The very low mass multiple system LHS 1070. A testbed for model atmospheres for the lower end of the main sequence 

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The Basics Properties of M-dwarfs

Introduction to M-dwarfs

Within less than two decades the study of low-mass stars and brown dwarfs has bloomed into one of the most active fields in astronomy. The low-mass end of the main sequence from M, L, T and Y dwarfs includes objects spanning several orders of magnitude in temperature, from 4000 K down to room temperature, and nearly fills the entire temperature gap between the coolest stars and our Solar System’s giant planets. Stars known as red-dwarfs and red subdwarfs are main sequence stars, a classification typically meant to include all main sequence objects of spectral subtype K5 to M9. Their masses range from 0.08M⊙ ≤ M⊙ ≤ 0.8M⊙, based on their estimated metallicity (Chabrier et al. 2000). Despite their intrinsic faintness, M-dwarfs constitute a large fraction of the detectable baryonic matter in the Galaxy. They are the dominant stellar component in the Galaxy, comprising ∽ 70% of all stars (Chabrier 2003) and nearly half the stellar mass of the Galaxy which make the lower end of the Hertzsprung-Russel diagram very important. These stars are found in any population, from young metal-rich M-dwarfs in open clusters (Reid 1993; Leggett et al. 1994) to the several billion years old metal-poor dwarfs in the galactic halo (Green & Margon 1994) as well as in globular clusters (Cool et al. 1996; Renzini et al. 1996). Such low mass stars are an important probe for our Galaxy; as they carry fundamental information regarding stellar physics and about the structure, formation and dynamics of the Galaxy. The M-dwarfs span very long life time in the universe. Some have lifetime much greater than the estimated age of the universe, which makes them an important fossil record of Galactic history of great value in probing the structure and evolution of the Milky Way.
Recent improvements in kinematic modelling and magnetic activity analysis have provided enhanced statistical age estimates for populations of low-mass dwarfs (West et al. 2006). When coupled with information about metallicity, these ages can provide valuable insight into the history of the chemical evolution of the Milky Way. Their huge number in the Galaxy makes M-dwarfs very important in the study of various process such as the formation and evolution of stars. Because of their ubiquity, cool dwarfs may represent the largest population of stars which have orbiting planets, especially low-mass planets in their respective habitable zones, which with relatively tight orbits for a cool dwarf system. In addition, the fact that the exis-tence of brown dwarfs or planets has been discovered and confirmed around M-dwarfs (Butler et al. 2004; Bonfils et al. 2012) plays an important role in understanding the formation of brown dwarfs and planets. M-dwarfs are also very important to derive various quantities such as Initial mass function (IMF), and the present day mass function. These frequently used functions are derived by using the luminosity. However, the historic deficiency of data for M-dwarfs was primarily due to their intrinsic faintness, a consequence of their low mass. The situation has been radically altered in the last decade, as deep surveys covering large areas of the sky have been carried out. Projects such as the Solan Digital Sky surveys (SDSS, York et al. 2000), the Two-Micron All Sky Surveys (2MASS, Skrutskie et al. 2006) and the Deep Near-Infrared Survey of the Southern Sky (DENIS, Epchtein et al. 1999) can trace their root back to photo-graphic surveys. An important by-product of recent transit surveys has been the discovery of many eclipsing binaries with M-dwarf components (e.g., Coughlin et al. 2011; Harrison et al. 2012; Birkby et al. 2012). These systems have traditionally been the most favourable for deter-mining the basic properties of late-type stars, including their masses, radius, temperature, and luminosity. Unfortunately, most newly discovered systems tend to be faint, so the problem for accurate determinations continues to be that of carrying out accurate spectroscopy.
In general, it is necessary to obtain the spectra of low mass M-dwarf candidates selected by using photometry or a study of proper motions in order to confirm their spectral types; this limits the temperature and mass of a suitable candidate. Low resolution spectra are normally preferred for the initial followup of candidates, since they are adequate for the measurement of broad molecular absorption bands of late-type M-dwarfs, while also providing the high-est signal-to-noise ratios. Most of the well observed M-dwarfs are relatively nearby and their observed trigonometric parallaxes are therefore quite reliable, so that accurate absolute lumi-nosities are known. Methods have been derived to find their mass, their location and density in the Galaxy, their age (involving effective temperature), bolometric corrections, absolute visual magnitude and several colour indices for them have been established. However, the measure-ment of the chemical compositions of M-dwarfs is still limited, as it require lot of telescope time to obtain very high quality spectra for them. The current factor limiting the determination of accurate chemical compositions for M-dwarfs is the lack of a accurate atmosphere models reliable enough to interpret the complex spectra of these stars.

A Survey of the Properties of M-dwarfs

Determining the fundamental properties of M-dwarfs, is a challenge from both observational and theoretical perspectives. Empirical values for M-dwarfs masses, luminosities, temperatures and radii can be extracted by studying the orbits of M-dwarf binaries (Leinert et al. 2000). How-ever, the intrinsic faintness of these systems makes their observation challenging and analysis of known binaries reveals systematic variations in inferred temperatures or radii. Theoretical constraints on M-dwarf atmospheric parameters have similarly been difficult to obtain. Ac-curate modelling of the deep convective zones in M-dwarf interiors and of the formation of the molecules and grains that dominate M dwarf atmospheres (Tsuji et al. 1996b; Allard et al. 2000) requires significant computational resources as well as an extensive database of oscillator strengths and opacities obtained from laboratory experiments.

Physical properties

The theory of the evolution of low mass stars is mainly based on a detailed study of the variation with time of bolometric luminosity, effective temperature, radius and angular momentum, for a given stellar mass. Theoretical models of stellar interiors and atmospheres have made predic-tions for the temporal evolution of the first three parameters, while other structure (e.g., winds, disk) may produce loss of angular momentum. 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. The temperature of M-dwarfs ranges from 4000 to 2300 K and the surface gravity, ranging from ∽ 4.5 – 5.5, allows the forma-tion of various molecules. At these low temperature the structure of M-dwarfs is affected by atomic and molecular opacity and convection. The atmosphere thus become more sensitive to the strong opacity due to molecules such as TiO, H2O, so that this molecular opacity eventu-ally becomes the main source of absorption. With their complex description of atmospheric physics and chemistry the observations have now reached a high level of sophistication, while the theoretical model side has fallen behind. In particular, precise observational calibrations of the basics physical properties of M-dwarfs, such as their mass, age, radius, luminosity or surface gravity is still missing. Unfortunately the degeneracy in the age-temperature relation for M-dwarfs makes it difficult to make an unambiguous determination of their physical prop-erties. Direct size measurements of low-mass stars represent vital tests of theoretical models of stellar evolution, structure, and atmospheres. As seen in the results of Berger (2006), notable disagreements exist between interferometrically determined radii and those calculated in low-mass stellar models such as those of Chabrier & Baraffe (1997) and Siess & Livio (1997) in the sense that interferometrically obtained values for the stellar diameters are systematically larger by more than 10% than those predicted from models. Developments on both the observational and theoretical fronts are thus essential in order to obtain meaningful and important estimates of the physical properties of M-dwarfs (see the review from Allard et al. 1997, 2012a; Chabrier et al. 2000).

Photometric Properties

SDSS, 2MASS and DENIS have had great success in discovering M-dwarfs. If the images are deep enough and an appropriate combination of filters is used, it is actually easier to iden-tify cool M-dwarfs than many other classes of astronomical objects, because of the distinctive nature of their spectral energy distribution (SED), which is due to the presence of strong molec-ular absorption bands. The colours of M-dwarfs provide insight into the processes operating in their atmospheres. Because of their intrinsic faintness, moderate- to high-resolution spec-troscopy may not be performed on all of the cool M-dwarfs which have been discovered by these surveys. Thus, analyses of cool M dwarf colours could be essential in providing infor-mation on their physical properties. As is well known, the chemical composition of the stellar photosphere (or its metallicity) affects the stellar energy distribution. Systematic trends have also been identified in colour-colour diagrams using the known correlation between kinematic population and metallicity. Alternatively, the location of a star in a colour-colour diagram can be used as a metallicity indicator: the metal-poor subdwarfs stars are usually sub-luminous in such a diagram (fig. 2.1).
The reason for this behaviour is that the decreased metallicity leads to a decreased atmo-spheric opacity. This effect means that a star of fixed mass ‘moves‘ in the H-R diagram to a position of higher Teff and higher luminosity. For very cool M-dwarfs, broadband photometry at near-IR wavelengths is primarily detecting the strong molecular bands of H2O, CH4, CO, and H2. Broadband photometry at optical wavelengths (λ ≤ 1µm) measures very different spec-trophotometric features. Despite the faintness of cool dwarfs, the multicolour photometry of M-dwarfs has proven to be sufficient for the determination of the normal colours, bolometric corrections, and Teff for them. Optical and near infrared photometry can be useful as a diag-nostic tool for finding the potential candidate of very low mass stars, but it is not possible to disentangle the parameters when addressing different populations of very low mass stars.

Spectroscopic properties

The H-R diagram is the most important map in stellar astronomy. It provides a relatively straightforward method for separating different stellar luminosity classes. The theoretical study of stars is usually divided into separate parts dealing with stellar interiors and stellar atmo-spheres. Although they are interesting objects in their own right, M-dwarfs have a wider po-tential which at present is largely unrealized, because investigation of their properties is largely hampered by the complex lines and bands of diatomic and triatomic molecules which appear in their observed spectra. The effects of temperature and of reduced gravity modify the chemical and physical properties of their atmospheric layers, producing the peculiar spectroscopic fea-tures that have been identified in the optical spectra of M-dwarfs. In an M-dwarf atmosphere most of the hydrogen is locked into H2 and most of the carbon into CO. With decreasing tem-perature, M dwarf spectra show an increase in abundances of diatomic and triatomic molecules which contributes to the optical and the near-infrared spectra (such as SiH, CaH, CaOH, TiO, VO, CrH, FeH, OH, H2O, CO). The TiO bands in the optical region and the H 2O bands in the infrared have complex and extensive band structures, leaving no window for the true continuum and creating a pseudo-continuum which allows observation of only the strongest (often reso-nance) atomic lines such as those from Ca II, Na I and K I (Allard 1990a; Allard & Hauschildt 1995a).
The spectral transition from low-mass M dwarfs to the latest type brown dwarfs is notewor-thy for demonstrating how a considerable transformation of the spectral features can be due to a small change in the effective temperature. The spectral transition is characterized by i) the condensation onto seeds of strong opacity-causing molecules such as CaH, TiO and VO, which govern the entire visual to near-infrared part (0.4-1.2 µm) of the spectral energy distribution (hereafter SED); ii) a ’veiling’ due to Rayleigh and Mie scattering from sub-micron to micron-sized aerosols; iii) a weakening of the infrared water vapour bands owing to oxygen-rich grain condensation and to the greenhouse (or blanketing effect) caused by silicate dust; iv) methane and ammonia band formation in T and Y dwarfs; v) water vapour condensation in Y dwarfs (Teff ≤ 500 K). Condensation begins to occur in M dwarfs with Teff ≤ 3000 K. In T dwarfs and brown dwarfs the visual to red part of the SED is dominated by the wings of the Na I D and 0.77 µm K I alkali doublets, which form out to as much as 2000 Å from the line centre (Allard et al. 2007a). The SED of those dwarfs is therefore dominated by molecular opacities and resonance atomic transitions under pressure (∽3 bars) broadening conditions, leaving no window for the continuum (Allard 1990a; Allard et al. 1997, 2012a).

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Despite their extreme faintness (10−2−10−5L⊙) in V bandpass, M-dwarfs yield spectroscopic features which can still provide us with information about basic atmospheric properties such as luminosity, metallicity and temperature. For example i) The CaOH bands around 0.54-0.556 µm in dwarfs later than M3 are a very good temperature indicator and a good discriminant between M-dwarfs and backgrounds red giant stars (Gizis 1997; Reid & Gizis 2005; Martin et al. 1996). ii) An atomic spectral feature such as that of Ca I (6162 Å) can possibly be used to distinguish subdwarfs from dwarfs. iii) Hydride bands such as those of CaH at 6380 Å and 6880 Å decreases in strength with decreasing temperature, whereas the NaI doublet at 8183 Å and 8195 Å is relatively strong for earlier type M-dwarfs but relatively weaker for later type. iv) The KI doublet at 7665 Å and 7699 Å is very strong and is useful for making gravity determination. v) The saturation of the TiO band strength in M-dwarfs later than M5 and the introduction of the VO to TiO band strength index is now used to classify M-dwarfs and substellar candidates later than M5 (Henry et al. 1994; Kirkpatrick et al. 1995; Martin et al. 1996). Figure 2.2 shows the optical to red SED of M-dwarfs from M0 to M9.5, observed at Siding Spring Observatory (SSO) at a spectral resolution of 1.4 Å (Rajpurohit et al. 2013). Molecular band spectra are much more complex than atomic spectra and dominate the spectral regions in which they are located. TiO has an especially distributed and complex spectrum and it dominates M dwarf spectra in the spectral regions traditionally used to determine the chemical compositions of solar-type stars. This can be seen in fig. 2.2, where the M dwarf spectra show a significant deviation, primarily due to TiO absorption, from the predominantly smooth continuum spectra of earlier type stars.
Figures 2.3 to 2.6 shows the IR spectra of M-dwarfs (Cushing et al. 2005). It can be seen that the dominant near infrared features are due to photospheric absorption by water vapour, FeH, neutral metals, carbon monoxide, and OH. The absorption lines of neutral metals, as well as the bands of water and CO, become stronger with decreasing temperature. In the optical region, metal-poor stars show strong features relative to the strength of the molecular TiO bands. However, in the infrared regime the dominant molecular features are due to water, and this single metal species will not show the same level of decrease as the double metal TiO. The atomic spectral lines such as those of Fe I, Ca I, Na I, K I, Si I, Mg I, Al II, along with some hydride bands such as those of FeH, can be seen in the J-band spectra with equivalent widths of 2-2.5 Å and 1.52 Å, respectively; but most of these features weaken in the spectra of mid-to late-type M-dwarfs. The H band is the most difficult wavelength range in which to identify features in the spectra of early M-dwarfs, because it contains many relatively weak absorption features which defy definite identification. Only a few doublets and triplets of Mg, Si, Al, and K are clearly evident, with the possible exception of OH (1.689 µm). H2O bands define the shape of the J and H band peaks. Water absorption is most obvious in the J-band at 1.33 µm and strengthens through the later M-dwarf types. The K-band spectra of early M-dwarfs also exhibit atomic features due to Ca, Mg, Al, Si, Na, Ti, and Fe and also shows strong CO bands. These spectral features all weaken with decreasing temperature. H2O absorption bands also appear on either side of the K-band at a spectral type of ∽ M4 and strengthen through the M, L, and T sequences.

Stellar Parameters of M-dwarfs

Effective Temperature

An effective temperature measurement for a low-mass star or brown dwarf is important to deter-mine flux or luminosity which then can be used to confirm whether a given object is hot or cool. The empirical temperature scale for cool stars is generally well established and temperatures are now known with reasonable precision for stars covering the range of spectral type from A to M. The M dwarf temperature scale has been a subject of some interest for several decades now, especially since the development of detectors with suitable sensitivity in the infrared spectral region has made it possible to obtain the relevant observational data. Empirical temperatures for metal-deficient and metal rich stars had been virtually non-existent, but recently the infra-red flux method (IRFM) has been applied by Casagrande et al. (2008) to a sample of M-dwarfs, providing approximate Teff values for them. Empirical measurement of M dwarf temperature can be obtained by the information extracted from the orbits of M dwarf binaries. As shown by the results of Irwin et al. (2011) and Kraus et al. (2011), radii and temperatures of low-mass stars obtained from eclipsing binaries are systematically larger and cooler (respectively) for given mass. This is mainly due to the intrinsic faintness of these low-luminosity systems, and the analyses of known binaries reveal systematic offsets in inferred temperatures and radii that correlate with both orbital period and magnetic activity. Strong magnetic field can prevent convection, thus giving larger radii for a given Teff or lower Teff for a given radius (Casagrande et al. 2008). The presence of numerous large spots at the surface can thus lower the Teff of the star.
Significant advances have also been made in atmospheric modelling for cool stars, by incor-porating improved metal-line and molecular line source of opacity in the models. The effective temperature of cool M-dwarfs can be estimated from their spectral type and from the fitting of observed spectral lines to the synthetic spectra predicted using a model atmosphere. Synthetic photometry generated using the model atmosphere show good agreement with the empirical temperature scales and now allows us to extend the temperature calibrations confidently to stars over the full range of parameter space. As an important first step, a conversion between spectral type and temperature is required.
The resulting scale may give results which differ significantly from an accurate conversion rule, but in the absence of a robust determination of the temperature scale at young star ages (e.g., from eclipsing binaries), this scale offers a reasonable way of interpreting spectral types and luminosities in terms of star masses and ages within current evolutionary models. The de-termination of M dwarf effective temperatures has been refined considerably since the work of Veeder (1974); Pettersen (1980); Bessell (1991). They fitted blackbody curves through broad-band colours and the points of an assumed observed continuum. Tsuji et al. (1996b) provided, good Teff values using IRFM. Casagrande et al. (2008) provided a modified IRFM T eff for dwarfs, including M-dwarf. The Teff scale of M-dwarfs can be developed by using a set of evolutionary models. Luhman (1999) initially adopted a Teff which is based on the NextGen and AMES-Dusty evolutionary models of (Baraffe et al. 1998a) and (Chabrier et al. 2000), re-spectively. Luhman et al. (2003) then adjusted this Teff scale further, so that the sequences of IC 348 and Taurus at ≤ M9 were parallel to those model isochrones on the Hertzsprung-Russell diagram. Their Teff conversion is likely to be inaccurate at some level, as it falls between the scales for dwarfs and giants. However, even the current empirical methods (Berriman et al. 1992; Jones et al. 1994) still assume that nearly pure thermal radiation escapes from an M-dwarf atmospheres at some wavelength. Such an assumption is reliable only for optically thick layers of a non-convective atmosphere but models strongly suggest that M dwarf atmospheres are convective out to optical depths as low as τ ∽ 10−3. The photospheric structure of an M dwarf is much more sensitive to opacity caused by TiO and H2O. Thanks to the large improve-ment in knowledge about the source of atomic and molecular line opacities, particularly for TiO (which dominate the optical spectral range) and for H2O (which dominates in near-infrared range), as well as to revised estimates of solar abundances (Asplund et al. 2009; Caffau et al. 2011), there now appears to be much improvement in the Teff scales obtain using a given model atmosphere over entire spectral sequence of M dwarfs (Rajpurohit et al. 2013).

Table of contents :

1. Motivation 
2. The Basics Properties of M-dwarfs 
2.1. Introduction to M-dwarfs
2.2. A Survey of the Properties of M-dwarfs
2.2.1. Physical properties
2.2.2. Photometric Properties
2.2.3. Spectroscopic properties
2.3. Stellar Parameters of M-dwarfs
2.3.1. Effective Temperature
2.3.2. Gravity
2.3.3. Metallicity
2.4. M-subdwarfs
3. A Model Atmosphere For Low Mass Stars 
3.1. Introduction
3.2. Historical Overview
3.3. Model Construction
3.4. Molecular Opacities in M dwarfs
3.5. Convective energy transport
3.6. Dust Grain and Atmospheric composition in M dwarfs
3.7. Current Model Atmospheres for Low Mass stars
3.7.1. BT-Dusty and BT-Settl
3.7.2. MARCS
3.7.3. DRIFT
4. The very low mass multiple system LHS 1070. A testbed for model atmospheres for the lower end of the main sequence 
4.1. Introduction
4.2. Observations and data reduction
4.2.1. Photometry
4.2.2. Spectroscopic observations
4.2.3. Spectroscopic features
4.3. Physical Parameters Determination
4.3.1. Atmosphere models
8 Table of contents
4.3.2. Spectral Type
4.3.3. Metallicity
4.3.4. Gravity
4.3.5. Effective Temperature and Radius
4.3.6. Age and mass
4.4. Results
4.5. Discussion and Conclusion
5. The effective temperature scale of M dwarfs 
5.1. Introduction
5.2. Observations
5.3. Model atmospheres
5.4. Teff determination
5.5. Comparison between models and observations
5.5.1. Spectroscopic confrontation
5.5.2. Photometric confrontation
5.5.3. The Teff scale of M dwarfs
5.6. Conclusion
6. High resolution spectroscopy of Msubdwarfs: Effective temperature and metallicity
6.1. Introduction
6.2. A high resolution spectral atlas of M subdwarfs
6.2.1. Observation and data reduction
6.2.2. Molecular features
6.2.3. Atomic lines
6.3. Model atmospheres
6.4. Comparison with model atmospheres
6.4.1. Molecular bands
6.4.2. Atomic lines
6.4.3. Stellar parameters determination
6.5. Discussion
6.6. Conclusion
7. Conclusion and future perspectives


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