Crowdsourcing Gravitational Waves from Superradiant Axions

Abstract

Black hole superradiance is a powerful probe of ultralight axions. If nature contains a boson with a mass of order $10^{-12}\,$eV, $\textit{mere vacuum fluctuations}$ will lead to its efficient production around spinning stellar mass black holes, forming a gravitational atom that both drains the black hole spin and decays to produce near-monochromatic gravitational waves. Existing superradiance constraints derive primarily from spin measurements of a handful of identified black holes. Here we instead present a detailed study of the population level effect: gravitational waves arising from both the 100 million black holes in the Milky Way and the stochastic signal from axion clouds throughout the universe. We study the impact of a broad range of systematic uncertainties on the black hole properties and compute the projected axion sensitivity for LIGO, as well as the future instruments Einstein Telescope, Cosmic Explorer, and a high-frequency Magnetic Weber Bar. We demonstrate that LIGO can robustly probe axion masses from roughly $10^{-13}\,$eV to $4 \times 10^{-12}\,$eV. If the black hole population extends to masses slightly below $5\,M_{\odot}$ - as hinted for by LIGO inspiral observations - LIGO would approach $10^{-11}\,$eV. Under that same assumption we show that a future high-frequency detector could push considerably higher, potentially beyond $10^{-10}\,$eV in the most optimistic scenarios, reaching towards the lowest masses within the projected sensitivity of axion dark matter searches.

Figures (14)

• Figure 1: The projected sensitivity of GW searches for axion superradiance as a function of the axion mass $\mu$, for galactic (left) and extragalactic (right) analyses. Results are shown for LIGO O5 and for a wide range of systematic variations to the underlying treatment of the BH population parameters and also the theoretical treatment of superradiance. Broadly, GW searches are well placed to complement and potentially extend existing analyses focusing on the spin-down of individual BHs with spins inferred from X-ray and LIGO observations (gray regions), which are subject to systematic uncertainties orthogonal to those of a population analysis. The dashed sensitivity on the left would be obtained only if LIGO sensitivity was extended to higher frequencies as discussed in the text.
• Figure 2: The two key timescales for axion superradiance: cloud growth, $T_c$, and cloud decay, $T_h$. We show the timescales as a function of the axion mass, $\mu$, for the first five modes associated with a BH with an initial mass and spin of $10\,M_{\odot}$ and $0.95$. From this example we see that lower modes grow faster, higher modes probe larger $\mu$, and eventually $T_h < T_c$ which shuts off the cloud growth and the signal's observability.
• Figure 3: Projected sensitivity to an axion of mass $\mu$ under our fiducial astrophysical galactic model, assuming a coherent integration time of $T_{\rm int} = 4$ hr and a total observation time $T_{\rm obs} = 1$ yr. We show results for each the observatories considered in this work: LIGO O1, LIGO O5, Einstein Telescope, Cosmic Explorer, and MWBs. For LIGO O5, the impact of modifying our fiducial model for the BH population is shown in Fig. \ref{['fig:fig_1']}, with the details of the variations specified in Tab. \ref{['tab:configs_GA']}. Other details are as in Fig. \ref{['fig:fig_1']}.
• Figure 4: Projected sensitivity to the axion mass $\mu$ under our fiducial extragalactic model for four observatories considered in this work: LIGO O1, LIGO O5, Einstein Telescope and Cosmic Explorer. Higher frequency detectors like the MWB, which are not competitive for the lower frequency extragalactic searches, are not shown. In all cases we show the sensitivity to a stochastic signal after one year of integration. The definition of our fiducial model for the BH parameters is provided in Tab. \ref{['tab:configs_EG']}; for the impact of variations in these choices for LIGO O5 and other details, see Fig. \ref{['fig:fig_1']}.
• Figure 5: Sensitivity for two systematic configurations of our galactic BH ensemble particularly conducive to obtaining sensitivity to higher axion masses. These two systematic configurations correspond to the inclusion of higher modes in addition to the Gaussian mass distribution (Config. 1), along with the DM Collapse BH mass distribution (Config. 2). For both configurations, we also adopt the log age distribution for BH ages. We compare the sensitivities across all of our considered observatories, with $T_{\rm int}$ now $\mu$-dependent, reflecting higher frequency drifts at high $\mu$, as discussed in the text. Recall the dashed curves correspond to assuming the interferometers can extend their sensitivity range to higher frequencies.