# Stochastic and resolvable gravitational waves from ultralight bosons

## TL;DR

This paper calculates the stochastic gravitational-wave background from ultralight bosons around black holes, showing it could be detectable by LIGO and LISA, and may help constrain axion-like particles.

## Contribution

First computation of the stochastic gravitational-wave background from superradiant bosonic condensates around black holes using numerical solutions and astrophysical models.

## Key findings

- Background potentially observable by Advanced LIGO and LISA.
- LIGO O1 data may already constrain certain axion masses.
- Semicoherent searches could detect dozens of resolvable sources.

## Abstract

Ultralight scalar fields around spinning black holes can trigger superradiant instabilities, forming a long-lived bosonic condensate outside the horizon. We use numerical solutions of the perturbed field equations and astrophysical models of massive and stellar-mass black hole populations to compute, for the first time, the stochastic gravitational-wave background from these sources. In optimistic scenarios the background is observable by Advanced LIGO and LISA for field masses $m_s$ in the range $\sim [2\times 10^{-13}, 10^{-12}]\,{\rm eV}$ and $\sim 5\times[ 10^{-19}, 10^{-16}]\,{\rm eV}$, respectively, and it can affect the detectability of resolvable sources. Our estimates suggest that an analysis of the stochastic background limits from LIGO O1 might already be used to marginally exclude axions with mass $\sim 10^{-12.5}{\rm eV}$. Semicoherent searches with Advanced LIGO (LISA) should detect $\sim 15~(5)$ to $200~(40)$ resolvable sources for scalar field masses $3\times 10^{-13}$ ($10^{-17}$) eV. LISA measurements of massive BH spins could either rule out bosons in the range $\sim [10^{-18}, 2\times 10^{-13}]$ eV, or measure $m_s$ with ten percent accuracy in the range $\sim[10^{-17}, 10^{-13}]$ eV.