3. Distinguishing YOUNG Brown Dwarfs from stars

Stars and BDs can have identical temperatures and luminosities when they are young (though the star would have to be older than the BD). “Young” in this context extends up to several gigayears. We therefore require a more direct test of the substellar status of a young BD candidate before it can be certified. Since the difference between BDs and VLMS lies in the nuclear behavior of their cores, it is natural to look for a nuclear test of substellarity. There is a straightforward diagnostic that is fairly simple both theoretically and observationally: the “lithium test”. In addition to verifying substellar status, observations of lithium can be used to assess the age of stars in clusters, which is helpful in the application of the lithium test itself. Lithium observations of very cool objects can be useful in constraining the nature of BD candidates in clusters, in the field, and in star forming regions.

3.1 The Principle of the Lithium Test

In simplest terms, stars will burn lithium in at most a little over 100 Myr (megayears), while most BDs will never reach the core temperature required to do so. This stems from the fact that even before hydrogen burning commences, core temperatures in a star reach values that cause lithium to be destroyed. On the other hand, in most BDs the requisite core temperature is never reached because of core degeneracy (see Chabrier; this volume). Furthermore, at masses near and below the substellar boundary the objects are all fully convective, so that surface material is efficiently mixed to the core. Finally, the surface temperatures of young candidates are favorable for observation of the neutral lithium resonance line, which is strong and occurs in the red. There are some subtleties to be considered in the application of the test, as discussed below. A more comprehensive review of this subject is provided by Basri (1998a).

The idea behind the lithium test was implicit in calculations of the central temperature of low mass objects by D'Antona and Mazzitelli (1985) and others. They found that the minimum lithium burning temperature was never reached in the cores of objects below about 60 jupiters. On the other hand, all M stars on the main sequence are observed to have destroyed their lithium. The first formal proposal to use lithium to distinguish between substellar and stellar objects was made by Rebolo et al (1992). This induced Nelson et al (1993) to provide more explicit calculations useful in the application of the lithium test.

The theory of lithium depletion in VLM objects is comparatively simple. Because the objects are fully convective, their central temperature is simply related to their luminosity evolution. The semi-analytic study of lithium depletion by Bildsten et al (1997) is a particularly revealing exposition of the heart of the problem. The physical complications in VLM objects, including partially degenerate equations of state and very complicated surface opacities, do not obscure the basic relation between the effective temperature and lithium depletion. The complications of mixing theory, which lead to many fascinating effects in the observations of surface lithium in higher mass stars, are simply not relevant for fully convective objects.

Pavlenko et al (1995) studied lithium line formation at very cool temperatures. Their basic result, that the lithium line should be quite strong in the 1500-3000K range, is confirmed by observations. NLTE effects and the effect of chromospheric activity have been considered by them and by Stuik et al (1997), and found to be of secondary importance. The strength of the resonance line means that it does not begin to desaturate until more than 90% of the initial lithium has been depleted. The timescale over which the lithium line disappears is about 10 Myr, which is roughly 10% of the age at which it occurs in substellar objects. But the observational disappearance of the line occurs even more rapidly (after desaturation).

Based on the clear possibility of using the lithium test to confirm substellar status, the group at the IAC embarked on an effort to apply it to the best existing BD candidates. They used 4-m class telescopes at spectral resolutions of 0.05 nm for a brighter initial sample (Magazzù et al 1993) and 0.2-0.4 nm (Martín et al 1995). This latter resolution is lower than ideal, but the observations are very difficult due to the faintness of VLM objects. They were unable to detect lithium in any of the candidates. For most targets (since the ages aren't known) this implied a lower mass limit greater than 60 jupiters, but did not resolve whether they are BDs.

The results were puzzling for their Pleiades candidates. These were drawn from the Hambly et al (1993) list of very faint proper motion objects, and those authors had already suggested BD candidacy based on the color-magnitude position of the objects compared to evolutionary tracks for the age of the Pleiades (thought to be 70 Myr). Martín et al (1995) realized that there was an inconsistency between the inferred mass of these Pleiades members and the lack of lithium. The situation was even more striking in the results of Marcy et al (1994), who observed a yet fainter Pleiades member (HHJ 3) with better upper limits on the lithium line (using the newly commissioned Keck 10-m telescope).

3.2 The Lithium Test in Young Clusters

The first application of the lithium test to a BD candidate with a positive result came in the study of PPL 15 by Basri et al (1996). PPL 15 is an object only slightly fainter than HHJ 3, and was the faintest known Pleiades member at the time of the study. Basri et al reported a detection of the lithium line, but apparently weaker than expected for undepleted lithium in an M6.5 star (based on high resolution model spectra). At the same time, they confirmed that PPL 15 had the right radial velocity and Ha strength to be a cluster member (it was discovered by Stauffer et al (1994) in a photometric, rather than proper motion, survey). More recently Hambly et al (1999) have also confirmed that it is a proper motion member of the cluster.

To explain how lithium could appear in PPL 15 but not in HHJ 3, Basri et al used an empirical bolometric correction to convert to luminosity. The solution becomes apparent in a luminosity-age diagram, with the lithium depletion region displayed (eg. Fig. 1). This shows that the lithium test is more subtle than presented above. One wrinkle is that it takes stars a finite amount of time to deplete their lithium. Thus, if an object is sufficiently young, it will show lithium despite having a mass above the hydrogen-burning limit (giving the possibility of a false positive in the test). On the other hand, the minimum mass for lithium destruction is below the minimum mass for stable hydrogen burning. Thus, if we wait long enough, the high mass BDs will deplete their lithium too (giving the possibility of a false negative in the test).

Basri et al resolved the problem of the non-detection of lithium in HHJ 3 and its presence in PPL 15 by suggesting that the Pleiades is substantially older than previously thought. They showed that with an age of 115 Myr (rather than the classical age of 70 Myr), the behavior of both stars makes sense. The inferred mass of VLM Pleiades members is thereby raised (since they have longer to cool to the observed temperatures), with PPL 15 just about at the substellar boundary. The prediction was that any cluster members that are fainter than PPL 15 would show strong lithium.

This prediction was tested in short order on Teide 1, a fainter M8 Pleiades member with apparently good cluster membership credentials. Field M8 stars are quite unlikely to be young enough to show lithium. Rebolo et al (1996) used the Keck telescope to confirm strong lithium in both Teide 1 and a very similar object (Calar 3). As these are well below PPL 15 in luminosity, they must be considered ironclad BDs in the cluster. They have masses in the range 55-60 jupiters (given the new age for the cluster; they would be substantially lower using the classical age).

3.2.1 The Age Scale for Young Clusters

The work of Basri et al (1996) suggested that a new method of determining ages of clusters has been found: lithium dating. Stauffer et al (1999a) pursued such a program for the Pleiades, and obtained very clear confirmation of the lithium boundary found by Basri et al. They agreed that the explanation is that the cluster is more than 50% older (125 Myr) than its classical age. Further progress has occurred for several clusters. Basri & Martín (1999) found lithium in a (previously known) member of the a Per cluster, and determined that the classical age of a Per should be corrected substantially upward. More objects were needed to pin down the lithium boundary, and Stauffer et al (1999b) provide them. They conclude that the age of a Per is about 85 Myr, rather than the classical age of 50 Myr (a similar correction as in the Pleiades). Barrado y Navascués et al (1999) also find that the younger cluster IC 2391 needs a correction of less than 50% to its classical age (being 50 Myr old instead of 35 Myr) on the basis of lithium dating.

Lithium dating is fundamentally a nuclear age calibrator. In that sense, it is like the upper-main sequence turnoff age, which is the “classical” means of assessing cluster ages. There is reason to regard the lithium ages as more reliable than the classical method for young clusters. That is because the stars turning off the main sequence in young clusters are massive enough that they have convective nuclear burning cores. The issue of convective overshoot is then quite crucial – the more there is, the more hydrogen from the convectively stable envelope that can be enlisted into the main sequence phase. This will increase the main sequence lifetime of the star, and thus the age inferred from the turn-off. Stellar evolution theory had already been grappling with this problem; a review of the topic in this context is in Basri (1998b). The treatment of convective overshoot is quite uncertain, and the problem must be inverted to find observational constraints to what is otherwise an essentially free parameter.

In lithium dating, on the other hand, the details of convection are rendered unimportant by the fully convective nature of the objects (which are then forced to adiabatic temperature gradients). The precision of lithium dating is limited by the width of the depletion boundary, errors in the conversion of magnitudes to luminosities (due to bolometric corrections and cluster distances), and possible corrections to the age scale because of opacity issues in very cool objects. But it probably has similar precision to, and greater accuracy than, classical dating methods. Indeed, this may prove one of the most powerful methods to finally provide a value for the convective overshoot in high mass stars. Lithium dating can only work up to about 200 Myr, when the lowest mass object that can deplete lithium will have done so. Furthermore, the correction for core convective overshoot can only apply for clusters younger than about 2 Gyr; stars leaving the main sequence in older clusters have radiative cores.

As a cluster gets older, the luminosity of the lithium depletion boundary gets fainter. Thus, while the Hyades is one-third the distance of the Pleiades, its lithium boundary is at fainter apparent magnitudes. Searches for BDs here have been less successful (cf. Reid & Hawley 1999). Although a Per is further away, its youth means that the apparent magnitude of the lithium boundary is similar to the Pleiades. Given a correct age, the luminosity of the substellar boundary can then be inferred from models. This will not be coincident with the depletion boundary in general (only at the age of the Pleiades). Once the boundary is established, the search for BDs can proceed to fainter objects using cluster membership as the sole criterion.

3.3 The Lithium Test in the Field

Can the lithium test be used for field objects, given that one will not generally know the age of an object? Clearly it works to distinguish main sequence M stars from BDs less massive than 60 jupiters (that was the original idea). Basri (1998a) refined the discussion of how to apply the lithium test in the field. Fig. 1 shows that the lithium depletion region, taken with the observed luminosity or temperature of the object, provides a lower bound to the mass and age (jointly) if lithium is not seen. Conversely, it provides an upper bound to the mass and age if lithium is seen. The temperature at which an object at the substellar limit has just depleted lithium sets a crucial boundary. It is the temperature below which, if lithium is observed, the object must automatically be substellar. More massive (stellar) objects will have destroyed lithium before they can cool to this temperature. A substellar mass limit of 75 jupiters implies a temperature limit of about 2700K for lithium detection, which roughly corresponds to a spectral type of M6. Thus, any object M7 or later which shows lithium must be substellar. This form of the test is easier to apply than that employing luminosity, which requires one to know the distance and extinction to an object. Otherwise they are equivalent.

For instance, since the spectral type of the object 269A (Thackrah et al 1997) is M6, one cannot be sure it is a BD even though it shows lithium (though it certainly lies in the region where it might be a BD; the age would have to be known to be sure). A more definitive case is provided by LP 944-20 (Tinney 1998). It is sufficiently cool (M9) that the fact that lithium is detected guarantees it is a BD, even though we know little about its age (the lithium detection provides an upper limit on the age). This is also be true for the enigmatic object PC0025+0447 (M9.5), which displays prodigious Ha emission. Martín et al (1999a) claim a lithium detection for it during a less active state, which would imply that it is a (probably very young) BD. The objects in Hawkins et al (1996) were originally suggested to have luminosities around 10^-4 solar. If they were confirmed to be below that level, then they would be BDs independent of a lithium observation (since that is the minimum main sequence luminosity). They are cool enough that if they showed lithium, they would definitely be BDs. Unpublished observations by Basri and Martín find that the brightest of them does not show lithium, and recent work by Reid (1999) makes it unlikely that these are actually BDs (they are apparently further away, and so more luminous). As discussed in Section 4, the lithium test has been applied quite successfully to objects which are cooler than M; those which show lithium (about a third of them so far) must certainly be substellar.

3.4 Brown Dwarfs in Star Forming Regions

The lithium test is less obviously useful in star forming regions (SFR). Even clear-cut stars have not had time to deplete lithium yet. Nonetheless, there have been numerous reports of BDs in SFR. They are identified as BDs on the basis of their position in color-magnitude or HR diagrams, using pre-main sequence evolutionary tracks. One must worry whether the pre-main sequence tracks for these objects are correct, or if there are residual effects of the accretion phase. If one of these candidates doesn't show lithium, it can be immediately eliminated as being a non-member of the SFR. The lithium test as applied in the field still works: if a member of a SFR is cooler than about M7 (here we should be careful that the pre-main sequence temperature scale might be a little different) and the object shows lithium, then it must be substellar. Indeed, for an object to be so cool at such an early age pushes it very comfortably into the substellar domain.

Good BD candidates have now been found in a number of SFRs, including Taurus (Briceño et al 1998), Chameleon (Neuhauser & Comeron 1999), r Oph (Williams et al 1995; Wilking et al 1999), the Trapezium cluster (Hillenbrand 1997), IC 348 (Luhman et al 1998), the s Ori cluster (Bejar et al 1999), and others. Some very faint/cool objects have been found whose substellar status seems relatively firm (if they are members). The lowest of these may be as small as 10-15 jupiters (Tamura et al 1998). Spectroscopic confirmation of these candidates is imperative, as has been done for a BD near the deuterium-burning boundary in s Ori (Zapatero-Osorio et al 1999). Such observations indicate that the substellar mass function may extend right down through the lowest mass BDs. It is natural to wonder how far it goes below that, since there is no obvious reason why it should stop where we have defined the boundary between BDs and planets.