Optical counterparts of ultraluminous X-ray sources identified from archival HST WFPC2 images

We present a systematic analysis of archival HST WFPC2 Association'' data sets that correlate with the Chandra positions of a set of 44 ultraluminous X-ray sources (ULXs) of nearby galaxies. The main motivation is to address the nature of ULXs by searching for optical counterparts. Sixteen of the ULXs are found in early-type galaxies (RC3 Hubble type < 3). We have improved the Chandra/HST relative astrometry whenever possible, resulting in errors circles of 0.3-1.7 in size. Disparate numbers of potential ULX counterparts are found, and in some cases none are found. The lack of or low number of counterparts in some cases may be due to insufficient depth in the WFPC2 images. Particularly in late-type galaxies, the HST image in the ULX region was often complex or crowded, requiring source detection to be performed manually. We therefore address various scenarios for the nature of the ULX since it is not known which, if any, of the sources found are true counterparts. The optical luminosities of the sources are typically in the range 10(4)-10(6) L-circle dot, with (effective) V magnitudes typically in the range 22-24. In several cases color information is available, with the colors roughly tending to be more red in early-type galaxies. This suggests that, in general, the (potential) counterparts found in early-type galaxies are likely to be older stellar populations and are probably globular clusters. Several early-type galaxy counterparts have blue colors, which may be due to younger stellar populations in the host galaxies, however, these could also be background sources. In spiral galaxies the sources may also be due to localized structure in the disks rather than bound stellar systems. Alternatively, some of the counterparts in late-type galaxies may be isolated supergiant stars. The observed X-ray/optical flux ratio is diluted by the optical emission of the cluster in cases where the system is an X-ray binary in a cluster, particularly in the case of a low-mass X-ray binaries in an old cluster. If any of the counterparts are bound systems with similar to 10(4)-10(6) stars and are the true counterparts to the ULX sources, then the X-ray luminosities of the ULX are generally well below the Eddington limit for a black hole with mass similar to 0.1% of the cluster mass. Finally, we find that the optical flux of the counterparts is consistent with being dominated by emission from an accretion disk around an intermediate-mass black hole if the black hole happens to have a mass greater than or similar to 10(2) M-circle dot and is accreting at close to the Eddington rate, unless the accretion disk is irradiated (which would result in high optical disk luminosities at lower black hole masses).