# Searching for ultralight bosons within spin measurements of a population of binary black hole mergers

## TL;DR

This paper proposes a hierarchical Bayesian method to combine multiple gravitational-wave black hole spin measurements, enabling stronger constraints on ultralight boson masses within a specific range, despite individual measurement uncertainties.

## Contribution

It introduces a novel hierarchical Bayesian inference approach to improve constraints on ultralight bosons using multiple black hole spin measurements from gravitational-wave data.

## Key findings

- Hundreds of high SNR detections can exclude certain boson mass ranges.
- Current LIGO/Virgo data are insufficient for conclusive constraints.
- The method's effectiveness depends on black hole spin distribution and boson mass.

## Abstract

Ultralight bosons can form clouds around rotating black holes if their Compton wavelength is comparable to the black hole size. The boson cloud spins down the black hole through a process called superradiance, lowering the black hole spin to a characteristic value. It has been suggested that spin measurements of the black holes detected by ground-based gravitational-wave detectors can be used to constrain the mass of ultralight bosons. Unfortunately, a measurement of the individual black hole spins is often uncertain, resulting in inconclusive results. Instead, we use hierarchical Bayesian inference to combine information from multiple gravitational-wave sources and obtain stronger constraints. We show that hundreds of high signal-to-noise ratio gravitational-wave detections are enough to exclude (confirm) the existence of non-interacting bosons in the mass range $\left[10^{-13},3\times 10^{-12}\right]~\rm{eV}$ $\left([10^{-13},10^{-12}]~\rm{eV}\right)$. The precise number depends on the distribution of black hole spins at formation and the mass of the boson. From the few uninformative spin measurements of binary black hole mergers detected by LIGO and Virgo in their first two observing runs, we cannot draw statistically significant conclusions.