Discovering the QCD Axion with Black Holes and Gravitational Waves

TL;DR

The paper investigates how rotating black holes can reveal ultra-light bosons through superradiance, forming macroscopic axion clouds that emit monochromatic gravitational waves via level transitions and annihilations. It develops a hydrogen-like gravitational-atom framework, estimates signal strengths and event rates for Advanced LIGO/VIRGO and future detectors, and maps out axion-mass parameter space exclusions from BH spin measurements. The work highlights that aLIGO could detect a handful of transition signals and thousands of annihilation events for favorable axion masses, while low-frequency detectors could probe even lighter axions around supermassive BHs, potentially constraining or discovering the QCD axion. Environmental effects from companion stars and disks are found to be subdominant, making BH superradiance a robust search channel for light bosons with gravitational couplings.

Abstract

Advanced LIGO may be the first experiment to detect gravitational waves. Through superradiance of stellar black holes, it may also be the first experiment to discover the QCD axion with decay constant above the GUT scale. When an axion's Compton wavelength is comparable to the size of a black hole, the axion binds to the black hole, forming a "gravitational atom." Through the superradiance process, the number of axions occupying the bound levels grows exponentially, extracting energy and angular momentum from the black hole. Axions transitioning between levels of the gravitational atom and axions annihilating to gravitons can produce observable gravitational wave signals. The signals are long-lasting, monochromatic, and can be distinguished from ordinary astrophysical sources. We estimate up to O(1) transition events at aLIGO for an axion between 10^-11 and 10^-10 eV and up to 10^4 annihilation events for an axion between 10^-13 and 10^-11 eV. In the event of a null search, aLIGO can constrain the axion mass for a range of rapidly spinning black hole formation rates. Axion annihilations are also promising for much lighter masses at future lower-frequency gravitational wave observatories; the rates have large uncertainties, dominated by supermassive black hole spin distributions. Our projections for aLIGO are robust against perturbations from the black hole environment and account for our updated exclusion on the QCD axion of 6*10^-13 eV < ma < 2*10^-11 eV suggested by stellar black hole spin measurements.

Figures (16)

• Figure 1: Superradiance times of levels $\ell = 1$ to $4$ (left to right) for spins $a_* = 0.99$ and $0.90$, fixing $m=\ell$ and $n = \ell + 1$. Time in years is shown for a $10\, M_{\odot}$ black hole as a function of boson mass $\mu_a$; on the right axis, we show the dimensionless superradiance rate $\Gamma_{\rm{sr}} r_g$ as a function of the gravitational coupling $\alpha$ (top axis).
• Figure 2: Effect of superradiance for a QCD axion with mass $\mu_a = 10^{-11}\,\mathrm{eV}$ and decay constant $f_a = 6\times 10^{17}\,\mathrm{GeV}$. Shaded regions correspond to BH parameters which would result in spin down within a binary lifetime ($10^6$ years), for $\ell=1$ (dark blue) to $\ell=5$ (light blue) levels. We also show an example evolution of a $6M_{\odot}$ black hole with initial spin $a_* = 0.95$.
• Figure 3: Time evolution of ground and excited levels' occupation numbers (left $y$-axis) and the resulting gravitational wave signal strain (right $y$-axis) for the $6g\rightarrow 5g$ transition around a $10\,M_{\odot}$ black hole with spin $a_* = 0.9$, 10 kpc away. The peak signal is larger when $\Gamma_e > \Gamma_g$ (left, $\alpha = 1$) than the case $\Gamma_e < \Gamma_g$ (right, $\alpha = 1.25$). The initial occupation numbers of both levels are set to 1 when $t = 0$, and while the time in years differs significantly, the characteristic timescales for the signals are set by the superradiance rates (top axes) in both cases.
• Figure 4: Transition signal strains for different level transitions from a $10 M_{\odot}$ black hole system 10 kpc away ($a_* = 0.99$, $\alpha/\ell = 0.3$), assuming $25$ hr integration time. The bottom axis shows the corresponding GW frequency. We focus on the starred ($^*$) transitions as most promising for GW detection. The strain shown here is approximate; we also make the simplistic assumption that in each case only two SR rates dominate.
• Figure 5: Number of $6g\rightarrow 5g$ and $7h\rightarrow 6h$ transition events expected at aLIGO as a function of the axion mass, assuming a monochromatic search with $121\times 250$ hr integration time and $C_{\rm{tf}} =10$. Each event typically lasts several decades. We assume $4.1M_{\odot}$ minimum BH mass; if the minimum BH mass is smaller the curves would shift to higher axion masses. The three lines correspond to varying the BH mass distribution width, from narrow (solid) to wide (dotted). The bands around the central curves correspond to optimistic and pessimistic estimates of other astrophysical uncertainties (see text). The vertical shaded regions are disfavored by the observation of rapidly spinning BHs, for bosons with coupling equal to that of the QCD axion (light gray) or stronger (dark gray) (see section \ref{['sec:spin_limit']}).