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(τ) ∝ τ ^ατ with slope −1 ≲ α_τ ≲ −0.35 and a minimum delay time of τ_min = 10 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^+9.4_-5.5 × 10⁻⁶ M _⊙^{− 1} and this yield dropped to 0.134^{+ 1.6}_-0.127 × 10⁻⁶ M_⊙⁻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 〈 log 10 (Z/Z_⊙ ) 〉= −0 .3^+0.3_-0.4 , 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.