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Non-LTE Models for Hot Stars
Added ComplicationsComplete Linearization
Line Blanketed, Non-LTE Models
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Massive Hot Starswww.ster.kuleuven.ac.be/~coralie/ghost3_bouret.pdf
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Interesting Complications
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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 + …)
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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
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Model Atmospheres for Hot Stars
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TLUSTY/SYNSPEC
• OSTAR2002:Lanz & Hubeny 2003, ApJS, 146, 417
• BSTAR2006:Lanz & Hubeny 2007, ApJS, 169, 83
• Web site:http://nova.astro.umd.edu/
• TLUSTY – atmosphereSYNSPEC – detailed spectrum
• Versions available for accretion disks
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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 ofcrucial – full CL treatment andALI – use fast ALI treatment
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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
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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)
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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
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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
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OSTAR2002: Lyman Jump & Teff
• Top to bottom:Teff = 55, 50, 45, 40, 35, 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
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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
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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)
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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)
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OSTAR2002 &
BSTAR2006• grad/g vs.Teff and log g
Thick and dashed line = Eddington limitfor 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)
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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
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BSTAR2006 vs. ATLAS
• NLTE effects most important for analysis of specific lines(NLTE – black,LTE – red)