We are examining properties of cool stars having effective temperatures below 4000 K. It is distinguished between cool dwarfs (log g > 3.5) and cool giants (log g < 3.5).
There are basic model grids encompassing the coolest known M dwarfs, M subdwarfs and brown dwarf candidates having a wide range of paremeters: 500 <= Teff <= 4000 K, 3.5 <= log g <= 5.5 and -4.0 <= [M/H] <= +0.5. The equation of state includes 105 molecules and up to 27 ionization stages of 39 elements. In the spectra, there are over 300 molecular bands of TiO, VO, CaH and FeH in the JOLA approximation and about 2 million spectral lines out of 42 million atomic and 700 million molecular (H2, CH, NH, OH, MgH, SiH, C2, CN, CO, SiO) lines included. The models are calculated assuming LTE, plane-parallel atmosphere, energy conversion and hydrostatic equilibrium.
In the case of giant star models (log g < 3.5) the assumption of a plane-parallel atmosphere is not appropriate anymore, so spherical hydrostatic and radiative transfer is needed. Another model grid has been calculated encompassing the parameter range 2000 <= Teff <= 6800 K, 0.0 <= log g <= 3.5 and [M/H] = 0.0, -0.3, -0.5, -0.7. In the associated part of the HR-diagram one can find some long-periodic variables (LPV) like Cepheids and Miras which are pulsating. Due to the use of hydrostatic calculations, the pulsating mechanism cannot be reproduced yet.
Low resolution synthetic spectra of the models are suitable for a temperature estimation of observed spectra whereas gravity has no significant influence. In order to do abundance analysis, NLTE-Models are preferred.
Non-local thermal equilibrium (NLTE)
There exist mainly LTE-models but also some NLTE-calculations in order to determine the departure coefficients of several element lines. Chemical abundances and also time-dependent effects occuring in variable giants can be examined better in NLTE.
NLTE-effects change the profile of individual lines and in some cases they may change the structure of the spectrum itself significantly. For example, in cool stars TiO forms a pseudo-continuum due to vibrational bands. Departures from LTE of the Ti I atom indirect changes the concentration of TiO. A Ti I model atom with 395 levels and 5279 primary bound-bound transitions has been used to determine the departure. It has been shown that LTE is a poor approximation for Ti I formation.
Treatment of dust
At low temperatures (Teff < 3000 K) dust formation takes place. Depending of the chemical composition of the atmosphere, the formation of over 600 gas-phase species and 1000 liquids and crystals and the opacities of 30 different types of grains (e.g. Al2O3, MgAl2O4, iron, MgSiO3, Mg2SiO4, amorphous carbon, SiC, some calcium silicates) are considered in PHOENIX. The programm is able to consider four scenarios:
- Cond models: Dust formation takes place, but all of the dust falls into deep atmosphere layers and does not contribute to the opacity.
- Settling models:A fraction of grains sediment out of the current layer using condensation, coagulation, sedimentation and mixing (in convective zones).
- Dusty models:Dust opacities are calculated from the dust cloud base up to the uppermost atmospheric layer. The distribution depends on the grain size, the radiative acceleration and the dust porosity factor.
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Non-local thermodynamic equilibrium effects of Ti I in M dwarfs and giants,Hauschildt, P.H. 1997, ApJ, 488, 428
The NextGen model atmosphere grid. II.
Spherically symmetric model atmospheres for giant stars with effective temperatures between 3000 and 6800 K, Hauschildt, P.H. 1999, ApJ, 525, 871
Limiting effects of dust in brown dwarf model atmospheres Allard, F. AJ, 556, 357
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Model atmospheres for M (sub)dwarf stars. I. The base model grid, Allard, F. 1995, ApJ, 445, 433
Stellar pulsations accross the HR-diagram: Part 1+2 Gautchy, A. 1995, ARA&A, 33, 75, Gautchy, A. 1996, ARA&A, 34, 551