Event Rate Density and Luminosity Function of Newborn-Magnetar-Driven X-Ray Transients from Neutron Star Binary Mergers

TL;DR

This study estimates the event rate density and luminosity function of newborn-magnetar-driven X-ray transients from neutron star mergers, providing predictions for detection rates with the upcoming Einstein Probe mission.

Contribution

It introduces a new analysis combining population synthesis and observational data to characterize the luminosity function and event rate density of these transients, with implications for future observations.

Findings

Local event rate density of ~300 Gpc^-3 yr^-1

Luminosity function characterized by a broken power-law

Estimated Einstein Probe detection rate of ~31 per year

Abstract

X-ray transients (XTs) driven by newborn magnetars from mergers of neutron star binaries (NSBs) were occasionally detected in the narrow-field {\it Chandra} Deep Field-South survey (CDF-S) and the {\it Swift}/XRT observations of short gamma-ray bursts (sGRBs). Quantifying their event rate density (ERD) and luminosity function (LF) is critical for understanding NSB coalescence and magnetar formation. Utilizing population synthesis calculations incorporating various equations of state (EoS), we derive a local ERD of $\sim 300\,{\rm Gpc^{-3}\,yr^{-1}}$ and a redshift-dependent ERD profile peaking at $z=1.81$ followed by rapid decline beyond $z \sim 4$. Constructing an XT sample based on CDF-S and {\it Swift} observations, we characterize the LF by a single power-law function at $L \leq 4.75 \times 10^{46}\;{\rm erg\;s^{-1}}$ with a slope of $-1.03$, following by a broken power-law function in which the break luminosity is $L_{\rm b} = 4.38 \times 10^{47}\;{\rm erg\;s^{-1}}$ and the slopes are $-0.28$ and $-1.66$. Based on the ERD and the LF, we estimate that the {\it Einstein Probe} ({\it EP}) detection rate is $\sim 31\;{\rm yr^{-1}}$, adopting a conservative threshold flux of $10^{-9}\;{\rm erg}\;{\rm s^{-1}}$, an luminosity range of $L \in [2\times 10^{44},2\times 10^{49}]\;{\rm erg\;s^{-1}}$, and a correction for jet opening angle of $\sim 16^{\circ}$. This detection rate is consistent with the {\it EP} observations during its first-year operation. It is important to note that our estimation is subject to uncertainties arising from the LF derivation. Future {\it EP} observations of these XT events will be crucial in reducing these uncertainties.