## 5. ConclusionKerins (1997), referred to as Paper I, has suggested that low mass stars could provide the substantial dark matter fraction indicated by the combined 1st- and 2nd-year MACHO gravitational microlensing results. Whilst observations from Hubble Space Telescope (HST) and other instruments have been interpreted as excluding such stars from having a significant halo density, Paper I shows that their density could in fact be substantial if they are grouped into globular-cluster configurations. The motivation for such clusters comes from some baryonic dark matter formation scenarios. Paper I calculates the constraints on such clusters (assuming they comprise low-mass stars of primordial metallicity) which arise from MACHO microlensing results, dynamical constraints on massive halo objects, and observations from 20 HST fields obtained by Gould et al. (1996). However, the results of Paper I apply only to the spherically-symmetric cored isothermal halo model investigated there. In the present study, the number of HST fields utilised has been increased to 51, and now incorporates the Hubble Deep Field and Groth Strip fields (Gould et al. 1997). The model dependency of the results in Paper I has been tested by adopting 5 of the reference halo models employed in the MACHO collaboration's analysis of its microlensing results. One of the models is similar to the halo investigated in Paper I whilst the other 4 are drawn from a self-consistent family of power-law halo models and comprise spherically-symmetric haloes with a rising rotation curve, a falling rotation curve and a flat curve, as well as a flattened (E6) halo model. The 51 HST fields contain just 145 candidates with colours between 1.2 and 1.7 (spanning the colour range predicted for zero-metallicity stars with masses between the hydrogen-burning limit and ) against the tens or hundreds of thousands predicted for the halo models. From this one concludes that the halo fraction in unclustered low-mass stars is at most with 95% confidence, depending on the halo model, and in all cases falls well short of providing even the lower-limit halo fraction inferred by MACHO. However, in the cluster scenario there exists a wide range of cluster masses and radii which can allow a halo fraction consistent with the lower limit derived from MACHO microlensing results whilst remaining compatible with dynamical limits and HST observations. Consistency with the preferred microlensing halo fraction, rather than the lower limit, requires fine tuning of the cluster parameters (as found in Paper I), but is possible for all models investigated. The one potentially serious problem for the cluster scenario is that the strong constraints on unclustered stars imply that an overwhelming fraction of all stars, at least 95%, must still reside in clusters at the present day. This is higher than expected from generic cluster evaporation considerations for much of the permitted cluster mass range, though it may still be consistent with clusters comprising stars with initially anisotropic orbits. In any case, these limits assume that stars which have already evaporated from clusters now form a perfectly smooth distribution which traces the halo density profile. If instead these stars still have a lumpy distribution, reflecting the fact that they previously resided in clusters, then the cluster fraction limits are too strong. Probably the only way to definitively exclude or confirm the cluster scenario is to obtain several deep fields as close to the Galactic centre as is practical, where the strong dynamical constraints severely restrict the range of feasible cluster parameters. © European Southern Observatory (ESO) 1997 Online publication: March 24, 1998 |