Detectability of Population III stellar remnants as X-ray binaries from tidal captures in the local Universe

We assess the feasibility of detecting the compact object remnants from Population III (Pop III) stars in nearby dense star clusters, where they become luminous again as X-ray binaries (XRBs) and tidal disruption events (TDEs) via strong tidal encounters. Analytically modelling the formation of Pop III stars, coupled with a top-heavy initial mass function predicted by numerical simulations, we derive the number of (active) Pop III XRBs and TDEs in the present-day Milky Way (MW) nuclear star cluster as $\sim 0.06-0.3$ and $\lesssim 4\times 10^{-6}$, rendering any detection unlikely. The detection probability, however, can be significantly boosted when surveying all massive star clusters from the MW and neighboring galaxy clusters. Specifically, we predict $\sim 1.5-6.5$ and $\sim 40-2800$ active Pop III XRBs in the MW and the Virgo cluster, respectively. Our Pop III XRBs are dominated ($\sim 99\%$) by black holes with a typical mass and luminosity of $\sim 45$ $\rm M_{\odot}$ and $\sim 10^{36}$ $\rm erg\ s^{-1}$. Deep surveys of nearby ($\lesssim 30-300$ $\rm Mpc$) galaxy clusters for such Pop III XRBs are well within reach of next-generation X-ray telescopes, such as ATHENA and LYNX.