# The effective spin-redshift correlation of field binary black hole mergers and how 3G gravitational-wave detectors can constrain it

### Authors:

Bavera, Fishbach, Zevin, Zapartas, Fragos (2022)

### Abstract:

Understanding the origin of merging binary black holes is currently one of the most pressing quests in astrophysics. In this research article, we showed that if isolated binary evolution dominates the formation mechanism of merging binary black holes, one should expect a correlation between the effective spin parameter, and the redshift (distance) of the merger 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. We compared our model predictions with population predictions based on the current catalog of observed binary black hole mergers and find that current data favor a positive correlation of the effective spin parameter and merger redshift, as predicted by our model of isolated binary evolution.

The Figure shows the effective spin parameter, $\chi_\mathrm{eff}$, intrinsic distribution of binary black holes formed from isolated binary evolution in the Universe as a function of redshift, $z$. Our model predicts that binary black hole systems merging at larger redshifts have on average larger effective spin parameters.