file: masters.98 = Rob Rutten's course at CAUP Master's autumn 1998 last: Nov 20 1998 students -------- Alison Boyle email alison@astro.up.pt graduated in physics in Galway Fernando Jorge Guti'errez Pinheiro email fjp@astro.up.pt graduated in astronomy in Porto Ulrike Riemenschneider email ulrike@astro.up.pt graduated in applied mathematics in Galway course content (summary) = Chapts 2+5 RTSA, Chapt 8 GTR ------------------------------------------------------- photon-atom interactions (Chapt 2 RTSA) bb, bf, ff, Thomson, Rayleigh photon creation, destruction, scattering, conversion Planck function; Boltzmann, Saha distributions local thermal (LTE) versus nonthermal nonlocal (scattering, conversion) radiation quantities (Chapt 2 RTSA) definitions I, J, F; j, alpha, S; tau, tau_rad S = (1-eps) J + eps B radiative transfer (Chapt 2 RTSA) differential transport equation thin line formation integral solution, Eddington-Barbier approximation thick line formation curve of growth stellar atmospheres (Chapt 5 RTSA) empirical model determination classical stellar photospheres in LTE, HE, RE chromospheric line formation coronal ionization equilibrium coronal energy equilibrium stellar environments (Chapt 8 GTR) P Cygni profiles hot-star winds Zanstra mechanism planetary nebulae Bowen pumping mechanism lecture notes ------------- RTSA = "Radiative TRansfer in Stellar Atmospheres" dark-blue notes STELLAR ATMOSPHERES Astrofysica 2B January 6 1998 = Utrecht version of the RTSA notes (slightly better than the current WWW version of RTSA which I will renew in December) Utrecht course: 3rd year astronomy students (30 hours + exercises) one copy to each student one copy to CAUP library Chapter 2 = quantities, processes, basic RT = summary of GTR Chapter 5 = classical stellar atmospheres GTR = "Generation and Transport of Radiation" light-blue notes March 1995 = Dan Kiselman's paste Peterson translation + Chapts 2,3 IART Utrecht: 2nd year astronomy + physics students (24 hours, Dutch version) no electronic version yet available one copy in library left last year (but I can't find it) Chapt 2-5 = RTSA Chapt 2 but much more extended (RTSA Chapt 2 = summary of these GTR lecture notes) Chapter 8 = "Applications" copied and handed out (except coronal radio emission) books (+/- = present/not present in CAUP library) ----- see more extensive descriptions in introduction to RTSA + Rybicki & Lightman (CAUP library QB461 R88) + Gray (CAUP library QB809 G67) + Boehm-Vitense series lower level than RTSA but quite good; recommended + Shu I, II (CAUP library QB461 S5;1 and S5;2) higher level than RTSA - Novotny (out of print) - Mihalas (out of print) and one that I hadn't seen before: + Don Emerson (CAUP library QB 465 E44) Interpreting Astronomical Spectra John Wiley & Sons 1996 looks quite good daily log --------- ----------------------------------------------------------------------- 1 = Monday Nov 16: radiation processes (Chapt 2 RTSA; Chapts 5 + 6 GRT) ----------------------------------------------------------------------- What is the spectrum of the white board with lights off? solar with slight modification from blue sky = Rayleigh scattering Thermodynamic Equilibrium (TE) distribution functions (RTSA 2.5; GTR 4) atoms and other fermions Maxwell distribution (over velocity and speed) Boltzmann distribution (over different excitation levels) Saha distribution (over different ionization stages) photons (= bosons: no exclusion principle) Planck function Wien approximation Rayleigh-Jeans approximation peak shift = color = Wien displacement law area = integrated intensity = Stefan Boltzmann all these share exp(-energy/kT) character (statistical mechanics) atom-photon interactions (RTSA 2.3-2.4; GTR 5, 6) bound-bound processes = discrete energy up/down => spectral lines radiative excitation collisional excitation spontaneous radiative deexcitation collisional deexcitation stimulated radiative deexcitation profile (= wavelength dependence cross-section): narrow spike center part = Doppler core = Gaussian Dopplershifts from thermal motions Dopplershifts from "turbulence" = fudge for fine detail wings = damping wings = Lorentzian = Coulomb perturbations bound-free processes = ionization/recombination => continua same five basic possibilities profile: zero below threshold energy, drop-off above free-free processes = atom/ion + free electron => continua same five basic possibilities profile: no threshold, decrease with energy "atom" may also be ions, molecules, hadrons etc special: H-minus bf and ff = neutral hydrogen atom + second electron provides dominant continuous extinction in photospheres cool stars continuum scattering = redirection of photon, keeps energy (wavelength) Thomson scattering = photon + free electron no wavelength dependence of cross-section provides dominant continuous extinction in photospheres hot stars Rayleigh scattering = photon + bound electron (in atom or molecule) wavelength dependence of cross-section: lambda^4 makes our sky blue and sunsets red Exercise = Payne-like Saha-Boltzmann for Schadee atom and hydrogen Ulrike off to examination IDLDE = windows version of IDL demo, similar to PC student version completed --------------------------------------------------------------------- 2 = Tuesday Nov 17: definitions I,J,F; alfa,j,S; transport equation (Chapt 2 RTSA; Chapts 2 + 3 GRT) --------------------------------------------------------------------- Are there Na D lines in the whiteboard spectrum? (Chapt 1 GRT) yes, just like in solar irradiance spectrum. Atmosphere doesn't change solar lines since no free sodium atoms. Rayleigh scattering leaves frequency of scattered photon the same, so the solar line spectrum is not changed, only the continuum distribution (blue sky). Plus addition of molecular absorption lines such as H2O lines next to the Na D lines. Kirchhoff-Bunsen sodium-in-flame experiments (Chapt 1 RTSA) flame: Na D emission lines = coll exc + rad deexc plus background illumination: absorption lines due to scattering = redirection away from line of sight line strength increases with amount of Na diagnostic of presence and quantity of Na at a distance basic process combinations (for bb but same for bf and ff) (Chapt 1 GRT) coll exc + rad deexc = photon creation rad exc + coll deexc = photon destruction these two are thermal and local rad exc + rad deexc = photon scattering nonthermal, nonlocal rad exc + further exc to other levels etc = photon conversion nonthermal, nonlocal, non-monochromatic macroscopic quantities (Chapt 2+3 GRT, Chapt 2 RTSA) intensity flux mean intensity emission coefficient extinction coefficient optical thickness optical depth source function fully thermal: S=B fully scattering: S=J two-level atom: S = (1-eps) J + eps B transport equation nature of source function sets difficulty; if eps << 1 non-local integro-differential equation exercise = Minnaert-like Schuster-Schwarzschild line formation until Voigt profile computation --------------------------------------------------------------------- 3 = Wednesday Nov 18: LTE/NLTE thick line formation (Chapt 2 RTSA; Chapt 3 GRT) --------------------------------------------------------------------- overnight Leonid score: Alison: 5 Ulrike: 2 Fernando: 1 certain, 1 questionable Rob: 0 (2 in Brasil in 1966 - out of 10000/hour alas) repeat definitions and transport equations = Eqs. 2.1-2.24 RTSA formal integral "solution" of radiative transfer equation (RTE) RTE solution for homogeneous medium (Eq. 2.26, Fig. 2.2 RTSA) optically thick object: no spectral lines optically thin object: emission/absoprtion lines depending on S/I(0) solar limb darkening (Fig 2.4 RTSA) solar limb brightening continuous extinction in solar photosphere through spectrum UV: metal edges; visual: H minus bf; infrared: H minus ff Fig 8.1 page 82 GTR (edges wrong though) (also in Figs 6.14-6.18 RTSA but Vitense confusograms hard to read) formal integral solution RTE for optically thick inhomogeneous atmosphere emergent intensity from plane-parallel atmosphere Eddington-Barbier approximation stellar line formation with EB approximation ("four-panels" Fig 2.5 RTSA) absorption lines = decreasing S(h) emission lines = increasing S(h) LTE (Local Thermodynamic Equilibrium): S = B absorption lines = decreasing T(h) solar photosphere in visual emission lines = increasing T(h) solar chromosphere in UV and IR NLTE (Non-LTE): S = (1-eps)J + eps B + ?? example: Ca II K line much stronger than Halpha due to Boltzmann-Saha funny little peaks ("reversals") requires hump in S (Fig 2.5 RTSA) peaks are good magnetometers for cool stars but not understood Colloquium: movie of solar 171 Angstrom Fe IX/X images from TRACE bright = optically thin Fe IX/X emission at T = 10^6 K dark = H I, He I, He II bf scattering at T = 10^4 - 10^5 K solar corona is not exactly plane-parallel... Exercise: rest Minnaert-like = equivalent width, curve of growth --------------------------------------------------------------------- 4 = Thursday Nov 19: classical stellar photospheres (Chapt 5 RTSA, books Boehm-Vitense and Gray) --------------------------------------------------------------------- empirical modeling of the solar temperature stratification - Planck function inversion = inverted continuum extinction (Chap 8 GRT) - inversion of observed spectral line profiles - inversion of observed continua UV - IR - inversion of center-limb intensity variation historical identification Hminus as major continuum provider theoretical modeling of stellar temperature stratification - ideal gas: N -> P - chemical composition + Saha: N_e -> N_g - hydrostatic equilibrium (HE): g, T(tau) -> N_e(tau) - radiative equilibrium (RE): T_eff -> T(tau) exercise: problems 1 + 2 RTSA (page 213) --------------------------------------------------------------------- 5 = Friday Nov 20: chromospheres, coronae, winds, planetary nebulae (Chapt 8 GRT, copied and handed out) --------------------------------------------------------------------- classical photospheres versus chromospheres and coronae subsurface: LTE, HE (except convection), RE (except convection) photosphere: LTE, HE, RE chromosphere: NLTE = scattering in strong resonance lines no RE since transparant to the stallar flux no HE but acoustic waves and shocks onset of domination magnetic pressure over gas pressure corona: two components - hot (10^6 K) loops emitting X-ray lines thin layer without irradiation since B(T=5000K) negligible at X rays coronal equilibrium = collisional excitation, radiative deexcitation each photon lost, so far from LTE although thermal photon creation total photon loss equals coronal heating coronal heating mechanism unknown - cool matter (10^4 K) extinction in HI, HeI, HeII bf continua thick layer with scattering bf scattering = redirection and also wavelength change hot stars versus cool stars hydrogen ionized hydrogen neutral continuous etinction = Thompson (NLTE) H-minus bf and ff = LTE radiatively driven wind wind = coronal evaporation large mass loss negligible mass loss no convection convection no magnetic field (presumably) solar type magnetic fields no chromosphere or corona chromospheres and coronae hot-star winds (Chapt 8 GRT) P-Cygni profiles thin layer case with Dopplershift mapping radiative acceleration planetary nebulae (Chapt 8 GRT) Zanstra mechanism: observe bright Balmer lines due to Lyman continuum from hot central star counting Balmer line photons nebular yields estimate of star Ly cont Bowen mechanism: pumping through line coincidences Exercise: problem 3 RTSA (printout with answers 1-4 copied and handed out)