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 _merge ≈ 1. Because GWs are inefficient at shrinking the binary orbit, some of these BBH systems likely experienced long delay times τ between the formation of their progenitor stars at z _form and their GW merger at z _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 ≲ α _τ ≲ -0.35 and a minimum delay time of ${\tau }_{\min }=10\,\mathrm{Myr}$ . We use these predicted delay time distributions to infer the formation redshifts of the ~70 BBH events reported in the third GW transient catalog GWTC-3 and the formation rate of BBH progenitors. For our default α _τ = -1 delay time distribution, we find that GWTC-3 contains at least one system (with 90% credibility) that formed earlier than z _form > 4.4. Comparing our inferred BBH progenitor formation rate to the star formation rate, we find that at z _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 _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 _form = 4 was $\langle {\mathrm{log}}_{10}(Z/{Z}_{\odot })\rangle =-{0.3}_{-0.4}^{+0.3}$ , although the inferred metallicity can vary by a factor of ≈3 for different assumptions about the BBH yield. Our results highlight the promise of current GW observatories to probe high-redshift star formation.