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Pop II and the Dark Matter Halo (1Jun94)
(from NOAO HIGHLIGHTS!, NOAO Newsletter No. 38, 1 June 1994)

Explorations of the faint end of the luminosity function in nearby
globular clusters are improving understanding of topics ranging from
the structure of stars near the hydrogen-burning limit to the nature of
the dark matter halo (DMH) of the Galaxy.  The inferred mass of the
DMHs in galaxies like the Milky Way can provide about 0.05 to 0.1 of
the density required to close the Universe.  Hot Big Bang
nucleosynthesis calculations suggest about this mass in baryons was
formed in the early Universe, thus it is reasonable to suppose that the
DMH of the Galaxy is made of ordinary matter.  One obvious possibility
is that low-mass stars from the Pop II field contain sufficient mass to
explain the various dynamical effects suggestive of a DMH.  Stars near
0.1 Mo have M/L ratios ranging from 1500 to 4000 more than "dark"
enough to explain the DMH M/L of between 30 and 100.  The observational
problem is to measure the luminosity and mass function for the Pop II
field for M <  0.5 Mo.

         		  [Figure not included]

In situ studies of the Pop II luminosity function (LF) are difficult
because of the intrinsic faintness of low-mass stars.  Even surveys
with very faint limiting magnitudes sample only a small volume of
space.  Further complications are the large population of faint
galaxies in deep surveys and the difficulties of retrieving distance
and [Fe/H] information given only broad-band colors and brightnesses.
Nevertheless, such studies have been undertaken and may soon provide
some valuable constraints (one such ambitious and recent program is
described in Richer and Fahlman, 1992, Nature, 358, 383).

An alternative is to look where there are large numbers of low-mass Pop
II stars at a known distance and metallicity - the Galactic globular
clusters.  Although there is considerable uncertainty in the connection
between cluster and the field LFs, most theoretical studies suggest
that the LF measured in current-day clusters probably represents a
conservative limit on the population of low-mass stars in clusters.
Recent faint LFs based on I band observations in the clusters M13, NGC
5139 (j Centauri), and NGC 6752 have indicated a sharp increase in the
number of stars below 0.4 Mo (Richer et al. 1991, ApJ, 359, L11).  In
the single-color study of NGC 6752 there was no sign of a turnover in
the LF down to the Richer et al.  faint limit corresponding to ~ 0.17
Mo.  If the Pop II field has as steep a slope as that seen in NGC 6752
and it extends to masses as low as 0.02 Mo this could explain the
Galactic DMH if it indeed has the shape of the Pop II spheroid and a
M/L ~ 30.

A effort was begun in June 1993 using the CTIO 4-m + PFCCD by Bolte (U.
of California, Santa Cruz), Hesser and Stetson (NRC/Dominion Astrophys.
Obs.), and VandenBerg (U. of Victoria) to verify and extend to faint
luminosities and lower masses the Richer et al. work in NGC 6752.  The
program involves very deep imaging in two bands (V and I) and avoids
many of the uncertainties of single bandpass studies.  The
color-magnitude diagram shown in the figure is the result of ALLFRAME
(Stetson 1994, PASP in press) reductions of 10 X 900 seconds exposures
in V and 10 X 600 seconds exposures in I.  The main sequence of stars
in NGC 6752 is unambiguously defined to V = 24, corresponding to Mv
11.5.  Even with the rough calibration that was used to generate the
figure, it is clear that the inflection of the main sequence at faint
Mv (seen at V ~ 22.5) predicted by the Bergbusch and VandenBerg (1992,
ApJS, 81, p.163) isochrones does occur in real clusters.  Determining
LFs to the limit of the data requires an extensive battery of
artificial star experiments; however, the preliminary result is that
the Richer et al. steep LF in NGC 6752 is verified.  Time has been
granted in July 1994 to extend these observations to even lower
masses.  Although the extremely steep mass-luminosity relationship for
stars with M <  0.2 Mo makes it very difficult to test directly whether
or not the mass function will extend to 0.02 Mo it will be possible to
explore to the hydrogen burning limit.  If the steep LF continues to
0.1 Mo then at the very least the Pop II low-mass stars must be
considered as an important (5-20%) constituent of the Galactic DMH.

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