Astron. Astrophys. 322, 709-718 (1997)

1. Introduction

Recent advances in attempts to detect or constrain the nature of dark matter (DM) in the halo of our Galaxy have led to a variety of constraints on both baryonic and non-baryonic candidates (Carr 1994 ; Jungman et al. 1996 ).

The microlensing rate observed by the MACHO collaboration (Alcock et al. 1997) towards the Large Magellanic Cloud (LMC) indicates that the likely halo DM fraction in compact form is around 40%, and comprises objects in the mass range , though the inferred fraction and mass range are sensitive to the assumed halo distribution function. This therefore suggests that the halo may comprise a roughly equal mixture of baryonic and non-baryonic matter, though there are non-baryonic candidates, such as primordial black holes and shadow matter, which can also explain the microlensing events. In any case, the MACHO results imply that no single candidate, baryonic or non-baryonic, can explain all of the halo DM unless the halo distribution function departs significantly from the usual assumption of an isothermal sphere.

If the DM responsible for the observed microlensing is baryonic then the inferred mass range implicates either white-dwarf remnants of an early generation of stars or very low-mass (VLM) stars close to the hydrogen-burning limit. However, in our Galaxy the number density of halo white dwarfs is strongly constrained by the present-day helium and metal abundances of the interstellar medium (Carr et al. 1984 ; Ryu et al. 1990 ; Adams & Laughlin 1996 ) and, assuming the white dwarfs are younger than 18 Gyr, by number counts of high-velocity white dwarfs (Chabrier et al. 1996 ). Counts of high-redshift galaxies also appear to rule out white dwarfs from contributing significantly to halo DM in other galaxies (Charlot & Silk 1995 ).

VLM stars are currently even less favoured since photometric surveys appear to place even stronger limits on their contribution (e.g. Gilmore & Hewett 1983 ; Richstone et al. 1992 ; Bahcall et al. 1994 , hereafter BFGK; Graff & Freese 1996 , hereafter GF; Flynn et al. 1996 ). The latest MACHO results also appear to argue against most of the DM comprising sub hydrogen-burning brown dwarfs unless the DM is distributed more like a maximal disc, in which case any halo must have a very low total mass interior to the LMC in order to remain consistent with local surface-density and rotation-curve constraints. Within the context of standard halo models therefore, there is great difficulty in explaining the high halo fraction detected by MACHO by invoking a single baryonic candidate.

In this paper I re-examine the VLM star hypothesis for the case where the stars have zero-metallicity, as may be the case if the halo is formed from primordial matter. In this case their colours will be different than assumed by previous studies, so constraints from these studies need not necessarily apply to zero-metallicity stars. I also examine the possibility of DM clustering, and how that effects number counts and microlensing statistics. Such clustering is predicted by some DM formation theories.

The plan of the paper is as follows: Sect.  2 calculates the space density constraints for a smoothly distributed population of zero-metallicity VLM stars imposed by number counts from 20 of the 22 HST fields obtained by BFGK. These calculations adopt the latest numerical predictions for zero-metallicity VLM star photometry. It will be shown that the limits on such a population are comparable to those for populations of non-zero metallicity, with the allowed halo fraction being at most 1.4%. Sect.  3 extends the analysis to include the effect of clustering and, using a combination of the HST number-count limits, MACHO observations and dynamical constraints on the permitted mass and radius of clusters, places upper limits on the cluster space density. It will be shown that whilst dynamical constraints strongly limit the allowed mass and radius of clusters, they nonetheless permit a cluster DM fraction which can simultaneously explain the MACHO and HST observations, though both the required mass M and radius R need to be finely tuned (,  pc). I further show that the microlensing signatures of these clusters are essentially indistinguishable from the unclustered scenario, and in particular are not expected to modify the inferred halo fraction. Finally in this section, I use the halo DM fraction inferred by MACHO to compute the efficiency with which VLM stars must be clustered in order to remain compatible with HST observations. The required efficiency, better than 92% at the present day, places the strongest demand on the scenario. The main findings of the paper are discussed in Sect.  4.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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