Analytic joint priors of effective spin parameters and inference of the spin distribution of binary black holes

Iwaya, Masaki, Kobayashi, Kazuya, Morisaki, Soichiro, Hotokezaka, Kenta and Kinugawa, Tomoya 2025. Analytic joint priors of effective spin parameters and inference of the spin distribution of binary black holes. Physical Review D (particles, fields, gravitation, and cosmology) 111 (10) , 103046. 10.1103/PhysRevD.111.103046

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Abstract

We derive an analytic form of the joint prior of effective spin parameters, and , assuming an isotropic and uniform-in-magnitude spin distribution. This is a vital factor in performing hierarchical Bayesian inference for studying the population properties of merging compact binaries observed with gravitational waves. In previous analyses, this was evaluated numerically using kernel density estimation (KDE). However, we find that this numerical approach is inaccurate in certain parameter regions, where both and are small. Our analytic approach provides accurate computations of the joint prior across the entire parameter space and enables more reliable population inference. Employing our analytic prior, we reanalyze binary black holes in the gravitational-wave transient catalog 3 (GWTC-3) by the LIGO-Virgo-KAGRA collaboration. While the results are largely unchanged, log-likelihood errors due to the use of the inaccurate prior evaluations are , implying the bias is already at the concerning level if one adopts a log-likelihood variance cut. Since the systematic bias from the numerical method accumulates with the increasing number of events, our analytic prior will be more crucial in future analyses.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Physics and Astronomy
Publisher:	American Physical Society
ISSN:	2470-0010
Date of First Compliant Deposit:	6 June 2025
Date of Acceptance:	25 April 2025
Last Modified:	24 Jun 2025 11:15
URI:	https://orca.cardiff.ac.uk/id/eprint/178672

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