1. 1 Model Atmosphere Results (Kurucz 1979, ApJS, 40, 1) Kurucz ATLAS LTE code Line Blanketing Models, Spectra Observational Diagnostics

2. 2 ATLAS by Robert Kurucz (SAO) Original paper and updated materials (kurucz.cfa.harvard.edu) have had huge impact on stellar astrophysics LTE code that includes important continuum opacity sources plus a statistical method to deal with cumulative effects of line opacity (“line blanketing”) Other codes summarized in Gray

3. 3 ATLAS Grid T eff = 5500 to 50000 K No cooler models since molecular opacities largely ignored. Models for T eff > 30000 K need non-LTE treatment (also in supergiants) log g from main sequence to lower limit set by radiation pressure (see Fitzpatrick 1987, ApJ, 312, 596 for extensions) Abundances 1, 1/10, 1/100 solar

4. 4 Line Blanketing and Opacity Distribution Functions Radiative terms depend on integrals Rearrange opacity over interval: DF = fraction of interval with line opacity < ℓ ν Same form even with many lines in the interval

5. 5 ODF Assumptions Line absorption coefficient has same shape with depth (probably OK) Lines of different strength uniform over interval with near constant continuum opacity (select freq. regions carefully)

6. 6 ODF Representation DF as step functions Pre-computed for grid over range in: temperature electron density abundance microturbulent velocity (range in line opacity) T = 9120 K

7. 7 Line Opacity in Radiation Moments

8. 8 Atmospheric Model Listings Tables of physical and radiation quantities as a function of depth All logarithms except T and 0 (c.g.s.)

9. 9

10. 10 Emergent Fluxes (+ Intensities)

11. 11

12. 12 Temperature Relation with Line Blanketing With increased line opacity, emergent flux comes from higher in the atmosphere where gas is cooler in general; lower I ν, J ν Radiative equilibrium: lower J ν → lower T Result: surface cooling relative to models without line blanketing

13. 13 Temperature Relation with Line Blanketing To maintain total flux need to increase T in optically thick part to get same as gray case Result: backwarming

14. 14 Flux Redistribution (UV→optical): opt. F ν ~ hotter unblanketed model

15. 15 Temperature Relation with Convection Convection: Reduces T gradient in deeper layers of cool stars

16. 16 Geometric Depth Scale Physical extent large in low density cases (supergiants)

17. 17 Observational Parameters Colors: Johnson UBVRI, Strömgren ubvy (Lester et al. 1986, ApJS, 61, 509) Balmer line profiles (Hα through Hδ)

18. 18 Flux Distributions Wien peak Slope of Paschen continuum (3650-8205) Lyman jump at 912 (n=1) Balmer jump at 3650 (n=2) Paschen jump at 8205 (n=3) Strength of Balmer lines

19. 19

20. 20

21. 21 H 912He I 504He II 227

22. 22

23. 23 Comparison to Vega

24. 24 IDL Quick Look IDL> kurucz,teff,logg,logab,wave,flam,fcont INPUT: teff = effective temperature (K, grid value) logg = log gravity (c.g.s, grid value) logab = log abundance (0,-1,-2) OUTPUT: wave = wavelength grid (Angstroms) flam = flux with lines (erg cm -2 s -1 Angstrom -1 ) fcont = flux without lines IDL> plot,wave,flam,xrange=[3300,8000],xstyle=1

25. 25 Limb Darkening Eddington-Barbier Relationship S=B(τ=1) S=B(τ=0)

26. 26 How Deep Do We See At μ=1? Answer Depends on Opacity T(τ=0) T(τ=1) low opacity T(τ=1) high opacity Limb darkening depends on the contrast between B(T(τ=0)) and B(T(τ=1))

27. 27 Limb Darkening versus T eff and λ Heyrovský 2007, ApJ, 656, 483, Fig.2 u increases with lower λ, lower T eff Both cases have lower opacity → see deeper, greater contrast between T at τ=0 and τ=1 Linear limb-darkening coefficient vs T eff for bands B (crosses), V (circles), R (plus signs), and I (triangles)