## 2. Limits on zero-metallicity VLM starsSaumon et al. (1994 ) have computed a grid of fully non-gray
atmospheric models for zero-metallicity () VLM
stars and brown dwarfs in the mass range . Their
calculations take account of all the major sources of opacity for a
pure H+He mixture including H In particular, Saumon et al. find that the expected colour for zero-metallicity VLM stars ranges between 1.27 for 0.2- stars to 1.57 at the hydrogen-burning limit (). This is somewhat below the threshold values assumed by BFGK, GF and Flynn et al. (1996 ) in their analyses, whose inferences are based on the number counts of stars with . Whilst one can not say for sure whether any dark halo population has a metallicity substantially less than that of the spheroid, there is clearly a need to re-examine the HST data using the zero-metallicity predictions of Saumon et al. in order to close up this last remaining 'loophole'. The positions of the 22 HST fields are tabulated in Gould et al.
(1996 ), along with the corresponding minimum and maximum The limiting maximum In computing the minimum and maximum observable distances for each
VLM star mass, and for each field, I follow Gould et al. (1996 ) in
converting the The halo mass within the volume defined by the minimum and maximum distances , , and the solid angle per field sr, is calculated assuming a spherically-symmetric softened isothermal halo density distribution of the form where The integral can be performed analytically though the resulting expression is long. Note that the integral limits in Eq. 2 are implicit functions
of the VLM star mass for The median value for is found to range from 330 pc for 0.092- stars up to 1 kpc for 0.2- stars. For the median values are 3.3 kpc and 10.1 kpc for 0.092- and 0.2- stars, respectively. Applying Eq. 3 to VLM stars at the hydrogen-burning limit mass of , one finds an expectation number of stars in the HST fields of 6 310, and for 0.2- objects the expectation is nearly an order of magnitude larger at 60 100 stars. These numbers take account of the fact that data from one-third of field 4 (i.e. data from one of the three detector chips) had to be discarded by Gould et al. (1996 ) due to problems with receiving the data from HST, and that as much as 2% of each of the fields was discarded due to emission from background galaxies. The number of stars detected in the 20 fields with values in the range 1.2 to 1.7, spanning the range predicted by Saumon et al. (1994 ), is only 75. The 95% CL (Confidence level) upper limit on the average, for a realisation of 75 stars, is 91. Therefore, even if one assumes that all of the stars detected by HST are halo VLM stars right on the hydrogen-burning limit, their contribution to the halo DM can be no more than 1.4% at the 95% CL, and the limit is correspondingly stronger than this for more massive objects. In fact it is likely that a significant fraction of these objects may belong to the disc or spheroid. The limit of 1.4% is stronger than that inferred by BFGK for solar-metallicity VLM stars from their analysis of one of the HST fields. Their results translate to a 95% CL upper limit of less than 4% for stars with , adopting . The 95% upper limit inferred by GF for low-metallicity stars with corresponds to a halo fraction of less than 0.9% for the same field. However, both of these studies exclude from their analyses stars with , so the limits presented here, which are derived from 20 fields, constitute a completely independent check on previous results. The conclusion is that, regardless of their metallicity, VLM stars do not contribute significantly to the halo DM, at least under the assumption that they are smoothly distributed in the halo. © European Southern Observatory (ESO) 1997 Online publication: June 5, 1998 |