1. Non-LTE Models for Hot Stars
Added Complications Complete Linearization Line Blanketed, Non-LTE Models

3. Massive Hot Stars www.ster.kuleuven.ac.be/~coralie/ghost3_bouret.pdf

4. Interesting Complications

5. Complete Linearization (CL) (Auer & Mihalas 1969)
Linearized versions of - transfer equation - radiative equlilibrium - hydrostatic equilibrium - conservation of particle number - statistical equilibrium
Use matrix operations in a Newton – Raphson correction scheme (iterative)
Used for H + He models (Mihalas + …)

6. Complete Linearization (Auer & Mihalas 1969)
Always works but expensive in computer time …varies as (NF+NL+NC)3 x ND x Niter
NF = # frequency points (~106)
NL = # atomic energy levels
NC = # constraint equations (~3)
ND = # depth points
Niter = # iterations to convergence

7. Model Atmospheres for Hot Stars

8. TLUSTY/SYNSPEC OSTAR2002: Lanz & Hubeny 2003, ApJS, 146, 417
BSTAR2006: Lanz & Hubeny 2007, ApJS, 169, 83
Web site:
TLUSTY – atmosphere SYNSPEC – detailed spectrum
Versions available for accretion disks

9. Line Blanketed Non-LTE Models for Hot Stars by Hubeny & Lanz (1995, ApJ, 439, 875)
Uses hybrid CL + ALI scheme (Accelerated Lambda Iteration: solve for J = Λ[S] using approximate Λ-operator plus a correction term from prior iteration)
Divide frequency points into groups of crucial – full CL treatment and ALI – use fast ALI treatment

10. Non-LTE Opacity Distribution Functions
Group all transitions: parity energy
Make superlevels for each group (~30 per ion)
Assign single NLTE departure coefficient to each superlevel

11. Non-LTE Opacity Distribution Functions
For each pair of superlevel transitions, get total line opacity in set frequency intervals
Represent in model as an ODF
Alternatively use Opacity Sampling (Monte Carlo sampling of superline cross sections)

12. Line Blanketing: OSTAR2002
Low tau: top curves are for an H-He model, and the temperature is progressively lower when increasing the metallicity
Large tau: reverse is true at deeper layers

13. NLTE populations: OSTAR2002
He (left), C (right) ionization vs. tau for Teff = 30, 40, 50 kK (top to bottom)
LTE = dashed lines
NLTE: numbers tend to be lower in lower stages (overionized by the strong radiation field that originates in deep, hot layers) and conversely higher in higher stages

14. OSTAR2002: Lyman Jump & Teff
Top to bottom: Teff = 55, 50, 45, 40, , and 30 kK
Lyman jump gradually weakens with increasing temperature and disappears at 50 kK
Weakening and disappearance of Lyα, Si IV 1400, C IV 1550, etc. at hot end

15. OSTAR2002: Lyman Jump & g
Top to bottom, > 912 Å: log g = 4.5, 4.25, 4.0, 3.75, 3.5
Order reversed for < 912 Å
Saha eqtn.: low ne, low neutral H, less b-f opacity

16. Lyman Jump & metallicity
Z / ZSUN = 2, 1, 1/2, 1/5, 1/10 (bold line)
Strong absorption 1000 – 1600 Å balanced by higher flux < 912 Å in metal rich cases (flux constancy)

17. NLTE (TLUSTY) vs. LTE (ATLAS)
(Teff, log g) = (40 kK, 4.5), (35 kK, 4.0), (30 kK, 4.0) (thick lines), compared to Kurucz models with the same parameters (thin histograms)

18. OSTAR2002 & BSTAR2006
grad/g vs.Teff and log g Thick and dashed line = Eddington limit for solar and zero metallicity
BSTAR2006 grid (filled) and OSTAR2002 grid (open)
Evolutionary tracks (Schaller et al. 1992) are shown for initial masses of 120, 85, 60, 40, 25, 20, 15, 12, 9, 7, 5, and 4 MSUN (left to right)

19. BSTAR2006 vs. ATLAS
(Teff, log g) = (25 kK, 3.0), (20 kK, 3.0), (15 kK, 3.0) (black lines); compared to Kurucz models, same parameters (red histograms)
In near UV, LTE fluxes are 10% higher than NLTE
Lower NLTE fluxes result from the overpopulation of the H I n = 2 level at the depth of formation of the continuum flux, hence implying a larger Balmer continuum opacity

20. BSTAR2006 vs. ATLAS
NLTE effects most important for analysis of specific lines (NLTE – black, LTE – red)