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A dozen X-ray supernova shock breakout (SN SBO) candidates were reportedrecently based on XMM-Newton archival data, which increased the X-ray selectedSN SBO sample by an order of magnitude. Assuming they are genuine SN SBOs, westudy the luminosity function (LF) by improving upon the method used in ourprevious work. The light curves and the spectra of the candidates were used toderive the maximum volume within which these objects could be detected withXMM-Newton by simulation. The results show that the SN SBO LF can be describedby either a broken power law (BPL) with indices (at the 68$\%$ confidencelevel) of $0.48 \pm 0.28$ and $2.11 \pm 1.27$ before and after the breakluminosity at $\log (L_b/\rm erg\,s^{-1})=$ $45.32 \pm 0.55$ or a single powerlaw (SPL) with index of $0.80 \pm 0.16$. The local event rate densities of SNSBOs 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 offast X-ray transients of SN SBO origin can be significantly increased by thewide-field X-ray telescopes such as the Einstein Probe.

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