Gravitational-wave population inference at past time infinity

TL;DR

This paper introduces a method for population inference of stellar-mass black-hole binaries at past time infinity, addressing inconsistencies in reference frequency and spin estimation to improve astrophysical insights.

Contribution

It models black-hole populations and selection effects at past time infinity, providing a consistent reference frame for gravitational-wave population studies.

Findings

Current measurement uncertainties mask the impact of reference frequency.

Ignoring spins in selection effects causes overestimation of spin alignment.

Modeling at past time infinity improves population inference accuracy.

Abstract

Population studies of stellar-mass black-hole binaries have become major players in gravitational-wave astronomy. The underlying assumptions are that the targeted source parameters refer to the same quantities for all events in the catalog and are included when modeling selection effects. Both these points have so far been neglected when estimating the orientations of the black-hole spins. In particular, the detector-frame gravitational-wave frequency used to define frequency-dependent quantities (e.g., 20 Hz) introduces an inconsistent reference between events at the population level. We solve both issues by modeling binary black-hole populations and selection effects at past time infinity, corresponding to the well-defined reference frequency of 0 Hz. We show that, while current gravitational-wave measurement uncertainties obfuscate the influence of reference frequency in population inference, ignoring spins when estimating selection effects leads to an over-prediction of spin alignment in the underlying astrophysical distribution of merging black holes.