LIGO-Virgo-KAGRA's Oldest Black Holes: Probing star formation at cosmic noon with GWTC-3

Abstract

In their third observing run, the LIGO-Virgo-KAGRA gravitational-wave (GW) observatory was sensitive to binary black hole (BBH) mergers out to redshifts $z_{\mathrm{merge}}\approx 1$. Because GWs are inefficient at shrinking the binary orbit, some of these BBH systems likely experienced long delay times $\ddot{I}„$ between the formation of their progenitor stars at $z_{\mathrm{form}}$ and their GW merger at $z_{\mathrm{merge}}$. In fact, the distribution of delay times predicted by isolated binary evolution resembles a power law $p(\ddot{I}„)\propto \ddot{I}{„}^{\hat{I}{\pm }_{\ddot{I}}„}$ with slope $-1\lesssim \hat{I}{\pm }_{\ddot{I}}„\lesssim -0.35$ and a minimum delay time of $\ddot{I}{„}_{\min }=10$ Myr. We use these predicted delay time distributions to infer the formation redshifts of the $\sim 70$ BBH events reported in the third GW transient catalog GWTC-3 and the formation rate of BBH progenitors. For our default $\hat{I}{\pm }_{\ddot{I}}„=-1$ delay time distribution, we find that GWTC-3 contains at least one system (with 90\% credibility) that formed earlier than $z_{\mathrm{form}}>4.4$. Comparing our inferred BBH progenitor formation rate to the star formation rate (SFR), we find that at $z_{\mathrm{form}}=4$, the number of BBH progenitor systems formed per stellar mass was $6.4_{-5.5}^{+9.4}\times 10^{-6}{M}_{\odot }^{-1}$ and this yield dropped to $0.134_{-0.127}^{+1.6}\times 10^{-6}{M}_{\odot }^{-1}$ by $z_{\mathrm{form}}=0$. We discuss implications of this measurement for the cosmic metallicity evolution, finding that for typical assumptions about the metallicity-dependence of the BBH yield, the average metallicity at $z_{\mathrm{form}}=4$ was $⟨{\log }_{10}(Z/Z_{\odot })⟩=-0.3_{-0.4}^{+0.3}$, although the inferred metallicity can vary by a factor of $\approx 3$ for different assumptions about the BBH yield. Our results highlight the promise of current GW observatories to probe high-redshift star formation.

Updates to some calculations following helpful referee comments. Accepted by ApJL. 17 pages, 8 figures