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

In their third observing run, the LIGO-Virgo-KAGRA gravitational-wave (GW) observatory was sensitive to binary black hole (BBH) mergers out to redshifts $z_\mathrm{merge}\approx1$. Because GWs are inefficient at shrinking the binary orbit, some of these BBH systems likely experienced long delay times $\tau$ 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 $p(\tau)\propto\tau^{\alpha_\tau}$ with slope $-1\lesssim\alpha_\tau\lesssim-0.35$ and a minimum delay time of $\tau_\mathrm{min}=10$ Myr. We use these predicted delay time distributions to infer the formation redshifts of the $\sim70$ BBH events reported in the third GW transient catalog GWTC-3 and the formation rate of BBH progenitors. For our default $\alpha_\tau=-1$ 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 $6.4^{+9.4}_{-5.5}\times10^{-6}\,M_\odot^{-1}$ and this yield dropped to $0.134^{+1.6}_{-0.127}\times10^{-6}\,M_\odot^{-1}$ 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 $\langle\log_{10}(Z/Z_\odot)\rangle=-0.3^{+0.3}_{-0.4}$, although the inferred metallicity can vary by a factor of $\approx3$ for different assumptions about the BBH yield. Our results highlight the promise of current GW observatories to probe high-redshift star formation.