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 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 α τ 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 − 5.5 + 9.4 × 10 − 6 M ⊙ − 1 and this yield dropped to 0.134 − 0.127 + 1.6 × 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 − 0.4 + 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.