Luminosity function and event rate density of XMM-Newton-selected supernova shock-breakout candidates

A dozen X-ray supernova shock breakout (SN SBO) candidates were reported recently based on XMM-Newton archival data, which increased the X-ray selected SN SBO sample by an order of magnitude. Assuming they are genuine SN SBOs, we study the luminosity function (LF) by improving upon the method used in our previous work. The light curves and the spectra of the candidates were used to derive the maximum volume within which these objects could be detected with XMM-Newton by simulation. The results show that the SN SBO LF can be described by either a broken power law (BPL) with indices (at the 68$\%$ confidence level) of $0.48 \pm 0.28$ and $2.11 \pm 1.27$ before and after the break luminosity at $\log (L_b/\rm erg\,s^{-1})=$ $45.32 \pm 0.55$ or a single power law (SPL) with index of $0.80 \pm 0.16$. The local event rate densities of SN SBOs above $5\times 10^{42}$ $\rm erg\,s^{-1}$ are consistent for two models, i.e., $4.6 ^{+1.7}_{-1.3} \times 10^4$ and $4.9 ^{+1.9}_{-1.4} \times 10^4$ $\rm Gpc^{-3}\,yr^{-1}$ for BPL and SPL models, respectively. The number of fast X-ray transients of SN SBO origin can be significantly increased by the wide-field X-ray telescopes such as the Einstein Probe.