10.2 Baryonic Dark Matter

Instead of these exotic candidates it is possible that dark halos are made up of ordinary baryonic material. In this case, there are various constraints on the form that such baryonic DM can take. Most of these constraints come from considerations of the Milky Way halo. The majority of studies have concluded that the only viable candidates are brown dwarfs and sufficiently massive black holes (e.g. Carr 1990; De Rújula, Jetzer and Massó 1992). Hot gas in halos would generate too many X-rays (Hegyi 1984), whereas cold gas can be ruled out immediately since it would tend to settle in a disk. Hydrogen snowballs (solid hydrogen objects with sub-planetary masses) can also be ruled out (Hills 1986). M dwarfs are excluded by source counts limits (Gilmore and Hewitt 1983). More recent work by Richstone et al. (1992) illustrates that very few stars at the low-mass end of the visible stellar spectrum are present in the Milky Way halo. Other stellar remnants conflict with nucleosynthesis and background light constraints (McDowell 1986; Hegyi and Olive 1986).

The brown dwarf and black hole options have often been criticized on the grounds that observations of current star formation do not find significant numbers of such objects. This is hardly surprising. We know that there is very little DM in the disk of the Milky Way (cf. Section 2 above), so, without making any further observations, we also know that there is very little DM in current star-forming regions. One can not draw detailed conclusions about the nature of dark halos from studies of star formation in the disk of the Milky Way. It seems to me that this point has been misunderstood, since one still sees papers which claim to contain dreadful news for brown dwarfs as DM candidates due to the lack of evidence for such objects in star-forming regions. Even more extraordinary are the aspersions cast on brown dwarfs based on the lack of such objects in binary star sytems with visible primaries. Limits on brown dwarfs in binaries have little to do with a hypothetical dark halo of brown dwarfs in the Milky Way, since this would require the 10¹¹ M of DM in the Milky Way halo to be accompanied by visible binary companions with a total mass around 10¹² M! (Admittedly it would be reassuring to find some brown dwarfs, just to determine whether such objects can form at all, but the above observations do not provide any direct constraints on the nature of the DM in galactic halos.)

The easiest way of putting a lot of mass into dark objects is to suppose that, at earlier epochs, the stellar IMF was skewed to either low-mass or high-mass objects. In either case, one simply needs to truncate the IMF. For instance, imposing an upper mass around the hydrogen burning limit of 0.08 M ensures that all objects that form are brown dwarfs. In the high-mass case, truncation prevents the formation of stars that will produce too many metals or still be on the main sequence today. The pollution problem requires that only stars with masses greater than about 200 M form. Such objects collapse to black holes without ejecting too many metals (Carr, Bond and Arnett 1984; Carr 1990).

Ryu, Olive and Silk (1990) resurrected an alternative to brown dwarfs or black holes. They pointed out that white dwarfs have the advantage of being known to exist. The problem is that to avoid forming M dwarfs that would still be around today, and more massive stars that would pollute the Milky Way with metals, Ryu et al. (1990) had to assume that the IMF was strongly peaked around 4 M. In other words, they invoked a stellar IMF that contained only stars that evolved to white dwarfs.

Whether white dwarfs are more attractive than the brown dwarf or black hole option is partly a matter of taste. It is worth noting, however, that the model of Ryu et al. (1990) suffers from other drawbacks. Smecker and Wyse (1991) studied additional constraints based on the occurence of Type Ia supernovae. In a halo dominated by white dwarfs, mergers of such objects in binaries would produce Type Ia explosions as well as the associated helium and metals. Smecker and Wyse (1991) concluded that if white dwarfs constitute the halo DM, their precursors must have formed with a much lower binary fraction than is typical. Again, one could argue that since the required star formation is already atypical, this need not be an added worry. Admirers of simplicity, on the other hand, probably regard these results as another nail in the coffin of white dwarf dark halos.

Theoretical ideas on the mass spectrum of the first generation of stars are not very enlightening. Carr (1990) has pointed out that there are highly plausible reasons to suppose that the first stars were very massive, leading to black hole remnants, and equally compelling arguments that the first generation of objects might have been sub-stellar brown dwarfs. Other ideas also seem to produce more confusion than clarity. For instance, it has sometimes been argued that the minimum stellar fragmentation mass and the minimum mass for hydrogen burning are set by different physical processes, so that it is unlikely that the two scales are the same. Since stars are observed to have a mass spectrum that reaches down to the hydrogen-burning limit, the inference is that brown dwarfs must exist. Direct calculations of the minimum fragmentation mass give values around 0.004 M (Palla, Salpeter and Stahler 1983), thereby supporting this assertion. However, this argument is countered by the claim that star formation is an accretion process that is only halted when protostellar winds turn on. Since such winds require deuterium burning to have commenced, this suggests only visible stars form. The counter-counterargument is that the first stars that form in a protogalaxy will heat the gas and prevent accretion onto other protostellar cores, thereby ensuring that most gas forms brown dwarfs. From this one concludes that there is a lot to learn about star formation.

Lacey and Ostriker (1985) took a more empirical approach and suggested that the ``puffing up'' of the Galactic disk might be due to black holes with masses around 10⁶ M in the Milky Way halo. This could explain the increase in the stellar velocity dispersion with age, as well as the ratios of the radial, azimuthal and vertical velocity dispersions. In fact, this places an upper mass of around 10^6.3 M on black holes (or any other population of dark objects), since higher masses would overheat the disk.

The Lacy and Ostriker (1985) scenario suffers from a couple of drawbacks. Firstly, there is a tendency for such massive black holes to get dragged into the Galactic nucleus through the effects of dynamical friction. Secondly, as such objects cross the Milky Way disk they would gas from the interstellar medium leading to excessive X-ray emission. These considerations led Carr and Lacey (1987) to suggest that dark clusters with masses around 10⁶ M might be more promising candidates. Such objects get disrupted before causing a major build-up of material in the Galactic center. This disruption requires that the components of the clusters have masses less than about 10 M, which favors brown dwarfs, although black holes are still a possibility. Formation mechanisms for such clusters have been discussed by Carr and Lacey (1987) and Ashman (1990b).

Rix (1992) has used the disk-heating argument to rule out black holes and dark clusters at somewhat lower masses. By considering the heating effects of such objects on the dwarf irregular galaxy DDO 154, he finds that dark constituents must satisfy M < 10⁵ M. Limits from the Draco dwarf spheroidal imply an even tighter constraint of M < 10⁴ M.

The black hole option has recently undergone an intriguing revival. Gnedin and Ostriker (1992) have suggested that the DM in halos is made up of the black hole remnants of supermassive objects (SMOs). The novel twist is that the SMOs, which are assumed to form pregalactically, produce considerable amounts of radiation in the young Universe (see also Carr, Bond and Arnett 1984). This radiation alters the abundances of the light elements that are used to constrain the baryonic density of the Universe. Thus primordial nucleosynthesis calculations are not being compared to the true primordial abundances of these elements. The consequence is that _b is higher than the usual limits mentioned above. Eventually, the black hole remnants cluster to form galactic halos.

Evidence for brown dwarfs in the Milky Way halo comes from observations of globular clusters. Some studies of the stellar mass function within these objects have revealed evidence for a steepening at low masses (Richer and Fahlman 1986; 1992). This implies that globular clusters have a higher fraction of low-mass stars than other stellar systems and raises the possibility that they might contain significant numbers of brown dwarfs. Richer and Fahlman (1989) carried out star counts in the globular cluster M71. They concluded that between 50% and 90% of the cluster mass was in stars fainter than their limiting magnitude. While stellar remnants might constitute the unobserved objects, Richer and Fahlman (1989) found that stars with masses below 0.33 M were more likely candidates.

Fahlman et al. (1989) and Richer et al. (1990) continued this work and extended the mass function down to about 0.2 M in M13, M71 and NGC 6397. These results supported the earlier claim that the mass function steepens below about

0.4 M. Interestingly, Richer et al. (1990) found that M13 had the steepest mass function at low-luminosities and thus the largest fraction of low-mass stars. M13 also appears to have undergone less dynamical evolution than the other two globular clusters (see also Richer et al. 1991). Such evolution is expected to produce mass segregation through energy equipartition. This process causes lower mass stars to migrate to the outer regions of the cluster, or possibly to be lost from the cluster altogether. These observations are consistent with the idea that globular clusters initially contained a large number of low-mass stars and brown dwarfs which have since been lost. Richer et al. (1990) speculate that brown dwarfs lost from globular clusters might explain the halo DM. More recent work on M13 has suggested that around 50% of the mass of M31 may presently be in the form of low-mass stars and brown dwarfs (Leonard, Richer and Fahlman 1992).

The idea that the stellar mass function in globular clusters is steep at the low-mass end has received some support from theoretical studies. N-body simulations of the evolution of globular clusters in the Milky Way suggest that steep stellar mass functions may be required for the clusters to survive to the present epoch (Chernoff and Weinberg 1990). Putting more mass into low-mass stars reduces the total amount of mass-loss from the cluster due to stellar evolution, thereby keeping the cluster bound. This is a double-edged sword for proponents of brown dwarfs in the Milky Way halo, since the clusters that are likely to be destroyed and provide the mass of a smooth halo have shallower mass functions and fewer brown dwarfs. Even so, if brown dwarfs are initially present in significant numbers in globular clusters, it seems inevitable that dynamical evolution will lead to many of these objects ending up in the halo.

Other evidence for cosmologically significant numbers of brown dwarfs is provided by cluster cooling flows. X-ray observations of many clusters of galaxies suggest that large amounts of gas are flowing onto a central galaxy (Fabian, Nulsen and Canizares 1984; Fabian 1990). If this gas is forming stars, then the colors and luminosities of the accreting galaxies suggest that most of the gas is forming dark objects. The only candidates appear to be very low-mass stars or brown dwarfs. Some support for this interpretation is provided by observations of a cooling flow galaxy that has a massive near-infrared envelope. Johnstone and Fabian (1989) claim this is consistent with a population of low-mass stars formed from the accreting gas. Ashman and Carr (1988; 1991) and Thomas and Fabian (1990) have suggested that similar quasistatic gas flows may produce galactic halos of brown dwarfs at earlier epochs.

Galaxy clusters also provide more general evidence in favor of baryonic DM, since there is evidence that the DM distribution in these objects is centrally concentrated. This is usually regarded as being indicative of dissipation. In particular, Eyles et al. (1991) have found a centrally peaked DM distribution in the Perseus cluster through X-ray observations. Gravitational lensing of background galaxies also indicate DM distributions that are more concentrated than galaxy distribution in some clusters (Lynds and Petrosian 1989; Tyson 1992).

Despite this circumstantial evidence, attempts to detect brown dwarfs in the halo of the Milky Way have failed so far. Notably, searches for brown dwarfs in the IRAS database have revealed no firm candidates. This does not provide a stringent constraint, although it does illustrate that if brown dwarfs do constitute the halo DM they are extremely elusive.