MODEL ATMOSPHERES OF VERY LOW MASS STARS AND BROWN DWARFS

France Allard,¹ ­ Peter H. Hauschildt,² ­ David R. Alexander,¹ and ­ Sumner Starrfield³ ­

¹Department of Physics, Wichita State University, Wichita, Kansas 67260-0032; e-mail: allard@eureka.physics.twsu.edu ; dra@twsuvm.uc.twsu.edu

ABSTRACT	Section:	ChooseTop of pageABSTRACT <<INTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

Abstract  As progressively cooler stellar and substellar objects are discovered, the presence first of molecules and then of condensed particulates greatly complicates the understanding of their physical properties. Accurate model atmospheres that include these processes are the key to establishing their atmospheric parameters. They play a crucial role in determining structural characteristics by setting the surface conditions of model interiors and providing transformations to the various observational planes. They can reveal the spectroscopic properties of brown dwarfs and help establish their detectability. In this paper, we review the current state-of-the-art theory and modeling of the atmospheres of very low mass stars, including the coolest known M dwarfs, M subdwarfs, and brown dwarfs, i.e. T_eff 4,000 K and 4.0 [M/H] +0.0. We discuss ongoing efforts to incorporate molecular and grain opacities in cool stellar spectra, as well as the latest progress in (a) deriving the effective temperature scale of M dwarfs, (b) reproducing the lower main sequences of metal-poor subdwarfs in the halo and globular clusters, and (c) results of the models related to the search for brown dwarfs.

INTRODUCTION	Section:	ChooseTop of pageABSTRACTINTRODUCTION <<GENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

The crop of extremely cool stars and substellar objects has been meager until very recently, when marked improvements in detection ability have finally started to yield a rich harvest. Stars with masses as low as 0.1M and white dwarfs as cool as 5000 K (Paresce et al 1995, Richer et al 1995, Cool et al 1996, Renzini et al 1996) have been resolved in nearby globular clusters using the Wide Field/Planetary Camera 2 on board the Hubble Space Telescope (HST). Charge-coupled device (CCD) astrometry has unveiled uncharted M dwarfs in the immediate vicinity of our Solar System (Henry et al 1995, Stone et al 1996, Tinney 1996). Growing numbers of halo carbon dwarfs have been discovered by deep multicolor CCD surveys (Heber et al 1993, Warren et al 1993, Deutsch 1994, Liebert et al 1994). Young deuterium-burning brown dwarfs have been identified in nearby open clusters (Rebolo et al 1995, Basri et al 1996, Rebolo et al 1996) and in the solar neighborhood (Thackrah et al 1997) using the Keck telescope. Cryogenic coronographic imaging and astrometric surveys are revealing cool, evolved brown dwarfs hiding in the solar neighborhood (Nakajima et al 1995, Oppenheimer et al 1995, Mazeh et al 1996, Williams et al 1997), and high signal/noise radial velocity and astrometric surveys are now sensitive to massive planets around nearby Sun-like stars (Mayor & Queloz 1995, Butler & Marcy 1996, Marcy & Butler 1996a, b, Butler et al 1997, Marcy et al 1997). These exciting developments, and those of the MACHO, EROS, and OGLE microlensing surveys (Aubourg 1995, Alcock et al 1996), will soon enable a reconstruction of the faint end of the galactic initial mass function and the determination of the baryonic fraction of the missing mass (Chabrier et al 1996b, Flynn et al 1996, Graff & Freese 1996). Very low mass (VLM) stars and brown dwarfs are probably the most numerous objects in the galaxy (Gould et al 1996, Méra et al 1996a). Nevertheless, until recently, little about their atmospheres, evolution, or spectral characteristics was clearly understood. The presence of both a wide variety of molecular absorbers (each with hundreds of thousands to millions of spectral lines) and numerous condensates greatly complicates accurate modeling of these cool stellar atmospheres. The extension of the convection zone to the outermost photospheric layers means that evolutionary models depend critically on accurate handling of the surface boundary. Recently, theoretical calculations of important molecular absorbers such as H₂O, TiO, CN, and CO, as well as grain opacities, have made it possible to generate greatly improved models of cool stellar and brown dwarf atmospheres, their high resolution spectra, and their evolution. In view of the latest progress both on the observational and theoretical fronts, it seems timely to summarize here our present understanding of the atmospheres and spectroscopic properties of cool VLM stars and substellar brown dwarfs. Previous reviews of these topics can be found in Liebert & Probst (1987), Stevenson (1991), Bessell & Stringfellow (1993), Burrows & Liebert (1993), Gustafsson & Jørgensen (1994).

GENERAL SPECTROSCOPIC PROPERTIES OF COOL DWARFS	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO... <<A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

A VLM star generally refers to a main sequence star with a spectral type ranging from mid K to late M and a mass from about 0.6 M to the hydrogen-burning minimum mass (0.0750.085 M, depending on metallicity). Such stars span a wide range of populations, from the youngest metal-rich M dwarfs in open clusters such as the Pleiades (Simons & Becklin 1992, Hambly et al 1993, Williams et al 1996, Zapatero Osorio et al 1997), the Hyades (Leggett & Hawkins 1989, Reid 1993, Bryja et al 1994, Leggett et al 1994), Ophiuchus (Cameron et al 1993), Persei (Zapatero Osorio et al 1996), and the galactic disk (Gliese & Jahreiss 1991), to the several billionyear-old metal-poor subdwarfs of the galactic halo (Green et al 1991, Monet et al 1992, Green & Margon 1994) and globular clusters (Paresce et al 1995, Richer et al 1995, Cool et al 1996, Renzini et al 1996). Even within the solar neighborhood, M dwarfs do not form a homogeneous sample of unique age and metallicity, but rather they span up to 10³ years in age and ±0.51.0 dex around the solar value in metallicity (Burrows & Liebert 1993).

In VLM star and brown dwarf atmospheres, most of the hydrogen is locked in H₂ and most of the carbon in CO, with excess oxygen bound in molecules such as TiO, VO, and H₂O. The energy distribution of a typical late-type M dwarf is entirely governed by the absorption of TiO and VO in the optical, and H₂O in the infrared, leaving no window of true continuum in the emergent spectrum. With their extremely low intrinsic faintness (10 ² 10 ⁵ L), in particular in the V bandpass, the painstaking spectral classification of the nearby stars aiming toward a complete census of the luminosity function is still in progress (Reid 1994, Kirkpatrick & Beichman 1995, Liebert et al 1995, Reid et al 1995a). Fortunately, the groundwork necessary to construct an effective temperature scale at the lower end of the main sequence has already been laid by Boeshaar (1976) in the visual (0.440.68 m), with (a) the first identification of CaOH bands at 0.540.556 m in dwarfs later than about M3.5 (these bands are excellent temperature indicators and good discriminants between field M dwarfs and background red giant stars); (b) the first report of a saturation of the visual TiO band strengths in M dwarfs later than M5; and (c) the introduction of the VO to TiO band strength index now being used to classify M dwarfs and substellar candidates later than M5 (Henry et al 1994, Kirkpatrick et al 1995, Martín et al 1996). Boeshaar's classifications soon were extended beyond even the limits of the classical Morgan & Keenan spectral sequence, i.e. to types M9.5>M10, by Kirkpatrick et al (1995) in the optical to near-infrared regime (0.651.5 m) and by Davidge & Boeshaar (1993), Jones et al (1994), Leggett et al (1996) in the near infrared (1.12.5 m).

Figure 1 summarizes a typical near-infrared spectral sequence of M dwarfs to brown dwarfs. The near-infrared water vapor bands become slowly stronger with the spectral type of M dwarfs. The CO overtones near 2.3 m (and 4.5 m, not shown in Figure 1) are still apparent, although much weaker than in late-type giant stars due to the stronger H₂O "continuum" in the dwarfs. At the hydrogen-burning limit, i.e. at a spectral type of M10.5 and a T_eff of about 2000 K (Baraffe et al 1995), the peculiar spectral distribution of GD 165B (Zuckerman & Becklin 1992, Kirkpatrick et al 1993a) suggests that all signs of the TiO bands disappear from the optical spectral distribution, leaving only atomic lines and perhaps VO bands (Davis 1994, Kirkpatrick et al 1995), CaH, CaOH, and/or FeH bands. As the effective temperature drops into the brown dwarf regime, methane (CH₄) features begin to appear (Tsuji et al 1995, Allard et al 1996, Marley et al 1996), and corundum (Al₂O₃), perovskite (CaTiO₃), iron, enstatite (MgSiO₃), and forsterite (Mg₂SiO₄) clouds may form, enhancing the carbon:oxygen abundance ratio and profoundly modifying the thermal structure and opacity of the photosphere (Sharp & Huebner 1990, Fegley & Lodders 1996).

View larger version (59K) Figure 1 A near-infrared spectral sequence of M dwarfs to brown dwarfs. The observed spectral distributions ( full lines) were obtained at UKIRT for the M dwarfs by Jones et al (1994), and for the brown dwarf Gl229B by Geballe et al (1996). A comparison to OS models with, from top to bottom, Teff = 3400, 3000, 2700, 2600, 2000, and 1000 K (F Allard & PH Hauschildt, in preparation) (dotted lines) reveals a growing overestimation of water vapor band strengths with decreasing mass. The peculiar optical spectrum of GD 165B forces an arbitrary choice of the model parameters (here set to those of a star at the hydrogen-burning limit) for this object.

The chemistry of cool dwarf atmospheres is, therefore, a complex nonlinear problem requiring a detailed knowledge of the concentration of atoms and molecules, which prevents a straightforward derivation of quantities such as excitation temperatures and metallicities from line ratios, as is possible for hotter stars. The most reliable way to estimate effective temperatures and metallicities of VLM stars and to identify substellar brown dwarfs is by a direct comparison of observed and model spectra.

A BRIEF HISTORY OF THE MODELS	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO... <<MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

Advances in atmospheric modeling of cool stars have been slowed by the twin bottlenecks of (a) incomplete molecular opacity data bases and (b) the inability to handle convection rigorously. Once these problems are addressed reasonably well, we still face other challenges: incorporating the effects of photospheric grain formation, chromospheres, magnetic fields, departures from local thermodynamic equilibrium, spatial variations in atmospheric structure due to starspots, cloud formation, and eventually weather patterns. Model atmospheres incorporating such processes have only become possible within the past two decades with the work of Mould (1975, 1976), Allard (1990), Kui (1991), Brett & Plez (1993), Allard & Hauschildt (1995b), Brett 1995a, b, Tsuji et al (1996a) for M dwarfs; Saumon et al (1994) for zero-metallicity subdwarfs; and Tsuji et al (1995, 1996b), Allard et al (1996), Marley et al (1996) for substellar brown dwarfs.

Mullan & Dermot (1987) have reviewed early efforts in modeling M dwarf atmospheres. Mould (1975, 1976) was the first to produce an extensive grid of convective M dwarf model atmospheres between 4750 and 3000 K. The models effectively combined the ATLAS code (Kurucz 1970), TiO band model opacities and chemical equilibrium by Tsuji (1966, 1973), H₂O opacities by Auman (1967), and a mixing-length treatment of convection (Bøhm-Vitense 1958, Kippenhan 1962). Mould also incorporated atomic line blanketing in the form of an Opacity Distribution Function (ODF; see Kurucz 1970, Mihalas 1978). However, the coarseness of his opacity grid kept him from adequately reproducing the observed spectral characteristics of the coolest M dwarfs.

It took another 15 years before model calculations finally broke the "3000-K barrier" in T_eff, with the work of Allard (1990), Kui (1991). Both adapted their model codes from that of Wehrse (1972), who had treated the more extreme atmospheric conditions of cool white dwarfs (T_eff 7000 K). Both authors also handled molecular opacity using band models and straight mean (SM) techniques that made it possible to includebeyond the dominant TiO and H₂O opacitiesa number of important molecular bands such as those of the hydrides (CaH, MgH, SiH, OH, CH), which are important in low-metallicity subdwarfs, as well as the red and infrared bands of VO (Keenan & Schroeder 1952) and CO, respectively, which act as sensitive temperature indicators (Henry et al 1994, Kirkpatrick et al 1995, Martín et al 1996). From the Allard (1990) grid, Kirkpatrick et al (1993b) derived a revised temperature sequence for M dwarfs that casts new light on traditional results based on blackbody methods. This new sequence yielded values of T_eff as much as 500-K higher at a given luminosity and shifted the positions of the late-type dwarfs in the HR diagram from cooling tracks to the blue side of theoretical lower main sequences (D'Antona & Mazzitelli 1985, Burrows et al 1989, 1993). This made it more likely that field late-type M dwarfs were hydrogen-burning stars rather than young, contracting, substellar brown dwarfs. Subsequent improvements to these modelssuch as the introduction of (a) laboratory oscillator strengths for the TiO bands (Davis et al 1986) instead of the smaller (by a factor of 23) empirically derived astrophysical values of Brett (1989, 1990) and (b) the FeH Wing-Ford bands near 0.98 m (Phillips et al 1987)allowed Allard (1994) to resolve most of the remaining discrepancies in the optical model spectra that had been pointed out by Kirkpatrick et al (1993b), Gustafsson & Jørgensen (1994), Jones et al (1994).

Despite the initial successes, comparison with observed near-infrared spectra uncovered another problem: The models failed to match the infrared spectrum governed by the water vapor opacity profile (Allard & Hauschildt 1995b, Bessell 1995, Tinney et al 1995). This situation is illustrated in Figure 1, which shows that the water bands are clearly too strong in the metal-rich models. The peak of the energy distribution of M dwarfs is located in the near infrared, at around 1 m. For brown dwarfs, most of the emitted flux emerges between 1 and 10 m. One difficulty in determining the quality of model spectra is due to telluric absorption in the Earth's atmosphere. Telluric water bands filter the light of these faint objects over most of the infrared range. While some near-infrared spectra from about 0.92.5 m can be obtained from ground-based facilities (e.g. the UKIRT spectra of Figure 1), these are unreliable in intervals where the water bands are strongest. A proper calibration of the measured fluxes becomes even more delicate for faint brown dwarfs in close binary systems (for an illustration of the uncertainties in calibrating the "K" band fluxes in the spectrum of Gl 229B, see e.g. Oppenheimer et al 1995, Matthews et al 1995, Geballe et al 1996). Beyond 2.5 m, the Earth's atmosphere is nearly opaque and red dwarfs must be observed with infrared space-based facilities such as the HST, NICMOS, ISO, and the planned SIRTF, NGST, and DARWIN missions. But while there remain uncertainties in the absolute calibration of ground-based spectrophotometry of faint M dwarfs, these cannot completely account for the observed flux discrepancy in the infrared spectra of M dwarfs. For example, Figure 1 indicates that the predicted H₂O bands grow in strength more rapidly with decreasing T_eff than those of observed M dwarfs (Kirkpatrick et al 1995). This comparison supports the conclusion that there are shortcomings in the models. One of those shortcomings is clearly the treatment of opacity in very cool atmospheres.

MOLECULAR OPACITIES	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIES <<GRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

Most of the molecules that play an important role in cool star atmospheres have been known since the early 1930s from the work of Russell (1934) and later De Jager & Neven (1957). Some of the most extensive studies of cool stellar atmosphere chemistry are by Vardya (1966), Morris & Wyller (1967), Tsuji (1973), Gurvich (1981) who published equilibrium constants for an extensive list of diatomic and polyatomic species. More recent studies such as those of Sauval & Tatum 1984, Rossi et al (1985), Irwin (1987, 1988), Cherchneff & Barker (1992), Neale & Tennyson (1995), Sharp & Huebner (1990) provide partition functions for most molecules directly, which allows for more flexible atmospheric calculations.

In the absence of detailed lists of transitions, or sometimes to cope with restricted computational facilities, atmospheric modelers often resort to band models or to average opacities such as the Just Overlapping Line Approximation (JOLA), SM, or ODF techniques, which approximate (by a continuum distribution) the absorption within a band or a predefined wavelength bin (Kurucz 1970, Mihalas 1978, Tsuji 1994). While computationally economical, they make the assumption that the rotational fine structure is smeared out; i.e. the lines overlap without being saturated. Such conditions are never truly met even for the strongest bands of TiO and H₂O in the densest of the VLM stellar atmospheres, and these methods tend to overestimate the resulting molecular blanketing by trapping photons that would have otherwise escaped from between the lines. A far more accurate account of molecular and atomic opacities in model atmospheres is achieved by applying an Opacity Sampling (OS) treatment of transitions lists on a prespecified fine grid of wavelengths (Peytremann 1974, Sneden et al 1976). This can be done either dynamically within the atmospheric calculations (Kurucz 1992b, Hauschildt et al 1992, Allard & Hauschildt 1995b) or be pretabulated as a function of pressure, temperature, isotopic ratios, and wavelengths (Plez et al 1992, Brett 1995a, Kipper et al 1996). While the advantage of a dynamical approach lies in the flexibility of handling depth-dependent mechanisms such as pressure broadening, departures from local thermodynamic equilibrium, microturbulence, and abundance variations, the more efficient pretabulation of the OS opacities gives the modeler freedom to incorporate his or her choice of complete line lists.

In an attempt to address the too-strong infrared water band problem in M dwarf models, Brett & Plez (1993), Allard et al (1994, 1996), Brett (1995a, b), and F Allard & PH Hauschildt (in preparation) used the OS treatment of molecular opacities to compute a new generation of M dwarf model atmospheres, which brought important breakthroughs in the understanding of M dwarf atmospheres. In the next sections, we summarize the most significant improvements in the treatment of opacities due to TiO and H₂O.

Optical Bands

The strengths of TiO bands define the optical (0.41.2 m) spectral distribution of late K to M stars. Together with the VO bands and a few other optical spectral features, they constitute the primary T_eff indicators in very cool stars. There currently exist three TiO line lists generated (a) from first principles by Collins & Faÿ (1974) and more recently extended for isotopic species and the system by Jørgensen (1994), (b) empirically from molecular levels assigned in laboratory experiments by Kurucz (1993), and (c) by Plez et al (1992). While substantial errors in the Kurucz (1993) line list have been acknowledged by the author, the Plez et al (1992), Jørgensen (1994) line lists lead to great improvements upon previous models based on SM treatment of opacities (Mould 1975, Kui 1991, Allard & Hauschildt 1995b) in the modeling of M dwarfs. Each TiO line list applied in an OS treatment of the opacities leads to better agreement with the observed optical absolute magnitudes of M dwarfs (see e.g. Brett 1995a, b, Chabrier et al 1996a). The new models also show excellent agreement with the measured parameters of the only two known M dwarfs in eclipsing binaries (see Section 9 below; also see Bessell 1991, 1995, Chabrier & Baraffe (1995).

Unfortunately, the TiO line lists of Plez et al (1992), Jørgensen (1994) give poor line positions and relative band strengths that prevent accurate high-resolution spectral syntheses of M dwarfs (Piskunov et al 1996, Schweitzer et al 1996). They also fail to reproduce the optical R-I colors of late-type dwarfs (F Allard & PH Hauschildt, in preparation), which may reflect either some remaining inaccuracies in the current estimates of the oscillator strengths (Davis et al 1986, Doverstal & Weijnitz 1992, Hedgecock et al 1995) or an incomplete account of VO or other opacity in the "R" bandpass. Indeed, despite the existence of a few spectroscopic studies of VO systems (Davis 1994, Merer et al 1987, Bauschlicher & Langhoff 1986), no list of transitions and oscillator strengths adequate for stellar atmosphere modeling is yet available for this important molecule. The Berkeley program has generated extensive line lists for FeH (Phillips et al 1987, Phillips & Davis 1993; see also Balfour & Klynning 1994), which, however, lack matching oscillator strengths. Moreover, the complexity of the FeH molecule has prevented theoretical models (Langhoff & Bauschlicher 1990, 1991) from reproducing the observed spectrum of FeH (Langhoff & Bauschlicher 1994). A similar situation also prevails for the electronic systems of CaOH (Bernath & Brazier 1985, Ziurys et al 1992, 1996), despite their importance as one of the strongest visual bands in the spectra of M-type dwarfs. Modelers have resorted to band models for most of these molecular systems (Brett 1989, 1990, Brett & Plez 1993, Allard & Hauschildt 1995b), which overestimate the resulting opacity and compromise both high-resolution spectral analysis and the determination of accurate atmospheric parameters. Fortunately, a new ab initio calculation of TiO is currently under way (SR Langhoff & CW Bauschlicher, Jr, in preparation), which should soon enable improved modeling of some aspects of cool M dwarfs.

H₂O Bands

In view of the initial success obtained with an OS treatment of the TiO opacities for the optical spectral distribution of M dwarfs, Alexander et al (1989) and later Plez et al (1992) developed an OS table of randomly distributed H₂O lines derived from line strength and line spacing data measured in the laboratory Ludwig 1971. (Brett & Plez 1993, Brett 1995a, b) then used the Plez et al (1992) table in their models of M dwarfs, but this treatment still failed to reproduce the infrared spectra and colors of M dwarfs (Bessell & Stringfellow 1993, Bessell 1995).

In retrospect, this result was to be expected because H₂O lines overlap more than those of TiO, so SM treatment of opacities is more appropriate for H₂O. Schryber et al (1995) therefore argued, based on results of their ab initio calculations for H₂O, that the H₂O laboratory cross sections obtained by Ludwig (1971), used by both groups in the form of either SM (Allard & Hauschildt 1995b) or OS (Plez et al 1992, Brett & Plez 1993, Brett 1995a, b) may be intrinsically overestimated when applied to gas hotter than about 1500 K. Theoretical lists of transitions that include "steam" or "hot" band transitionsbased on molecular levels assigned in laboratory experiments (semiempirical; e.g. Kurucz 1992a) or on a molecular model from first principles (ab initio; e.g. Miller et al 1994)are of far greater relevance for atmospheric calculations and are essential for an adequate account of molecular opacities in cool star and brown dwarf atmospheres. Over the past decade, efforts have converged in the development of improved theoretical opacity data for molecules of astrophysical interest with the creation of the Kurucz (1992a) and SCAN (Jørgensen 1992) data bases, and with the fruitful work of the University of the College of London (Miller et al 1994) and NASA Ames (Langhoff & Bauschlicher 1994) centers of quantum chemistry calculations.

Theoretical line lists for hot H₂O from three independent sources have recently been released by Jørgensen et al (1994), Miller et al (1994), Partridge & Schwenke (1997). The Miller et al (1994) list (6.2 million lines) uses a laboratory potential surface (Jensen 1989), while the Partridge & Schwenke (1997) list (300 million lines) uses a purely theoretical potential but the same computational approach. Both preliminary lists were computed up to J values of about 30; i.e. they do not include all the necessary hot or steam bands. The Jørgensen et al (1994) list (20 million transitions) on the other hand, while also based on the Jensen (1989) potential energy functions, was computed with the goal of completeness for the atmospheres of cool giants with some compromise on the treatment of the molecular binding. For example, they use a rigid rotator approximation with an a posteriori correction to the Hamiltonian. The three data sets lead to very different opacity profiles, with the Jørgensen et al and Partridge & Schwenke lists reproducing the results obtained previously with the Ludwig opacities. Only the Miller et al line list led to an improved fit of the infrared spectral distribution of M dwarfs (Allard et al 1994, Jones et al 1995, 1996, Leggett et al 1996), as well as to an excellent agreement of early-type M dwarfs with a whole new generation of evolutionary models that include improved non-gray surface boundary conditions (Baraffe et al 1995, 1997, Chabrier et al 1996a, Leggett et al 1996). However, none of the current H₂O line lists can explain the apparent saturation of the water vapor bands observed in the latest-type M dwarfs and illustrated in Figure 1. The cause of those discrepancies may therefore lie elsewhere, as is discussed in Section 5 below. A more accurate knowledge of the water vapor opacity profile is clearly needed and is now being addressed by the work of Viti et al (1995), Partridge & Schwenke (1997).

GRAINS	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINS <<LINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

The current generation of M dwarf model atmospheres (Brett 1995b, Allard et al 1996) does not include the condensation of molecules to grains. Condensation clearly must be included in the calculations as indicated by the work of Sharp & Huebner (1990), who report the abundance of condensates as a function of the gas conditions. If ZrO₂ one of the first condensates to appear at gas temperatures 2000 Kis not an important species in M dwarf atmospheres, the condensation of corundum at 1800 K and iron, VO, and enstatite at 1600 K most certainly affects the spectral distribution of late M dwarfs and brown dwarfs because of the large extinction of solid particles. The importance of condensation in the atmospheres of late-type M dwarfs and brown dwarfs has been confirmed by Tsuji et al (1996a, b), Fegley & Lodders (1996), who find large concentrations of such condensates in their model atmospheres.

The impact of condensation on the spectral distribution and atmosphere of a cool dwarf is to gradually deplete the gas phase abundance of titanium, iron, vanadium, and oxygen. If we ignore for the moment the opacity of the grains, the result is a more transparent optical spectral distribution because the TiO-, VO-, FeH-, and metal-line opacities decline with decreasing effective temperature of the star. This should be reflected by an observed saturation of these molecular bands in the latest-type M dwarfs and brown dwarfs, a behavior that is presently difficult to ascertain without accurate model atmospheres that incorporate the effects of condensation. Perhaps a confirmation can be found in the peculiar optical spectrum of the coolest known M dwarf, GD 165B, mentioned in Section 2 above. However, the true nature of GD 165B's atmosphere is uncertain because this object, the companion of an old pulsating DA white dwarf within an orbital distance of 128 AU (Becklin & Zuckerman 1988, Bergeron & McGraw 1990, Zuckerman & Becklin 1992, Bergeron et al 1993, Kirkpatrick et al 1993a), may be more metal-poor and/or more carbon-rich than other nearby stars as a result of the white dwarf's prior evolution.

Tsuji et al (1996a) were the first to calculate model atmospheres for M dwarfs and brown dwarfs including not only grain formation but also grain opacities, the so-called dusty models. Their results showed that including corundum, iron, and enstatite opacities, while assuming arbitrarily spherical grains with sizes set to 0.1 m, could heat the photospheric layers and change the overall structure of the atmosphere. The resulting dusty spectral distributions of late-type M dwarfs were redder with weaker molecular spectral features than models without grain opacities, and they were shown to reproduce the infrared broadband fluxes of the latest-type M dwarfs, including GD 165B. If confirmed, this greenhouse effect, caused by the presence of photospheric grains, may help explain the observed saturation of the near-infrared water vapor bands discussed in Section 4 and illustrated in Figure 1, as well , as well as perhaps the R-I colors (see Section 4.1) of late-type dwarfs, which the grainless models of Allard & Hauschildt (1995b), Brett (1995a, b) fail to reproduce. The calculations presented by Tsuji et al (1996a), however, are coarse, and a better treatment of both the molecular and grain opacities, as well as the formal inclusion of dust scattering in the solution of the radiative transfer equation, can be achieved.

Early attempts to compute the opacity of grains were made by Cameron & Pine (1973), Alexander 1975. More detailed calculations including the effects of chemical equilibrium calculations and grain-size distributions were reported by Alexander et al (1983), Pollack et al (1985). Alexander & Ferguson (1994a, b) have described the computation of the opacity of grains with the inclusion of equilibrium condensation abundances, the effects of the distribution of grain sizes, and the effect of grain shape through the continuous distribution of the ellipsoid model of Bohren & Huffman (1983). These calculations include the absorption and scattering due to magnesium silicates, iron, carbon, and silicon carbide grains for a wide range of chemical compositions down to temperatures of 700 K. The direct inclusion of the equilibrium calculations of Sharp & Huebner (1990) in the future will allow for more detailed treatment of the effects of trace condensates, lower temperature opacity sources, and the effects of different elemental abundances. The inclusion of high-temperature condensates such as Al₂O₃ and CaTiO₃ may have significant effects on the opacity in cool star atmospheres, even though their abundance is quite small because of the high absorption and scattering efficiency of grains. For lower temperatures, the optical effects of species such as FeS, Fe₃O₄, and H₂O need to be included. Pollack et al (1994) have produced opacities for water, ammonia, methane, and other low-temperature condensates. They assume complete condensation of all condensible species and extend the temperature range down to 300 K. These opacities offer an excellent basis for future brown dwarf and Jovian-type planet atmosphere calculations. However, the extinction caused by grains in a stellar atmosphere depends critically on the rate of grain formation and the resulting size distribution.

Moreover, constraints imposed by the lack of detection of cloud layers in Jupiter by the Galileo atmospheric probe (Isbell & Morse 1996, Keane et al 1996), and of any trace of scattering by grains in the evolved brown dwarf Gl 299B (Allard et al 1996, Tsuji et al 1996b), may imply an inhomogeneous vertical and/or horizontal distribution of the grains, such as scarce cloud distribution, gravitational settling, and sedimentation and rains of condensates in substellar dwarf atmospheres. While grains are likely to be destroyed by the radiative and convective heat in the inner layers of the atmosphere, the main effects of the sedimentation and rains of condensates should be a radial abundance gradient (Muchmore 1987, Guillot et al 1994) and a gradual depletion of the upper photosphere from its condensible elements over time.

The effect of grain formation and of its opacity on the atmospheric structure of M dwarf atmospheres will, therefore, not be fully understood until grain formation and time-dependent grain growth calculations incorporating the effects of sedimentation, diffusion, coagulation, and coalescence are included. Gail & Sedlmayr (1988), Dominik et al (1989) (see references therein) have developed a formalism to account for the phenomena in the outflows from cool giants (Beck et al 1992), supergiants (Seab & Snow 1989), and nova atmospheres (Beck et al 1995). Grain growth models have also been developed for the atmospheres of cool carbon-rich white dwarf (Zubko 1987) and Jovian planet (Rossow 1978, Dobrijevic et al 1992) atmospheres. However, as yet, no results have been obtained for oxygen-rich dwarf atmospheres.

LINE ABSORPTION	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTION <<CONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

The contribution of atomic and ionic line transitions to photospheric opacities is relatively less important for M dwarfs than for cool giants and hotter stars. This result arises not only from the fact that molecular absorption bands dominate opacity, but also because the lower photospheric temperatures cause the number densities (N_i ) of atoms in higher excitation and ionization levels, such as those of the hydrogen Balmer series, to be quenched (N_i e ^{_i /kT} , where T is the gas temperature and _i is the excitation potential or ionization energy relative to the ground state). Moreover, the "locking" of elements into molecular compounds and further condensation of such elements to grains also reduces the available abundances of atomic species, as is the case for hydrogen, which is about 7085% H₂ in the photospheres of M dwarfs.

As a result, only the strongest resonance and subordinate lines, with the low excitation energy of mostly alkali and earth-alkali elements, prevail in the spectra of M dwarfs. Those lines can be very broad owing to van der Waals (vdW) pressure broadening, and they often contrast greatly with the narrow emission and weak absorption lines that originate in the chromospheric layers of active M stars (such as the Balmer series and the Ca H and K lines). Only a few of the atomic lines that are created in the photospheric layers can be detected within the haze of molecular lines and provide diagnostics of the photospheric parameters. Examples include the Na ID lines at 5889,5896 Å, as well as other Na I resonance transitions at 8183,8195 Å and 10746,10749,10835 Å and those of K I at 6911,6939, 7665,7699, 9950,9954, and 10480,10482,10487 Å. Lines of Rb I at 7950 Å and Ba I at 7911,7913 Å are also particularly strong (relative to the local continuum) in late-type M dwarfs and brown dwarf candidates.

Despite the relative scarcity of directly observable atomic lines in their spectra, an accurate modeling of M dwarf atmospheres nevertheless requires the use of a complete atomic line list that includes lines of ionized elements for a complete account of the opacity in the hotter layers (typically about 8000 K in M dwarfs) of the inner atmosphere. A failure to do so may result in atmospheric structures that are too cool globally, as the efficient convection zone assures the transfer of inner atmospheric heat to the outer photospheric layers. The most complete list of atomic transitions currently available is that by Kurucz (1994) and its revisions. Several other line lists, such as those generated from first principle model atoms of the Opacity Project (Seaton 1992, Seaton et al 1992) or semiempirically using atomic levels assigned in laboratory experiments (see Verner et al 1996 and revisions), are also available but are still too incomplete for the purpose of model atmosphere calculations.

Line Broadening Mechanisms

The high densities prevailing in VLM star atmospheres cause strong spectral lines to be significantly broadened. Because the gas temperatures are not high enough to sustain a significant amount of ionization, the electron and proton densities are much smaller than the densities of the most important neutral and molecular species. Consequently, the contribution of Stark broadening to the total damping constant is very small, even in stars with very low metallicities. The total thermal plus microturbulent line widths are always much smaller than the line width owing to vdW broadening:

(1)

which describes the interaction between two different, unpolarized neutral particles within the impact or static approximation, with _vdW the full-width half-maximum damping constant of the resulting Lorentz profile, v the relative velocity between perturber and absorber, and N_p the number density of perturbers. While the interaction constant C ₆ can be determined exactly for both the ground and excited states of a perturbed atom when the perturber is atomic hydrogen (Michelis 1976), no exact method has yet been developed for the case of collisions with the much slower molecular hydrogen perturbers that dominate the atmospheres of VLM stars, brown dwarfs, and Jovian-type planets (Guillot et al 1994). In those cases, the collisions are not instantaneous and the profiles not strictly Lorentzian (Kunde et al 1982, Goody & Yung 1989), but in the absence of accurate alternatives, modelers often resort to using the hydrogenic approximation formulated by Unsöld (1955) for collisions with neutral hydrogen with some ad hoc modifications:

(2)

where Z is the charge of the absorber, E the ionization energy (e.g E _H = 13.6 eV), and E_l and E_u the lower and upper level excitation energies of the absorber. Investigations by Weidemann (1955), for instance, showed that the values as calculated above are in good agreement with observed line widths for alkali metals but not for other elements, such as iron (Kusch 1958). This has led to the introduction of correction factors to the "classical" formula, which can range from 10 C ₆ in the Sun (Takeda et al 1996) to 10^1.8 C ₆ in white dwarfs for nonalkali-like species (Wehrse & Liebert 1980). No corrections are required for alkali elements. The Unsöld (1955) approximation, combined with this correction factor for non-alkali elements and with an explicit account of the different polarizabilities of each perturber ( _p/ _H) C ₆, where the subscript p refers to the perturber), leads to improved profiles that appear to describe well the atomic lines observed in late-type M dwarfs (Schweitzer et al 1996). The most abundant perturbers in M dwarfs and their polarizabilities are given by Weast (1988), Schweitzer et al (1996).

While the situation is poor for atomic line broadening, it is even worse for molecular lines, for which only a few sources and techniques exist (Lazarev & Pnomarev 1992, Kurucz 1993, Guillot et al 1994). Fortunately, individual molecular lines are usually not saturated, so that broadening is less important for them than for strong atomic lines. Moreover, molecular lines often overlap so strongly that their wings are completely masked (Schweitzer et al 1996), and only the Gaussian line cores of the strongest molecular transitions are observed. The atmospheres of VLM stars and brown dwarfs are therefore only weakly sensitive to the adopted value of the vdW damping constant in the bands of several of the most important molecular absorbers (e.g TiO and H₂O). This may, however, not be the case for some hydride bands and for the infrared CO overtones that show larger typical line spacings (Kui 1991, Davis 1994, Tsuji 1994).

CONVECTION	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTION <<STELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

The thin radiative skin above the convective region in an M dwarf determines the surface boundary conditions for the entire temperature structure of the fully convective photosphere and interior. This radiative zone is often limited to the outermost optically thin regions of the photosphere in early-type M dwarfs (Allard 1990, Kui 1991, Burrows et al 1993, Allard & Hauschildt 1995b): i.e. to optical depths below about 10 ³. Figure 2 illustrates how the outer atmosphere of a typical M dwarf is affected by the atomic and molecular opacities and convection. At such low optical depths ( = 10 ³ corresponds to log P _gas 3.8 in this model), the structure of the atmosphere is sensitive to the strong opacities of TiO and H₂O. Early-type M dwarf atmospheres, spectra, colors, and even their evolution are, therefore, very dependent upon elemental abundances and the treatments of molecular opacities and possibly convection (see Section 9 below; see Baraffe et al 1995 for an illustration of these effects). Early-type M dwarfs should serve as excellent stellar laboratories in which to study convection.

View larger version (49K) Figure 2 The influence of the molecular and atomic opacities and convection upon the atmospheric structure of a typical model atmosphere; here the T eff = 2800 K, log g = 5.0, and solar metallicity model of Allard & Hauschildt (1995b). A corresponding gray structure without convection (bold dot-dashed) is also shown for comparison. While the complete neglect of H2O opacities causes a dramatic cooling (by CO) of the atmosphere (long-dashed curve), uncertainties by a factor of two in the H2O opacity cross sections cause only negligible changes in the atmospheric structure (thin dot-dashed relative to dotted curve). A similar drop in the opacity cross section of TiO, however (thin short-dashed relative to dotted curve), causes a much more significant cooling of the atmosphere.

The standard mixing length theory (Bøhm-Vitense 1958, Kippenhan 1962, Mihalas 1978) used to model convective energy transport in stars is only a crude approximation. While nonlocal treatments of convection exist (for review, see Chan et al 1991, Gustafsson & Jørgensen 1994, Grossman 1996, Kim et al 1996) that may be better suited to the optically thin medium of cool stellar atmospheres, they are very computationally prohibitive and have not been applied to models of M dwarfs. Fortunately or sadly, depending on your point of view, the large opacities in M dwarfs mean convection is nearly adiabatic for values of the mixing length () comparable to the atmospheric pressure scale height. The atmospheres and synthetic spectra of M dwarfs therefore show very little sensitivity to changes in over the range typical of solar-type atmospheres; i.e. H_P = 1.2 to 2.2 (Brett 1995a, Baraffe et al 1997). Moreover, models indicate that the convection zone gradually retreats with decreasing mass in late-type M dwarfs because of their decreasing luminosity and with decreasing metallicity due to decreasing photospheric opacities (Allard 1990). In cool brown dwarf models such as those computed for Gl 229B, for example, the convection zone reaches no higher than optical depths of about unity (although models show signs of a second, separate convective layer closer to the surface in such cool objects). The spectroscopic and photometric properties of late-type M dwarfs, metal-poor subdwarfs, and possibly brown dwarfs are therefore relatively insensitive to the details of convection (see e.g. Brett 1995a). This means that standard mixing length approximations are probably suitable for these stars (which is good news for brown dwarf modelers), but that these same stars are not very good laboratories to study convection (which is bad news for convection modelers).

STELLAR ACTIVITY	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITY <<THE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

The "solar dynamo" model, also known as the alpha-omega dynamo, which operates at the radiative convective boundary layer in the solar interior, predicts a correlation of activity with rotation that is observed in solar-type stars (Noyes et al 1984, Marilli et al 1986, Rutten 1986). When coupled with the decrease of the rotation rate as the star ages (owing to loss of angular momentum during its lifetime), a rotation-activity-age correlation is expected and has also been observed (Wilson & Skumanich 1964). The fully convective lowest mass stars, however, like premain-sequence solar-type stars, are known to be very active even if no spot-cycle variability can yet be confirmed in any of them. Several flare periodically [see e.g. Linsky et al (1995) for a report of recent flare outbursts in VB10], and a large fraction of them (up to 60% in M5 dwarfs) show chromospheric H emission. The dynamo generation of their fields must therefore occur from a different, or at least modified, mechanism. And indeed, the surface activity in the M dwarfs has been observed to exhibit general characteristics that contrast with those of solar-type stars: 1. The incidence of chromospheric and coronal activity in M dwarfs grows with decreasing stellar mass (Joy & Abt 1974, Giampapa & Liebert 1986, Reid et al 1995a, b, Hawley et al 1996). 2. The coronal and chromospheric luminosity and the luminosity that occurs in flares all decrease with stellar mass (Fleming 1988, Peterson 1989); however, the fraction of the luminosity that appears in these magnetic indicators relative to the total stellar luminosity (L_H /L_bol, L_X/L_bol, hereafter "activity level") remains nearly constant (Fleming et al 1995, Reid et al 1995a, Mullan & Fleming 1996). 3. While, as in solar-type stars, M dwarfs show little or no activity when the rotation rate reaches below a certain threshold (5 km/s; cf Marcy & Chen 1992), stars with rotation rates above this threshold show weak or no correlation between rotation and the activity level for both chromospheric and coronal emissions (Stauffer & Hartmann 1986, Rutten et al 1989, Hawley et al 1996). 4. Coronal and chromospheric activity show a correlation with scale height from the galactic plane, metallicity, and probably age of the star (Fleming et al 1995, Reid et al 1995a, Hawley et al 1996).

M dwarfs are therefore more active than solar-type stars. This clearly indicates that some change in the magnetic field generation and/or the interaction of the field with the stellar atmosphere has occurred. Two possible ideas have been suggested to explain the differing M dwarf behavior: 1. Noyes et al (1984) and later Peterson (1989) pointed out that the volume of the convection zone is an important parameter in the generation of the magnetic field, and this volume begins to decrease in proportion to the mass once the stars are mostly convective (in M dwarfs). The field strength may become saturated in the lowest mass stars, and hence no strong rotation-activity connection would be expected (see e.g. Rosner et al 1985, Stauffer et al 1991). Moreover, the relative neutrality of the gas in M dwarfs compared with hotter stars may also alter the behavior of magnetic field lines (P Ulmschneider, private communication). Direct measurements of the magnetic field strength and its stellar surface coverage have been obtained, using Zeeman splitting of highly magneto-sensitive lines, by Robinson (1980), Gray (1984), Saar (1988), Mathys & Solanki (1989), Basri & Marcy (1994) for a number of late-type stars, which confirm the presence of strong magnetic fields in M dwarfs. Saar (1994), Johns-Krull & Valenti (1996), for example, report magnetic field strengths for the dMe dwarfs AD Leo, EV Lac, and AU Mic of 4.04.3 kG with covering factors between 55 and 85%. 2. On the other hand, the propagation of acoustic shocks (which originate at the convective-radiative surface boundary), and the resulting acoustic heating of the chromosphere, should become most efficient in the strongly convective M dwarf photospheres and may therefore play an important role in the energy budget of their atmospheres and coronae (Schrijver 1987, Mathioudakis & Doyle 1992, Mullan & Cheng 1993). Since the extension of the convection zone depends sensitively on the atmospheric parameters (see Section 7 above), a correlation of the chromospheric activity with metallicity and age in M dwarfs would therefore be likely. The first steps in integrating detailed photosphere models with acoustically heated M dwarf chromospheres were taken by Buchholz (1995), Mullan & Cheng (1993, 1994). Mullan & Cheng (1994) report a more effective penetration of acoustic waves into the coronae of M dwarfs compared with the case of more massive solar-type stars. They find that acoustic heating can maintain a corona with a temperature on the order of 0.71 10⁶ K and a surface X-ray flux as large as 10⁵ ergs cm ² s ¹, and they suggest that relatively inactive M dwarfs that display X-ray emissions below this limit may be candidates for acoustically maintained coronae.

However, these ideas still leave some unanswered questions. How can we explain, for example, stars of the same age or the same mass and rotation rates above the threshold but with widely different activity levels? In an attempt to explain the dilemma raised by the two M9.5-type field dwarfs PC 0025+ 0447 (Graham et al 1992) and BRI 0021 012 (Tinney 1993) that have widely different activity levels, Basri & Marcy (1995) suggested that there could also be a threshold temperature below which acoustic and Alfvén waves become inefficient and stellar activity subsides. Below this temperature threshold, the heating of the chromosphere and corona and the wind generation would be sufficiently prohibited to prevent the formation of chromospheric emission lines and to slow the rotation of the star. However, this interpretation still leaves the case of hotter stars unaddressed. An example is the triple VLM star system LHS 1070 (Leinert et al 1994; F Allard et al, in preparation), in which the two faint companions of the same age and metallicity are also similar both in mass (0.085 M) and T_eff (26002700 K), but where only the faintest of the three components is inactive. Several other systems have been observed where only the more massive primary star is active (Hawley et al 1996). While most cases can be explained if the primaries are in fact unresolved close-binary stars in which enhanced rotation (and activity) is maintained by tidal interactions, this does not seem to explain the lack of activity in the close-binary star LHS 1070C.

Modeling an M dwarf chromosphere is a complex problem owing to the complexity of the radiative transfer calculations in such a cool, dense environment. Cram & Mullan (1985) modeled an M dwarf chromosphere using hydrogen Balmer emission line observations. Giampapa et al (1982) used Ca II observations to model M dwarf chromospheres, with limited success. Houdebine & Panagi (1990) investigated the effects of changing the model hydrogen atom used in the calculations, but they did not fit their models to data. Hawley & Fisher (1994) have developed chromospheric flare models, which incorporate a full nonlocal thermodynamic equilibrium (NLTE) treatment of the statistical equilibrium and radiative transfer in the important optically thick chromospheric lines and a helium ionization equilibrium computed self-consistently with the downward X-ray flux from the corona. Yet they were unsuccessful at fitting both the Ca II and hydrogen Balmer lines in their quiescent and flare observations. More recently, Mauas & Falchi (1996) were also unable to match both the observed hydrogen Balmer line strengths in their quiescent model of a well-observed active M dwarf. To date, no model has successfully predicted all the major chromospheric lines observed in an active M dwarf atmosphere.

The success of chromospheric modeling may be limited by these workers' assumptions of monotonically rising atmospheres or even two-component models. (Hawley et al 1996) found that active M dwarfs in the field show systematic spectral differences relative to nonactive stars, which may lead to a better understanding of the atmospheric heating mechanisms: Early-type dMe appear (a) brighter by 0.5 mag from V-K, (b) 0.1-mag redder in (V-I) and (V-K), and (c) to show systematic differences in the relative strengths of some near-infrared TiO subbands compared with those of nonactive dM stars of the same spectral type. These effects may in part be expected if dMe stars are systematically younger with larger radii. However, they are only observed in the most massive M dwarfs. On the other hand, while direct effects of magnetic fields on the structure of the atmosphere (e.g. through the magnetic pressure term) and the Zeeman splitting of atomic lines are negligible for all but the outermost photosphere, the impinging radiation upon the upper photosphere by a magnetically or acoustically heated chromosphere can be important. The radiation temperature of the chromosphere is generally much higher than that of the photosphere, and even a relatively small irradiation of the photosphere (0.1% of the total flux of the star) by the chromosphere can introduce important NLTE effects that may change the temperature structure of the outermost layers. Since the outermost thin radiative skin of an M dwarf regulates the entire structure of the convective photosphere and interior (see Section 7 above), these effects may couple back to the dynamo-generated magnetic and acoustic heating. Systematic development of (magneto) hydrodynamical studies of chromospheric activity must be tied to realistic photosphere models to truly understand cool dwarfs.

THE Teff SCALE OF M DWARFS	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF... <<THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

While bolometric luminosities can be derived from a careful integration of the observed stellar radiation for single stars within the accuracy of their known parallaxes (Tinney et al 1993, 1995), and stellar masses can be derived for close binaries down to the hydrogen-burning limit (Henry & McCarthy 1993), the calibration of the observed magnitudes and spectral types as a function of the physical atmospheric parameters of the stars still remains difficult. The determinations of M dwarf effective temperatures have been refined considerably since the work of Veeder (1974), Peterson (1980), Reid & Gilmore (1984), who fit blackbody curves through broadband colors and points of assumed observed continuum. But even the current empirical methods (Berriman et al 1992, Jones et al 1994) still assume that nearly pure thermal radiation escapes from dM atmospheres at some wavelength(s). Such an assumption is secure only for optically thick layers of a nonconvective atmosphere, but models strongly suggest that M dwarf atmospheres are convective out to optical depths as low as 10 ³ (see Section 7 above). The hazards of any type of Planck flux fitting to an M dwarf spectrum are apparent from Figure 3 and have been emphasized by Allard & Hauschildt (1995a), who showed how strong molecular absorption and flux redistribution obliterate all evidence of the original continuum shape.

View larger version (53K) Figure 3 Spectral distributions of emerging fluxes at the stellar surface for 3000 K models of metallicities corresponding roughly to the solar neighborhood ([M/H] = 0.0), halo ([M/H] = 2.0), and Population III ([M/H] = 4.0) stars. A blackbody of the same effective temperature (smooth curve) is shown for comparison.

Fortunately, two double-line spectroscopic and eclipsing M dwarf binary systems can offer some guidance in the subsolar mass regime: CM Draconis and YY Geminorum. Lacy (1977) and later Habets & Heintze (1981) determined the T_eff of M dwarfs in these systems based on the observed masses and radii. Figure 4 compares the latest OS models of Brett (1995b), F Allard & PH Hauschildt (in preparation), and Kurucz 1992b to these fundamental stellar calibrators. The T_eff scales derived from the spectral synthesis of individual stars of Kirkpatrick et al (1993b) [using the SM models of Allard (1990)] and Leggett et al (1996) [using OS synthetic spectra drawn from the Allard & Hauschildt (1995b) model structures] are also shown, which illustrate the tendency of theoretical T_eff to become cooler with developments in the treatment of opacities in the models.

View larger version (50K) Figure 4 The M dwarf Teff scale. Current model-dependent effective temperature scales for cool stars down to the hydrogen-burning limit. Open triangles feature results from spectral synthesis of selected stars from the works of Kirkpatrick et al (1993b), Leggett et al 1996 as indicated. The new generation of OS models by Brett (1995b) and F Allard & PH Hauschildt (in preparation), as interpolated onto theoretical isochrones by Chabrier et al (1996a), reproduce closely the independently determined positions of M dwarfs in the eclipsing binaries CM Dra and YY Gem (Habets & Heintze 1981). Much uncertainty remains, however, in the lowermost portion of the main sequence where effects of grain formation can become important.

As an inspection of Figure 2 reveals, M dwarf photospheric structures are much more sensitive to TiO opacities than to the current uncertainties in the H₂O opacity profiles discussed in Section 4. The result of the use of an OS treatment of the main molecular opacities, in particular for TiO, appears therefore to be a breakthrough in the agreement of modeled T_eff scales with observations of early-type M dwarfs. Note that the OS models of Kurucz (1992b), on the other hand, suffer from an inaccurate TiO absorption profile and a complete lack of H₂O opacities, and the models are therefore clearly inadequate in the regime of VLM stars (i.e. below T_eff 4500 K and M 0.8 M), where molecular opacities dominate the stellar spectra and atmospheric structures.

However, the situation still remains uncertain at T_eff 3500 K, where the SM models of Allard & Hauschildt (1995b) seem to yield a better agreement, both with the current T_eff estimate for CM Draconis and with the VRI colors of the Leggett (1992) disk stars sample. This could be understood in terms of an incompleteness of current optical opacities (see Section 4.1 for details). The SM technique used for the treatment of TiO opacities in the models of Allard & Hauschildt (1995b) compensates for missing optical opacities and may represent a better intermediate solution in this regime. Kinematics indicate that CM Draconis is most likely an old disk system and may be slightly metal-depleted compared with young-disk main-sequence stars (Rucinski 1978, Saumon et al 1995a, Chabrier & Baraffe 1995). Recently, new determinations of the masses and radii of CM Draconis have been obtained by Metcalfe et al (1996), and a revision of the effective temperatures and metallicity of the system is under way (Viti et al 1996), which may help improve the temperature estimate for CM Draconis and shed some light on this region of the lower main sequence.

The models of F Allard & PH Hauschildt (in preparation) and Brett (1995a, 1995b) presently neglect the effects of both condensation and grain opacities that may affect stars cooler than 2700 K. The preliminary dusty models of Tsuji et al (1996a) (also shown in Figure 4) indicate that condensation effects may drive the T_eff scale of these M dwarfs to cooler values at a given color. Tsuji et al's models also indicate that when grain opacities begin to alter the thermal equilibrium of the atmosphere, the lowest-mass stars become gradually hotter and redder, mimicking more closely the behavior of blackbodies.

Much uncertainty remains, therefore, at the lowermost portion of the main sequence. The effects of grain formation and more complete opacities of TiO promise a better understanding of the stars and brown dwarfs in the vicinity of the hydrogen-burning limit [the location of which is roughly indicated in Figure 4 by the termination point of the Allard & Hauschildt model sequence], but they still remain to be ascertained. These questions are currently being addressed by Tsuji et al (1996b) and F Allard & PH Hauschildt (in preparation).

THE DETECTABILITY OF BROWN DWARFS	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW... <<THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited

Brown dwarfs are substellar objects not massive enough to sustain stable nuclear fusion and therefore cannot successfully stabilize on the hydrogen-burning main sequence (Burrows et al 1993, Saumon et al 1995a). While this boundary between stars and brown dwarfs is fairly well defined, the recently reported massive extrasolar planets, some of which have orbital eccentricities more reminiscent of stellar binary systems (e.g. e = 0.4 for 70 Vir; see Marcy & Butler 1996b), blur the distinction between planets and brown dwarfs. The minimum mass for deuterium burning (13 M _J ) may represent a more physically meaningful criterion to distinguish Jovian planets from classical brown dwarfs (Saumon et al 1994).

To develop search strategies for substellar objects, we propose three categories for objects in the brown dwarf regime: (a) transitional objects: massive brown dwarfs (M 0.06 M) younger than about 10⁹ years that are burning deuterium or even hydrogen temporarily; (b) lithium brown dwarfs: low-mass brown dwarfs ( M 0.06 M) younger than about 10⁷ years that are still burning deuterium but have not depleted their initial reservoir of lithium and beryllium; and (c) evolved brown dwarfs: brown dwarfs older than 10⁷ 10⁹ years that have exhausted their nuclear fuel and have cooled and faded below the parameters of the coolest main-sequence stars [i.e. T_eff = 2000 K and L= 10 ⁴ L (Burrows et al 1993, Baraffe et al 1997)]. Many brown dwarfs of all types are expected to be in the solar neighborhood and nearby clusters, so it was puzzling that concerted searches did not reveal any (Martín et al 1994, Marcy et al 1994, Henry 1996).

Transitional Objects

If it is massive enough, a brown dwarf can initiate thermonuclear fusion early in its evolution, before fading to invisibility as a component of the dark matter (Burrows et al 1993). Such young objects can approach atmospheric conditions similar to those of M dwarf stars (T_eff 3000 K) and can easily be confused with them. An extrapolation of the observed massspectral type relation of red dwarfs in short-period binary systems seems to support the existence of a large population of unrecognized brown dwarfs among red dwarfs with spectral types later than M7 (Henry & McCarthy 1993, Henry et al 1994, Kirkpatrick et al 1994, 1995, Kirkpatrick & McCarthy 1994). However, further extensions of the Henry & McCarthy (1993) mass-spectral type relation and new evolution models (Baraffe & Chabrier 1996) reveal a sharp drop in the mass-luminosity and mass-color relations from about 0.1 M to the hydrogen-burning limit, which rules out this naive extrapolation. The possibility that such objects may masquerade as known field M dwarfs must still be confirmed.

Transitional objects in the field with unknown age and mass should betray their youth with the following signatures that distinguish them from more massive M dwarfs: (a) a lower surface gravity (log g < 5.0), since the brown dwarf is still early on its evolutionary track, and (b) a higher rotation rate accompanied by more chromospheric and coronal activity. Unfortunately, both these criteria are difficult to apply in practice: Metal-rich model spectra for the latest-type dwarfs show very little sensitivity to changes in gravity (Allard & Hauschildt 1995a). Moreover, the wings of resonance lines that are sensitive to the pressure stratification of the photosphere are also sensitive to slightly increased T_eff and/or metallicity that can compensate for a lower gravity (Schweitzer et al 1996). As for rotation, the relation between age, rotation, and activity in late-type dwarfs is very poorly understood (see Section 8 above) and is not a reliable discriminant of transitional objects either. This situation is best illustrated by the striking contrast between the candidates PC 0025+0447 (classified dM9.5; Graham et al 1992), which shows one of the strongest H emission lines of the lower main sequence, and the brown dwarf candidate BRI 0021012 (classified <dM9.5; Tinney et al 1993), which rotates 20 times faster than other field nonemission M stars (Basri & Marcy 1995). Faced with these ambiguities, nobody has yet been able to confirm any transitional object in the field. Young stellar clusters, however, have yielded more positive results (see below).

Lithium Brown Dwarfs

The key to recognizing such substellar objects is in their spectra. Since an M dwarf is completely convective, the entire star is mixed and the surface abundances reflect the elemental abundances in the core. If the central temperatures are low enough or the star is young enough, then nuclei should survive in the atmosphere that would otherwise be completely destroyed in hotter, more massive stars. This is the case for ⁷Li nuclei, which are destroyed by proton captures at relatively low temperatures of a few (2) million degrees in the interior. Therefore, if you can detect and measure the strength of ⁷Li lines in a stellar spectrum and you are armed with accurate atmospheric and evolution models, you should be able to estimate the mass and age of the star (Rebolo et al 1992, Maggazzú et al 1993).

To date, the detection of Li I lines is the most decisive spectral indicator of substellarity for young brown dwarfs with masses below about 0.06 M. This test is best used for nearby young clusters where the age is reasonably well known and the 6707-Å region can be studied at relatively high dispersion to obtain a precise abundance of lithium. If the cluster is old enough that only the very lowest mass stars should retain any surface lithium, as is the case for the Pleiades, then this is a very powerful test of substellarity. The fact that early searches for Li I in Pleiades brown dwarf candidates yielded no detections prompted (Pavlenko et al 1995) and later (Allard & Hauschildt 1995a, b) to investigate a number of concurrent physical processes that could prevent the Li I 6708 Å doublet from being seen in those objects. They explored possible molecular bonding involving lithium and departures from LTE in the Li I lines, all with negative results: The Li I lines should be observable in young brown dwarfs. Indeed, recent spectroscopic observations of Teide 1, Calar 3, and PPl 15 (Rebolo et al 1995, Zapatero Osorio et al 1997, Stauffer et al 1994) show that they are cluster members, have low luminosities, and have retained lithium at their surface (Basri et al 1996, Rebolo et al 1996). Teide 1 and Calar 3 are most likely brown dwarfs with estimated masses of 55 ± 15 M _J Zapatero Osorio et al 1997. One more candidate, the first found in the field, has also been confirmed to have Li in its atmosphere Thackrah et al 1997. Several more Pleiades candidates may soon be confirmed (or rejected) by the Li test Martín et al 1996.

Accurate estimation of brown dwarf masses depends critically upon an understanding of the depletion of lithium at the surface as a function of mass Nelson et al 1993. This in turn requires evolutionary calculations for low-mass stars that include the most modern equations of state and non-gray atmospheres for their outer boundary conditions, as have been performed by (Baraffe et al (1995, 1997), Chabrier & Baraffe (1995), Chabrier et al (1996a), Baraffe & Chabrier (1996), Allard et al (1996). The evolutionary calculations are largely sensitive to the treatment of the equations of state, which requires the inclusion of the thermodynamic properties of a strong-coupled Coulomb plasma, electron degeneracy, and pressure ionization (Dorman et al 1989, Nelson et al 1993, Burrows et al 1993). Non-gray atmospheres were found to cause the interiors to become systematically cooler (and the hydrogen-burning minimum mass smaller) than when using gray models such as those of Burrows et al (1993) for a given mass. This is because energy is transported in the interiors of these objects by convection, and their structure can be approximated by that of a polytrope of index, n = 1.5 [see Burrows & Liebert (1993) for a discussion of the polytropic nature of low mass stars and brown dwarfs]. The polytropic interior characteristics are only specified once the atmospheric structure is determined, and improvements in the atmospheric properties, therefore, directly impact the determinations of the ages, masses, and location in the Hertzprung-Russell (HR) diagram of these stars. A proper treatment of the atmosphere is therefore essential to the predicted massLi abundance relation as a function of the age of brown dwarfs (Chabrier et al 1996a).

EVOLVED BROWN DWARFS

A major breakthrough in finding the missing link between Jovian planets and low mass stars was the discovery of the first evolved field brown dwarf Gliese (Gl) 229B by Oppenheimer et al (1995), Nakajima et al (1995). Unfortunately, Gl 229Band other candidates like the astrometrically discovered HD 114762 (Mazeh et al 1996, Williams et al 1997), the ZZ Ceti companion GD 165B (Becklin & Zuckerman 1988, Zuckerman & Becklin 1992), and the massive extrasolar giant planet candidate around 70 Vir (Marcy & Butler 1996b)are all binary companions that are too faint and too close to their stellar primaries to be tested for an optical lithium signature. Fortunately, their low temperatures offer an advantage, since unique changes in molecular chemistry that occur across the temperature transition from the coolest M dwarfs (2000 K) to the Jovian planets (150 K) result in distinctive spectral signatures.

There currently exist three sets of model atmospheres and synthetic spectra for the T_eff regime of cool brown dwarfs: (a) The Tsuji et al (1996a, b) models cover the range from 4000 K (although only from 2700 K with grains) to 1000 K; (b) the Allard et al (1996) models reach down (from 10,000 K) to 800 K; and (c) the Marley et al (1996) models cover the range from 1000 K to the temperature of Jupiter, i.e. 150 K. Tsuji et al (1995) were the first to introduce detailed models and synthetic spectra for cool brown dwarfs. While unsuitable for high-resolution spectral synthesis, their models (based on a band model treatment of the molecular opacities) predict the growing intensity of infrared CH₄ bands with T_eff  cooler than about 1800 K. This signature was later identified in the near-infrared spectral distribution of the brown dwarf Gl 229B (Matthews et al 1995, Geballe et al 1996) and helped confirm the substellar nature of the brown dwarf. The study of Gl 229B also led to the important realization that, although grain formation must occur in such cool photospheres and may indeed affect the spectroscopic properties of late M dwarfs (Tsuji et al 1996a), none of the predicted greenhouse effects of grain opacities seem to be present in Gl 229B Allard et al (1996), Tsuji et al (1996b). These authors showed that grainless models provide a better description of the spectral distribution of the brown dwarf when a homogeneous atmosphere is assumed (see Section 5 above for details; Tsuji et al 1996b). The grainless brown dwarf models of Tsuji et al (1995), however, are based on band-model opacities that tend to overestimate the strength of molecular features and cannot be used reliably to derive accurate atmospheric parameters and absolute fluxes for evolved brown dwarfs.

The brown dwarf model atmospheres of Allard et al (1996), on the other hand, are based on a direct OS treatment of an ab initio line list for H₂O (Miller et al 1994) and lists of transitions observed in planetary atmospheres [e.g. the RADEN, GEISA, HITRAN, and ATMOS projects by Farmer & Norton (1989), Husson et al (1992), Rothman et al (1992), Farmer & Norton (1989), Kuznetsova et al (1993), respectively] and that reproduce more accurately the spectroscopic properties of evolved brown dwarfs. This can be appreciated in Figure 1, where the most recent observations of the brown dwarf Gl 229B by Geballe et al (1996) are compared to the best fitting model of Allard et al (1996). Their models, combined with the latest brown dwarf evolution models, led to a T_eff of 9001000 K and a mass of about 3050 M _J for Gl 229B. The lack of condensation in their calculations, however, prevented them from completely covering the range of relevant brown dwarfs parameters; i.e. brown dwarfs cooler than about 800 K, in which water vapor begins to condense out of the gas phase, leaving profoundly transformed photospheres and synthetic spectra. This limitation was avoided by Marley et al (1996) by simply neglecting elements that are expected to be condensed at the effective temperatures of Jovian planets and by including only the H₂, He, CH₄, NH₃, H₂O, and H₂S species in their chemical equilibrium calculations. This allowed them to compute models that cover the regime of brown dwarfs and extrasolar planets cooler than 1000 K. Despite their approximations in the treatment of molecular opacities (K-coefficient technique) and convection (adiabatic mixing only), their model successfully reproduced most of the observed spectral characteristics of the brown dwarf Gl 229B.

The models of Allard et al (1996), Marley et al (1996) are compared in Figure 5 to summarize the predicted absolute fluxes that brown dwarfs would have at a distance of 50 parsec (pc). Both the model spectra and blackbody distributions of the same T_eff are shown, which indicate the range of possible spectroscopic characteristics of brown dwarfs (from a grainless to a fully dusty atmosphere). As can be seen in that figure, brown dwarfs are most readily detected at 4.5 m: the peak of their spectral energy distribution. At 5 m, the hotter (younger or more massive) brown dwarfs and stars show strong CO bands that cause their flux to drop by nearly 0.5 dex relative to that at 4.5 m. Between 4.5 and 10 m, opacities of CH₄ (and H₂O in the hot brown dwarfs) cause the flux to drop by 0.51.0 dex. Searches in the 4.55 m region and redwards of 10 m should therefore offer the best possibilities for finding and resolving brown dwarfs in binaries. The detection limits of current and planned ground-based and space-based telescopes (from Saumon et al 1994) are also indicated in Figure 5, which show that brown dwarfs (dusty or not) within 50 pc would be easily detected by Space Infrared Telescope Facility in the 4.55.0 m region. The drop in sensitivity of the various instruments redward of 10 m implies, however, that only brown dwarfs as hot as or hotter than Gl 299B have a good chance of detection at that distance.

View larger version (58K) Figure 5 Predicted absolute fluxes of brown dwarfs at 50 pc as compared with the sensitivity of ground- and space-based platforms that will be or are currently applied to the search for brown dwarfs and extrasolar planets. The latter are values reported for the 5 detection of a point source in 1 h of integration, except for the three NICMOS cameras where the integration is limited to 40 min (see Saumon et al 1994 for details). Models of both Allard et al (1996) (solid line) and Marley et al (1996) (dotted line) are shown, which simulate (a) a brown dwarf near the hydrogen-burning limit (top-most spectrum: Teff = 2000 K), (b) an evolved brown dwarf similar to Gl 229B (central spectra: Teff = 900 K and 960 K), and (c) a brown dwarf closer to the deuterium-burning limit (lower-most spectrum: Teff = 500 K). The corresponding blackbody (dashed line) are also shown for comparison.

The general spectral distributions of brown dwarfs hotter than about 800 K are relatively well reproduced by current models. In contrast, the incompleteness of lists of observed molecular transitions for several important molecular absorbers may introduce uncertainty in the predicted absolute fluxes and colors of cooler brown dwarfs where water is no longer the dominant infrared opacity. Opacities for CH₄, for example, are clearly incomplete because only the strongest lines of CH₄ are available from the Gestion et Etude des Informations Spectroscopiques Atmospheriques and High Resolution Transmision data bases, while none are available blueward of 1.6 m where systems of CH₄ are known to cause strong absorption features in the spectra of planets [e.g. in Jupiter and Titan; see Mickelson & Larson 1992, Bernath et al 1995, Baines et al 1993, Strong et al 1993, Larson & Mickelson 1997]. The complexity of the CH₄ compound has so far prevented the accurate modeling of the methane spectrum beyond 2000 cm ¹ (see e.g. Tyuterev et al 1994), where a significant fraction of the flux emerges from a brown dwarf or Jovian planet.

THE METAL-DEFICIENT VLM STARS	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S... <<CONCLUSIONSAcknowledgmentsLiterature Cited

Accurate knowledge of the compositions of metal-poor VLM subdwarf M (hereafter sdM) stars and their positions in the Hertzprung-Russell diagram is essential to a full understanding of the chemical history of our Galaxy. The reconstruction of the initial mass function in the old disk, halo, and globular clustersfounded on an accurate mass-luminosity relation that is a sensitive function of the stellar chemical composition (Chabrier et al 1996a, D'Antona & Mazzitelli 1996, von Hippel et al 1996)also depends upon it.

Unfortunately the metallicity, atmospheric parameters, and mass-luminosity relation of sdM stars have long remained uncertain owing to the lack of VLM stellar model atmospheres and the resulting lack of bolometric corrections and synthetic photometry to transform theoretical evolution models into various empirical planes such as color-magnitude diagrams (see e.g. Greenstein 1989 for details).

This situation began to change in the early 1990s with the Allard Allard (1990) grid of VLM models that explored a wide range of parameter space with metallicities ranging from solar values to as low as 1/10,000th solar (i.e. a logarithmic ratio of metal to hydrogen abundances of [M/H]= 4.0). This encompassed all relevant age/metallicity populations of cool dwarfs, including disk, halo, and even unobserved Population III VLM subdwarfs. These models were later updated by Allard & Hauschildt (1995b), for an OS treatment of more complete atomic opacities, and most recently by F Allard & PH Hauschildt (in preparation), for an OS treatment of the molecular opacities as well. Figure 3 presents three typical model-flux distributions obtained by F Allard & PH Hauschildt (in preparation) for 3000-K dwarfs: one for metal-rich conditions of young disk dwarfs, the other two for their higher-gravity halo and Population III subdwarf counterparts. The collision-induced absorption (CIA) of H₂-H₂, H₂-H, and H₂-He (Borysow et al 1989, Borysow & Frommhold 1989, 1990, Zheng & Borysow 1994) defines the near-infrared continuum in these low-metallicity subdwarfs. Centered at 2 m, H₂ CIA depresses the infrared continuum such that most of the flux emerges only in bluer passbands. Molecular absorption bands of hydrides such as MgH and CaH are the predominant features in the optical region when double metals such as TiO and VO are depleted (Mould & Wyckoff 1978, Boeshaar 1976, Bessell 1982). The optical spectrum of an sdM is therefore much more transparent than that of a metal-rich M dwarf, where the continuum is defined by H opacity. The result is a spectral distribution that becomes bluer with decreasing stellar metallicity.

Figure 6 illustrates the behavior of metal-poor VLM stars in the M _V (V-I) color-magnitude diagram. As can be seen, the work of Monet et al (1992), Dahn et al (1995) have revealed a number of old disk and halo subdwarfs, some of which are nearly two magnitudes bluer than previously known field sdM stars. D'Antona (1995) suggested that the extreme subdwarfs of the Monet et al (1992) sample belong to the galactic halo. But despite the availability of VLM model atmospheres and synthetic spectra, it has still proven difficult to untangle the effects of reduced metallicity from those of increased gravity or reduced effective temperature, which all affect the pressure structure of the photosphere in similar ways (Allard 1990, Kui 1991, Allard & Hauschildt 1995b). This difficulty, combined with the lack of accurate line lists for molecular hydride absorption bands, has hampered efforts to obtain the atmospheric parameters of observed M subdwarfs (sdM) via spectral synthesis. Thus far, only a few stars have been analyzed in any detail (cf Dahn et al 1995).

View larger version (39K) Figure 6 Color-magnitude diagram of the lower main sequence for disk to globular clusters stars. The excellent agreement obtained by Baraffe et al (1997) to the [Fe/H] = 1.9 globular cluster NGC6397 of Cool et al (1996) (small dots to the blue of the diagram) illustrates the recent success of synthetic photometry and evolution models to reproduce metal-poor VLM stars. Two model sequences by Baraffe et al Baraffe et al (1997) are shown for [M/H] = 1.5 [Fe/H] = 1.9 ( full line) and for [M/H] = 1.3 i.e. [Fe/H] = 1.0 (dot-dashed line). Points along the theoretical sequences are labeled with the stellar mass, in units of the solar mass. The latter isochrone gives a correct description of the most metal-poor halo subdwarfs of Monet et al (1992) ( full circles). The disk stars of Monet et al (1992) (crosses) and Dahn et al (1995) (small dots) to the red and the zero-metallicity models of Saumon et al (1994) (dashed line) to the blue display the possible range of so-called subluminosity for metal-poor VLM subdwarfs.

The M subdwarfs in binary and multiple systems, for which the metallicity of the hotter primary is known, and clusters with VLM stars of the same age and metallicity offer more promise to test Population II evolutionary and atmosphere models. Two early-type M subdwarfs in binary systems have been recently reported by Martín et al (1995): the faint, wide proper-motion companion to G116-009 and the fourth and faintest (M _V = 12.2) companion in the [M/H] = 1.7±0.4 multiple system G176-46 (see also Laird et al 1988, Latham et al 1992). A spectral synthesis of these M subdwarfs with the most recent OS model atmospheres should soon permit calibration of the T_eff scale of similar halo subdwarfs (F Allard & PH Hauschildt, in preparation).

One of the unique contributions of the HST to the understanding of the lower main-sequence star formation in the early Universe and the contribution of low-mass stars to the universal dark matter has been the recent detection of large numbers of VLM stars and white dwarfs in the nearest globular clusters (Paresce et al 1995, Richer et al 1995, Cool et al 1996, Renzini et al 1996). Figure 6 depicts the globular cluster NGC6397 as observed with the Wide Field/Planetary Camera 2 by Cool et al (1996). This cluster displays a genuine Fe underabundance of [M/H] = 1.9 (i.e. 1/80 times solar) and must have formed some 15 10 ³ years ago. Its main sequence is narrow and well defined, without the age, activity, and metallicity dispersion characteristic of samples of field stars. Fits to that main sequence below about 0.5 M do not suffer from the same high sensitivity to assumed values of the helium abundance fraction and mixing length as do fits to more massive parts of the main sequence (cf Baraffe et al 1997). Two characteristic kinks also typical of the mass-luminosity relation shape the lower portion of the main sequence. The first kink at 0.4 M is caused by H₂ dissociation (Copenland et al 1970). The second, below 0.1 M, is close to the HST detection limit for several clusters and was first revealed in the Population II models of D'Antona (1987, 1990, 1995). The first kink is due to the onset of electron degeneracy in the interior, which is also the cause for the sharp drop in the mass-luminosity relation below this threshold (Chabrier & Baraffe 1997). Its exact location depends upon the pressure structure and hence the opacities of the atmospheres (see also Section 7). The shape of the lower main sequence of globular clusters represents a nearly parameter-free test bed for stellar evolution and atmospheric physics in a metallicity regime where models are less prone to the incompleteness of H₂O and TiO opacities.

D'Antona & Mazzitelli (1985), D'Antona (1987) laid the ground work for the theoretical modeling of VLM stars down to the hydrogen-burning limit, and their models long provided among the best descriptions of the lower main sequence of VLM stars. More recently, D'Antona & Mazzitelli (1994, 1996) have computed a series of premain-sequence tracks for Population II stars with masses ranging from 0.0152.5 M using both standard mixing-length theory and the Canuto & Mazzitelli (1991, 1992) theory of turbulent convection. However, a critical element to the handling of convection that describes the stellar structures in these fully convective objects comes (a) from the equations of state, i.e. the adiabatic gradient (Saumon et al 1995b), and (b) from the treatment of the surface boundary, i.e. the atmosphere as we pointed out in Sections 7 and 10. Even with updated versions of the Magni & Mazzitelli (1979) equations of state, the models of D'Antona & Mazzitelli D'Antona & Mazzitelli (1996) are still systematically too hot by 200 K across the VLM range and could not reproduce the observed lower main sequences of globular clusters.

Recently, Alexander et al (1997), Baraffe et al (1997) computed evolution models based on the equation of state of Saumon et al (1995b) and found a remarkable agreement of their models with the observed main sequence of the cluster NGC6397 all the way down to the detection limit, corresponding to masses of 0.13 M. This success is illustrated in Figure 6, where the models of Baraffe et al (1997) are plotted over the photometry. (Note that the dispersion in the diagram at magnitudes fainter than 14.5 mag is likely due to foreground stars.) The two groups, however, disagree on the metallicity of NGC6397: Alexander et al (1997) use bolometric corrections and synthetic colors of Allard & Hauschildt (1995b) and find [M/H] = 2.0. Baraffe et al (1997) use the more recent, less blanketed (F Allard & PH Hauschildt, in preparation) models both as surface boundary conditions and for color transformations, and they find agreement for [M/H] = 1.5, a value that is more consistent with a history of oxygen and other enrichment in old stellar populations (Ryan et al 1991 and references therein). On the other hand, the halo subdwarfs of Monet et al (1992) ( full circles in Figure 6) show a wider dispersion in metallicity. Baraffe et al (1995), Alexander et al (1997) derived isochrones for the most extreme subdwarfs of the Monet et al (1992) sample and obtained a metallicity of [M/H] = 1.5, while the analysis of Baraffe et al (1997) (shown in Figure 6) led to consistant values of [M/H] = 1.3 to 1.5 for the same subdwarfs. Clearly, these results illustrate the progress brought about by more accurate stellar equations of states, model atmospheres, and synthetic photometry to the understanding of the lower main sequence of halo and globular cluster stars.

These successes increase our confidence that the present Population II stellar models are now sufficiently accurate to derive reliable mass-luminosity relations and the stellar mass functions that rely upon them. The mass function in the stellar halo has been derived from the Dahn et al (1995) luminosity function by Méra et al (1996b, c), Chabrier et al (1996b), using the theoretical mass-luminosity relations drawn from the Baraffe et al (1995, 1997) evolution models. These authors found a halo mass function which is rising all the way down to the hydrogen-burning limit, suggesting a large population of substellar objects in the halo. But to determine exactly the amount of dark mass in the form of metal-poor substellar brown dwarfs, we need to extrapolate the mass function into the substellar domain. Indeed, despite all the advances in cool star models and detection techniques, we still have identified only a handful of halo M subdwarfs and none below the hydrogen-burning limit. A hint of the nature of the missing mass in the halo is nevertheless already provided by the frequency of events reported by the EROS and MACHO microlensing surveys: The average time of recorded events indicates the existence of a rich population of halo objects with masses of at least 0.30.5 M (Aubourg 1995, Alcock et al 1996). Metal-poor brown dwarfs seem therefore eliminated as a strong contender for the missing mass (measured to be 10¹² M, i.e. 10 times the visible mass) in the halo. Rather, the average masses of the microlenses suggest at least two possibilities, either main sequence VLM subdwarf stars or white dwarf stellar remnants. However, although the results of astrometric surveys like 2MASS, DENIS, and more accurate parallaxes for nearby stars from, for example, the USNO, CCD, and HIPPARCOS surveys may give us larger halo samples in the near future, HST pencil surveys and the Dahn et al (1995) luminosity function of the halo seem for now to eliminate the possibility of a large population of VLM stars in the halo (Bahcall et al 1994, Elson et al 1996, Flynn et al 1996, Gould et al 1996, Graff & Freese 1996).

CONCLUSIONS	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONS <<AcknowledgmentsLiterature Cited

Realistic model atmospheres of VLM stars and brown dwarfs are essential if we are ever to fully understand the population of the lower main sequence, the mass-luminosity relation, and the initial mass function and its dependance on the chemical history of the Galaxy. The last few years have brought significant improvements in the models, as well as the first convincing detections of substellar objects that can be used to test the models. This progress on both theoretical and observational fronts has led to several noteworthy advances in our knowledge of the lower main sequence, including the following:

1.	The spectroscopic properties of brown dwarfs and their luminosities as a function of mass and age can now be reliably predicted. We confidently expect that most brown dwarfs within 50 pc of the Sun are within detection range of either existing instruments or facilities planned for the next decade. This bodes well for studies of the low-mass end of the initial mass function for the solar neighborhood.
2.	The mass-luminosity relation for cool field stars of solar metallicity is now reproducible by models, and the underlying physics is well understood (Chabrier et al 1996a). The sharp drop in the relation at masses below 0.1 M due to the onset of electron degeneracy in the interior provides a natural explanation for the corresponding drop in the observed luminosity function as one approaches the hydrogen-burning limit. These models and the results of microlensing observations all point to a rising-disk mass function all the way down to the hydrogen-burning limit and suggest a substantial number of brown dwarfs in the galactic disk (Han & Gould 1996, Méra et al 1996a, c).
3.	It is clear that non-gray model atmospheres must be invoked to handle correctly the evolution and internal structure of M dwarfs, brown dwarfs, and metal-poor VLM stars. The first major victory in attacking these problems has occured not in the field, but in metal-poor globular clusters. The lower main sequences of such clusters can now be fitted by interior models using the latest non-gray surface boundary and color transformations. In light of this success, we can confidently assert that the Monet et al (1992) subdwarfs are low-luminosity members of the galactic halo with metallicities of [M/H] 1.5±0.2 (i.e. [Fe/H] 1.9±0.2) and that, if current stellar luminosity functions for the halo are accurate, such main-sequence subdwarfs cannot make up a significant fraction of the halo missing mass.

The progress outlined above and the good agreement among brown dwarf model spectra generated by various independent model codes is reassuring, but we cannot afford to be complacent at this stage. While the effective temperature scale of low mass stars is now reasonably well determined for T_eff 3500 K, it is still poorly defined for M dwarfs and young brown dwarfs with spectral types later than M6, and it will remain so until more complete opacities become available. These opacities must include better treatments of TiO, H₂O, and CH₄ molecules (including hot bands), grain size distributions, and grain growth time scales appropriate to the high pressures and oxygen-rich conditions found in cool dwarf atmospheres.

While we labor to understand the outer layers of M dwarfs, we must also remember that the interior models that define such sequences suffer their own uncertainties, and that interior and atmospheric properties are intimately coupled in these objects. With fully convective interiors, their radiation fields play the role of an energy valve that regulates both the internal structure and the hydrodynamical (either magnetic or acoustic) heating of their chromospheres. Systematic development of classical atmosphere models (in which molecular opacity calculations and laboratory molecular data are tested) must be tied to (magneto) hydrodynamical studies of chromospheric activity and applied to interior models to truly understand cool dwarfs. The fact that researchers are taking these first steps is an encouraging sign that our field is finally "coming of age" after a long but fruitful adolescence.

Acknowledgments	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgments <<Literature Cited

We thank Drs. Hugh RA Jones and Tom R Geballe for providing UKIRT near-infrared spectra of M dwarfs and Gl 299B and Sandy K Leggett, Mike S Bessell, John M Brett, T Tsuji, MS Marley, Didier Saumon, DC Monet, Conard C Dahn, and Adrienne M Cool for providing data in electronic form. We would also like to express our gratitude to Suzanne Hawley and Peter Ulmschneider for instructive discussions on activity in M dwarf stars and to Francesca D'Antona, Isabelle Baraffe, and Gilles Chabrier for discussions about VLM star evolution and equations of state, as well as for providing their theoretical isochrones in a numerical form. We are also particularly indebted to Jaymie Matthews for generously proofreading the manuscript and to the Cornell Theory Center (CTC) and the San Diego Supercomputer Center (SDSC) for their allocation of computer time, which made possible some of the calculations and conclusions presented in this review.

This work is funded by grants from the National Science Foundation (NSF) (AST-9217946) to Indiana University, NASA LTSA (NAG5-3435) to Wichita State University, NASA LTSA and ATP to the University of Georgia in Athens, and NASA LTSA (NAGW2628), ATP (NAG53068), and NSF (AST94-17057) to the Arizona State University.

Literature Cited	Section:	ChooseTop of pageABSTRACTINTRODUCTIONGENERAL SPECTROSCOPIC PRO...A BRIEF HISTORY OF THE MO...MOLECULAR OPACITIESGRAINSLINE ABSORPTIONCONVECTIONSTELLAR ACTIVITYTHE Teff SCALE OF M DWARF...THE DETECTABILITY OF BROW...THE METAL-DEFICIENT VLM S...CONCLUSIONSAcknowledgmentsLiterature Cited <<

1.	Alcock C, ­ Allsman RA, ­ Axelrod TS, ­ Bennett DP, ­ Cook KH,­ et al. 1996. Ap. J. 461:84103   [CrossRef] [ISI] [ADS]
2.	Alexander DR. ­ 1975. Ap. J. Suppl. 29:363   [CrossRef] [ADS]
3.	Alexander DR, ­ Augason GC, ­ Johnson HR. ­ 1989. Ap. J. 345:101421   [CrossRef] [ISI] [ADS]
4.	Alexander DR, ­ Brocato E, ­ Cassisi S, ­ Castellani V, ­ Ciacio F, ­ DeglíInnocenti S. ­ 1997. Astron. Astrophys. 317:90   [ADS]
5.	Alexander DR, ­ Ferguson JW. ­ 1994a. In Molecules in the Stellar Environment, ed. UG Jørgensen, Lect. Notes Phys., pp. 14962. Berlin/Heidelberg: Springer-Verlag
6.	Alexander DR, ­ Ferguson JW. ­ 1994b. Ap. J. 437:87991   [CrossRef] [ISI] [ADS]
7.	Alexander DR, ­ Rypma RL, ­ Johnson HR. ­ 1983. Ap. J. 272:77380   [CrossRef] [ISI] [ADS]
8.	Allard F. ­ 1990. Model atmospheres for M dwarfs. PhD thesis. RuprechtKarls University, Heidelberg, Germany
9.	Allard F. ­ 1994. In Molecular Opacities in the Stellar Environment, ed. P Thejll, U Jørgensen, IAU Colloq. 146, pp. 15. Copenhagen: Niels Bohr Inst.; Nordita
10.	Allard F, ­ Hauschildt PH. ­ 1995a. See Tinney 1995, pp. 3244
11.	Allard F, ­ Hauschildt PH. ­ 1995b. Ap. J. 445:43350   [CrossRef] [ISI] [ADS]
12.	Allard F, ­ Hauschildt PH, ­ Baraffe I, ­ Chabrier G. ­ 1996. Ap. J. Lett. 465:L12327   [CrossRef] [ADS]
13.	Allard F, ­ Hauschildt PH, ­ Miller S, ­ Tennyson J. ­ 1994. Ap. J. Lett. 426:L39L41   [CrossRef] [ADS]
14.	Aubourg E. ­ 1995. Astron. Astrophys. 301:15   [ADS]
15.	Auman JJ. ­ 1967. Ap. J. Suppl. 14:171   [CrossRef] [ADS]
16.	Bahcall JN, ­ Flynn C, ­ Gould A, ­ Kirkhakos S. ­ 1994. Ap. J. 435:L51L54   [CrossRef] [ISI] [ADS]
17.	Baines KH, ­ West RA, ­ Giver LP, ­ Moreno F. ­ 1993. J. Geophys. Res. 98:551729   [ISI] [ADS]
18.	Balfour WJ, ­ Klynning L. ­ 1994. Ap. J. 424:104953   [CrossRef] [ISI] [ADS]
19.	Baraffe I, ­ Chabrier G. ­ 1996. Ap. J. 461:L51L54   [CrossRef] [ISI] [ADS]
20.	Baraffe I, ­ Chabrier G, ­ Allard F, ­ Hauschildt PH. ­ 1995. Ap. J. Lett. 446:L35L38   [CrossRef] [ADS]
21.	Baraffe I, ­ Chabrier G, ­ Allard F, ­ Hauschildt PH. ­ 1997. Ap. J. In press
22.	Basri G, ­ Marcy GW. ­ 1994. Ap. J. 431:84449   [CrossRef] [ISI] [ADS]
23.	Basri G, ­ Marcy GW. ­ 1995. Astron. J. 109:76273   [CrossRef] [ISI] [ADS]
24.	Basri G, ­ Marcy GW, ­ Graham JR. ­ 1996. Ap. J. 458:6009   [CrossRef] [ISI] [ADS]
25.	Bauschlicher CWJ, ­ Langhoff SR. ­ 1986. J. Chem. Phys. 85:5936   [CrossRef] [ISI] [ADS]
26.	Beck HKB, ­ Gail H-P, ­ Henkel R, ­ Sedlmayr E. ­ 1992. Astron. Astrophys. 265:62642   [ADS]
27.	Beck HKB, ­ Hauschildt PH, ­ Gail H-P, ­ Sedlmayr E. ­ 1995. Astron. Astrophys. 294:195205   [ADS]
28.	Becklin EE, ­ Zuckerman B. ­ 1988. Nature 336:65658   [ISI] [ADS]
29.	Bergeron P, ­ Fontaine G, ­ Brassard P, ­ Lamontagne R, ­ Wesemael F,­ et al. 1993. Ap. J. 106:198799   [CrossRef] [ADS]
30.	Bergeron P, ­ McGraw JT. ­ 1990. Ap. J. Lett. 352:L45L48   [CrossRef] [ADS]
31.	Bernath PF, ­ Black JH, ­ Brault JW. ­ 1995. Preprint.
32.	Bernath PF, ­ Brazier CR. ­ 1985. Ap. J. 288:37376   [CrossRef] [ISI] [ADS]
33.	Berriman G, ­ Reid IN, ­ Leggett SK. ­ 1992. Ap. J. Lett. 392:L31L33   [CrossRef] [ADS]
34.	Bessell MS. ­ 1982. Publ. Astron. Soc. Austr. 4:41719   [ADS]
35.	Bessell MS. ­ 1991. Astron. J. 101:662   [CrossRef] [ISI] [ADS]
36.	Bessell MS. ­ 1995. See Tinney 1995, pp. 12331
37.	Bessell MS, ­ Stringfellow GS. ­ 1993. Astron. Astrophys. Rev. 31:43371   [Abstract]
38.	Boeshaar PC. ­ 1976. The spectral classification of M dwarf stars. PhD thesis. Ohio State Univ., Columbus, OH.
39.	Bøhm-Vitense E. ­ 1958. Zh. Astrophys. 46:108   [ADS]
40.	Bohren CF, ­ Huffman DR. ­ 1983. Absorption and Scattering of Light by Small Particles. New York: Wiley & Sons. 541 pp.
41.	Borysow A, ­ Frommhold L. ­ 1989. Ap. J. 341:54955   [CrossRef] [ISI] [ADS]
42.	Borysow A, ­ Frommhold L. ­ 1990. Ap. J. Lett. 348:L41L43   [CrossRef] [ADS]
43.	Borysow A, ­ Frommhold L, ­ Moraldi M. ­ 1989. Ap. J. 336:495503   [CrossRef] [ISI] [ADS]
44.	Brett JM. ­ 1989. MNRAS 241:24757   [ISI] [ADS]
45.	Brett JM. ­ 1990. Astron. Astrophys. 231:44052   [ADS]
46.	Brett JM. ­ 1995a. Astron. Astrophys. 295:73654   [ADS]
47.	Brett JM. ­ 1995b. Astron. Astrophys. Suppl. 109:26364   [ADS]
48.	Brett JM, ­ Plez B. ­ 1993. Publ. Astron. Soc. Austr. 10:25053   [ADS]
49.	Bryja C, ­ Humphreys RM, ­ Jones TJ. ­ 1994. Astron. J. 107:24653   [CrossRef] [ISI] [ADS]
50.	Buchholz B. ­ 1995. Acoustically heated chromospheres of late type stars. PhD thesis. Univ. Heidelberg. 135 pp.
51.	Burrows A, ­ Hubbard WB, ­ Lunine JI. ­ 1989. Ap. J. 345:93958   [CrossRef] [ISI] [ADS]
52.	Burrows A, ­ Hubbard WB, ­ Saumon W, ­ Lunine JI. ­ 1993. Ap. J. 406:15871   [CrossRef] [ISI] [ADS]
53.	Burrows A, ­ Liebert J. ­ 1993. Mod. Phys. Rev. 65:301   [CrossRef] [ISI] [ADS]
54.	Butler RP, ­ Marcy GW. ­ 1996. Ap. J. Lett. 464:L15356   [CrossRef] [ADS]
55.	Butler RP, ­ Marcy GW, ­ Williams E, ­ Hauser H, ­ Shirts P. ­ 1997. Ap. J. Lett. 474:11518   [CrossRef] [ADS]
56.	Cameron AGW, ­ Pine MR. ­ 1973. Icarus 18:377   [ISI] [ADS]
57.	Canuto VM, ­ Mazzitelli I. ­ 1991. Ap. J. 370:295311   [CrossRef] [ISI] [ADS]
58.	Canuto VM, ­ Mazzitelli I. ­ 1992. Ap. J. 389:72430   [CrossRef] [ISI] [ADS]
59.	Chabrier G, ­ Baraffe I. ­ 1995. Ap. J. Lett. 451:L29L32   [ADS]
60.	Chabrier G, ­ Baraffe I. ­ 1997. Astron. Astrophys. In press
61.	Chabrier G, ­ Baraffe I, ­ Plez B. ­ 1996a. Ap. J. Lett. 459:L91L94   [ADS]
62.	Chabrier G, ­ Segretain L, ­ Méra D. ­ 1996b. Ap. J. 468:L21L24   [CrossRef] [ISI] [ADS]
63.	Chan KL, ­ Nordlun A, ­ Steffen M, ­ Stein RF. ­ 1991. Solar Interior and Atmosphere, pp. 22374. Tucson, AZ: Univ. Ariz. Press
64.	Cherchneff I, ­ Barker JR. ­ 1992. Ap. J. 394:70316   [CrossRef] [ISI] [ADS]
65.	Collins JG, ­ Faÿ TDJ. ­ 1974. J. Quant. Spectrosc. Radiat. Transfer 14:1259   [CrossRef] [ISI]
66.	Comeron F, ­ Rieke GH, ­ Burrows A, ­ Reike MJ. ­ 1993. Ap. J. 416:185203   [CrossRef] [ISI] [ADS]
67.	Cool AM, ­ Piotto G, ­ King IR. ­ 1996. Ap. J. 468:65562   [CrossRef] [ISI] [ADS]
68.	Copenland H, ­ Jensen JO, ­ Jørgensen HE. ­ 1970. Astron. Astrophys. 5:12   [ADS]
69.	Cram LE, ­ Mullan DJ. ­ 1985. Ap. J. 294:62633   [CrossRef] [ISI] [ADS]
70.	Dahn CC, ­ Liebert J, ­ Harris HC, ­ Guetter HH. ­ 1995. See Tinney 1995, pp. 23948
71.	D'Antona F. ­ 1987. Ap. J. 320:65362   [CrossRef]
72.	D'Antona F. ­ 1990. In Physical Processes in Fragmentation of Star Formation, ed. RC Dolcetta, C Choisi, A Di Fazio, pp. 36779. Dordrecht: Kluwer
73.	D'Antona F. ­ 1995. See Tinney 1995, pp. 1323
74.	D'Antona F, ­ Mazzitelli I. ­ 1985. Ap. J. 296:50213   [CrossRef]
75.	D'Antona F, ­ Mazzitelli I. ­ 1994. Ap. J. Suppl. 90:467500   [CrossRef]
76.	D'Antona F, ­ Mazzitelli I. ­ 1996. Ap. J. 456:32936   [CrossRef]
77.	Davidge TJ, ­ Boeshaar PC. ­ 1993. Ap. J. Lett. 403:L47L50   [CrossRef] [ADS]
78.	Davis SP. ­ 1994. In Molecules in the Stellar Environment, ed. UG Jørgensen, Lect. Notes Phys., pp. 397411. Berlin/Heidelberg: Springer-Verlag
79.	Davis SP, ­ Littleton JE, ­ Phillips JG. ­ 1986. Ap. J. 309:44954   [CrossRef] [ISI] [ADS]
80.	De Jager C, ­ Neven L. ­ 1957. Liège R. Soc. Mem. 18:257
81.	Deutsch RW. ­ 1994. PASP106:113437
82.	Dobrijevic M, ­ Goutoulli L, ­ Toublanc D, ­ Parisot JP, ­ Brillet J. ­ 1992. In Titan, ESA Symp. Ser., pp. 32932, II Univ. Bordeaux, France
83.	Dominik C, ­ Sedlmayr E, ­ Gail H-P. ­ 1989. Astron. Astrophys. 223:22736   [ADS]
84.	Dorman B, ­ Nelson LA, ­ Chau WJ. ­ 1989. Ap. J. 342:1003818   [CrossRef] [ISI] [ADS]
85.	Doverstal M, ­ Weijnitz P. ­ 1992. Mol. Phys. 75:1357   [ISI]
86.	Elson RAW, ­ Santiago BX, ­ Gilmore GF. ­ 1996. New Astron. 1:1   [CrossRef] [ISI] [ADS]
87.	Farmer CB, ­ Norton RH. ­ 1989. A High-Resolution Atlas of the Infrared Spectrum of the Sun and the Earth Atmosphere from Space, Vol. 1: The Sun, NASA Ref. Publ. 1224. Washington, DC: NASA
88.	Fegley BJ, ­ Lodders K. ­ 1996. Ap. J. Lett. 472:L37L39   [ADS]
89.	Fleming TA. ­ 1988. Ap. J. 331:95873   [CrossRef] [ISI] [ADS]
90.	Fleming TA, ­ Schmitt JHMM, ­ Giampapa MS. ­ 1995. Ap. J. 450:40110   [CrossRef] [ISI] [ADS]
91.	Flynn C, ­ Gould A, ­ Bahcall J. ­ 1996. Ap. J. Lett. 466:L55L58   [CrossRef] [ADS]
92.	Gail H-P, ­ Sedlmayr E. ­ 1988. Astron. Astrophys. 206:15368   [ADS]
93.	Geballe TR, ­ Kulkarni SR, ­ Woodward CE, ­ Sloan GC. ­ 1996. Ap. J. Lett. 467:L1014   [CrossRef] [ADS]
94.	Giampapa MS, ­ Liebert J. ­ 1986. Ap. J. 305:78494   [CrossRef] [ISI] [ADS]
95.	Giampapa MS, ­ Worden SP, ­ Linsky JL. ­ 1982. Ap. J. 258:74060   [CrossRef] [ISI] [ADS]
96.	Gliese W, ­ Jahreiss H. ­ 1991. Astron. Rechen-Inst. Heidelberg Mitt. Ser. A 224:16164
97.	Goody RM, ­ Yung YL. ­ 1989. Atmospheric Radiation. London/New York: Oxford Univ. Press. 2nd ed.
98.	Gould A, ­ Bahcall JN, ­ Flynn C. ­ 1996. Ap. J. 465:75968   [CrossRef] [ISI] [ADS]
99.	Graff DS, ­ Freese K. ­ 1996. Ap. J. Lett. 467:L65L68   [CrossRef] [ADS]
100.	Graham JR, ­ Matthews K, ­ Greenstein JL, ­ Neugebauer G, ­ Tinney CG, ­ Persson SE. ­ 1992. Astron. J. 104:201621   [CrossRef] [ISI] [ADS]
101.	Gray DF. ­ 1984. Ap. J. 277:64047   [CrossRef] [ISI] [ADS]
102.	Green PJ, ­ Margon B. ­ 1994. Ap. J. 423:72332   [CrossRef] [ISI] [ADS]
103.	Green PJ, ­ Margon B, ­ MacConnell DJ. ­ 1991. Ap. J. Lett. 380:L31L34   [CrossRef] [ADS]
104.	Greenstein JL. ­ 1989. Pac. Astron. Soc. Publ. 101:787810   [CrossRef] [ISI] [ADS]
105.	Grossman SA. ­ 1996. MNRAS 279:30536   [ISI] [ADS]
106.	Guillot T, ­ Gautier D, ­ Chabrier G, ­ Mosser B. ­ 1994. Icarus 112:33753   [CrossRef] [ISI] [ADS]
107.	Gurvich LV. ­ 19781981. Thermodinamicheskie Svoistva Individuak'nikh Vershev, Vol. 13. Moscow: Sovit Acad. Sci.
108.	Gustafsson B, ­ Jørgensen UG. ­ 1994. Astron. Astrophys. Rev. 6:1965   [ISI] [ADS]
109.	Habets GMHJ, ­ Heintze JRW. ­ 1981. Astron. Astrophys. Suppl. 46:193237   [ADS]
110.	Hambly NC, ­ Hawkins MRS, ­ Jameson RF. ­ 1993. Astron. Astrophys. Suppl. 100:60740   [ADS]
111.	Han C, ­ Gould A. ­ 1996. Ap. J. 467:54045   [CrossRef] [ISI] [ADS]
112.	Hauschildt PH, ­ Wehrse R, ­ Starrfield S, ­ Shaviv G. ­ 1992. Ap. J. 393:30728   [CrossRef] [ISI] [ADS]
113.	Hawley SL, ­ Fisher GH. ­ 1994. Ap. J. 426:387403   [CrossRef] [ISI] [ADS]
114.	Hawley SL, ­ Reid IN, ­ Gizis JE. ­ 1997. Astron. J. In press
115.	Heber U, ­ Bade N, ­ Jordan S, ­ Voges W. ­ 1993. Astron. Astrophys. 267:L31L34   [ADS]
116.	Hedgecock LM, ­ Naulin C, ­ Costes M. ­ 1995. Astron. Astrophys. 304:66777   [ADS]
117.	Henry TJ. ­ 1996. Sky Telescope 91:24   [ADS]
118.	Henry TJ, ­ Kirkpatrick JD, ­ Ianna PA, ­ Jahreiss H. ­ 1995. Bull. Am. Astron. Soc. 187:7022   [ADS]
119.	Henry TJ, ­ Kirkpatrick JD, ­ Simons DA. ­ 1994. Astron. J. 108:143744   [CrossRef] [ISI] [ADS]
120.	Henry TJ, ­ McCarthy DW. ­ 1993. Astron. J. 106:77389   [CrossRef] [ISI] [ADS]
121.	Houdebine ER, ­ Panagi PM. ­ 1990. Astron. Astrophys. 231:45965   [ADS]
122.	Husson N, ­ Bonnet B, ­ Scott NA, ­ Chedin A. ­ 1992. J. Quant. Spectrosc. Radiat. Transfer 48:509   [CrossRef] [ISI] [ADS]
123.	Irwin AW. ­ 1987. Astron. Astrophys. 182:34858   [ADS]
124.	Irwin AW. ­ 1988. Astron. Astrophys. Suppl. 74:14560   [ADS]
125.	Isbell D, ­ Morse D. ­ 1996. NASA press release 96-10
126.	Jensen P. ­ 1989. J. Mol. Spectrosc. 133:438   [ISI]
127.	Johns-Krull C, ­ Valenti J. ­ 1996. Ap. J. Lett. 459:L95L98   [ADS]
128.	Jones HRA, ­ Longmore AJ, ­ Allard F, ­ Hauschildt PH. ­ 1996. MNRAS 280:7794   [ISI] [ADS]
129.	Jones HRA, ­ Longmore AJ, ­ Allard F, ­ Hauschildt PH, ­ Miller S, ­ Tennyson J. ­ 1995. MNRAS 277:76776   [ISI] [ADS]
130.	Jones HRA, ­ Longmore AJ, ­ Jameson RF, ­ Mountain CM. ­ 1994. MNRAS 267:41323   [ISI] [ADS]
131.	Jørgensen UG. ­ 1992. Rev. Mex. Astron. Astrofis. 23:4962   [ISI] [ADS]
132.	Jørgensen UG. ­ 1994. Astron. Astrophys. 284:17986   [ADS]
133.	Jørgensen UG, ­ Jensen P, ­ Sorensen GO. ­ 1994. In Molecular Opacities in the Stellar Environment, ed. P Thejll, U Jørgensen, IAU Colloq. 146, pp. 5154. Copenhagen: Bohr Inst., Nordita
134.	Joy AH, ­ Abt HA. ­ 1974. Ap. J. Suppl. 28:118   [CrossRef] [ADS]
135.	Keane TC, ­ Yuan F, ­ Ferris JP. ­ 1996. Icarus 122:205   [CrossRef] [ISI] [ADS]
136.	Keenan PC, ­ Schroeder LW. ­ 1952. Ap. J. 115:82   [CrossRef] [ISI] [ADS]
137.	Kim YC, ­ Fox PA, ­ Demarque P, ­ Sofia S. ­ 1996. Ap. J. 461:499506   [CrossRef] [ISI] [ADS]
138.	Kippenhan R. ­ 1962. Proc. XXVIII Course, Tech. Rep., Int. School Enrico Fermi
139.	Kipper T, ­ Jørgensen UG, ­ Klochkova VG, ­ Panchuk VE. ­ 1996. Astron. Astrophys. 306:489   [ADS]
140.	Kirkpatrick JD, ­ Beichman CA. ­ 1995. Bull. Am. Astron. Soc. 187:7512   [ADS]
141.	Kirkpatrick JD, ­ Henry TJ, ­ Liebert J. ­ 1993a. Ap. J. 406:7017   [CrossRef] [ISI] [ADS]
142.	Kirkpatrick JD, ­ Henry TJ, ­ Simons DA. ­ 1995. Astron. J. 109:797807   [CrossRef] [ISI] [ADS]
143.	Kirkpatrick JD, ­ Kelly DM, ­ Rieke GH, ­ Liebert J, ­ Allard F, ­ Wehrse R. ­ 1993b. Ap. J. 402:64354   [CrossRef] [ISI] [ADS]
144.	Kirkpatrick JD, ­ McCarthy DWJ. ­ 1994. Astron. J. 107:33349   [CrossRef] [ISI] [ADS]
145.	Kirkpatrick JD, ­ McGraw JT, ­ Hess TR, ­ Liebert J, ­ McCarthy DW J. ­ 1994. Ap. J. Suppl. 94:74988   [CrossRef] [ADS]
146.	Kui R. ­ 1991. Model atmospheres for M-dwarfs. PhD. thesis. Natl. Univ. Aust.
147.	Kunde V, ­ Hanel R, ­ Maguire W, ­ Gautier D, ­ Baluteau JP,­ et al. 1982. Ap. J. 263:44367   [CrossRef] [ISI] [ADS]
148.	Kurucz RL. ­ 1970. Smithsonian Astrophys. Obs. Spec. Rep. 309. Washington, DC: Smithsonian Astrophys. Obs.
149.	Kurucz RL. ­ 1992a. Rev. Mex. Astron. Astrofis. 23:45   [ISI] [ADS]
150.	Kurucz RL. ­ 1992b. Rev. Mex. Astron. Astrofis. 23:187   [ISI] [ADS]
151.	Kurucz RL. ­ 1993. Molecular data for opacity calculations, Kurucz CD-ROM No. 15
152.	Kurucz RL. ­ 1994. Atomic data for opacity calculations, Kurucz CD-ROM No. 1
153.	Kusch HJ. ­ 1958. Z. Astrophys. 45:1   [ADS]
154.	Kuznetsova LA, ­ Pazyk EA, ­ Stolyarov AV. ­ 1993. Russ. J. Phys. Chem. 67:2046
155.	Lacy CH. ­ 1977. Ap. J. 218:444   [CrossRef] [ISI] [ADS]
156.	Laird JB, ­ Carney BW, ­ Latham DW. ­ 1988. Astron. J. 95:1843   [CrossRef] [ISI] [ADS]
157.	Langhoff SR, ­ Bauschlicher CW. ­ 1990. J. Mol. Spectrosc. 141:243   [ISI]
158.	Langhoff SR, ­ Bauschlicher CWJr . ­ 1991. Ap. J. 375:843   [CrossRef] [ISI] [ADS]
159.	Langhoff SR, ­ Bauschlicher CWJr . ­ 1994. In Molecules in the Stellar Environment, ed. UG Jørgensen, Lect. Notes Phys., pp. 31025. Berlin/Heidelberg: Springer-Verlag
160.	Larson LE, ­ Mickelson ME. ­ 1997. Preprint
161.	Latham DW, ­ Mazeh T, ­ Stefanik RP, ­ Davis RJ, ­ Carney BW,­ et al. 1992. Astron. J. 104:77495   [CrossRef] [ISI] [ADS]
162.	Lazarev VV, ­ Pnomarev YN. ­ 1992. Optics Lett. 17:1283   [ISI] [ADS]
163.	Leggett SK. ­ 1992. Ap. J. Suppl. 82:35194   [CrossRef] [ADS]
164.	Leggett SK, ­ Allard F, ­ Berriman G, ­ Dahn CC, ­ Hauschildt PH. ­ 1996. Ap. J. Suppl. 104:117   [CrossRef] [ADS]
165.	Leggett SK, ­ Harris HC, ­ Dahn CC. ­ 1994. Astron. J. 108:944   [CrossRef] [ISI] [ADS]
166.	Leggett SK, ­ Hawkins MRS. ­ 1989. MNRAS 238:145   [ISI] [ADS]
167.	Leinert C, ­ Weitzel N, ­ Richichi A, ­ Eckart A, ­ Taccono-Garman LE. ­ 1994. Astron. Astrophys. 291:L47   [ADS]
168.	Liebert J, ­ Kirkpatrick JD, ­ Beichman C, ­ Reid IN, ­ Monet DC, ­ Dahn CC. ­ 1995. Bull. Am. Astron. Soc. 187:7502   [ADS]
169.	Liebert J, ­ Probst RG. ­ 1987. Astron. Astrophys. Rev. 25:473   [Abstract]
170.	Liebert J, ­ Schmidt G, ­ Lesser M, ­ Stephanian JA, ­ Lipovetsky VA, ­ Chaffe FH, ­ Foltz CB, ­ Bergeron P. ­ 1994. Ap. J. 421:733   [CrossRef] [ISI] [ADS]
171.	Linsky JL, ­ Wood BE, ­ Brown A, ­ Giampapa MS, ­ Ambruster C. ­ 1995. Ap. J. 455:670   [CrossRef] [ISI] [ADS]
172.	Ludwig CB. ­ 1971. Appl. Opt. 10(5):1057
173.	Maggazzú A, ­ Martín EL, ­ Rebolo R. ­ 1993. Ap. J. 404:L17   [CrossRef] [ADS]
174.	Magni G, ­ Mazzitelli I. ­ 1979. Astron. Astrophys. 72:134   [ADS]
175.	Marcy G, ­ Basri G, ­ Graham JR. ­ 1994. Ap. J. Lett. 428:L57   [CrossRef] [ADS]
176.	Marcy GW, ­ Butler RP. ­ 1996a. Ap. J. Lett. 464:L147   [CrossRef] [ADS]
177.	Marcy GW, ­ Butler RP. ­ 1996b. Ap. J. Lett. 464:L151   [ADS]
178.	Marcy GW, ­ Butler RP, ­ Williams E, ­ Bildsten L, ­ Graham J. ­ 1997. Ap. J. In press
179.	Marcy GW, ­ Chen GH. ­ 1992. Ap. J. 390:550   [CrossRef] [ISI] [ADS]
180.	Marilli E, ­ Catalano S, ­ Trigilio C. ­ 1986. Astron. Astrophys. 167:297   [ADS]
181.	Marley MS, ­ Saumon D, ­ Guillot T, ­ Freedman R, ­ Hubbard WB,­ et al. 1996. Science 272:1919   [Medline] [ISI] [ADS]
182.	Martín EL, ­ Rebolo R, ­ Magazzú A. ­ 1994. Ap. J. 436:262   [CrossRef] [ISI] [ADS]
183.	Martín EL, ­ Rebolo R, ­ Zapatero Osorio MR. ­ 1995. See Tinney 1995, pp. 25356
184.	Martín EL, ­ Rebolo R, ­ Zapatero Osorio MR. ­ 1996. Ap. J. 469:706   [CrossRef] [ISI] [ADS]
185.	Mathioudakis M, ­ Doyle JG. ­ 1992. Astron. Astrophys. 262:523   [ADS]
186.	Mathys G, ­ Solanki SK. ­ 1989. Astron. Astrophys. 208:189   [ADS]
187.	Matthews K, ­ Nakajima SR, ­ Oppenheiner BR. ­ 1995. IAU Circ. 6280:1   [ADS]
188.	Mauas PJD, ­ Falchi A. ­ 1996. Astron. Astrophys. 310:245   [ADS]
189.	Mayor M, ­ Queloz D. ­ 1995. Nature 378:355   [ISI] [ADS]
190.	Mazeh T, ­ Latham DW, ­ Stefanik RP. ­ 1996. Ap. J. 466:415   [CrossRef] [ISI] [ADS]
191.	Méra D, ­ Chabrier G, ­ Baraffe I. ­ 1996a. Ap. J. 459:L87   [ISI] [ADS]
192.	Méra D, ­ Chabrier G, ­ Schaeffer R. ­ 1996b. Europhys. Lett. 33:327   [ISI]
193.	Méra D, ­ Chabrier G, ­ Schaeffer R. ­ 1996c. Astron. Astrophys. In press
194.	Merer AJ, ­ Huang G, ­ Cheung AS-C, ­ Taylor AW. ­ 1987. J. Mol. Spectrosc. 125:465   [ISI]
195.	Metcalfe TS, ­ Mathieu RD, ­ Latham DW, ­ Torres G. ­ 1996. Ap. J. 456:356   [CrossRef] [ISI] [ADS]
196.	Michelis CHP. ­ 1976. A study of van der Waals broadening for lines of astrophysical interest. PhD thesis. Texas Univ., Austin
197.	Mickelson ME, ­ Larson LE. ­ 1992. Bull. Am. Astron. Soc. 24:990   [ADS]
198.	Mihalas D. ­ 1978. Stellar Atmospheres. San Francisco: Freeman. 2nd ed.
199.	Miller S, ­ Tennyson J, ­ Jones HRA, ­ Longmore AJ. ­ 1994. In Molecules in the Stellar Environment, ed. UG Jørgensen, Lect. Notes Phys., pp. 296309. Berlin/Heidelberg: Springer-Verlag
200.	Monet DG, ­ Dahn CC, ­ Vrba FJ, ­ Harris HC, ­ Pier JR,­ et al. 1992. Astron. J. 103:638   [CrossRef] [ISI] [ADS]
201.	Morris S, ­ Wyller A. ­ 1967. Ap. J. 150:877   [CrossRef] [ISI] [ADS]
202.	Mould JR. ­ 1975. Astron. Astrophys. 38:283   [ADS]
203.	Mould JR. ­ 1976. Ap. J. 210:402   [CrossRef] [ISI] [ADS]
204.	Mould JR, ­ Wyckoff S. ­ 1978. MNRAS 182:63   [ISI] [ADS]
205.	Muchmore D. ­ 1987. Ap. J. 278:769   [CrossRef] [ADS]
206.	Mullan DJ, ­ Cheng QQ. ­ 1993. Ap. J. 412:312   [CrossRef] [ISI] [ADS]
207.	Mullan DJ, ­ Cheng QQ. ­ 1994. Ap. J. 420:392   [CrossRef] [ISI] [ADS]
208.	Mullan DJ, ­ Dermot J. ­ 1987. In NASA Wash. M-Type Stars, pp. 45579
209.	Mullan DJ, ­ Fleming TA. ­ 1996. Ap. J. 464:890   [CrossRef] [ISI] [ADS]
210.	Nakajima T, ­ Oppenheimer BR, ­ Kulkarni SR, ­ Golimowski DA, ­ Matthews K, ­ Durrance ST. ­ 1995. Nature 378:463   [ISI] [ADS]
211.	Neale L, ­ Tennyson J. ­ 1995. Ap. J. Lett. 454:L169   [ADS]
212.	Nelson LA, ­ Rappaport S, ­ Chiang E. ­ 1993. Ap. J. 413:364   [CrossRef] [ISI] [ADS]
213.	Noyes RW, ­ Hartmann LW, ­ Balinunas SL, ­ Duncan DK, ­ Vaughan AH. ­ 1984. Ap. J. 279:763   [CrossRef] [ISI] [ADS]
214.	Oppenheimer BR, ­ Kulkarni SR, ­ Nakajima T, ­ Matthews K. ­ 1995. Science 270:1478   [Medline] [ISI] [ADS]
215.	Paresce F, ­ De Marchi G, ­ Romaniello M. ­ 1995. Ap. J. 468:655
216.	Partridge H, ­ Schwenke DW. ­ 1997. J. Chem. Phys. In press
217.	Pavlenko YV, ­ Rebolo R, ­ Martín EL, ­ Garcia-Lopez RJ. ­ 1995. Astron. Astrophys. 303:807   [ADS]
218.	Peterson BR. ­ 1980. Astron. Astrophys. 82:53   [ADS]
219.	Peterson BR. ­ 1989. Sol. Phys. 121:299   [ADS]
220.	Peytremann E. ­ 1974. Astron. Astrophys. 33:203   [ADS]
221.	Phillips JG, ­ Davis SP. ­ 1993. Ap. J. 409:860   [CrossRef] [ISI] [ADS]
222.	Phillips JG, ­ Davis SP, ­ Lindgren B, ­ Balfour WJ. ­ 1987. Ap. J. Suppl. 65:721   [CrossRef] [ADS]
223.	Piskunov N, ­ Valenti J, ­ Johns-Krull C. ­ 1996. Bull. Am. Astron. Soc. 188:4407
224.	Plez B, ­ Brett JM, ­ Nordlund A. ­ 1992. Astron. Astrophys. 256:551   [ADS]
225.	Pollack JB, ­ Hollenbach D, ­ Beckwith S, ­ Simonelli DP, ­ Roush T, ­ Fong W. ­ 1994. Ap. J. 421:615   [CrossRef] [ISI] [ADS]
226.	Pollack JB, ­ McKay CP, ­ Christofferson BM. ­ 1985. Icarus 64:471   [CrossRef] [ISI] [ADS]
227.	Rebolo R, ­ Martín EL, ­ Basri G, ­ Marcy GW, ­ Zapatero Osorio MR. ­ 1996. Ap. J. 469:L53   [CrossRef] [ISI] [ADS]
228.	Rebolo R, ­ Martín EL, ­ Maggazzú A. ­ 1992. Ap. J. 389:L83   [CrossRef] [ISI] [ADS]
229.	Rebolo R, ­ Zapatero Osorio MR, ­ Martín EL. ­ 1995. Nature 377:129   [ISI] [ADS]
230.	Reid IN. ­ 1994. Astrophys. Space Sci. 217:57   [ISI] [ADS]
231.	Reid IN, ­ Gilmore RF. ­ 1984. MNRAS 206:19   [ISI] [ADS]
232.	Reid IN, ­ Hawley SL, ­ Gizis JE. ­ 1995a. Astron. J. 110:1838   [CrossRef] [ISI] [ADS]
233.	Reid IN, ­ Hawley SL, ­ Mateo M. ­ 1995b. MNRAS 272:828   [ISI] [ADS]
234.	Reid N. ­ 1993. MNRAS 265:785   [ISI] [ADS]
235.	Renzini A, ­ Bragaglia A, ­ Ferraro FR, ­ Gilmozzi R, ­ Ortolani S,­ et al. 1996. Ap. J. 465:23   [CrossRef] [ISI] [ADS]
236.	Richer HB, ­ Fahlman GG, ­ lbata RA, ­ Stetson PB, ­ Bell RA,­ et al. 1995. Ap. J. 451:17   [ADS]
237.	Robinson RD. ­ 1980. Ap. J. 239:961   [CrossRef] [ISI] [ADS]
238.	Rosner R, ­ Golub L, ­ Vaiana G. ­ 1985. Astron. Astrophys. Rev. 23:413   [Abstract]
239.	Rossi SCF, ­ Marciel WJ, ­ Benevides-Soares P. ­ 1985. Astron. Astrophys. 148:93   [ADS]
240.	Rossow WB. ­ 1978. Icarus 36:1   [CrossRef] [ISI] [ADS]
241.	Rothman LS, ­ Gamache RR, ­ Tipping RH, ­ Rinsland CP, ­ Smith MAH,­ et al. 1992. J. Quant. Spectrosc. Radiat. Transfer 48:469   [CrossRef] [ISI] [ADS]
242.	Rucinski SM. ­ 1978. Acta Astron. 28:167   [ADS]
243.	Russell HM. ­ 1934. Ap. J. 79:317   [CrossRef] [ADS]
244.	Rutten RGM. ­ 1986. Astron. Astrophys. 159:291   [ADS]
245.	Rutten RGM, ­ Zwaan C, ­ Schrijver CJ, ­ Duncan DK, ­ Mewe R. ­ 1989. Astron. Astrophys. 219:239   [ADS]
246.	Ryan SG, ­ Norris JE, ­ Bessell MS. ­ 1991. Astron. J. 102:303   [CrossRef] [ISI] [ADS]
247.	Saar SH. ­ 1988. Ap. J. 324:441   [CrossRef] [ISI] [ADS]
248.	Saar SH. ­ 1994. In Infrared Solar Physics, ed. DM Rabin et al, IAU Colloq. 154, p. 493. Dordrecht: Kluwer
249.	Saumon D, ­ Bergeron P, ­ Lunine JI, ­ Hubbard WB, ­ Burrows A. ­ 1994. Ap. J. 424:333   [CrossRef] [ISI] [ADS]
250.	Saumon D, ­ Burrows A, ­ Hubbard WB. ­ 1995a. See Tinney 1995, pp. 312
251.	Saumon D, ­ Chabrier G, ­ Van Horn HM. ­ 1995b. Ap. J. Suppl. 99:713   [CrossRef] [ISI] [ADS]
252.	Saumon D, ­ Hubbard WB, ­ Burrows A, ­ Guillot T, ­ Lunine JI, ­ Chabrier G. ­ 1996. Ap. J. 460:993   [CrossRef] [ISI] [ADS]
253.	Sauval AJ, ­ Tatum JB. ­ 1984. Ap. J. Suppl. 56:193   [CrossRef] [ADS]
254.	Schryber HS, ­ Miller S, ­ Tennyson J. ­ 1995. J. Quant. Spectrosc. Radiat. Transfer 53:373   [CrossRef] [ISI]
255.	Schweitzer A, ­ Hauschildt PH, ­ Allard F, ­ Basri G. ­ 1996. MNRAS 283:82129   [ISI] [ADS]
256.	Seab GC, ­ Snow TP. ­ 1989. Ap. J. 347:479   [CrossRef] [ISI] [ADS]
257.	Seaton JM. ­ 1992. Rev. Mex. Astron. Astrofis. 23:180   [ISI] [ADS]
258.	Seaton JM, ­ Zeippen CJ, ­ Tully JA, ­ Pradhan AK, ­ Mendoza C,­ et al. 1992. Rev. Mex. Astron. Astrofis. 23:19   [ISI] [ADS]
259.	Sharp CM, ­ Huebner WF. ­ 1990. Ap. J. Suppl. 72:417   [CrossRef] [ADS]
260.	Simons DA, ­ Becklin EE. ­ 1992. Ap. J. 390:431   [CrossRef] [ISI] [ADS]
261.	Sneden L, ­ Johnson HR, ­ Krupp BM. ­ 1976. Ap. J. 204:281   [CrossRef] [ISI] [ADS]
262.	Stauffer J, ­ Hamilton D, ­ Probst R. ­ 1994. Astron. J. 108:155   [CrossRef] [ISI] [ADS]
263.	Stauffer JR, ­ Giampapa MS, ­ Herbst W, ­ Vincent JM, ­ Hartmann LW, ­ Stern RA. ­ 1991. Ap. J. 374:142   [CrossRef] [ISI] [ADS]
264.	Stauffer JR, ­ Hartmann LW. ­ 1986. Ap. J. Suppl. 61:531   [CrossRef] [ADS]
265.	Stevenson DJ. ­ 1991. Astron. Astrophys. Rev. 29:163   [Abstract]
266.	Stone RC, ­ Monet DG, ­ Monet AKB, ­ Walker RL, ­ Ables HD. ­ 1996. Astron. J. 111:1721   [CrossRef] [ISI] [ADS]
267.	Strong K, ­ Taylor FW, ­ Calcutt SB, ­ Remedios JJ, ­ Ballard J. ­ 1993. J. Quant. Spectrosc. Radiat. Transfer 50:363   [CrossRef] [ISI] [ADS]
268.	Takeda Y, ­ Kato K-I, ­ Watanabe Y, ­ Sadakane K. ­ 1996. Publ. Astron. Soc. Jpn. 48:511   [ISI] [ADS]
269.	Thackrah A, ­ Jones HRA, ­ Hawkins M. ­ 1997. MNRAS. In press
270.	Tinney CG. ­ 1993. The faintest stars. PhD thesis. Calif. Inst. Technol., Pasadena
271.	Tinney C,­ ed. 1995. The Bottom of the Main Sequenceand Beyond. ESO Astrophys. Symp. Berlin/Heidelberg: Springer-Verlag
272.	Tinney CG. ­ 1996. MNRAS 281:644   [ISI] [ADS]
273.	Tinney CG, ­ Mould JR, ­ Reid IN. ­ 1993. Astron. J. 105:1045   [CrossRef] [ISI] [ADS]
274.	Tinney CG, ­ Reid IN, ­ Gizis J, ­ Mould JR. ­ 1995. Astron. J. 110:3014   [CrossRef] [ISI] [ADS]
275.	Tsuji T. ­ 1966. Publ. Astron. Soc. Jpn. 18:127   [ISI] [ADS]
276.	Tsuji T. ­ 1973. Astron. Astrophys. 23:411   [ADS]
277.	Tsuji T. ­ 1994. In Molecules in the Stellar Environment, ed. UG Jørgensen, Lect. Notes Phys., pp. 7997. Berlin/Heidelberg: Springer-Verlag
278.	Tsuji T, ­ Ohnaka K, ­ Aoki W. ­ 1995. See Tinney 1995, pp. 4552
279.	Tsuji T, ­ Ohnaka K, ­ Aoki W. ­ 1996a. Astron. Astrophys. 305:L1   [ADS]
280.	Tsuji T, ­ Ohnaka K, ­ Aoki W, ­ Nakajima T. ­ 1996b. Astron. Astrophys. 308:L29   [ADS]
281.	Tyuterev VG, ­ Babikov YL, ­ Tashkun SA, ­ Perevalov VI, ­ Nikitin A,­ et al. 1994. J. Quant. Spectrosc. Radiat. Transfer 52:459   [CrossRef] [ISI] [ADS]
282.	Unsöld A. ­ 1955. Physik der Sternatmosphären. Berlin/Göttingen/Heidelberg: Springer-Verlag. 2nd ed.
283.	Vardya MS. ­ 1966. MNRAS 134:347   [ISI] [ADS]
284.	Veeder GJ. ­ 1974. Astron. J. 79:1056   [CrossRef] [ISI] [ADS]
285.	Verner DA, ­ Verner EM, ­ Ferland GJ. ­ 1996. Bull. Am. Astron. Soc. 188:5418   [ADS]
286.	Viti S, ­ Jones HRA, ­ Tennyson J, ­ Polyansky OL, ­ Miller S,­ et al. 1995. Bull. Am. Astron. Soc. 187:10314   [ADS]
287.	von Hippel T, ­ Gilmore G, ­ Tanvir N, ­ Robinson D, ­ Jones D. ­ 1996. Astron. J. 112:192   [CrossRef] [ADS]
288.	Warren SJ, ­ Irwin MJ, ­ Evans DW, ­ Liebert J, ­ Osmer PS, ­ Hewett PC. ­ 1993. MNRAS 261:185   [ISI] [ADS]
289.	Weast RC,­ ed. 1988. Handbook of Chemistry and Physics. Boca Raton, FL: CRC Press. 2nd ed.
290.	Wehrse R. ­ 1972. Astron. Astrophys. 19:453   [ADS]
291.	Wehrse R, ­ Liebert J. ­ 1980. Astron. Astrophys. 86:139   [ADS]
292.	Weidemann V. ­ 1955. Z. Astrophys. 36:101   [ADS]
293.	Williams DM, ­ Boyle RP, ­ Morgan WT, ­ Rieke GH, ­ Stauffer JR, ­ Rieke MJ. ­ 1996. Ap. J. 464:238   [CrossRef] [ISI] [ADS]
294.	Williams E, ­ Butler R, ­ Marcy G. ­ 1997. Ap. J. In press
295.	Wilson OC, ­ Skumanich A. ­ 1964. Ap. J. 140:1401   [CrossRef] [ISI] [ADS]
296.	Zapatero Osorio MR, ­ Rebolo R, ­ Martín EL. ­ 1997. Astron. Astrophys. 317:164   [ADS]
297.	Zapatero Osorio MR, ­ Rebolo R, ­ Martín EL, ­ Garcia Lopez RJ. ­ 1996. Astron. Astrophys. 305:519   [ADS]
298.	Zheng C, ­ Borysow A. ­ 1994. Ap. J. 441:960   [CrossRef] [ISI] [ADS]
299.	Ziurys LM, ­ Barclay WLJ, ­ Anderson MA. ­ 1992. Ap. J. 384:63   [CrossRef] [ADS]
300.	Ziurys LM, ­ Fletcher DA, ­ Anderson MA, ­ Barclay WLJ. ­ 1996. Ap. J. Suppl. 102:425   [CrossRef] [ADS]
301.	Zubko VG. ­ 1987. On the Microstructure Theory of a Condensate Layer in a White Dwarf Atmosphere. Kiev: Acad. Sci. Ukrainian SSR
302.	Zuckerman B, ­ Becklin EE. ­ 1992. Ap. J. 386:260   [CrossRef] [ISI] [ADS]