The $χ_\mathrm{eff}-z$ correlation of field binary black hole mergers and how 3G gravitational-wave detectors can constrain it

Abstract

Understanding the origin of merging binary black holes is currently one of the most pressing quests in astrophysics. We show that if isolated binary evolution dominates the formation mechanism of merging binary black holes, one should expect a correlation between the effective spin parameter, χ eff , and the redshift of the merger, z, of binary black holes. This correlation comes from tidal spin-up systems preferentially forming and merging at higher redshifts due to the combination of weaker orbital expansion from low metallicity stars given their reduced wind mass loss rate, delayed expansion and have smaller maximal radii during the supergiant phase compared to stars at higher metallicity. As a result, these tightly bound systems merge with short inspiral times. Given our fiducial model of isolated binary evolution, we show that the origin of a χ eff − z correlation in the detectable LIGO-Virgo binary black hole population is different from the intrinsic population, which will become accessible only in the future by third-generation gravitational-wave detectors such as Einstein Telescope and Cosmic Explorer. Given the limited horizon of current gravitational-wave detectors, z 1, highly rotating black hole mergers in the LIGO-Virgo observed χ eff − z correlation are dominated by those formed through chemically homogeneous evolution. This is in contrast to the subpopulation of highly rotating black holes in the intrinsic population, which is dominated by tidal spin up following a common evolve event. The different subchannel mixture in the intrinsic and detected population is a direct consequence of detector selection effects, which allows for the typically more massive black holes formed through chemically homogeneous evolution to be observable at larger redshifts and dominate the LIGO-Virgo sample of spinning binary black holes from isolated evolution at z > 0.4. Finally, we compare our model predictions with population predictions based on the current catalog of binary black hole mergers and find that current data favor a positive correlation of χ eff − z as predicted by our model of isolated binary evolution.

The Binary Black Hole Spin Distribution Likely Broadens with Redshift

“…This effect may be enhanced by the lower metallicities present at high redshifts, which diminish the strength of stellar winds and hence prevent binary orbits from widening and avoiding tidal spin-up. Bavera et al (2022) corroborate this prediction using population synthesis simulations, finding that an increasing fraction of systems undergo tidal spin-up in close orbits at high redshifts. Because there are systems that do not meet the criteria for efficient tidal spin-up at all redshifts, they find that the spin distribution both broadens and increases in mean.…”

“…The mean of the aligned population is restricted to 0.1 < μ a < 1, in While the posterior for the redshift-correlated population is consistent with primary mass being the sole source of correlation, the opposite is not true. order to represent systems formed via isolated binary evolution in the field (Gerosa et al 2018;Qin et al 2018;Zaldarriaga et al 2018;Bavera et al 2020;Belczynski et al 2020;Bavera et al 2021Bavera et al , 2022 The posterior on the mixture fraction is again very similar to the one obtained with the first prior choice in Figure 10. Since the mixture fraction increases with redshift for all three prior choices, the second Gaussian added on top of the bulk distribution always contributes more at high redshifts, consistent with the conclusion that the χ eff distribution broadens with increasing redshift.…”

“…The third model defined in Section 4.2, for example, serves as a proxy for this scenario. In this case, the symmetric χ eff component centered at zero might serve to capture binaries assembled dynamically in dense stellar environments (Portegies Zwart & McMillan 2002;Rodriguez et al 2015;Antonini & Rasio 2016;Gerosa & Berti 2017;Rodriguez et al 2019;Kimball et al 2020;Gerosa & Fishbach 2021), while the preferentially positive χ eff component corresponds to a subpopulation of systems formed via isolated binary evolution in the field (Gerosa et al 2018;Qin et al 2018;Zaldarriaga et al 2018;Bavera et al 2020;Belczynski et al 2020;Bavera et al 2021Bavera et al , 2022. However, such a mixture between two subpopulations generally leads to a shift in the mean of the χ eff distribution with redshift.…”

Signatures of mass ratio reversal in gravitational waves from merging binary black holes

“…Last, recently several authors have suggested the existence of redshift-evolution in the binary black hole (effective) spin distribution: finding at higher redshifts both a larger fraction of binary black holes with nonnegligible spin and a broadening in the black hole spin magnitude distribution Bavera et al (2022); Biscoveanu et al (2022). This positive spin-redshift correlation matches the expected behavior in our model assumptions.…”

No evidence that the majority of black holes in binaries have zero spin

“…Our priors on µ eff and σ eff are listed in Table 2. This model was proposed in Roulet & Zaldarriaga (2019) and Miller et al (2020) and has been employed and extended in Abbott et al (2021a), Abbott et al (2021b), Callister et al (2021b, Biscoveanu et al (2022), andBavera et al (2022).…”