SOLAR SPECTRUM FORMATION

Transcription

1 SOLAR SPECTRUM FORMATION Robert J. Rutten [Sterrekundig Instituut Utrecht & Institutt for Teoretisk Astrofysikk Oslo] Texts: R.J. Rutten, Radiative Transfer in Stellar Atmospheres (RTSA), my website D. Mihalas, Stellar Atmospheres, 1970, 1978 G.B. Rybicki and A.P. Lightman, Radiative Processes in Astrophysics, 1979, 2004 M. Stix, The Sun, 1989, 2002/2004 examples of local, nonlocal, converted photons: white light corona coronium lines EUV corona EUV bright/dark [Zanstra & Bowen PN lines] radiative transfer basics: basic quantities constant S ν plane-atmosphere RT Eddington-Barbier cartoons LTE 1D solar radiation escape: Planck continuous opacity LTE continuum Boltzmann-Saha LTE line equations LTE line cartoons solar ultraviolet spectrum VALIIIC temperature solar spectrum formation Ca II H&K versus Halpha NLTE 1D solar radiation escape: bb processes bb rates bb equilibria scattering solar radiation processes VAL3C continuum formation radiative cooling VAL3C radiation budget realistic line cartoon Na D1 Ca II 8542 versus Halpha MHD-simulated essolar radiation escape: Ca II H in 1D Na D1 in 3D non-e hydrogen in 2D summary: RTSA rap

2 WHITE LIGHT CORONA Stix section Grotrian (1931): Thomson scattering 8000 km s 1 electrons (S ) ρ 2 = x 2 + y 2 ρ j(ρ) I(x) = 2 j(ρ) dy = 2 ρ2 x dρ 2 0 x N e from inverse Abel transform = isotropically scattered irradiation (S ) j(ρ) = 1 di/dx π x2 ρ dx = σ 1 2 T N e I (θ) dω 4π ρ

3 CORONIUM LINES Stix section Grotrian, Edlén 1942: forbidden lines high ionization stages (Stix Table 9.2 p. 398) name wavelength identification λ D v A ul previous ion χ ion green line nm [Fe XIV] nm 29 km/s 60 s 1 Fe XIII 355 ev yellow line [Ca XV] Ca XIV 820 red line [Fe XI] Fe IX 235 Coronal sky at Dome C

4 EUV CORONA Stix section bf equilibria: collisional ionization = radiative recombination only f(t ), not f(n e ) bb equilibria: collisional excitation = spontaneous deexcitation f(t, N e ) (S ) ( ) 1 dt n l C lu = n l N e σ lu f(v) v dv n u A ul hν n ion N e dz = Ne 2 dt EM v 0 dz

5 BRIGHT AND DARK IN EUV IMAGES iron lines Fe IX/X 171 Å: about 1.0 MK Fe XII 195 Å: about 1.5 MK Fe XIV 284 Å: about 2 MK bright collision up, radiation down thermal photon creation, NLTE equilibrium 171 Å: selected loops = special trees in forest dark radiation up, re-radiation at bound-free edge matter containing He +, He, H: K large opacity

6 BASIC QUANTITIES RTSA , Stix Monochromatic emissivity (Stix uses ε) de ν j ν dv dt dν dω units j ν : erg cm 3 s 1 Hz 1 ster 1 Monochromatic extinction coefficient di ν (s) = j ν (s) ds I ν : erg cm 2 s 1 Hz 1 ster 1 di ν σ ν n I ν ds di ν α ν I ν ds di ν κ ν ρ I ν ds units: cm 2 per particle (physics) cm 2 per cm 3 = per cm (RTSA) cm 2 per gram (astronomy) Monochromatic source function S ν j ν /α ν = j ν /κ ν ρ S tot ν = jν αν thick: (κ ν, S ν ) more independent than (κ ν, j ν ) S tot ν = jc ν + j l ν α c ν + α l ν = Sc ν + η ν S l ν 1 + η ν η ν α l ν/α c ν stimulated emission negatively into α ν, κ ν Transport equation with τ ν as optical thickness along the beam di ν ds = j di ν ν α ν I ν α ν ds = S ν I ν dτ ν α ν ds di ν dτ ν = S ν I ν Plane-parallel transport equation with τ ν as radial optical depth and µ as viewing angle dτ ν α ν dz τ ν (z 0 ) = z0 α ν dz µ cos θ µ di ν dτ ν = I ν S ν

7 CONSTANT SOURCE FUNCTION Transport equation along the beam (τ ν = optical thickness) di ν = S ν I ν I ν (τ ν ) = I ν (0) e τν + dτ ν τν 0 S ν (t ν ) e (τν tν) dt ν Invariant S ν I ν (D) = I ν (0) e τν(d) + S ν ( 1 e τ ν(d) ) example: S ν = B ν for all continuum and line processes in an isothermal cloud Thick object I ν (D) S ν Thin object I ν (D) I ν (0) + [S ν I ν (0)] τ ν (D) I ν (0)=0 : I ν (D) τ ν (D) S ν = j ν D

8 RADIATIVE TRANSFER IN A PLANE ATMOSPHERE Radial optical depth RTSA 2.2.2; Stix dτ ν = κ ν ρ dr r radial Hubený τ νµ κ ν cm 2 /gram α ν cm 1 = cm 2 /cm 3 σ ν cm 2 /particle Transport equation µ di ν dτ ν = I ν S ν Integral form I ν (τ ν, µ) = τν 0 S ν (t ν ) e (tν τν)/µ dt ν /µ I ν + (τ ν, µ) = + S ν (t ν ) e (tν τν)/µ dt ν /µ τ ν formal solution NB: both directions pm: Doppler anisotropy S ν Emergent intensity without irradiation I ν (0, µ) = (1/µ) 0 S ν (τ ν ) e τν/µ dτ ν Eddington-Barbier approximation I ν (0, µ) S ν (τ ν =µ) exact for linear S ν (τ ν )

9 SIMPLE ABSORPTION LINE extinction: bb process gives peak in α total = α c + α l = (1 + η ν ) α c optical depth: assume height-invariant α total linear (1 + η ν ) τ c source function: assume same for line (bb) and continuous (bf, ff) processes use Eddington-Barbier (here nearly exact, why?)

10 SIMPLE EMISSION LINE extinction: bb process gives peak in α total = α c + α l = (1 + η ν ) α c optical depth: assume height-invariant α total linear (1 + η ν ) τ c source function: assume same for line (bb) and continuous (bf, ff) processes use Eddington-Barbier (here nearly exact, why?)

11 SIMPLE ABSORPTION EDGE extinction: bf process gives edge in αν, c with αν c ν 3 if hydrogenic optical depth: assume height-invariant (unrealistic, why?) source function: assume same for the whole frequency range (unrealistic, why?) use Eddington-Barbier (here nearly exact, why?)

12 SIMPLE EMISSION EDGE extinction: bf process gives edge in αν, c with αν c ν 3 if hydrogenic optical depth: assume height-invariant (unrealistic, why?) source function: assume same for the whole frequency range (unrealistic, why?) use Eddington-Barbier (here nearly exact, why?)

13 SELF-REVERSED ABSORPTION LINE extinction: bb peak with height-dependent amplitude and shape optical depth: non-linear even in the log source function: decrease followed by increase (any idea why?) use Eddington-Barbier (questionable, why?)

14 DOUBLY REVERSED ABSORPTION LINE extinction: bb peak with height-dependent amplitude and shape optical depth: non-linear even in the log source function: decrease followed by increase followed by decrease (any idea why?) use Eddington-Barbier (questionable, why?)

15 DOUBLY REVERSED ABSORPTION LINE extinction: bb peak with height-dependent amplitude and shape optical depth: non-linear even in the log source function: decrease followed by increase followed by decrease (NLTE scattering) use Eddington-Barbier (questionable, why?)

16 SOLAR SPECTRUM FORMATION Robert J. Rutten [Sterrekundig Instituut Utrecht & Institutt for Teoretisk Astrofysikk Oslo] Texts: R.J. Rutten, Radiative Transfer in Stellar Atmospheres (RTSA), my website D. Mihalas, Stellar Atmospheres, 1970, 1978 G.B. Rybicki and A.P. Lightman, Radiative Processes in Astrophysics, 1979, 2004 M. Stix, The Sun, 1989, 2002/2004 examples of local, nonlocal, converted photons: white light corona coronium lines EUV corona EUV bright/dark [Zanstra & Bowen PN lines] radiative transfer basics: basic quantities constant S ν plane-atmosphere RT Eddington-Barbier cartoons LTE 1D solar radiation escape: Planck continuous opacity LTE continuum Boltzmann-Saha LTE line equations LTE line cartoons solar ultraviolet spectrum VALIIIC temperature solar spectrum formation Ca II H&K versus Halpha NLTE 1D solar radiation escape: bb processes bb rates bb equilibria scattering solar radiation processes VAL3C continuum formation radiative cooling VAL3C radiation budget realistic line cartoon Na D1 Ca II 8542 versus Halpha MHD-simulated essolar radiation escape: Ca II H in 1D Na D1 in 3D non-e hydrogen in 2D summary: RTSA rap

17 PLANCK RTSA Chapt. 2; Stix 4.5 Planck function in intensity units B ν (T ) = 2hν3 1 B c 2 e hν/kt λ (T ) = 2hc2 1 1 λ 5 e hc/λkt 1 B σ (T ) = 2hc 2 σ 3 1 e hcσ/kt 1 Approximations Wien: B ν (T ) 2hν3 e hν/kt Rayleigh-Jeans: B c 2 ν (T ) 2ν2 kt c 2

18 PLANCK FUNCTION VARIATIONS

19 CONTINUOUS OPACITY IN THE SOLAR PHOTOSPHERE bound-free RTSA Chapt. 8; Stix Fig. 4.5; figure from E. Böhm-Vitense optical, near-infrared: H UV: Si I, Mg I, Al I, Fe I (electron donors for H ) EUV: H I Lyman; He I, He II free-free infrared, sub-mm: H radio: H I electron scattering Thomson scattering (large height) Rayleigh scattering (near-uv) Rosseland average 1 κ = 0 1 κ ν db ν /dt db/dt dν

20 SOLAR OPTICAL AND NEAR-INFRARED CONTINUUM FORMATION Assumed: LTE, opacity only from H I bf+ff and H bf+ff, FALC model atmosphere Solar disk-center continuum: from Allen, Astrophysical Quantities, 1976 Does the Eddington-Barbier approximation hold?

21 Saha Boltzmann level populations Boltzmann distribution per ionization stage: n r,s N r = g r,s U r e χ r,s/kt partition function: U r s g r,s e χ r,s/kt Saha distribution over ionization stages: N r+1 = 1 ( ) 3/2 2 U r+1 2πme kt e χ r/kt N r N e U r h 2

22 Saha Boltzmann Schadeenium

23 LTE LINES continuum optical depth scale RTSA Chapt. 2; Stix η ν κ l /κ C dτ ν = dτ C + dτ l = (1 + η ν ) dτ C emergent intensity at disk center in LTE I ν (0, 1) = 0 B ν exp( τ ν ) dτ ν = 0 (1 + η ν ) B ν exp Eddington-Barbier: I ν (0, 1) B ν [τ ν =1] = B ν [τ C =1/(1+η ν )] ( τc 0 (1 + η ν ) dτ C ) dτ C line extinction coefficient shape = Maxwell [+ microturbulence ] Gauss damping Lorentz ν D ν 0 2RT γ + exp( (ν ν ) 2 / ν c A [+ξ2 D 2 t ] φ(ν) = ) 1 π νd [2π(ν ν 0 )] 2 + γ 2 /4 dν = H(a, v) π νd Voigt function v ν ν 0 ν D a γ 4π ν D H(a, v) a π + e y2 (v y) 2 + a 2 dy area in v: π line extinction coefficient σ l = hν 4π B lu φ(ν) = πe2 π e 2 m e c f f l l φ(ν) = H(a, v) m e c ν D A ul = g l f lu g u λ 2 s 1 (λ nm) κ l = σ l n LTE l (1 e hν/kt )/ρ = σ l µm H n i ni n ij n i n ijk n ij (1 e hν/kt ) i, j, k species, stage, lower level abundance, Saha, Boltzmann

24 STELLAR LTE ABSORPTION LINE extinction: large bb peak in α total (h) = α c (h) + α l (h), both decreasing with height optical depth: the inward integration τ ν = α ν dh along the line of sight reaches τ ν =1 at much larger height at line center than in the adjacent continuum source function: S ν (h) = B ν [T (h)] (neglect variation over the profile) intensity: the emergent profile is a two-sided mapping of B ν [T (h)] sampled at h(τ ν 1) Why are LTE lines with the same α c (h) and α l (h) deeper in the blue than in the red?

25 STELLAR LTE SELF-REVERSED LINE extinction: large bb peak in α total (h) = α c (h) + α l (h), both decreasing with height optical depth: the inward integration τ ν = α ν dh along the line of sight reaches τ ν =1 at much larger height at line center than in the adjacent continuum source function: S ν (h) = B ν [T (h)] (neglect variation over the profile) intensity: the emergent profile is a two-sided mapping of B ν [T (h)] sampled at h(τ ν 1)

26 SOLAR ULTRAVIOLET SPECTRUM Scheffler & Elsässer, courtesy Karin Muglach

27 VALIIIC MODEL Vernazza, Avrett, Loeser 1981ApJS V

28 SOLAR SPECTRUM FORMATION Avrett 1990IAUS A

29 H-α AND Ca II K IN THE SOLAR SPECTRUM solar abundance ratio: Ca/H = Assuming LTE at T = 5000 K, P e = 10 2 dyne cm 2 : Boltzmann H I: n 2 n 1 = Saha Ca II: N Ca II N Ca 1 Ca II (n=1) H I (n=2) =

30 Ca II H & Hα in LTE Leenaarts et al. 2006A&A L

31 SOLAR SPECTRUM FORMATION Robert J. Rutten [Sterrekundig Instituut Utrecht & Institutt for Teoretisk Astrofysikk Oslo] Texts: R.J. Rutten, Radiative Transfer in Stellar Atmospheres (RTSA), my website D. Mihalas, Stellar Atmospheres, 1970, 1978 G.B. Rybicki and A.P. Lightman, Radiative Processes in Astrophysics, 1979, 2004 M. Stix, The Sun, 1989, 2002/2004 examples of local, nonlocal, converted photons: white light corona coronium lines EUV corona EUV bright/dark [Zanstra & Bowen PN lines] radiative transfer basics: basic quantities constant S ν plane-atmosphere RT Eddington-Barbier cartoons LTE 1D solar radiation escape: Planck continuous opacity LTE continuum Boltzmann-Saha LTE line equations LTE line cartoons solar ultraviolet spectrum VALIIIC temperature solar spectrum formation Ca II H&K versus Halpha NLTE 1D solar radiation escape: bb processes bb rates bb equilibria scattering solar radiation processes VAL3C continuum formation radiative cooling VAL3C radiation budget realistic line cartoon Na D1 Ca II 8542 versus Halpha MHD-simulated essolar radiation escape: Ca II H in 1D Na D1 in 3D non-e hydrogen in 2D summary: RTSA rap

32 BOUND-BOUND PROCESSES AND EINSTEIN COEFFICIENTS Spontaneous deexcitation Radiative excitation Induced deexcitation A ul transition probability for spontaneous deexcitation from state u to state l per sec per particle in state u B lu J ϕ ν 0 number of radiative excitations from state l to state u per sec per particle in state l B ul J χ ν 0 number of induced radiative deexcitations from state u to state l per sec per particle in state u Collisional excitation and deexcitation C lu number of collisional excitations from state l to state u per sec per particle in state l C ul number of collisional deexcitations from state u to state l per sec per particle in state u

33 BOUND-BOUND RATES RTSA 2.3.1, 2.3.2, 2.6.1; Stix 4.2 Monochromatic bb rates expressed in Einstein coefficients (intensity units) n u A ul χ(ν)/4π n u B ul I ν ψ(ν)/4π n l B lu I ν φ(ν)/4π n u C ul n l C lu spontaneous emission stimulated emission radiative excitation collisional (de-)excitation Einstein relations g u B ul = g l B lu (g u /g l )A ul = (2hν 3 /c 2 ) B lu C ul /C lu = (g l /g u ) exp(e ul /kt ) General line source function j ν = hν 4π n u A ul χ(ν) required for TE detailed balancing with I ν = B ν, but hold universally α ν = hν 4π [n l B lu φ(ν) n u B ul ψ(ν)] S l = n u A ul χ(ν) n l B lu φ(ν) n u B ul ψ(ν) Simplified line source function CRD: χ(ν)=ψ(ν)=φ(ν) S l = n u A ul = 2hν3 1 n l B lu n u B ul c 2 g u n l 1 g l n u Boltzmann: S l = B ν (T ) Statistical equilibrium equations for level j N N n j R ji = n j R ij R ji = A ji + B ji J ji + C ji J ji 1 4π j i j i 4π 0 0 I ν φ(ν) dν dω time-independent population bb rates per particle in j total (= mean) mean intensity

34 BOUND-BOUND EQUILIBRIA RTSA missing; Stix LTE = large collision frequency interior, low photosphere up: mostly collisional = thermal creation (d + e) down: mostly collisional = large destruction probability (a) photon travel: honorary gas particles or negligible leak NLTE = statistical equilibrium or time-dependent chromosphere, TR photon travel: non-local impinging (pumping), loss (suction) two-level scattering: coherent/complete/partial redistribution multi-level: photon conversion, sensitivity transcription coronal equilibrium = hot tenuous coronal EUV up: only collisional = thermal creation (only d) down: only spontaneous (only d) photon travel: escape / drown / scatter bf H I, He I, He II

35 SCATTERING EQUATIONS RTSA Destruction probability coherent: ε ν αa ν α a ν + α s ν 2-level CRD: ε ν0 α a ν 0 α a ν 0 + α s ν 0 = C 21 C 21 + A 21 + B 21 B ν0 Elastic scattering coherent: S ν = (1 ε ν )J ν + ε ν B ν 2-level CRD: S ν0 = (1 ε ν0 )J ν0 + ε ν0 B ν0 Schwarzschild equation and Lambda operator J ν (τ ν ) I ν (τ ν, µ) dµ = S ν (t ν ) E 1 ( t ν τ ν ) dt ν Λ τν [S ν (t ν )] surface: J ν (0) 1 2 S ν(τ ν = 1/2) depth: J ν (τ ν ) S ν (τ ν ) diffusion: J ν (τ ν ) B ν (τ ν ) Scattering in an isothermal atmosphere coherent: S ν (0) = ε ν B ν 2-level CRD: S ν0 (0) = ε ν0 B ν0 Thermalizaton depth coherent: Λ ν = 1/ε 1/2 ν Gauss profile: Λ ν0 1/ε ν0 Lorentz profile: Λ ν0 1/ε 2 ν 0

36 EXPONENTIAL INTEGRALS RTSA figure 4.1

37 THE WORKING OF THE LAMBDA OPERATOR RTSA figure 4.1; Thijs Krijger production

38 GREY RE LTE SOLAR-TEMPERATURE ATMOSPHERE RTSA figure 4.9; Thijs Krijger production Temperature stratification: T (τ) T eff ( 3 4 τ ) 1/4

39 B, J, S FOR SOLAR-LIKE COHERENT LINE SCATTERING RTSA figure 4.11; Thijs Krijger production

40 CRD RESONANT SCATTERING IN AN ISOTHERMAL ATMOSPHERE RTSA figure 4.12; from Avrett 1965SAOSR A

41 IDEM FOR DIFFERENT LINE PROFILES RTSA figure 4.12; from Avrett 1965SAOSR A

42 IDEM WITH BACKGROUND CONTINUUM RTSA figure 4.13; from Avrett 1965SAOSR A

43 SOLAR ATMOSPHERE RADIATIVE PROCESSES bound-bound S ν, κ ν NLTE? PRD? neutral atom transitions ion transitions molecule transitions bound-free S ν, κ ν NLTE? always CRD H optical, near-infrared H I Balmer, Lyman; He I, He II Fe I, Si I, Mg I, Al I electron donors free-free S ν always LTE, κ ν NLTE H infrared, sub-mm H I radio RTSA Chapt. 8; Stix Fig. 4.5 electron scattering always NLTE, Doppler? Thomson scattering Rayleigh scattering collective p.m. cyclotron, synchrotron radiation plasma radiation

44 VALIIIC MODEL Vernazza, Avrett, Loeser 1981ApJS V

45 VAL3C CONTINUUM FORMATION

46 VAL3C CONTINUUM FORMATION

47 VAL3C CONTINUUM FORMATION

48 VAL3C CONTINUUM FORMATION

49 VAL3C CONTINUUM FORMATION

50 RADIATIVE COOLING RTSA Radiative equilibrium condition Φ tot (z) df rad(z) = 0 dz = 4π = 2π α ν (z) [S ν (z) J ν (z)] dν [j νµ (z) α νµ (z) I νµ (z)] dµ dν Net radiative cooling in a two-level atom gas Φ ul = 4πα l ν 0 (S l ν 0 J ν0 ) = 4πj l ν 0 4πα l ν 0 J ν0 = hν 0 [ nu (A ul + B ul J ν0 ) n l B lu J ν0 ] = hν 0 [n u R ul n l R lu ] Net radiative cooling in a one-level-plus-continuum gas Φ ci = 4π n LTE i b c σ ic (ν) ν 0 [ B ν ( 1 e hν/kt ) b i b c J ν ( 1 b )] c e hν/kt b i dν

51 VAL3C RADIATION BUDGET

52 VAL3C RADIATION BUDGET

53 REALISTIC SOLAR ABSORPTION LINE extinction: bb peak in η ν α l /α c becomes lower and narrower at larger height optical depth: τ ν α total ν dh increases nearly log-linearly with geometrical depth source function: split for line (bb) and continuous (bf, ff, electron scattering) processes intensity: Eddington-Barbier for S total ν = (α c S c + α l S l )/(α c + α l ) = (S C + η ν S l )/(1 + η ν )

54 SOLAR NaI D2 NSO disk-center FTS atlas Uitenbroek & Bruls 1992A&A U Na I D 2 is a good example of two-level scattering with complete redistribution: very dark Eddington-Barbier approximation: line-center τ = 1 at h 600 km chromospheric velocity response but photospheric brightness response What is the formation height of the blend line in the blue wing?

55 SOLAR NaI D2 Eddington-Barbier for the blends? Moore, Minnaert, Houtgast 1966sst..book...M: ATM H2O R ATM H2O R * ATM H2O R M * SS NA 1(D2) * ATM H2O R S" FE 1P S ATM H2O R ,26

56 Ca II 8542 VERSUS H-alpha IN 1D NLTE Cauzzi et al. 2007A&A C Kurucz model: radiative equilibrium FALC model: NLTE continuum fit Demonstration of difference in temperature sensitivity between Ca II nm and Hα. Each panel shows the temperature stratification of a standard solar model atmosphere and the resulting total source functions S λ at the nominal line-center wavelengths for Ca II nm and Hα, as function of the continuum optical depth at λ = 500 nm and with the source functions expressed as formal temperatures through Planck function inversion. The arrows mark τ = 1 locations. Lefthand panel: radiative-equilibrium model KURUCZ from Kurucz (1979, 1992a, 1992b). It was extended outward assuming constant temperature in order to reach the optically thin regime in Ca II nm. Righthand panel: empirical continuum-fitting model FALC of Fontenla et al. (1993). Its very steep transition region lies beyond the top of the panel but causes the near-vertical source function increases at left.

57 SAME WITH RADIATION FIELD Courtesy Han Uitenbroek Kurucz model: radiative equilibrium FALC model: NLTE continuum fit Two-level scattering with S ν0 = (1 ε ν0 )J ν0 + ε ν0 B ν0 dominates each source function

58 SOLAR SPECTRUM FORMATION Robert J. Rutten [Sterrekundig Instituut Utrecht & Institutt for Teoretisk Astrofysikk Oslo] Texts: R.J. Rutten, Radiative Transfer in Stellar Atmospheres (RTSA), my website D. Mihalas, Stellar Atmospheres, 1970, 1978 G.B. Rybicki and A.P. Lightman, Radiative Processes in Astrophysics, 1979, 2004 M. Stix, The Sun, 1989, 2002/2004 examples of local, nonlocal, converted photons: white light corona coronium lines EUV corona EUV bright/dark [Zanstra & Bowen PN lines] radiative transfer basics: basic quantities constant S ν plane-atmosphere RT Eddington-Barbier cartoons LTE 1D solar radiation escape: Planck continuous opacity LTE continuum Boltzmann-Saha LTE line equations LTE line cartoons solar ultraviolet spectrum VALIIIC temperature solar spectrum formation Ca II H&K versus Halpha NLTE 1D solar radiation escape: bb processes bb rates bb equilibria scattering solar radiation processes VAL3C continuum formation radiative cooling VAL3C radiation budget realistic line cartoon Na D1 Ca II 8542 versus Halpha MHD-simulated essolar radiation escape: Ca II H in 1D Na D1 in 3D non-e hydrogen in 2D summary: RTSA rap

59 Ca II H 2V GRAIN SIMULATION observation Lites, Rutten & Kalkofen 1993 sawtooth line-center shift triangular whiskers H 2V grains simulation Carlsson & Stein D radiation hydrodynamics subsurface piston from Fe I blend observer s diagnostics analysis (RR radiative transfer course) source function breakdown dynamical chromosphere H 2V grains = acoustic shocks

60 SHOCK GRAIN DIAGNOSIS Carlsson & Stein, ApJ 481, 500, 1997 I ν (0) = 0 S ν e τν dτ ν = 0 S ν τ ν e τν d ln τ ν dz dz

61 DYNAMIC LOWER CHROMOSPHERE Carlsson & Stein, ApJ 440, L29, 1995

62 3D NLTE-SE Na D1 IN 3D MHD SIMULATION Leenaarts et al. 2010ApJ L

63 SIMULATION PROPERTIES

64 MAGNETIC CONCENTRATION

65 COOL CLOUD

66 HOT FRONT

67 NON-E HYDROGEN IONIZATION Leenaarts et al. 2007A&A L time evolution along the two cuts in the 4th panel

68 SOLAR SPECTRUM FORMATION Robert J. Rutten [Sterrekundig Instituut Utrecht & Institutt for Teoretisk Astrofysikk Oslo] Texts: R.J. Rutten, Radiative Transfer in Stellar Atmospheres (RTSA), my website D. Mihalas, Stellar Atmospheres, 1970, 1978 G.B. Rybicki and A.P. Lightman, Radiative Processes in Astrophysics, 1979, 2004 M. Stix, The Sun, 1989, 2002/2004 examples of local, nonlocal, converted photons: white light corona coronium lines EUV corona EUV bright/dark [Zanstra & Bowen PN lines] radiative transfer basics: basic quantities constant S ν plane-atmosphere RT Eddington-Barbier cartoons LTE 1D solar radiation escape: Planck continuous opacity LTE continuum Boltzmann-Saha LTE line equations LTE line cartoons solar ultraviolet spectrum VALIIIC temperature solar spectrum formation Ca II H&K versus Halpha NLTE 1D solar radiation escape: bb processes bb rates bb equilibria scattering solar radiation processes VAL3C continuum formation radiative cooling VAL3C radiation budget realistic line cartoon Na D1 Ca II 8542 versus Halpha MHD-simulated essolar radiation escape: Ca II H in 1D Na D1 in 3D non-e hydrogen in 2D summary: RTSA rap

69 BASIC RADIATIVE TRANSFER EQUATIONS RTSA last page specific intensity I ν ( r, l, t) erg cm 2 s 1 Hz 1 ster 1 emissivity j ν erg cm 3 s 1 Hz 1 ster 1 extinction coefficient α ν cm 1 σ ν cm 2 part 1 κ ν cm 2 g 1 source function radial optical depth plane-parallel transport thin cloud thick emergent intensity S ν = j ν / α ν τ ν (z 0 ) = z 0 α ν dz µ di ν /dτ ν = I ν S ν I ν = I 0 + (S ν I 0 ) τ ν I + ν (0, µ) = 0 S ν (τ ν ) e τ ν/µ dτ ν /µ Eddington-Barbier I + ν (0, µ) S ν (τ ν = µ) mean mean intensity J ϕ ν 0 = I ν ϕ(ν ν 0 ) dµ dν photon destruction ε ν = α a ν/(α a ν + α s ν) C ul /(A ul + C ul ) complete redistribution isothermal atmosphere S l ν 0 = (1 ε ν0 ) J ϕ ν 0 + ε ν0 B ν0 S ν0 (0) = ε ν0 B ν0