Annu. Rev. Astron. Astrophys. 1994. 32: 531-590
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9.4. Evidence from Population I and Population II

Although it is difficult to observe brown dwarfs (BDs) themselves, one can study the IMF of stars in the mass range above the hydrogen-burning limit and infer whether its extrapolation would permit a lot of BDs. If one assumes that the IMF has the power-law form

Equation 9.1        (9.1)

(at least over some mass range), then most of the mass is in the smallest stars for x > 2 and in the largest ones for x < 2. Determining the value of x in the LMO range is difficult, partly because obtaining the luminosity function is hard and partly because there are large uncertainties in the mass-luminosity relation as one approaches the hydrogen-burning limit. Nevertheless, there does now seem to be a convergence of opinion (Bessell & Stringfellow 1993).

Let us first consider the possibility that the disk dark matter (if it exists) is in the form of BDs. Early studies of the luminosity function for nearby stars (Reid & Gilmore 1982, Gilmore & Reid 1983, Gilmore et al 1985) suggested that the IMF is too shallow for BDs to have an interesting density. These results were initially contradicted by the results of Hawkins (1985) and Hawkins & Bessell (1988), who went to somewhat fainter magnitudes and claimed that the observations were consistent with an IMF which steepened enough to put all the dark mass in BDs. However, the data of Tinney et al (1992, 1993) make it quite clear that the IMF flattens off below 0.2 Msun and, unless it rises again below 0.08 Msun, the contribution to the local dark matter must be small (Tinney 1993). This is also consistent with the results of Kroupa et al (1993), Comeron et al (1993), and Hu et al (1994). In particular Kroupa et al (1993), find x = 2.7 for m > 1 Msun, x = 2.2 for 0.5 < m < 1 Msun, and 0.7 < x < 1.8 for 0.08 Msun < m < 0.5 Msun. This suggests that stars of 0.5 Msun should dominate the disk density. BDs may dominate the number density but, unless the value of x changes below 0.08 Msun, they cannot contain more than 1% of the disk mass.

The situation is less clear-cut when one considers Population II stars. Richer et al (1991) claim that metal-poor globular clusters have x = 3.6 below 0.5 Msun down to at least 0.14 Msun, while Richer & Falman (1992) claim that stars in the Galactic Spheroid have x = 4.5 ± 1.2 in the same mass range. This does allow the possibility that most of the mass is in the smallest objects; indeed, BDs could explain all the halo dark matter if the IMF extended down to Mmin ~ 0.01 Msun. However, Richer & Falman also point out that the rotation curve of the Galaxy requires that the total spheroid mass cannot exceed 7 × 1010 Msun, which implies that the IMF cannot extend below 0.05 Msun. It is therefore unlikely that Population II stars themselves could explain the halo dark matter. As stressed by Lake (1992), the main point of these results is that they lend support to the suggestion that low metallicity enhances the fraction of mass in low mass objects.

It should be stressed that there is an important difference between attributing the disk and the halo dark matter to BDs. If the disk dark matter comprises BDs, one would expect them to represent the low mass tail of the Population I IMF since all disk stars presumably form at the same time. However, there may be no connection between the dark halo stars and Population II stars because they probably form at a different time and place. One should therefore be wary of attempts to exclude the halo from comprising BDs on the grounds that Population II stars have a particular IMF, as do Hegyi & Olive (1983, 1986, 1989).

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