Chandra ACIS Survey of X-ray Point Sources in Nearby Galaxies. II. X-ray
  Luminosity Functions and Ultraluminous X-ray Sources
  Based on the recently completed {\it Chandra}/ACIS survey of X-ray point
sources in nearby galaxies, we study the X-ray luminosity functions (XLFs) for
X-ray point sources in different types of galaxies and the statistical
properties of ultraluminous X-ray sources (ULXs). Uniform procedures are
developed to compute the detection threshold, to estimate the
foreground/background contamination, and to calculate the XLFs for individual
galaxies and groups of galaxies, resulting in an XLF library for 343 galaxies
of different types. With the large number of surveyed galaxies, we have studied
the XLFs and ULX properties across different host galaxy types, and confirm
with good statistics that the XLF slope flattens from lenticular
($\alpha\sim1.50\pm0.07$) to elliptical ($\sim1.21\pm0.02$), to spirals
($\sim0.80\pm0.02$), to peculiars ($\sim0.55\pm0.30$), and to irregulars
($\sim0.26\pm0.10$). The XLF break dividing the neutron star and black hole
binaries is also confirmed, albeit at quite different break luminosities for
different types of galaxies. A radial dependency is found for ellipticals, with
a flatter XLF slope for sources located between $D_{25}$ and 2$D_{25}$,
suggesting the XLF slopes in the outer region of early-type galaxies are
dominated by low-mass X-ray binaries in globular clusters. This study shows
that the ULX rate in early-type galaxies is $0.24\pm0.05$ ULXs per surveyed
galaxy, on a $5\sigma$ confidence level. The XLF for ULXs in late-type galaxies
extends smoothly until it drops abruptly around $4\times10^{40}$ erg s$^{-1}$,
and this break may suggest a mild boundary between the stellar black hole
population possibly including 30 $M_\odot$ black holes with super-Eddington
radiation and intermediate mass black holes.
