M dwarfs, L dwarfs and T dwarfs

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L dwarf spectral classification

L dwarf characteristics - photometry

L dwarf characteristics - temperature and mass

Spectral Classification of late-type dwarfs

1. Introduction

Spectral classification is astronomical botany: it is an ordering and organisation of observations based solely on appearance. The hope and expectation is that by undertaking this exercise, one is also producing a sequence whose order is determined by some underlying physical parameter (usually temperature). That expectation can be fulfilled through a sensible choice of morphological criteria - substantive variations rather than minutiae. When constructed correctly, spectral classification provides an astronomical shorthand communication system, allowing individual objects to be placed in the broader context in a simple and straightforward manner.

In practice, a spectral classification system is defined by a number of stars (or brown dwarfs) which are selected as fiducial standards, each representing a particular spectral class (M1, M2, M3, etc.). Program stars are classified based on either on differential comparison with those spectra, or by matching spectral indices against mean relations calibrated by data for those stars.

It is important that the act of classification is divorced from from theoretical interpretation of the spectra: classify, then interpret in terms of underlying physical paramters. The justification for this is obvious: theoretical models are ephemeral, periodically replaced with revised and improved analyses; the equivalent widths, line strengths and flux distribution of a given spectroscopic observation are, within observational uncertainty, fixed. A spectral classification system tied to physical parameters must change with each revision of the theoretical models, and a changing system makes it very difficult to establish the readily-understood common reference system which is essential for spectral types to be of any use.

In short, spectral classification is based on what an object looks like , not what it is.

The L-dwarf classification system described here is that outlined by Kirkatrick et al. (1999). That system follows in the steps of the Harvard and MK systems in adopting the philosophical approach outlined in the preceding paragraphs. In contrast, Martin et al (1999) have proposed an alternative scheme which violates those precepts in two important respects:

  1. spectral type, Ln, is tied to a theoretical temperature calibration, where
    n = (2300 - Teff)/100
  2. the scheme places stronger emphasis on colours than on morphology, so objects with very different energy distributions can be assigned the same numerical class.
In general, the Martin et al and the Kirkpatrick et al systems agree for spectral types earlier than ~L4, but diverge at later types (e.g. Denis0205 is type L5 on the Martin et al system, but L7 on K99). Our preference lies with the K99 system.

Given the discrepancies between these two systems, and the consequent possibility of confusion, one might enquire whether a preferred choice might be stipulated by an IAU commission. Past history in the field suggests that this is not likely. The Harvard system was only adopted as a `provisional' IAU standard in 1922 (almost 2 decades after its initial definition), and has never been elevated above that status. As for its successor,
"The MK system has no authority whatever; it has never been adopted as an official system by the International Astronomical Union - or by any other astronomical organisation. Its only authority lies in its usefulness; if it is not useful, it should be abandoned."
W. W. Morgan (1979)
In the same way, the system chosen to subdivide spectral class L (and T) will be decided informally, by use, rather than by mandate.

2. The M dwarf spectral-type sequence

2.1 A short history of type M

Spectral class M is characterised by the presence of strong absorption bands due to the diatomic molecule titanium oxide, TiO (Morgan, Keenan \& Kellman, 1943). The original classification scheme was based on photographic spectra of the blue-green region of the spectrum, reflecting the technology available at the time. At that tine, only a few M dwarfs were known sufficiently bright for high signal-to-noise spectroscopy, and all of those also have bright absolute magnitudes. As a result, while the M giant sequence was defined to spectral types M6, the original MK system extends only to M2 for main sequence stars. Another consequence of choosing (or being forced to choose) the blue-green region of the spectrum for classification purposes concerns TiO absorption: while M0 is formally defined as marking the onset of TiO absorption at blue-green wavelengths, absorption bands due to that molecule are already strong at red wavelengths. Thus, K7 and even K5 dwarfs can have noticed TiO 7050\AA absorption. This may also be relevant for L dwarf classification, as discussed further in section 4.

Mirroring to some extent the present situation with L dwarfs, two spectral type systems for classifying M dwarfs came into general use in the 1940s: the Yerkes system (Morgan, 1938; Kuiper 1842); and the Mt. Wilson system (Joy, 1947). The Yerkes system used TiO bandstrengths between 5800 and 6500 A as the primary classification; the Mt. Wilson system (lke the MK system) used the blue-green region of the spectrum (see Figure L1.1). The net result was different spectral types for the same star (e.g. Wold 359 was M8, Yerkes, but M6e, Joy). Reconciling these differences to produce a single system was clearly desireable.

Figure l1.1: An M-dwarf spectral sequence for the blue-green region covered by the original MK classification scheme.

M dwarfs are low-luminosity, red stars; given the general scarcity of photons, it makes sense to define a classification system at redder wavelengths, maximising the signal-to-noise in observations. (There is a caveat: the spectral region should also contain suitable atomic or molecular features - see further below regarding near-infrared observations.) Keenan & MacNeill (1976) and Boeshaar (1976) produced the first attempts at such an extension, but both studies remained limited to wavelengths shortward of 6800 A by the detector technology of the time, and neither provides calibration beyond class M6.

The solidification of M-dwarf system came with the wider availablity of red-sensitive detectors - GaAs SITS, image tubes and, particularly, CCDs. As in the 1940s, two systems emerged: Mike Bessell (1991) defined a system tied on Wing's (1973) giant-star system, based on TiO bandstrengths for earlier-type M dwarfs and VO for later-types; at the same time, Kirkpatrick, Henry & McCarthy (1991) devised a system based a point-by-point least-squares comparison of individual, low-resolution (12 A) spectra (6300 to 9000 A) against a grid of standards, normalising the spectra at 7500 A. This classification technique uses both the relative strengths of atomic and molecular features (TiO, VO, CaH) and the overall shape of the spectrum. The KHM system has an extensive list of standards, all accessible from northern hemisphere observatories, and, probably partly for that reason, that system has become the de facto standard. Its main properties are outlined in the following section.

2.2 The M dwarf sequence

Figure L1.2: The main molecular and atomic spectral features at far red wavelengths in M dwarfs.

Figure L1.2 shows the far-red spectrum of the M3 dwarf Gl 752A (the companion to VB10), marking the main moleculare and atomic features. The most prominent TiO bands are at 6322, 6569, 6651, 7053, 7666, 8206 and 8432 Angstroms; CaH occurs at 6346, 6382 and 6750 A; VO is present in late M dwarfs at 7334 and 7851 A. The most prominent atomic features are H-alpha, often found in emission in later dwarfs, the potassium resonance doublet at 7665/7699 Angstroms and the sodium doublet at 8183/8195 Angstroms.

Figure L1.3: Early-type M dwarfs in the KHM system

The original KHM classification paper lists 39 primary spectral standards and 38 secondary standards. Henry et al. (1995) extend the observations to include most of the late-K and M dwarfs in the 8-parsec sample, with typical uncertainties of +/-0.5 spectral classes. The Henry et al dataset includes 92 stars, all classified on the same system. This provides an important reference dataset for other analyses, as described further below. Figure L1.3 to L1.5 plot representative stars from that sample, mapping the gradual change in relative strength of the individual features.

Figure L1.4: Mid-type M dwarf standards in the KHM system

Figure L1.5: Late-type M dwarf standards in the KHM system

The calibration techniques defined by KHM, and applied by Henry et al, use the overall slope of the spectrum as one of the criteria in determining the final spectral type. This sets relatively stringent requirements on the accuracy of the spectrophotometric calibration over the full 6300 to 9200 A span in wavelength. Systematic distortions introduced by, for example, differential chromatic refraction in the terrestrial atmosphere, or interstellar reddening along the line of sight, must be corrected before spectra can be calibrated. KHM discuss an alternative approach, based on matching the relative strength of atomic and molecular features in spectra which have been normalied by dividing by an estimated continuum. This method results in a very similar ordering of the primary and secondary standards, and almost identical types. The main disadvantage, as KHM point out, lies in the scarcity of even pseudo-continuum points in M dwarfs, particularly the later-type ultracool dwarfs (spectral types M7 and later).

Figure L1.6: The narrowband indices used to measure TiO, CaH and CaOH bandstrength in the PMSU survey, and the Vo-a index (from Kirkpatrick et al, 1999).

Figure L1.6 illustrates a partial solution to this problem: calibration by narrowband indices, designed to measure the strength of individual spectral features. Bandstrengths are determined by measuring the ratio between the flux within a small wavelength region centred on the particular feature, and a nearby pseudo-continuum point. Placing the pseudo-continuum reference point close (in wavelength) to the spectral feature ensures minimal sensitivity to large-scale flux calibration problems (such as interstellar reddening). Moreover, since data are collected simultaneously at all wavelengths, only accurate relative flux calibration is required, rather than the absolute calibration (and hence photometric conditions) demanded in conventional photometry.

Figure L1.7: TiO5 and VO-a indices as a function of spectral type on the KHM system (from Cruz & Reid, 2002).

Clearly, this technique can only work if one chooses appropriate spectral features. Figure L1.7 shows that both the TiO5 index, measuring the depth of the 7050 A TiO absorption band, and the VO-a index, measuring the depth of the 7400 A VO absorption band, are well correlated with spectral type, where the latter parameter has been defined using the KHM technique. The dispersion about the linear relations fitted is only ~0.5 spectral classes, comparable to the accuracy of the full-scale technique (see the NStars NLTT analysis and the PMSU survey for more details). Both indices are double-valued, reflecting first an increase and then a decrease in band strength with declining temperature (as discussed further below), but, since the two indices reverse at different spectral types, an analysis combining measurements from both indices can avoid the inherent ambiguities.

2.3 Luminosity class

Both TiO5 and VO-a are (primarily) temperature sensitive indices. Figure L1.6 also identifies the CaH2 index, measuring the strength of the 6830 A calcium hydride A-X band. That index serves as both a luminosity indicator, separating dwarfs and giants, and a measure of metallicity, discriminating between near-solar abundance disk dwarfs and metal-poor halo subdwarfs.

Figure L1.8: The M giant spectral sequence

The weaker CaH absorption is clearly evident at 6830 A, where the spectra are almost convex, and in the TiO bandhead at 6150 A, which is substantially sharper in giants than dwarfs. Note also the weaker KI 7665/7699 absorption in the lower-gravity atmospheres of the giants.

Figure L1.9: Comparison between giants and dwarfs at spectral types M2 and M5. Note the concvex shape near 6830 A and the sharper TiO band at 6300 A in the giants due to weaker CaH absorption.

The gravity sensitivity of metal hydride bands has been known for over six decades (Ohman, 1936; McCarthy, 1969; Mould, 1976). Calcium hydride is a particularly useful discriminant for M stars. As Figure L1.8 and L1.9 show, both the 6382 and 6830 bands are essentially indetectable in giants. Jones (1973) originally devised a scheme for measuring this effect, defining a series of narrowband (FWHM 30 A) filters centred on 6076, 6830, 7100 and 7460 A. Plotting m(6830)-m(7100) vs. m(6076)-m(7460) (effectively CaH-TiO vs R-I) gave excellent dwarf/giant discrimination.

Figure L1.10: Spectra of two carbon stars.

Photometric searches for low mass dwarfs, particularly those based on near-infrared colours, tend to turn up one other major contaminant - carbon stars. The majority of those (probably) are aymptotic giant branch stars, where dredge-up of nucleosynthesis products has changed the C/O abundance ratio from less than 1 to significantly greater than 1. A minority (at least in a magnitude-limited sample) are carbon dwarfs, where the increased C/O ratio probably reflects pollution by an evolved companion (since low-mass stars are not expected to undergo significant triple-alpha fusion reactions). Under those abundance conditions, oxygen bonds preferentially with carbon, rather than titanium, and the optical spectrum is dominated by absorption due to C2 and CN. Carbon stars also have significantly bluer optical/IR colours than late-type dwarfs.

2.4 M-dwarf Metallicities

The relative strength of the metal hydride bands and TiO absorption provides a means of identifying cool, metal-poor stars, and even deriving crude, but quantitative, abundance estimates. As the metal abundance decreases in a cool stellar atmosphere, the abundance of TiO decreases sharply, partly because TiO is a double metal, partly because Ti is competing with the much more abundant H (via H2O) for a decreasing supply of oxygen. The metal hydride bands are much less affected, since those are produced by a single metallic atom bonded with highly abundant hydrogen.

Figure L1.11: MgH in early-type M subdwarfs; see below for an outline of Gizis' (1997) sdM and esdM classification scheme

Magnesium hydride is the most prominent feature at optical wavelengths in K-type subdwarfs (Cottrell, 1978; Ake & Greenstein, 1980). As figure L1.11 shows, those features remain prominent at blue/green wavelengths in the earlier-type M subdwarfs. The three stars plotted have similar effective temperatures. There is an obvious decrease in strength of the 4960 A TiO bandhead relative to the 5200 A MgH feature as one moves from the near-solar abundance M3 dwarf Gl 251 to the intermediate subdwarf, LHS 320, and the extreme subdwarf, LHS 453.

Figure L1.12: CaH in M-type subdwarfs

These differential effects are also evident in the relative strengths of CaH and TiO bands at red wavelengths. Figure L1.12 compares red spectra of the near-solar abundance disk dwarf, Gl 83.1, the intermediate subdwarf, LHS 1024, and the extreme subdwarf, LHS 205a. All three of these stars have similar CaH bandstrengths, as measured by the CaH2 index (hence all three are type "4.5"), but the 7050 A TiO bands are clearly significantly weaker in the sdM, and almost indistinguishable in the esdM.

Figure L1.13: Calcium-hydride/TiO5 relations for main-sequence disk dwarfs (solid points), intermediate subdwarfs (open squares) and extreme subdwarfs (crosses).

The spectral classification scheme for late-type dwarfs was devised by Gizis (1997), and, as implied above, takes the calcium hydride bandstrength as the fiducial for type determination. Figure L1.13 plots two calcium hydride indices, CaH1, measuring the 6380 A band, and CaH2, measuring the 6830 A band, against TiO5, the full depth of the 7050 TiO bandhead. The overwhelming majority of nearby stars form a tight sequence in both of these diagrams, reflecting the relatively limited metallicity spread in the local Galactic Disk. Metal-poor subdwarfs scatter to the right of the disk sequence (lower TiO bandstrength for the same CaH absorption). These subdwarfs were identified through their having substantial proper motions and/or space velocities relative to the Sun; most are from Luyten's Half second (LHS) catalogue.

Gizis has divided the subdwarfs into two groups - intermediate subdwarfs, sdM, where TiO5 is moderastely reduced in strength; and extreme subdwarfs, esdM, where TiO5 is substantially weaker. Based on comparison of the photometric properties of these stars with the lower main-sequences of various globular clusters, the sdM dwarfs probably have an average abundace of [m/H]~-1, while theesdM dwarfs have [m/H] < -1.5.

Figure L1.14: The sdM sequence

Figure L1.15: The esdM sequence

Figures L1.14 and L1.15 show representative sdM and esdM sequences. The stars are taken from Gizis (1997) and Gizis & Reid (1997).

Figure L1.16: Subdwarfs in the (MV, (B-V)) and (MR, (R-I)) planes. Crosses mark disk stars with Hipparcos parallaxes; green and light blue points are F/G subdwarfs; magenta points are sdM and blue points esdm late-type subdwarfs.

Finally, the reduced TiO absorption in subdwarfs, as compared with disk dwarfs, leads to significantly different broadband colours at the same absolute magnitude. Figure L1.16 plots the (MV, (B-V)) and (MR, (R-I)) colour-magnitude diagrams for disk dwarfs and metal-poor subdwarfs. In (R-I), F, G and early-K subdwarfs are only marginally offset from the main sequence, since there are relatively few metallic features in these passbands at the appropriate temperatures. At lower temperatures, the reduced strength of (mainly) TiO leads to bluer colours at the same MR and the classic subluminous subdwarf sequence. In contrast, in (B-V), while the F, G and K subdwarfs fall below the main sequence, the later M-type subdwarfs actually cross over the disk sequence and have redder colours. This mainly reflects reduced absorption in the V-band, while hydride absorption continues to absorb much of the B-band flux (see Figure L1.11).


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