Model atmospheres for Red Giant StarsBertrand Plez

GRAAL, Université de Montpellier 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

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)

Tem

pera

ture

Optical depth

Classical model atmospheres

classical = LTE, 1-D, hydrostaticReal 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 observations

V-K vs. J-K

TiO vs. ZrO index

(VanEck et al. 2010)

At LTE, radiative energy balance requires:

At every level in atmosphereJ : radiation from (hotter) deeper atmosphere

B : local (cooler) radiation field

• In the blue JB >0 and in the red JB <0

=> if an opacity is efficient in upper atmospheric layers, heating (e.g. TiO) or cooling (e.g. H2O, C2H2).

• and backwarming, deeper.

Effect of lines on the thermal structure (line blanketing)

€

q = κ λ∫ (Jλ − Bλ )dλ = 0

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)

Interesting experiments:Effect of C/O in M-S-C models

0.5-0.99

0.99-2.40

TiO, H2O => C2, C2H2, HCN

the CO lock

C/O<1:if C/O increases => TiO, H2O decrease;Opacity decreases=> higher P

C/O>1if C/O increases => increase of C2, C2H2, ...Opacity increases => lower P

Pression

Tem

péra

ture

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

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

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

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

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

Other example

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 = RTeff4

• g = GM/R2

• Teff4 measures the flux per unit surface at a prescribed radius

(e.g. R(Ross)=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()=fobs()

Observations and stellar parameters spectroscopic accuracy

A good RGB case:

if g within 25% (logg=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 parameters what seismology can give

Seismology :

g = M/R2 = max.Teff0.5 (in solar units)

max 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 max and

• 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 radiationBUT 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