniform gravity and the other with
a gravity due to a point mass in spherical geometry. Taking the
electric current to be everywhere perpendicular to the gravitational
force, the fully three-dimensional problem is shown to be amenable
to analytic treatment. The equilibrium equations are reducible to a
single nonlinear scalar partial differential equation. The assumption
on the electric-current orientation is less restrictive than those
used to generate three-dimensional magnetostatic states in previous
studies. Consequently, the new magnetostatic solutions reported here
exhibit a rich variety of possible magnetic topologies. A subset of
these solutions have magnetic topologies identical to those of the
set of all potential magnetic fields. This subset of solutions are
analyzed as illustrative examples, with an application to model
the three-dimensional magnetic structure of cool plasma loops,
often observed in the EUV corona. The prospect for modeling realistic
structures in the solar atmosphere with observational inputs is pointed
out. The discussion relates the theoretical development to the property
of nonequilibrium discussed by Parker and others.
---------------------------------------------------------
Title: Modeling solar magnetic structures
Authors: Low, B. C.
1985svmf.nasa...49L Altcode:
Some ideas in the theoretical study of force-free magnetic fields
and magnetostatic fields, which are relevant to the effort of using
magnetograph data as inputs to model the quasi-static, large-scale
magnetic structures in the solar atmosphere are discussed. Basic
physical principles will be emphasized. An attempt will be made to
assess what we may learn, physically, from the models based on these
ideas. There is prospect for learning useful physics and this ought
to be an incentive for intensifying the efforts to improve vector
magnetograph technology and to solve the basic radiative-transfer
problems encountered in the interpretation of magnetograph raw data.
---------------------------------------------------------
Title: Three-dimensional magnetostatic models of coronal structures.
Authors: Bogdan, T. J.; Low, B. C.
1985BAAS...17Q.632B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Modeling solar magnetic structures.
Authors: Low, B. C.
1985NASCP2374...49L Altcode:
The author discusses some ideas in the theoretical study of force-free
magnetic fields and magnetostatic fields, which are relevant to the
effort of using magnetograph data as inputs to model the quasi-static,
large-scale magnetic structures in the solar atmosphere.
---------------------------------------------------------
Title: Theory of Coronal Mass Ejection Transients
Authors: Low, B. C.
1985spit.conf..988L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the large-scale magnetostatic coronal structures and
their stability
Authors: Low, B. C.
1984ApJ...286..772L Altcode:
A class of solutions to magnetostatic calculations is examined for
their fruitfulness in predicting the structures of solar coronal
loops and their hydromagnetic stability in the presence of linear
perturbations. An ideal, one-fluid, MHD equation describes a polytropic
plasma and stability is analyzed rigorously in terms of continuum
mechanics. It is noted that the polytropic approximation is crude,
since little is known of coronal heating processes, but that the
approach is transparent to easy physical interpretation. Attention is
focused on global closed magnetic fields and classical helmet-streamer
structures. Two classes of magnetostatic equilibrium solutions are
obtained, and the existence of an open magnetic field is shown to lead
to unstable equilibrium when the base length of the closed field region
reaches a critical magnitude. No conclusions could be drawn regarding
stability below the critical value.
---------------------------------------------------------
Title: An Analytic Model for Hydromagnetospheres
Authors: Tsinganos, K.; Low, B. C.
1984ESASP.207..289T Altcode: 1984plap.rept..289T
Steps needed to isolate a general solution of the complete hydromagnetic
equations are outlined. In this solution, the axisymmetric magnetosphere
that surrounds the central object consists of two regions. The first,
around the magnetic equator, is controled by closed and dipole-like
magnetic field lines wherein the plasma is in static equilibrium
with the magnetic and gravitational fields. The second, around the
magnetic axis, is controlled by flows along the open and monopole-like
magnetic field lines. The total pressure is continuous everywhere and
the solution is globally consistent. In the solar wind, for example,
coronal holes can be associated with the region of open field lines
and helmet streamer-type structures with the static regions of closed
lines. In cosmic jets the accretion disk can be associated with
the region of closed lines and the jet with the outflows along the
open magnetic lines. Similar considerations may apply to the pulsar
magnetosphere and bipolar flows from molecular clouds.
---------------------------------------------------------
Title: Self-Similar Magnetohydrodynamics - Part Four - the Physics
of Coronal Transients
Authors: Low, B. C.
1984ApJ...281..392L Altcode:
In this theoretical study, the white-light coronal transient is regarded
to be a fully developed magnetohydrodynamic flow that plows into a
preexisting ambient atmosphere. To keep the mathematical problem simple,
a model is considered where the ambient atmosphere has no magnetic
field whereas the outflow carries a substantial axisymmetric magnetic
field. A contact surface forms to drive a strong gasdynamic shock that
travels ahead and compresses the ambient atmosphere. Such a global
flow, with the effect of gravity included, is illustrated with a set of
exact, analytic, self-similar solutions of magnetohydrodynamics. The
governing nonlinear equations, derived in the first paper of this
series, are solved with a general technique, constructing explicitly
the gasdynamic shock and the trailing contact surface. Various types
of magnetic field configurations in the outflow behind the contact
surface are shown to give rise to plasma structures which resemble those
commonly observed in white-light transients, such as loops, voids,
and blobs. It is advocated that the coronal transient is a result of
a hydromagnetic system becoming gravitationally unstable in the low
corona. This takes place when the magnetic tension force and solar
gravity fail to counter the natural tendency of a magnetized plasma
to expand. A physical picture of this dynamic process is described,
and some quantitative properties to relate to observation are pointed
out. The original self-similar theory requires an adiabatic index γ =
4/3. It is shown that this constraint can be relaxed to γ ≠ 4/3,
raising interesting questions of heating and cooling in an expanding
plasma. For future interest, an appendix is attached to extend the
self-similar theory to allow for three-dimensional distributions of
the magnetic field and plasma and to incorporate Newtonian self-gravity.
---------------------------------------------------------
Title: Self-similar magnetohydrodynamics. III - The subset of
spherically symmetric gasdynamic flows. IV - The physics of coronal
transients
Authors: Low, B. C.
1984ApJ...281..381L Altcode:
A set of spherically symmetric, time-dependent self-similar gasdynamic
flows is presented. A polytropic gas with γ = 4/3 is assumed, and a
1/r<SUP>2</SUP> gravity is present. Explicit analytic solutions are
presented to illustrate the expansion of an atmosphere into vacuum as
well as into an ambient atmosphere. In the latter example, the outflow
is separated from the undisturbed ambient atmosphere by a strong
gasdynamic shock. Among the nonlinear properties illustrated are the
acceleration and deceleration of a shock in an extended atmosphere and
the acceleration of the outer layers of the atmosphere to high speeds
by the shock.
---------------------------------------------------------
Title: Three-dimensional magnetostatic atmospheres - Magnetic field
with vertically oriented tension force
Authors: Low, B. C.
1984ApJ...277..415L Altcode:
Further developments in a study of three-dimensional magnetostatic
equilibrium in the presence of a vertical uniform gravity are
reported. In an earlier study, a set of analytic solutions for
coronal structures was constructed with the constraint that
the three-dimensional magnetic field lies in parallel vertical
planes. This constraint is now relaxed, leading to geometrically more
realistic solutions. These equilibrium states are characterized by
the magnetic tension force being vertical everywhere and the total
pressure being a function of height only. The nonlinear equations
describing these special magnetic fields are derived with the use
of Euler potentials. Two illustrative examples are given in explicit
form, suggesting the quiescent prominence to be a highly inhomogeneous
structure, composed of local density enhancements and depletions
embedded in a three-dimensional sheared magnetic field.
---------------------------------------------------------
Title: Evolution of solar magnetic flux.
Authors: Boris, J. P.; DeVore, C. R.; Golub, L.; Howard, R. F.; Low,
B. C.; Sheeley, N. R., Jr.; Simon, G. W.; Tsinganos, K. C.
1984NASRP1120....3B Altcode:
Contents: Introduction. Appearance of magnetic flux: models for flux
emergence, unexplained observations. Dynamics of surface magnetic
flux: magnetic flux transport, magnetic flux structure. Disappearance
of magnetic flux: theoretical considerations, observations of flux
disappearance. Summary.
---------------------------------------------------------
Title: Coronal transients and their interplanetary effects.
Authors: Hundhausen, A. J.; Burlaga, L. F.; Feldman, W. C.; Gosling,
J. T.; Hildner, E.; House, L. L.; Howard, R. A.; Krieger, A. S.;
Kundu, M. R.; Low, B. C.; Sheeley, N. R., Jr.; Steinolfson, R. S.;
Stewart, R. T.; Stone, R. G.; Wu, S. T.
1984NASRP1120....6H Altcode:
Contents: 1. Introduction. 2. Background material: Ancient history -
solar flares and geomagnetic storms. Modern history - interplanetary
shock waves. Coronal transients or mass ejections. 3. The present:
Theoretical models. New observations of coronal mass ejections. 4. The
future: Solar origins. Interplanetary effects.
---------------------------------------------------------
Title: Nonlinear periodic solutions for the isothermal magnetostatic
atmosphere
Authors: Low, B. C.; Hundhausen, A. J.; Zweibel, E. G.
1983PhFl...26.2731L Altcode:
Zweibel and Hundhausen (1982) have obtained analytically a family
of isothermal, horizontally periodic, magnetostatic atmospheres
in a uniform gravitational field. The present investigation is
concerned with another set of period analytic solutions, taking into
account the equilibrium configuration of plasma condensations in an
otherwise everywhere uniform field. The physics of the support of
the condensations by the embedded magnetic field is of interest to
the study of solar prominences and interstellar clouds. Attention is
given to the nonlinear problem, the general results, models for plasma
condensations, and questions of stability.
---------------------------------------------------------
Title: Hydromagnetic Solar Wind in a Partially Open Magnetic Field
Authors: Low, B. C.; Tsinganos, K.
1983BAAS...15..995L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Energy of Electric Current Sheets - Part Two - the Magnetic
Free Energy and the Photospheric Magnetic Flux
Authors: Low, B. C.; Hu, Y. Q.
1983SoPh...84...83L Altcode:
The free energy associated with current sheets formed by displacing
magnetic dipoles in a highly conducting medium is discussed. Specific
models are illustrated, based on the idea that the free energy of a
magnetic field in the solar atmosphere is the energy librated after the
field has relaxed to a potential state that preserves the photospheric
flux distribution. Previous calculations by other authors based on
the consideration of discrete currents were incorrect because the
interaction between the atmospheric currents and the highly conducting
photosphere was not accounted for properly. It is shown that when this
interaction is included, the consideration of discrete currents leads
to the same result based on continuous magnetic field consideration.
---------------------------------------------------------
Title: Non Axisymmetric Magnetostatic Equilibrium - Part One -
a Perturbation Theory
Authors: Hu, W. R.; Hu, Y. Q.; Low, B. C.
1983SoPh...83..195H Altcode:
This paper considers the structural properties of a sunspot-like
magnetic flux tube which lacks perfect axisymmetry. The flux tube is
taken to be in static equilibrium with an atmosphere in a uniform
gravity. Assuming the departure from axisymmetry to be slight, the
equations for the first order non-axisymmetric part of the equilibrium
are derived in cylindrical coordinates. These first order equations
reduce to a linear second order hyperbolic partial differential
equation in the r-z plane. Whereas Cauchy type boundary conditions
are appropriate for hyperbolic equations, physical considerations
dictate the specification of boundary conditions on a closed surve
for our problem of interest. The construction of solutions to this
boundary value problem is illustrated with three analytically soluble
cases, where the zero-order axisymmetric equilibria are chosen to have
magnetic field geometry of different complexity. A physical discussion
of the results is given.
---------------------------------------------------------
Title: Expulsion of magnetized plasmas from coronae
Authors: Low, B. C.
1983IAUS..102..467L Altcode:
Recent MHD analytic treatments are adduced in a physical accounting
of the mechanism by which magnetized plasma is sporadically spilled
out of the sun's gravitational bounds. The same physical process is
suggested to occur in the white light transient phenomena of other
coronae. The coronal transient is interpreted as the outflow of a
gravitationally unbound, preexisting hydromagnetic structure in the
corona. The observed white light density structure is a part of this
moving, preexisting structure, and the ambient atmosphere is swept
upward and sideways by a large scale outflow.
---------------------------------------------------------
Title: Magnetostatic atmospheres with variations in three dimensions
Authors: Low, B. C.
1982ApJ...263..952L Altcode:
The static equilibrium of a fully ionized atmosphere with an
embedded magnetic field, in the presence of a uniform gravity, is
considered under the assumption that the magnetic field lines lie
in parallel vertical planes perpendicular to the x-axis in Cartesian
coordinates. The system is allowed to vary in all three dimensions. A
nonlinear, second-order hyperbolic partial differential equation having
y and z as independent variables is shown to be a necessary condition
on the magnetic surfaces for an equilibrium state to exist. Selected
explicit solutions are presented which illustrate various structural
properties of prominence-like density enhancements, coronal magnetic
arcades, as well as discrete bipolar plasma loops, for which explicit
equilibrium solutions with three-dimensional extensions are for the
first time presented.
---------------------------------------------------------
Title: The Energy of Electric Current Sheets - Part One - Models
with Moving Magnetic Dipoles
Authors: Hu, Y. Q.; Low, B. C.
1982SoPh...81..107H Altcode:
This paper treats two problems on the formation of electric current
sheets in the highly electrically conducting solar atmosphere. The
first problem concerns a vertical current sheet formed by decreasing
the distance between a pair of parallel magnetic line-dipoles lying
on the photosphere. The solution to this problem was given previously
by Priest and Raadu. With an interest in the flare phenomenon, they
derived a formula for the energy stored through the presence of the
current sheet. We show that this formula is incorrect. Firstly, there
is an error of sign in the derivation of Priest and Raadu, so that,
when corrected, the formula gives a negative value for the stored
energy. Secondly, the formula is shown to refer to an energy quite
different from the free energy associated with the current sheet. To
calculate for the current free energy, it is important to account for
the `frozen-in' condition in the highly conducting photosphere.
---------------------------------------------------------
Title: Self-similar magnetohydrodynamics. II - The expansion of a
stellar envelope into a surrounding vacuum
Authors: Low, B. C.
1982ApJ...261..351L Altcode:
The axisymmetric self-similar expansion of a stellar envelope into
a surrounding vacuum is treated. Two exact solutions are presented
to describe the time-dependent magnetohydrodynamics of the envelope,
assuming a polytrope with adiabatic index gamma equals 4/3. The boundary
conditions at the interface with vacuum are treated explicitly, and
a matching solution of Maxwell's equations is obtained to describe
the electromagnetic waves propagating into the vacuum, ahead of
the expanding envelope. As the envelope disperses to infinity, out
of the gravitational bound of the stellar core, the magnetic field
is stretched to a radial configuration. The energy properties are
discussed, showing, in particular, why the gamma equals 4/3 polytrope
exhibits self-similar expansion and how the total magnetic energy in
the envelope may be either decreasing or increasing with time during
the expansion, depending on the distribution of the plasma.
---------------------------------------------------------
Title: Magnetic Field Configurations Associated with Polarity
Intrusion in a Solar Active Region - Part One - the Force-Free Fields
Authors: Low, B. C.
1982SoPh...77...43L Altcode:
This paper presents a new class of exact solutions describing the
non-linear force-free field above a spatially localized photospheric
bipolar magnetic region. An essential feature is the variation in all
three Cartesian directions and this could not be modelled adequately
with previously known symmetric force-free fields. Sequences of
force-free fields are constructed and analyzed to simulate the slow
growth of a pair of spots on the photosphere. The axis connecting the
spots executes rotational motion, distorting the photospheric neutral
line separating fluxes of opposite signs. We show directly from the
analytic solutions that the resulting reversal of the positions
of the spots relative to the background field is associated with
(i) the creation of magnetic free energy, (ii) the severe shearing
of localized low-lying loops in the vicinity where the photospheric
transverse field aligns with the photospheric neutral line, and (iii)
the emergence and disappearance of flux from the photosphere at these
highly stressed regions. The model relates theoretically for the first
time these different magnetic field features that have been suggested
by observation and theoretical considerations to be flare precursors. A
general formula, based on the virial theorem, is also given for the
free energy of a force-free field, strictly in terms of the field value
at the photosphere. This formula has obvious practical application.
---------------------------------------------------------
Title: The initiation of a coronal transient
Authors: Low, B. C.; Munro, R. H.; Fisher, R. R.
1982ApJ...254..335L Altcode:
The coronal transient/eruptive prominence event of August 5, 1980,
observed by the Mauna Loa experiment system is analysed. This event
provided data on the early development of the transient in the
low corona between 1.2 and 2.2 solar radii, information that was
not available when earlier attempts were made to explain transient
phenomena. The transient's initial appearance in the form of a rising
density-depleted structure, before the eruption of the associated
prominence, is explained as an effect of magnetic buoyancy. The data
suggest that this transient has a density depletion of 17% to 33%
relative to an undisturbed corona which is approximately isothermal
with a temperature of 1.5 x 10 to the 6th K and a coronal density of
1.0 x 10 to the 9th/cu cm at the base of the corona.
---------------------------------------------------------
Title: Self-similar magnetohydrodynamics. I - The gamma = 4/3
polytrope and the coronal transient
Authors: Low, B. C.
1982ApJ...254..796L Altcode:
The full set of ideal magnetohydrodynamic (MHD) equations for a gamma
= 4/3 polytrope admits self-similar solutions which can be derived
by analytic methods. An axisymmetric magnetic field in a stratified
stellar atmosphere is assumed. The solutions admit a large variety
of magnetic structures, including those in the form of loops, moving
through the corona with large scale coherence and sharp small scale
features. The Lagrangian velocity of an individual transient feature is
found to accelerate or decelerate according to a positive or negative
gain in momentum by the plasma in a self-similar distribution of the
Lorentz force, the pressure gradient, and the gravitational force. In
both cases, the net force decreases with time so that, at large radial
distances, the motion becomes inertial. The physical implications are
discussed, arguring in favor of the transient beginning as a fully
nonlinear MHD motion that ejects both magnetic field and plasma out
of the gravitational bond of the sun.
---------------------------------------------------------
Title: Some nonlinear problems in astrophysics
Authors: Lerche, I.; Low, B. C.
1982PhyD....4..293L Altcode:
Astrophysical magnetic fields, in the hydromagnetic approximation, pose
a rich class of nonlinear problems. Of primary interest is the behavior
and properties of the magnetic field interacting with the plasma in the
presence of gravity. Substantial progress has been made recently with
these problems arising in the study of interstellar clouds, stellar
structures and magnetospheres, and structures on the Sun, such as
prominences, sunspots and coronal magnetic fields. This paper reviews
recent theoretical work, concentrating on steady state problems and
emphasizing the use of analytic methods. <P />The National Center for
Atmospheric Research is sponsored by the National Science Foundation.
---------------------------------------------------------
Title: Nonlinear force-free magnetic fields.
Authors: Low, B. C.
1982RvGSP..20..145L Altcode: 1982RvGeo..20..145L
The nonlinear properties of force-free magnetic fields are reviewed
with particular reference to the mechanisms for the sudden release of
stored energy in flares during the quasi-steady evolution of solar
fields. It is shown that in the solar atmosphere, force-free fields
with a nonconstant scalar function in the field equations are more
likely to occur than those with a constant scalar function, and the
nonlinear properties of these fields may give rise to many interesting
physical effects. Consideration is then given to two possible mechanisms
of field evolution: a model in which a force-free field in a medium
of infinite electrical conductivity evolves in response to slowly
changing boundary conditions brought about by photospheric motions in
the solar active region, and a model in which a field in a medium of
small finite electrical conductivity evolves in response to the slow
Ohmic dissipation of the electric current.
---------------------------------------------------------
Title: The Vertical Filamentary Structures of Quiescent Prominences
Authors: Low, B. C.
1982SoPh...75..119L Altcode:
We present a simple magnetostatic theory of the thin vertical filaments
that make up the quiescent prominence plasma as revealed by fine spatial
resolution Hα photographs. A class of exact equilibrium solutions
is obtained describing a horizontal row of long vertical filaments
whose weights are supported by bowed magnetic field lines. A free
function is available to generate different assortments of filament
sizes and spacings, as well as different density and temperature
variations. The classic Kippenhahn-Schlüter solution for a long
sheet without filamentary structures is a particular member of this
class of solutions. The role of the magnetic field in supporting and
thermally shielding the filament plasma is illustrated. It is found that
the filament can have a sharp transition perpendicular to the local
field, whereas the transition in the direction of the local field is
necessarily diffuse. A consequence of the filamentary structure is that
its support by the Lorentz force requires the electric current to have
a component along the magnetic field. This electric current flowing into
the rarefied region around the prominence can contain substantial energy
stored in the form of force-free magnetic fields. This novel feature
has implications for the heating and the disruption of prominences.
---------------------------------------------------------
Title: Eruptive solar magnetic fields
Authors: Low, B. C.
1981ApJ...251..352L Altcode:
The quasi-steady evolution of solar magnetic fields in response to
gradual photospheric changes is considered, with particular attention
given to the threshold of a sudden eruption in the solar atmosphere. The
formal model of an evolving, force-free field dependent on two Cartesian
coordinates is extended to a field which is not force free but in
static equilibrium with plasma pressure and gravity. The basic physics
is illustrated through the evolution of a loop-shaped electric current
sheet enclosing a potential bipolar field with footpoints rooted in the
photosphere. A free-boundary problem is posed and then solved for the
equilibrium configuration of the current sheet in a hydrostatically
supported isothermal atmosphere. As the footpoints move apart to
spread a constant photospheric magnetic flux over a larger region,
the equilibria available extend the field to increasing heights.
---------------------------------------------------------
Title: Equilibrium configuration of the magnetosphere of a star
loaded with accreted magnetized mass
Authors: Uchida, Y.; Low, B. C.
1981JApA....2..405U Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the Presence of Electric Currents in the Solar Atmosphere -
Part One - a Theoretical Framework
Authors: Hagyard, M.; Low, B. C.; Tandberg-Hanssen, E.
1981SoPh...73..257H Altcode:
An elementary analysis based on Ampére's Law is given to separate
the general magnetic field above the photosphere into two parts
B=B<SUB>1</SUB>+B<SUP>*</SUP>. The field B<SUB>1</SUB> is a potential
field due to electric currents below the photosphere. The field
B<SUP>*</SUP> is produced by electric currents above the photosphere
combined with the induced mirror currents. By symmetry, B<SUP>*</SUP>
has a set of field lines lying entirely in the plane z = 0 taken to be
the photosphere. This set of field lines can be constructed from given
vector magnetograph measurements and represents all the information
on the electric currents above the photosphere that a magnetograph can
provide. Theoretical illustrations are given and the implications for
data analysis are discussed.
---------------------------------------------------------
Title: A class of analytic solutions for the thermally balanced
magnetostatic prominence sheet
Authors: Low, B. C.; Wu, S. T.
1981ApJ...248..335L Altcode:
A theoretical study is presented for the nonlinear interplay between
magnetostatic equilibrium and energy balance in a Kippenhahn-Schlueter
type solar prominence sheet. A class of theoretical models is
presented, expressed in closed analytic forms, thus facilitating the
direct illustration of the nonlinear physical properties. The model
couples the equilibrium between magnetic field, plasma pressure,
and weight on the one hand, with the balance between a rho-squared T
radiative loss, a rho wave heating (where rho equals plasma density,
and T equals plasma temperature), and thermal conduction channeled
along magnetic field lines on the other. The steady solutions are
divided into three classes, and are characterized by the total wave
heating in the prominence sheet which is greater than, equal to,
or less than the total radiative loss. The compaction of the plasma
along the field lines, under its own weight, and the energy transport
effects determine which of the three basic behaviors obtains in a
particular situation. A discussion is presented of the implications
of the steady solutions for the formation of prominences.
---------------------------------------------------------
Title: The field and plasma configuration of a filament overlying
a solar bipolar magnetic region
Authors: Low, B. C.
1981ApJ...246..538L Altcode:
This paper presents an analytic model for a finite-size straight
filament suspended horizontally in a steady state over a bipolar
magnetic region. The equations of magnetostatic equilibrium are
integrated exactly. The solution obtained illustrates the roles played
by the electric current, magnetic field, pressure, and plasma weight
in the balance of force everywhere in space. A specific example of a
filament of diameter 50,000 km, with a density two orders of magnitude
over the corona and supported by a magnetic field of about 4 gauss
is included. The filament temperature can take values ranging from
a small fraction to a few times the coronal temperature, depending
on the internal electric current of the filament. To produce a cool
filament, such as the quiescent prominence, the solution is required
to have an internal field with a strong component along the filament,
giving rise to helical structures. A hot filament such as the X-ray
coronal loop can be produced as a twisted magnetic flux tube embedded
in a strong background field aligned parallel to the filament and
having lower density and temperature. The basic steps of construction
can be used to develop models more realistic than the ones presented
for their analytic simplicity.
---------------------------------------------------------
Title: On the Expulsion of Magnetised Plasmas through Solar and
Stellar Atmospheres
Authors: Low, B. C.
1981BAAS...13..837L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Magnetohydrodynamics of an Expanding Stellar Envelope
Authors: Low, B. C.
1981BAAS...13..792L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A Variational Approach to the Question of Temporal Stability of
Equilibrium Models of Solar Prominences - Part One - the Formal Theory
Authors: Lerche, I.; Low, B. C.
1981SoPh...69..327L Altcode:
Using a Lagrangian approach to the equations describing small amplitude
departures from equilibrium of solar prominences, we derive seven
quantities which, by analogy to the concepts of energy, momentum and
angular momentum, are conserved under circumstances corresponding to
ignorable coordinates of classical mechanics. In a pragmatic sense it
is expected that these conservation laws will be useful as criteria of
accuracy in obtaining eigen-frequencies for the perturbation equations
when numerical techniques are employed.
---------------------------------------------------------
Title: On the equilibrium of heated self-gravitating masses -
Cooling by conduction
Authors: Lerche, I.; Low, B. C.
1980ApJ...242.1144L Altcode:
An investigation is given of the equilibrium states available to a
self-gravitating mass of gas, cooling by conduction, and being heated
at a rate proportional to the local gas density. The plane geometry
situation is shown to be reducible to quadratures for the pressure,
density, temperature, and gravitational potential. For a constant
thermal conductivity it is shown that the gas density has either a
central maximum or a central minimum, depending on the ratio of the
thermal conductivity to a parameter taken to be a measure of the rate
of heating. For a thermal conductivity which is a positive power of
the temperature, it is shown that the gas density always has a central
minimum and a maximum at the outer boundary of the configuration. For
cylindrical and spherical geometrical configurations the same general
properties are obtained. The physical origin of this behavior is
discussed, and it is suggested that these exploratory calculations
provide an effect which may not only aid in understanding thin
filamentary structure observed in supernova remnants, but also help to
assuage the difficulties of producing maser activity in the interior
regions of 'cocoon' protostars.
---------------------------------------------------------
Title: On equilibrium states of heated self-gravitating gas clouds
cooling by conduction in an external gravitational field
Authors: Lerche, I.; Low, B. C.
1980ApJ...242.1156L Altcode:
Exact analytic solutions are presented for equilibrium states of
a self-gravitating one-dimensional cloud of gas, embedded in an
external gravitational field due to a plane of 'stars' being heated at
a rate proportional to the local gas density, and cooling by thermal
conduction. It is found that the general topology of the solutions
is such that the gas density has a minimum on the plane of 'stars',
rising to an infinite but integrable peak away from the plane so that
the total mass of gas in the cloud is finite. The results may be of
interest in investigations of interstellar molecular clouds and of
filamentary structures in supernova remnants as well as in the modeling
of gas distributions around 'cocoon' protostars.
---------------------------------------------------------
Title: The heating of a thermally conducting stratified medium. II. A
simple plane model on an atmosphere.
Authors: Lerche, I.; Low, B. C.
1980ApJ...241..459L Altcode:
Exact solutions of the following theoretical problem are presented:
A plane atmosphere is in hydrostatic equilibrium with a uniform
gravity. The ideal gas law is assumed. Heat is generated everywhere at a
rate proportional to the local density. The atmosphere is maintained in
a steady state through cooling by thermal conduction and radiation. This
problem is reducible to quadratures for a thermal conductivity which is
an arbitrary, but prescribed, function of the temperature, and for a
radiative loss which is expressible as the product of the density and
an arbitrary, but prescribed, function of the pressure. The analysis
is carried out for the case of power law thermal conductivity, and a
radiative loss proportional to the square of the density and to the
first power of the temperature. The radiative cooling function adopted
here has the basic mathematical form for an optically thin medium. The
solutions reproduce the macroscopic ordering of a hot 'corona' separated
from a 'photosphere' by a layer of temperature minimum. The analytic
solutions allow direct illustration of the interplay between steady
energy transport and the requirements of hydrostatic equilibrium.
---------------------------------------------------------
Title: Eruptive Solar Magnetic FIELDS#
Authors: Low, B. C.
1980BAAS...12..902L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the equilibrium structures of self-gravitating masses of
gas containing axisymmetric magnetic fields
Authors: Lerche, I.; Low, B. C.
1980MNRAS.192..611L Altcode:
The general equations describing the equilibrium shapes of
self-gravitating gas clouds containing axisymmetric magnetic fields
are presented. The general equations admit of a large class of
solutions. It is shown that if one additional (ad hoc) asumption is
made that the mass be spherically symmetrically distributed, then the
gas pressure and the boundary conditions are sufficiently constraining
that the general topological structure of the solution is effectively
determined. The further assumption of isothermal conditions for
this case demands that all solutions possess force-free axisymmetric
magnetic fields. It is also shown how the construction of aspherical
(but axisymmetric) configurations can be achieved in some special
cases, and it is demonstrated that the detailed form of the possible
equilibrium shapes depends upon the arbitrary choice of the functional
form of the variation of the gas pressure along the field lines.
---------------------------------------------------------
Title: On the resistive diffusion of force-free magnetic fields
Authors: Low, B. C.
1980JPlPh..24..181L Altcode:
Reid and Laing recently conjectured on the general behaviour of
resistive force- free magnetic fields in a slab model following a
numerical study. However, the basic properties of resistive force-free
magnetic fields had been established previously. We use and extend some
results from the previous work to show that the conjecture of Reid
and Laing is incorrect. A general analytic treatment of the problem
provides the correct physical properties that Reid and Laing were
unable to deduce from their numerical solutions. A criticism is also
given of the results presented in another numerical study treating
cylindrical resistive forcefree magnetic fields, by the same authors.
---------------------------------------------------------
Title: On the Equilibrium of a Cylindrical Plasma Supported
Horizontally by Magnetic Fields in Uniform Gravity
Authors: Lerche, I.; Low, B. C.
1980SoPh...67..229L Altcode:
We consider the mechanical equilibrium of a cylinder of plasma suspended
horizontally by magnetic fields in uniform gravity. This configuration
is what may be expected if a quiescent prominence were to condense in a
region initially filled with a uniform magnetic field. A set of exact
solutions describing the equilibrium situation is presented. Although
the plasma distribution is assumed to be cylindrically symmetric
to obtain tractibility of the problem, exact force balance between
plasma pressure, the Lorentz force and gravity is achieved everywhere
in space. The set of solutions covers a particular case of a uniform
temperature as well as cases where the temperature rises from zero
at the center of the plasma cylinder to rapidly reach a constant
asymptotic value outside the cylinder. The physical properties of these
solutions are described. A suggestion is made for future development,
based on the present work, to construct a prominence model in which the
requirements of both mechanical and radiative equilibrium are satisfied.
---------------------------------------------------------
Title: Exact Static Equilibrium of Vertically Oriented Magnetic Flux
Tubes - Part One - the Schluter-Temesvary Sunspot
Authors: Low, B. C.
1980SoPh...67...57L Altcode:
A method is prescribed for generating exact solutions of magnetostatic
equilibrium describing a cylindrically symmetric magnetic flux tube
oriented vertically in a stratified medium. Given the geometric shape
of the field lines, compact formulae are presented for the direct
calculation of all the possible distributions of pressure, density,
temperature and magnetic field strength compatible with these field
lines under the condition of static equlibrium. The plasma satisfies
the ideal gas law and gravity is uniform in space. A particular
solution is obtained by this method for a medium sized sunspot whose
magnetic field obeys the similarity law of Schlüter and Temesváry
(1958). With this solution, it is possible for the first time to
illustrate explicitly the confinement of the magnetic field of the
cool sunspot by the hotter external plasma in an exact relationship
involving both magnetic pressure and field tension as well as the
support of the weight of the plasma by pressure gradients. It is
found that the cool region of the sunspot is not likely to extend
much more than a few density scale heights below the photosphere. The
sunspot field approaches being potential in the neighbourhood of the
photosphere so that the Lorentz force exerting on the photosphere is
less than what the magnetic pressure would suggest. This accounts
for how the sunspot field can be confined in the photosphere where
its magnetic pressure is often observed to even exceed the normal
photospheric pressure. The energy mechanism operating in the sunspot
and the question of mechanical stability are not treated in this paper.
---------------------------------------------------------
Title: Evolving force-free magnetic fields. III - States of
nonequilibrium and the preflare stage
Authors: Low, B. C.
1980ApJ...239..377L Altcode:
The paper considers whether a neighboring magnetostatic equilibrium
exists to allow a magnetic field initially in a force-free configuration
to accommodate any imposed weak pressure. The following problem
is treated. The foot points of the field are fixed and the plasma
is frozen into the field lines under the approximation of infinite
electrical conductivity. A weak pressure is introduced. It is determined
infinitesimal plasma displacements exist to adjust the field lines to
a new equilibrium without changing the field line connectivity. The
analysis is carried out for the bipolar force-free fields forming one
of two evolutionary sequences modeling the development of the preflare
stage. It was found that for the force-free field corresponding to
the quasi-static stage of evolution, the neighboring magnetostatic
equilibrium always exists and the imposed gas pressure can be
accommodated with a slight departure of the field from being exactly
force free.
---------------------------------------------------------
Title: The heating of a thermally conducting stratified medium. I -
Self-gravitating gas threaded by magnetic fields
Authors: Lerche, I.; Low, B. C.
1980ApJ...239..360L Altcode:
Two theoretical problems are presented to illustrate the equilibrium
structure of a gravitating gas threaded by magnetic fields. The gas
is heated everywhere at a rate proportional to the local density
and cooled by thermal conduction channeled along the magnetic
field. Emphasis is placed on the influence of anisotropic thermal
conduction on the distribution of the gas. In the first problem, the
magnetic field has straight field lines that are nearly parallel. The
simple field line geometry allows us to calculate, in closed form, the
equilibria configurations of a gas slab which is cooled nonuniformly
by thermal conduction along field lines which leave the gas slab at
varying angles. The problem involves the gas having a free boundary,
which is one of the unknowns to be determined. A discussion is given
of the set of all possible equilibria so constructed. In the second
problem there is no electric current flowing in the gas but there is
a potential magnetic field having curved field lines. Exact solutions
of equilibriums are presented to illustrate the heating of stellar
and galactic coronas.
---------------------------------------------------------
Title: Analytic solutions for single and multiple cylinders of
gravitating polytropes in magnetostatic equilibrium
Authors: Lerche, I.; Low, B. C.
1980ApJ...238.1088L Altcode:
Exact analytic solutions for the static equilibrium of a gravitating
plasma polytrope in the presence of magnetic fields are presented. The
means of generating various equilibrium configurations to illustrate
directly the complex physical relationships between pressure, magnetic
fields, and gravity in self-gravitating systems is demonstrated. One
of the solutions is used to model interstellar clouds suspended by
magnetic fields against the galactic gravity such as may be formed by
the Parker (1966) instability. It is concluded that the pinching effect
of closed loops of magnetic fields in the clouds may be a dominant
agent in further collapsing the clouds following their formation.
---------------------------------------------------------
Title: Cylindrical Prominences and the Magnetic Influence of the
Photospheric Boundary
Authors: Lerche, I.; Low, B. C.
1980SoPh...66..285L Altcode:
We construct exact, non-linear, solutions for an horizontal,
cylindrical, current-carrying, prominence supported against solar
gravity by the action of a Lorentz force. The solutions incorporate
the photosphere boundary condition, proposed by van Tend and Kuperus
(1978), and analyzed by them for line filaments. Our solutions have
finite radius for the prominence material and, as well as satisfying the
equations of magnetostatic equilibrium, they allow for the continuity
of gas pressure, and of the normal and tangential components of magnetic
field across the circular prominence boundary. We show that an infinity
of solutions is possible and we illustrate the basic behavior by
investigation of a special case.
---------------------------------------------------------
Title: Exact Magnetostatic Models of Filament Prominences
Authors: Low, B. C.
1980BAAS...12..477L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On Magnetostatic Equilibrium in a Stratified Atmosphere
Authors: Low, B. C.
1980SoPh...65..147L Altcode:
This is a study of the relationship between a magnetic field and its
embedding plasma in static equilibrium in a uniform gravity. The ideal
gas law is assumed. A system invariant in a given direction is treated
first. We show that an exact integral of the equation for force balance
across field lines can be derived in a closed form. Using this integral,
exact solutions can be generated freely by integrating directly for
the distributions of pressure, density and temperature necessary to
keep a given magnetic field in equilibrium. Particular solutions are
presented for illustration with the solar atmosphere in mind. Extending
the treatment to the general system depending on all three spatial
coordinates, we arrive at the general form of a theorem of Parker
that a magnetic field in static equilibrium must possess certain
symmetries. We derive an equation involving the Euler potentials of
the magnetic field stipulating these necessary symmetries. Only those
magnetic fields satisfying this equation can be in static equilibrium
and for these fields, the endowed symmetries make the construction of
exact solutions an essentially two dimensional problem as exemplified
by the special case of invariance in a given direction.
---------------------------------------------------------
Title: The False Equilibrium of a Force-Free Magnetic Field
Authors: Low, B. C.
1980IAUS...91..283L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On exact equilibrium states in external gravitational fields
of heated, self-gravitating gas clouds cooling by conduction and
radiation.
Authors: Lerche, I.; Low, B. C.
1980PhyD...10..203L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Evolving force-free magnetic fields. IV. A variational
formulation of the problem.
Authors: Low, B. C.
1978ApJ...224..668L Altcode:
A theoretical model of evolving force-free magnetic fields is
reformulated by taking the distribution of photospheric footpoints
as the starting point of the model. A previously considered case
of two-dimensional geometry is treated, and the equations for the
force-free fields above the photosphere are derived from a variational
principle. It is shown that the approach adopted leads to a formidable
nonlinear boundary-value problem and that the physical relationship
between photospheric footpoint motions and magnetic-field evolution
can be more fruitfully investigated by using the original formulation
in which the starting point is to take as given the value of the
longitudinal field and a transverse field at the photosphere. The
questions of the existence and uniqueness of the solution to the
nonlinear boundary-value problem are briefly considered.
---------------------------------------------------------
Title: Evolving force-free magnetic fields. II. Stability of field
configurations and the accompanying motion of the medium.
Authors: Low, B. C.
1977ApJ...217..988L Altcode:
Two features of magnetic field evolution in the solar atmosphere are
examined for understanding solar flare phenomena. A stability analysis
of the force-free configurations of the magnetic field in Paper I
(1977), treated as static fields with their foot points rooted in the
photosphere, reveals that they are stable when subject to infinitesimal
perturbations which depend on two Cartesian coordinates. As a result,
the quasi-static evolution of intense magnetic fields in the solar
atmosphere may be understood in terms of successive infinitesimal
displacements of photospheric magnetic foot points and the relaxation
to a new stable force-free configuration following each infinitesimal
displacement of magnetic foot points. Furthermore, a kinematic approach
is described for obtaining information on the plasma motion during the
evolution of a magnetic field. The kinematic velocities that satisfy
the governing induction equation are found to have contrasting flow
patterns associated with qualitatively different mass transport.
---------------------------------------------------------
Title: A self-consistent model of a thermally balanced quiescent
prominence in magnetostatic equilibrium in a uniform gravitational
field.
Authors: Lerche, I.; Low, B. C.
1977SoPh...53..385L Altcode:
We present a theoretical model of quiescent prominences in the form of
an infinite vertical sheet. Self-consistent solutions are obtained
by integrating simultaneously the set of nonlinear equations of
magnetostatic equilibrium and thermal balance. The basic features of
the models are: (1) The prominence matter is confined to a sheet and
supported against gravity by a bowed magnetic field. (2) The thermal
flux is channelled along magnetic field lines. (3) The thermal flux
is everywhere balanced by Low's (1975b) hypothetical heat sink which
is proportional to the local density. (4) A constant component of
the magnetic field along the length of the prominence shields the
cool plasma from the hot surrounding. We assume that the prominence
plasma emits more radiation than it absorbs from the radiation fields
of the photosphere, chromosphere and corona, and we interpret the
above hypothetical heat sink to represent the amount of radiative loss
that must be balanced by a nonradiative energy input. Using a central
density and temperature of 10<SUP>11</SUP> particles cm<SUP>−3</SUP>
and 5000 K respectively, a magnetic field strength between 2 to 10
gauss and a thermal conductivity that varies linearly with temperature,
we discuss the physical properties implied by the model. The analytic
treatment can also be carried out for a class of more complex thermal
conductivities. These models provide a useful starting point for
investigating the combined requirements of magnetostatic equilibrium
and thermal balance in the quiescent prominence.
---------------------------------------------------------
Title: Evolving force-free magnetic fields. I. The development of
the preflare stage.
Authors: Low, B. C.
1977ApJ...212..234L Altcode:
Two boundary value problems are solved analytically to obtain
nonlinear force-free magnetic fields overlying given time-dependent
distributions of bipolar photospheric magnetic fields. We follow the
evolution in time of these two magnetic fields to show the development
of conditions likely to lead to solar flares. For the first magnetic
field, the photosphere moves as two almost rigid plates sliding past
each other along the magnetic neutral line. For the second magnetic
field, the photospheric velocity at large distances from the magnetic
neutral line has a growing uniform shear. The preflare stage for each
magnetic field is described. In particular, the model demonstrates that
the presence of large horizontal photospheric velocity shear across the
magnetic neutral line prior to a flare eruption is closely associated
with either a parallel or a perpendicular horizontal magnetic field
along the magnetic neutral line.
---------------------------------------------------------
Title: Dynamics of solar magnetic fields. VI. Force-free magnetic
fields and motions of magnetic foot-points.
Authors: Low, B. C.; Nakagawa, Y.
1975ApJ...199..237L Altcode:
A mathematical model is developed to consider the evolution of
force-free magnetic fields in relation to the displacements of their
foot-points. For a magnetic field depending on only two Cartesian
coordinates and time, the problem reduces to solving a nonlinear
elliptic partial differential equation. As illustration of the physical
process, two specific examples of evolving force-free magnetic fields
are examined in detail, one evolving with rising and the other with
descending field lines. It is shown that these two contrasting behaviors
of the field lines correspond to sheared motions of their foot-points
of quite different characters. The physical implications of these two
examples of evolving force-free magnetic fields are discussed.
---------------------------------------------------------
Title: Nonisothermal magnetostatic equilibria in a uniform gravity
field. II. Sheet models of quiescent prominences.
Authors: Low, B. C.
1975ApJ...198..211L Altcode:
We use the mathematical formulation of Low to construct magnetostatic
models of the quiescent prominence in the form of a vertical
infinite sheet of material which is both denser and cooler than its
surrounding. A magnetic field of about 2 gauss serves to support
the weight of the prominence and to confine the prominence material
in a thin sheet. By a suitable choice of a certain free function in
the mathematical model, the variation of the prominence temperature
corresponds to a medium with a 5/2 power-law thermal conductivity,
neglecting the magnetic effect on thermal conduction. It is shown that a
static balance obtains everywhere between the conducted heat input and
a hypothetical heat sink which is proportional to the local material
density. This heat sink simulates the effect of the radiative loss of
the prominence. The gross observed prominence features are reproduced.
---------------------------------------------------------
Title: Nonisothermal magnetostatic equlibria in a uniform gravity
field. I. Mathematical formulation.
Authors: Low, B. C.
1975ApJ...197..251L Altcode:
The magnetostatic equilibrium equations of a two-dimensional plasma in
a uniform gravity field are derived without assuming a constant gas
temperature. Pressure and temperature are transformed into functions
of the magnetic vector potential and the vertical height, and the
vector equilibrium equation for Cartesian and cylindrical coordinate
systems is reduced to a single scalar nonlinear elliptic partial
differential equation. The general properties of the derived equations
and their general implications are discussed, and it is shown that
photospheric conditions at any one time in general do not determine
unique magnetostatic equilibrium configurations above the photosphere.
---------------------------------------------------------
Title: Evolving Force-Free Magnetic Fields in Response to Photospheric
Motions
Authors: Low, B. C.; Nakagawa, Y.
1975BAAS....7..347L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Resistive diffusion of force-free magnetic fields in a passive
medium. IV. The dynamical theory.
Authors: Low, B. C.
1974ApJ...193..243L Altcode:
The subsequent resistive diffusion of an initially force-free magnetic
field in a tenuous medium, initially at rest, is considered. The
inertia of the medium is taken into account. The one-dimensional case
is treated by an expansion of both the momentum and the hydromagnetic
induction equations of the parameter epsilon = An/V<SUB>0</SUB> in
the limit of epsilon being much less than 1. Here A(-1) is a typical
length scale, n the constant resistive coefficient, and V<SUB>0</SUB>
the Alfven speed. It is found that within the Alfven transit time a
small nonzero Lorentz force sets in and accelerates the medium to move
in a manner such that the magnetic field may remain almost force-free
for an extended period of time.
---------------------------------------------------------
Title: Resistive Diffusion of Force-Free Magnetic Fields in a Passive
Medium. III. Acceleration of Flare Particle
Authors: Low, B. C.
1974ApJ...189..353L Altcode:
We have previously suggested that solar flares are triggered by
the resistive diffusion of force-free magnetic fields in a passive
medium. We consider a one-dimensional model in which an increasingly
large electric field is induced by a rapidly evolving magnetic field. We
estimate, in the case of solar flares, the energies to which protons
and electrons may be directly accelerated by such an induced electric
field. Sabject headings: flares, solar - hydromagnetics
---------------------------------------------------------
Title: Resistive diffusion of force-free magnetic fields in a
passive medium.
Authors: Low, B. C.
1974BAAS....6..264L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Erratum: Resistive Diffusion of Force-Free Magnetic Fields
in a Passive Medium
Authors: Low, B. C.
1973ApJ...186..775L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Resistive Diffusion of Force-Free Magnetic Fields in a Passive
Medium. 11. a Nonlinear Analysis of the One-Dimensional Case
Authors: Low, B. C.
1973ApJ...184..917L Altcode:
We investigate the force-free magnetic field B = [cos (z, t), sin
(z, t), 0] to ascertain when it may develop infinite field gradients
while undergoing resistive diffusion in a passive medium (Low). A
complete analysis of the nonlinear evolution of B is given, subject
to the conditions (i) 4L(z, 0) is an odd and increasing function of
the Cartesian coordinate z and (ii) ( I 00, t) = I o for all time,
where o is finite and independent of time. if the total rotation of
B along the z-axis exceeds half a revolution, i.e., > , we find
that B always develops infinite field gradients after a finite period
of time, irrespective of the initial distribution (z, 0). The modest
criterion > supports our suggestion that this type of instability
triggers the eruption of flares in the solar chromosphere. if < ,
we find that B always evolves toward a uniform field, irrespective of
the initial distribution (z, 0). The marginal case = admits an unstable
steady state. We use the properties of this steady state to show how a
quantitative theory of homologous flares might be constructed. Subject
headings: flares, solar - hydromagnetics
---------------------------------------------------------
Title: Resistive Diffusion of Force-Free Magnetic Fields in a
Passive Medium
Authors: Low, B. C.
1973ApJ...181..209L Altcode:
A force-free magnetic field B(x, t) satisfying V x B = aB for
nonconstant a will change its shape as it undergoes resistive
diffusion. We consider the resistive diffusion of such a force-free
magnetic field in a tenuous compressible medium, which is free to move
to accommodate the changing magnetic-field configuration. This process
is nonlinear, contrary to the usual magnetic field diffusion in a fixed
medium. We show that the force-free magnetic field may evolve slowly
for an extended period of time, whereupon it abruptly develops steep
gradients and passes into an explosive phase. We suggest that it is
this process that sets the stage for the onset of solar flares. Subject
headings: flares, solar - hydromagnetics - magnetic fields
---------------------------------------------------------
Title: Erratum: Root Mean Square Fluctuation of a Weak Magnetic
Field in an Infinite Medium of Homogeneous Stationary Turbulence
Authors: Low, B. C.
1972ApJ...178..277L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Root Mean Square Fluctuation of a Weak Magnetic Field in an
Infinite Medium of Homogeneous Stationary Turbulence
Authors: Low, B. -C.
1972ApJ...173..549L Altcode:
This paper considers the generation of magnetic field by statistically
homogeneous, stationary velocity turbulence. The generation of rms
magnetic fluctuation is explicitly demonstrated in the limit of short
turbulence correlation time. It is shown that the fluctuation ( B2)
associated with a growing or stationary mean field (B grows with time
such that ( B1)/( tends to a steady value, which is a monotonically
decreasing function of the growth rate of (B) As an application,
we estimate ( B1)/(B) to be of order one for the galactic medium,
in agreement with observational results. In the case of a decaying
(B), we show that the associated (bB1) eventually decays in time,
proceeding at a rate slower than that of the decay of (B).
---------------------------------------------------------
Title: Kinematic-Dynamo Action Under Incompressible, Isotropic
Velocity Turbulence
Authors: Lerche, I.; Low, B. C.
1971ApJ...168..503L Altcode:
We demonstrate that incompressible, isotropic velocity turbulence on its
own iii an infinite medium leads to regenerative dynamo action. Earlier
work has demonstrated that (i) incompressible velocity turbulence
possessing a net helicity generates dynamo action in an infinite medium;
(ii) isotropic, compressible velocity turbulence generates dynamo action
in an infinite medium. The present results show first that regenerative
dynamo action is not peculiar to the assumption of either nonisotropy or
compressibility, and second that the turbulent Lorentz force (which is
never isotropic no matter whether the velocity turbulence is isotropic
or not) is the main cause of purely turbulent dynamo action. The fact
that incompressible, isotropic turbulence generates dynamo activity
just underscores these facts.
