  Ultraluminous X-ray sources (ULXs) are some of the brightest phenomena found
outside of a galaxy's nucleus, and their explanation typically invokes
accretion of material onto a black hole. Here, we perform the largest
population study to date of ULXs in early-type galaxies, focusing on whether a
galaxy's large scale environment can affect its ULX content. Using the AMUSE
survey, which includes homogeneous X-ray coverage of 100 elliptical galaxies in
the Virgo cluster and a similar number of elliptical galaxies in the field
(spanning stellar masses of 1e8-1e12 M_sun), we identify 37.9 +/- 10.1 ULXs in
Virgo and 28.1 +/- 8.7 ULXs in the field. Across both samples, we constrain the
number of ULXs per unit stellar mass, i.e., the ULX specific frequency, to be
0.062 +/- 0.013 ULXs per 10^10 M_sun (or about 1 ULX per 1.6e11 M_sun of galaxy
stellar mass). We find that the number of ULXs, the specific frequency of ULXs,
and the average ULX spectral properties are all similar in both cluster and
field environments. Contrary to late-type galaxies, we do not see any trend
between specific ULX frequency and host galaxy stellar mass, and we show that
dwarf ellipticals host fewer ULXs than later-type dwarf galaxies at a
statistically meaningful level. Our results are consistent with ULXs in
early-type galaxies probing the luminous tail of the low-mass X-ray binary
population, and are briefly discussed in context of the influence of
gravitational interactions on the long-term evolution of a galaxy's (older)
stellar population.
