A comprehensive catalogue of high-mass X-ray binaries in the Large Magellanic Cloud detected during the first eROSITA all-sky survey

Context. The Magellanic Clouds, the closest star-forming galaxies to the Milky Way, offer an excellent environment to study high-mass X-ray binaries (HMXBs). While the Small Magellanic Cloud (SMC) has been thoroughly investigated with over 120 systems identified, the Large Magellanic Cloud (LMC) has lacked a complete survey due to its large angular size. Most prior studies targeted central or high-star-formation regions. The SRG/eROSITA all-sky surveys now enable a comprehensive coverage of the LMC, particularly due to its close vicinity to the south ecliptic pole. Aims. This work aims to improve our understanding of the HMXB population in the LMC by building a flux-limited catalogue. This allows us to compare sample properties with those of HMXB populations in other nearby galaxies. Methods. Using detections during the first eROSITA all-sky survey (eRASS1), we cross-matched X-ray positions with optical and infrared catalogues to identify candidate HMXBs. We assigned flags based on multi-wavelength follow-up observations and archival data, using properties of known LMC HMXBs. These flags defined confidence classes for our candidates. Results. We detect sources down to X-ray luminosities of a few $10^{34},\mathrm{erg,s^{-1}}$, resulting in a catalogue of 53 objects, including 28 confirmed HMXBs and 21 new eROSITA detections. Compared to the SMC, the LMC hosts fewer HMXBs and more systems with supergiant companions. We identify several likely supergiant systems, including a candidate supergiant fast X-ray transient with phase-dependent flares. We also find three Be stars with likely white dwarf companions. Two of the candidate Be/WD binaries show steady luminosities across four eROSITA scans, unlike the post-nova states seen in the majority of previous Be/WD reports. Conclusions. Our catalogue is the first to cover the entire LMC since the ROSAT era, providing a basis for statistical population studies. Using the HMXB population, we estimate the LMC star-formation rate to be $(0.22_{-0.07}^{+0.06}),M_{\odot},\mathrm{yr^{-1}}$, which is in agreement with results using other tracers.