Ultraluminous X-ray sources in nearby galaxies from ROSAT High Resolution Imager observations I.: Data analysis

X-ray observations have revealed in other galaxies a class of extranuclear X-ray point sources with X-ray luminosities of 10(39) - 10(41) ergs s(-1), exceeding the Eddington luminosity for stellar mass X-ray binaries. These ultraluminous X-ray sources (ULXs) may be powered by intermediate- mass black holes of a few thousand M-. or stellar mass black holes with special radiation processes. In this paper, we present a survey of ULXs in 313 nearby galaxies with D-25 > 1' within 40 Mpc with 467 ROSAT High Resolution Imager (HRI) archival observations. The HRI observations are reduced with uniform procedures, refined by simulations that help define the point source detection algorithm employed in this survey. A sample of 562 extragalactic X-ray point sources with L-X = 10(38) 10(43) ergs s(-1) is extracted from 173 survey galaxies, including 106 ULX candidates within the D-25 isophotes of 63 galaxies and 110 ULX candidates between 1D(25) and 2D(25) of 64 galaxies, from which a clean sample of 109 ULXs is constructed to minimize the contamination from foreground or background objects. The strong connection between ULXs and star formation is confirmed based on the striking preference of ULXs to occur in late-type galaxies, especially in star-forming regions such as spiral arms. ULXs are variable on timescales over days to years and exhibit a variety of long term variability patterns. The identifications of ULXs in the clean sample show some ULXs identified as supernovae ( remnants), H II regions/nebulae, or young massive stars in star-forming regions, and a few other ULXs identified as old globular clusters. In a subsequent paper, the statistic properties of the survey will be studied to calculate the occurrence frequencies and luminosity functions for ULXs in different types of galaxies to shed light on the nature of these enigmatic sources.