Ultraluminous X-ray sources in the first eROSITA survey I. Candidate catalogs
Ultraluminous X-ray sources (ULXs) are luminous non-nuclear X-ray point sources embedded in galaxies. Their luminosities exceeding 10^39 erg/s potentially require sub-Eddington accretion by objects with masses from ~10^2$M_{\odot}$ to ~10^4$M_{\odot}$ or supercritical accretion beyond the Eddington limit by stellar mass black holes or neutron stars. We identified ULXs by searching for X-ray counterparts in the ~10^5 galaxies of the HECATE catalog in the footprint of the first eROSITA all-sky survey, while excluding nuclear regions to avoid the selection of active galactic nuclei (AGN). We characterized the completeness of the sample and its contamination by unidentified AGN and determined the influence of source confusion. The catalog is unaffected by X-ray selection biases. We removed known contaminants such as supernovae, stars, and AGN, and manually vetted all candidates to further remove contaminants. We derived the X-ray selection function and fraction of unidentified AGN interlopers using a simulation with subsequent source detection. We present two samples of ULX candidates. The main sample consists of 90 sources with highly confident X-ray detections, 53 of which are identified for the first time. This sample is complete to a distance of ~7Mpc, contains at most 29% of unknown background AGN, and is mostly unaffected by source confusion. Several candidates are newly identified even though their locations have been observed by other instruments before, and some previously reported candidates we expected to identify are absent from our sample, demonstrating the transient behavior of ULXs. Based on our list of less confident detections, we also provide an extended catalog of 260 sources identified as potential candidates for further ULX identifications. Of these, 245 are identified as potential candidates for the first time. (Abridged)