file: masters.01 = Rob Rutten's course CAUP Masters December 2001 last: Dec 13 2001 students -------- Cristina Gon,calves crismurta@mail.pt Slawomir (Slawek) Gras slagras@hotmail.com Olga Moreira 95a015@astro.ma.fc.up.pt Bruno Silva silvab_@hotmail.com course material --------------- GTR = Generation and Transport of Radiation (CAUP library) RTSA = Radiative Transfer in Stellar Atmospheres (CAUP library /home/rutten/masters/rtsa http://www.astro.uu.nl/~rutten) SSA = Exercises Stellar Spectra A also in my CAUP dir and on my website SSB = Exercises Stellar Spectra B also in my CAUP dir and on my website textbooks: see end of this file course content (summary) = Chapts 2 RTSA, Chapt 8 GTR ------------------------ photon-atom interactions (Chapt 2 RTSA [= summary Chapt 4, 5, 6 GTR]) bb, bf, ff, Thomson, Rayleigh photon creation, destruction, scattering, conversion TE: 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 integral solution, Eddington-Barbier approximation line formation optically thick objects two-level scattering solar spectrum (Chapt 8 GTR) stellar environments (Chapt 8 GTR) solar coronal radiation hot star winds: P Cygni profiles planetary nebulae: Zanstra conversion books (+/- = present/not present in CAUP library in 2000) ----- more extensive book descriptions in introduction to RTSA + Rybicki & Lightman (CAUP library QB461 R88) GTR is a much extended version of Chapter 1 of this book (but Chapter 6 of GTR is a summary of all other chapters of this book) + 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; very good but pretty deep - 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 logs of what I taught =========================== Monday Dec 10 2001 = basic radiation physics ------------------ What is spectrum of the whiteboard with lights off? solar! non-local and radiation T >> local emission T lots of scattering on the way but that is all monofrequent so very non-local: photons carry signature of solar creation even though observed from whiteboard Na D lines in solar spectrum "all understood" but polarization still enigmatic total eclipse: white light without Na D lines due to Doppler smearing spectral classification Annie Cannon identification spectral type = temperature Saha-Boltzmann Cecilia Payne TE laws (RTSA 2; GTR 4) matter = Maxwell, Boltzmann, Saha radiation = Planck + regimes etc particle-photon interactions (RTSA 2, 3; GTR 1, 5, 6) bound-bound processes = discrete energy up/down => spectral lines radiative excitation collisional excitation spontaneous radiative deexcitation collisional deexcitation stimulated radiative deexcitation 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 ion, molecule, hadron etc Thomson scattering: free electrons, wavelength independent Rayleigh scattering: bound electrons, lambda^4 (blue sky) line broadening (RTSA 3) Doppler core = Gaussian from Maxwellian thermal motions damping core = Lorentzian wings from Coulomb interactions collisions natural broadening = heisenberg uncertainty basic process combinations (for bb but same for bf and ff) (GRT 1) 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 Kirchhoff-Bunsen sodium-in-flame experiments (RTSA 1; GTR 1) 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 definition radiation quantities I = intensity ergs / cm^2 s Hz ster = constant along ray J = mean intensity = average over all angles, same units F = net flux = sum in forward direction, cosine weighting solar line formation = mixture of scattering + thermal photon production thermal sample temperature at escape depth escape depth lies further out in line (smaller transparency) easy: production photons = B_\lambda (T) with outward decreasing temperature: absorption lines scattering needs evaluation of J = intensity averaged over all directions so needs I = radiative transport complex Tuesday Dec 11 2001 ------------------- radiation change quantities (RTSA 2, GTR 3) emissivity, extinction coefficient optical path length, optical depth source function bb transitions (RTSA 2, GTR 5) Einstein coefficients Einstein relations coherent scattering versus complete redistribution emissivity and extinction in Einstein coefficients stimulated emission as negative extinction general line source function radiative transfer equation (RTSA2, GTR 3) differential form integral from solution for emergent intensity from plane-parallel atmosphere Eddington-Barbier relation solar limb darkening/brightening (RTSA 2, GTR 3) line formation with the Eddington-Barbier approximation Wednesday Dec 12 2001 --------------------- extensive review of all equations sofar (RTSA 2 = your printout) > 100 eqs/hour... quickie introduction to numerical techniques: ALI (RTSA 5) two-level scattering: definition of epsilon (RTSA 2, GTR 7) two-level line source function S = (1-eps) J + eps B square-root eps law: S = sqrt(eps) B (surface of isothermal atmosphere) explanation of the solar spectrum (GTR 8) T_b continuum = inverse of continuous opacity continuous opacity visible and near-IR = H-minus (Chandrasekhar) 2nd electron from donor elements = lower ionization energy than H VALIII model with spectral feature formation height Avrett solar T_b plot with fractional opacity source whole spectrum Thursday Dec 13 2001 application (GTR 8) -------------------- brief equation review = radiative transfer rap (last page RTSA) NaD lines have dark cores due to scattering: sqrt(eps) law non-plane-parallel solar atmosphere: DOT movies sunspots, fluxtubes coronal emission white-light K corona = Thomson scattered, no spectral lines F corona = scattered by dust, including Fraunhofer lines X-ray = thermal emission, far from LTE due to optical thinness X-ray absorption = bound-free scattering out of passband coronal equilibrium excitation collisional up, radiation down: f(N_e,T) ionization idem, f(T) only recombination mostly di-electronic extended atmosphere: emission line ib flux from geometry expanding atmosphere: P Cygni profiles radiatio-driven stellar wind planetary nebulae: Zanstra mechanism for Balmer-line emission