The Transient Ultra-luminous X-ray Source, ULX-4, in M51

We present the results of a temporal and spectral analysis of the transient source ULX-4 in the galaxy M51. The data used were drawn from {\it Chandra}, {\it XMM-Newton} and {\it XRT} archives, spanning the years 2000-2019. The X-ray flux of the source is seen to vary by two orders of magnitudes within a month but a short-term variability was not observed. We find some evidence for the existence of a bi-modality feature in the flux distribution of ULX-4. The X-ray spectra from most of the data can be fitted by a simple {\it power-law} with a photon index in the range 1.44-2.0 suggesting that the source is in a hard state characterized by non-thermal emission. The presence of a soft component, in two {\it XMM-Newton} observations, is best described by the addition of a mekal component suggesting a contribution from a diffuse background source. We identified two optical sources as possible counterparts within an error radius of 0.18 arcsec at 95% confidence level for ULX-4 based on the archival {\it HST}/ACS and {\it HST}/WFC3 data. The absolute magnitude of these counterparts is -6.6 mag. Blackbody fits of the spectral energy distributions indicate the spectral type to be B-type stars. One of these counterparts exhibits a low-amplitude optical periodicity of 264 $\pm$ 37 days in the F606W filter; If we assume this apparent periodicity is associated with the orbital motion of the donor, then it is more likely that the donor is a red supergiant satisfying the long periodicity and accretion via Roche-lobe overflow. Consequently, the SED would then have to be interpreted as a superposition of emissions from a cold donor and a hot flow component, most likely from an accretion disk. If, on the other hand, the periodicity is super orbital in nature i.e., due to possible interactions of the compact object with a circumstellar disk, the donor could then be a Be/X star hosting a neutron star.