  Based on the archival data from the Chandra observations of nearby galaxies,
we study different sub populations of low-mass X-ray binaries (LMXBs) -
dynamically formed systems in globular clusters (GCs) and in the nucleus of M31
and (presumably primordial) X-ray binaries in the fields of galaxies. Our aim
is to produce accurate luminosity distributions of X-ray binaries in different
environments, suitable for quantitative comparison with each other and with the
output of population synthesis calculations. Our sample includes seven nearby
galaxies (M31, Maffei 1, Centaurus A,M81, NGC 3379, NGC 4697, and NGC 4278) and
the Milky Way, which together provide relatively uniform coverage down to the
luminosity limit of E35 erg/s. In total we have detected 185 LMXBs associated
with GCs, 35 X-ray sources in the nucleus of M31, and 998 field sources of
which ~ 365 are expected to be background AGN. We combine these data, taking
special care to accurately account for X-ray and optical incompleteness
corrections and the removal of the contamination from the cosmic X-ray
background sources, to produce luminosity distributions of X-ray binaries in
different environments to far greater accuracy than has been obtained
previously. We found that luminosity distributions of GC and field LMXBs differ
throughout the entire luminosity range, the fraction of faint (log(Lx) < 37)
sources among the former being ~ 4 times less than in the field population. The
X-ray luminosity function (XLF) of sources in the nucleus of M31 is similar to
that of GC sources at the faint end but differs at the bright end, with the M31
nucleus hosting significantly fewer bright sources. We discuss the possible
origin and potential implications of these results.
