Gravitational wave searches for ultralight bosons with LIGO and LISA

Abstract

Ultralight bosons can induce superradiant instabilities in spinning black holes, tapping their rotational energy to trigger the growth of a bosonic condensate. Possible observational imprints of these boson clouds include (i) direct detection of the nearly monochromatic (resolvable or stochastic) gravitational waves emitted by the condensate, and (ii) statistically significant evidence for the formation of "holes" at large spins in the spin versus mass plane (sometimes also referred to as "Regge plane") of astrophysical black holes. In this work, we focus on the prospects of LISA and LIGO detecting or constraining scalars with mass in the range $m_s\in [10^{-19},\,10^{-15}]$ eV and $m_s\in [10^{-14},\,10^{-11}]$ eV, respectively. Using astrophysical models of black-hole populations calibrated to observations and black-hole perturbation theory calculations of the gravitational emission, we find that, in optimistic scenarios, LIGO could observe a stochastic background of gravitational radiation in the range $m_s\in [2\times 10^{-13}, 10^{-12}]$ eV, and up to $10^4$ resolvable events in a $4$-year search if $m_s\sim 3\times 10^{-13}\,{\rm eV}$. LISA could observe a stochastic background for boson masses in the range $m_s\in [5\times 10^{-19}, 5\times 10^{-16}]$, and up to $\sim 10^3$ resolvable events in a $4$-year search if $m_s\sim 10^{-17}\,{\rm eV}$. LISA could further measure spins for black-hole binaries with component masses in the range $[10^3, 10^7]~M_\odot$, which is not probed by traditional spin-measurement techniques. A statistical analysis of the spin distribution of these binaries could either rule out scalar fields in the mass range $\sim [4 \times 10^{-18}, 10^{-14}]$ eV, or measure $m_s$ with ten percent accuracy if light scalars in the mass range $\sim [10^{-17}, 10^{-13}]$ eV exist.

Figures (10)

• Figure 1: Exclusion regions in the BH mass-spin plane (Regge plane) for a massive scalar field. For each mass $m_s$, the instability threshold is obtained by setting the superradiant instability time scales for $l=m=1,\,2,\,3$ equal to a typical accretion time scale, taken to be $\tau=50\,{\rm Myr}$ (see main text for details). Black data points (with error bars) are spin estimates of stellar and massive BHs obtained through the K$\alpha$ or continuum fitting methods Brenneman:2011wzMiddleton:2015osa. Red data points are GW measurements of the primary and secondary BHs from the three LIGO detections (GW150914, GW151226 and GW170104 TheLIGOScientific:2016peaAbbott:2017vtc). Blue, green and brown data points are projected LISA measurements under the assumption that there are no light bosons for three different astrophysical black hole population models (popIII, Q3 and Q3-nod from Klein:2015hvg), as discussed in the text. We assume a LISA observation time $T_{\rm obs}=1\,{\rm yr}$, and to avoid cluttering we only show events for which LISA spin measurement errors are relatively small ($\Delta \chi/\chi\leq 2/3$). The top horizontal line is a frequency scale corresponding to the BH mass, $f\approx\mu/\pi$ with $\mu\sim 0.2/M$ as a reference value.
• Figure 2: Flux for $\ell=m=1$ and taking the first two leading order terms in the flux $\tilde{\ell}=\tilde{m}=2$ and $\tilde{\ell}=3, \tilde{m}=2$ as a function of the scalar mass and for the spin computed at the superradiant threshold \ref{['finalspin']}. The numerical results computed in this work are compared with the analytic formula obtained in Brito:2014wla, labeled "Brito+", and the one obtained in Arvanitaki:2010sy, labeled "Arvanitaki+".
• Figure 3: Gravitational radiation time scale, instability time scale, and the signal duration $\Delta t$ [defined in Eq. \ref{['deltat']}] for detectable LISA sources and for different boson masses.
• Figure 4: Gravitational radiation time scale, instability time scale, and the signal duration $\Delta t$ [defined in Eq. \ref{['deltat']}] for detectable LIGO sources and for different boson masses. Dashed lines represent extragalactic sources and bold lines represent Galactic sources.
• Figure 5: Angle-averaged range $D_{\rm range}$ for LISA (top) and Advanced LIGO at design sensitivity (bottom) computed for selected initial BH spin ($\chi_i=0.998,\,0.95,\,0.7$). Left panels: the range is computed using a coherent search over an observation time $T_{\rm obs}=4$ yr (for LISA) and $T_{\rm obs}=2$ yr (for LIGO). Right panels: we assume a semicoherent search with ${\cal N}=121$ coherent segments of duration $T_{\rm coh}=250\,{\rm hr}$.