The Formation Rate and Luminosity Function of Fast X-ray transients from Einstein probe

Following its launch on 2024 January 9, the Einstein Probe (EP) telescope has detected hundreds of fast X-ray transients (FXTs), yet their physical origins remain elusive. Understanding their luminosity function and formation rate is crucial for elucidating their nature. Recently, the EP team has provided the latest catalog of EP-detected FXTs. Based on this catalog, we present a model-independent nonparametric approach to derive the luminosity function and formation rate of FXTs. Our analysis reveals significant cosmological luminosity evolution, characterized by a scaling relationship of $(1+z)^{3.58}$. After accounting for this evolution, we establish that the local luminosity function is best represented by a broken power law, with a break luminosity of $(4.17 \pm 0.34) \times 10^{46}$ erg/s. The formation rate exhibits a broken power law as $\rho(z) \propto (1+z)^{-4.25}$ at $z \lessapprox 0.9$ and $\rho(z) \propto (1+z)^{-0.26}$ at $z \gtrapprox 0.9$, yielding a local rate of approximately $153.8_{-95.1}^{+249.4}$ Gpc$^{-3}$ yr$^{-1}$. This rate is higher than that of long gamma-ray bursts (LGRBs). Our findings indicate that a component of FXTs is associated with LGRBs.