Model Construction

1. Model Construction The atmosphere connects the star to the outside world. All energy generated in the star has to pass through the atmosphere which itself usually does not produce additional energy. The photosphere is the region of the atmosphere where most of the radiation escapes from the star.

2. What needs to be done?

3. Parameters • There are many ways to construct model atmospheres. Using a fixed optical depth grid helps avoid pre-specifying the physical extension of the atmosphere. • Minimum independent parameters: • Effective temperature Teff • Gravity g(r) = G M / r2 • Mass, Radius or Luminosity L= 4πR2  Teff4 • Abundances of all elements i = ni / nT

4. Hydrostatic Equilibrium When mass loss is negligible, the total gas pressure in the atmosphere is: dP/dr = -g(r)  With the optical depth: d = - dr = -( + ) dr where , ,  are the extinction, absorption and scattering coefficients, we get: dP/d = g(r)  / 

5. Energy Conservation In plane-parallel geometry, we have: Frad + Fconv = ∫ F d =  Teff4 = cte Each volume element has emission = absorption: ∫  (J - S )d = 0 withJ the mean intensity (direction averaged) S the source function (simplest:B(T) ) The energy conservation determines essentially the T()structure!

6. Model Flow Chart Départ avec: T()= grey model (T4=3/4 Teff4 (+2/3)) Pout= 10-4 dyne/cm2 15 to 30 iterations Spectrum: ∫Frad d =  Teff4 > 30,000 pts UV  sbmm  = 0.01 Å

7. Opacities Absorption and scattering coefficients ∑ ij nij j: ionization stage i: energy level within each ionization stage ij: cross-section (cm2) nij: population density (cm-3) ∑ over all elements, processes, ionization stages, level. ijfrom QM, measurements

8. LTE • TE = thermodynamic Equilibrium • = detailed balance of all process • = state described by Pgas,T • If: • - Collisions dominate radiation • - Radiation field is Planckian • No scattering of radiation •  Local Thermodynamic Equilibrium (LTE) Not the case in exospheres of all stars and planets (radiation dominates) and in lines such as the Lyman series of hydrogen (scattering is important).

19. Comparison of Opacity Calculations

21. CO & CH4 are dominant molecules CO CH4

22. Beware of extrapolating polynomials beyond their intended temperature range

23. The role of atomic and molecular opacity increases at lower temperatures

24. H2O Abundance

25. Temperature Dependence of H2O Opacity

26. Sources of H2O opacities Empirical ‘02 Theoretical ‘90s Empirical ‘90s Lab. ‘70s

27. Line density variesamong different molecules

28. TiO only exists over a narrow temperature range

29. Temperature Dependence of TiO Opacity

30. Temperature Dependence of TiO Opacity

31. Even scarce molecules can affect model spectra

32. Line density is also importantin the visual spectrum

33. Hydrides can be important in dwarfs FeH abundance and spectrum

34. Conclusions Models rely upon only a few basic equations and several simplifying assumptions (hydrostatic eq., energy eq., LTE), valid only for the photospheres objects (Gas giant planets, brown dwarfs, stars older than 1 Myr). Improvements over the past 15 yrs: computer capacities  better opacities ! Complete atmosphere course online: http://www.hs.uni-hamburg.de/~stcd101/

35. References