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Model atmospheres for Red Giant Stars

Model atmospheres for Red Giant Stars. Bertrand Plez GRAAL, Université de Montpellier 2. RED GIANTS AS PROBES OF THE STRUCTURE AND EVOLUTION OF THE MILKY WAY Academia Belgica Roma, Nov 15-17-2010. outline. What is a model atmosphere (only 1D here) Ingredients

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Model atmospheres for Red Giant Stars

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  1. Model atmospheres for Red Giant Stars Bertrand Plez GRAAL, Université de Montpellier 2 RED GIANTS AS PROBES OF THE STRUCTURE AND EVOLUTION OF THE MILKY WAY AcademiaBelgica Roma, Nov 15-17-2010

  2. outline • What is a model atmosphere (only 1D here) • Ingredients • Examples of models and their use • Determination of stellar parameters : Teff, logg, … accuracy? • Seismology / spectroscopy

  3. Observed spectra This is not noise !

  4. Model spectra • Good fit! IR CO lines Optical spectrum (obs + mod) of a red SG (TiO) Not so good fit!

  5. What is a model? -> 1D examples in hydrostatic equilibrium (MARCS, Gustafsson et al. 2008) Temperature Optical depth

  6. Classical model atmospheres • classical = LTE, 1-D, hydrostatic • Real stars are not “classical” ! • But... • classical models include extremely detailed opacities • they serve as reference for more ambitious modeling (3-D, NLTE, ...) • cool star spectra very much affected by molecular lines • ... and are thus not yet all studied in detail even with classical models. • Note impressive recent developments : 3D convection (cf. talk by Ludwig), NLTE (e.g. Hauschildt et al.), pulsation-dust-wind LPVs (e.g. Hoefner et al.).

  7. Examples of MARCS 1D models (hydrostatic, LTE) Spectra for S type star mixtures (variable C/O and [s/Fe])

  8. Examples of MARCS 1D models (hydrostatic, ETL) Thermal structure, opacity effects (NB: 1bar=104cgs)

  9. M-S star photometry: models and observationsV-K vs. J-KTiO vs. ZrO index(VanEck et al. 2010)

  10. Effect of lines on the thermal structure (line blanketing) At LTE, radiative energy balance requires: At every level in atmosphere Jl : radiation from (hotter) deeper atmosphere Bl : local (cooler) radiation field • In the blue Jl-Bl >0 and in the red Jl-Bl <0 => if an opacity is efficient in upper atmospheric layers, heating (e.g. TiO) or cooling (e.g. H2O, C2H2). • and backwarming, deeper.

  11. Line blanketing: Heating in deep layers Cooling or heating in shallow layers Metal-rich Metal-poor

  12. Importance of line list completeness for the thermal structure (Jørgensen et al. 2001) 0 5 10 15 20 Depth (106km)

  13. 0.99-2.40 0.5-0.99 Interesting experiments:Effect of C/O in M-S-C models TiO, H2O => C2, C2H2, HCN the CO lock C/O<1: if C/O increases => TiO, H2O decrease; Opacity decreases=> higher P C/O>1 if C/O increases => increase of C2, C2H2, ... Opacity increases => lower P Température Pression

  14. Interesting experiments:Models for RSG and AGB of same L and Teff

  15. Interesting experiments:Models for RSG and AGB of same L and Teff

  16. Interesting experiments:Models for RSG and AGB of same L and Teff

  17. 1D models do a good job: Fit of a very cool red giant spectrum (lines of TiO, ZrO, and atoms) 1D model with obvious physical limitations in this case of an AGB star, but with very good line lists 1 is not the continuum level! From García-Hernández et al. 2007, A&A 462, 711

  18. Other example Observed spectra of M giants (Serote-Roos et al. 1996, A&AS, 117, 93)

  19. Observed spectra of M giants (Serote-Roos et al. 1996, A&AS, 117, 93), and MARCS model spectra (from Alvarez & Plez 1998, A&A 330, 1109)

  20. Models and stellar parameters • A 1D model atmosphere is defined by Teff, g, M (or R, or L), and chemical composition • L = 4pR2sTeff4 • g = GM/R2 • sTeff4measures the flux per unit surface at a prescribed radius (e.g. R(tRoss)=1) • The same radius is used for g • These are clear definitions. • What about observations?

  21. Observations and stellar parameters • Spectroscopy : Teff and g from lines. But NLTE ! 3D effects ! Line-broadening theory ! Errors in models ! • NB: line measurements to 1% -> errors in analysis/models dominate • Photometry / spectrophotometry : in principle same problems; uses global information (spectral shape) • Interferometry : what is the angular diameter ?! Real problem for red giants: wavelength dependency, limb-darkening, ... Must use models to derive diameter!! 3D better! • Use all and check inconsistencies! • Absolutely calibrated fluxes very useful ! => (R/d)2Fmod(l)=fobs(l)

  22. Observations and stellar parameters spectroscopic accuracy A good RGB case: if g within 25% (Dlogg=0.1), and Teff within 2.5% (100K at 4000K), parallax within 5%, and bol flux within 10% (.1 mag) => M within 55% ! Alternatively if angular diameter within 5%, parallax within 5%, and g within 25%, => M within 45% NB: For giants, isochrones pile up and do not allow high precision masses. Also, RGB, AGB, RSG degeneracy in L-Teff If good parallaxes (GAIA), and angular diameters, the problem is with g. => improve spectroscopic techniques! But how?

  23. Observations and stellar parameterswhat seismology can give Seismology : g = M/R2 = nmax.Teff0.5 (in solar units) nmax is known with high precision (<1%) and Teff (spectro) to 1-2%. If the scaling relation is accurate, we get a very good gravity! This allows detailed testing of e.g. NLTE effects on Fe : FeII/FeI balance is sensitive to g, an often used to determine g, although it is affected by NLTE. => derive corrections!

  24. Observations and stellar parameters • Questions: • Accuracy of scaling relations for nmax and Dn • Effect of metallicity? Prospect : Pop II stars • Does the surface chemical composition reflect the interior’s ? Should be OK for giants

  25. Conclusions • 1D model atmospheres account in great detail for chromaticity of opacity and radiation • BUT lack other crucial ingredients (3D, see Hans Ludwig’s talk) • great success in their use (stellar parameters, …) • BUT effects of NLTE, 3D ? • seismology brings fondamental information (gravity) to test this • in return, model atmospheres + spectroscopy => stellar parameters (Teff, chemical composition) • I have not discussed atmospheres as boundary conditions for the interior/evolution models

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