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

TL;DR

This study tackles the origin of fast X-ray transients (FXTs) by deriving their intrinsic luminosity function and formation rate from the Einstein Probe (EP) FXT catalog using nonparametric methods. By applying the Efron-Petrosian framework and Lynden-Bell's $c^-$ approach to 107 EP FXTs (with 31 secure redshifts), the authors quantify significant luminosity evolution as $L\propto(1+z)^{3.58}$ and obtain a local luminosity function described by a broken power law with break at $L_0^b=(4.17\pm0.34)\times10^{46}$ erg s$^{-1}$. The FXT formation rate is well fit by a broken power law, with $\rho(z)$ scaling as $(1+z)^{-4.25}$ for $z\lesssim0.9$ and $(1+z)^{-0.26}$ for $z\gtrapprox0.9$, giving a local rate of $\rho(0)\approx153.8^{+249.4}_{-95.1}$ Gpc$^{-3}$ yr$^{-1}$. The FXT rate is higher than that of long gamma-ray bursts and suggests a component linked to LL-LGRBs, linking FXTs to GRB-related phenomena while acknowledging limitations due to the sample size.

Abstract

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 $ρ(z) \propto (1+z)^{-4.25}$ at $z \lessapprox 0.9$ and $ρ(z) \propto (1+z)^{-0.26}$ 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.

Figures (4)

• Figure 1: The X-ray luminosity vs. redshift of 31 FXTs. The solid (black) curve shows the truncation boundaries assuming limiting X-ray flux of $F_{\rm limit} = 4.5 \times 10^{-11}$ erg cm$^{-2}$ s$^{-1}$ with a fixed photon index $\Gamma_{\rm WXT}= 1.59$. The associated set $M_i$ is shown in the red rectangle, and $N_i$ is shown in the blue rectangle.
• Figure 2: Left: value of test statistic $\tau$ as a function of $k$. The red dotted line is the best fit for $\tau = 0$, and the black dotted lines represent 1$\sigma$ errors. The optimal value is $k=3.58_{-0.51}^{+0.63}$ at a 1$\sigma$ confidence level. Right: nonevolving luminosity $L_{0,X} = L_{X}/(1 + z)^{3.58}$ of 31 FXTs. The black solid line represents the observational limit considering the impact of $k$.
• Figure 3: Left: cumulative luminosity function $\psi(L_{0,X})$. The scatter represents the cumulative number (N) with 1$\sigma$ error ($\sqrt{N}$), and the red line represents the best fit with a broken power-law model with the low-end index of $0.25 \pm 0.01$ and the high-end index of $0.71 \pm 0.03$, and the break luminosity is $4.17 \pm 0.34 \times 10^{46}$ erg/s. Right: cumulative redshift distribution of FXTs, $\phi(z)$.
• Figure 4: Left: comoving formation rate $\rho(z)$ of FXTs obtained from Equation (\ref{['eq:rho']}). It is normalized to unity at the first point, and the 1$\sigma$ error is also shown. The solid and dashed lines represent the single and double power-law forms of $\rho(z)$, respectively. Right: comparison between the formation rate of FXTs and other events. The red line represents the formation rate of FXTs. The yellow and blue lines represent the rates of short GRBs 2018ApJ...852....1Z and LGRBs 2015ApJS..218...13Y, respectively. The magenta line is the rates of FRBs 2024ApJ...973L..54C. The gray dots correspond to the observed SFR Hopkins_20062008MNRAS.388.1487L. Note that all formation rates are normalized at a redshift of $\sim 1$