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
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
Observed spectra This is not noise !
Model spectra • Good fit! IR CO lines Optical spectrum (obs + mod) of a red SG (TiO) Not so good fit!
What is a model? -> 1D examples in hydrostatic equilibrium (MARCS, Gustafsson et al. 2008) Temperature Optical depth
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.).
Examples of MARCS 1D models (hydrostatic, LTE) Spectra for S type star mixtures (variable C/O and [s/Fe])
Examples of MARCS 1D models (hydrostatic, ETL) Thermal structure, opacity effects (NB: 1bar=104cgs)
M-S star photometry: models and observationsV-K vs. J-KTiO vs. ZrO index(VanEck et al. 2010)
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.
Line blanketing: Heating in deep layers Cooling or heating in shallow layers Metal-rich Metal-poor
Importance of line list completeness for the thermal structure (Jørgensen et al. 2001) 0 5 10 15 20 Depth (106km)
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
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
Other example Observed spectra of M giants (Serote-Roos et al. 1996, A&AS, 117, 93)
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)
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?
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)
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?
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!
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
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