Stochastic and resolvable gravitational waves from ultralight bosons

TL;DR

Numerical solutions of the perturbed field equations and astrophysical models of massive and stellar-mass black hole populations are used to compute, for the first time, the stochastic gravitational-wave background from these 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.

Figures (3)

• Figure 1: GW strain produced by BH-boson condensates compared to the Advanced LIGO PSD at design sensitivity Aasi:2013wya and to the non-sky averaged LISA PSD Audley:2017drz (black thick curves), assuming a coherent observation time of $T_{\rm obs}=4\,{\rm yr}$ in both cases. Nearly vertical lines represent BHs with initial spin $\chi_i=0.9$. Each line corresponds to a single source at redshift $z\in(0.001,3.001)$ (from right to left, in steps of $\delta z=0.2$), and different colors correspond to different boson masses $m_s$. Thin lines show the stochastic background produced by the whole population of astrophysical BHs under optimistic assumptions (cf. main text for details). The PSD of DECIGO Kawamura:2006up (dashed line) is also shown for reference.
• Figure 2: Left panel: stochastic background in the LIGO and LISA bands. For LISA, the three different signals correspond to the "optimistic" (top), "less optimistic" (middle) and "pessimistic" (bottom) astrophysical models. For LIGO, the different spectra for each boson mass correspond to a uniform spin distribution with (from top to bottom) $\chi_i\in[0.8,1]$, $[0.5,1]$, $[0,1]$ and $[0,0.5]$. The black lines are the power-law integrated curves of Thrane:2013oya, computed using noise PSDs for LISA Audley:2017drz, LIGO's first two observing runs (O1 and O2), and LIGO at design sensitivity (O5) TheLIGOScientific:2016wyq. By definition, $\rho_{\rm stoch}> 1$ ($\rho_{\rm stoch}= 1$) when a power-law spectrum intersects (is tangent to) a power-law integrated curve. Right panel: $\rho_{\rm stoch}$ for the backgrounds shown in the left panel. We assumed $T_{\rm obs}=2\,{\rm yr}$ for LIGO and $T_{\rm obs}=4\,{\rm yr}$ for LISA.
• Figure 3: Resolvable events for the same astrophysical models used in Fig. \ref{['fig:background']}. Shaded areas correspond to exclusion regions from 4-year LISA massive BH spin measurements, using either the "popIII" (brown) or "Q3-nod" (light blue) models of Klein:2015hvg. For reference we also show with brackets the constraints that can be placed by spin measurements of massive/stellar-mass BHs Brenneman:2011wzArvanitaki:2014wva.