High-frequency gravitational wave transients from superradiance

Abstract

Ultralight bosons can form macroscopic gravitational-atom clouds around rotating black holes via superradiance, sourcing quasi-monochromatic gravitational waves through level transitions and annihilation. Primordial black holes provide a natural setting for such systems in a frequency range relevant for resonant-cavity experiments. We present a unified treatment of gravitational-wave emission from both isolated and binary-perturbed gravitational atoms in this regime. For isolated systems, we derive analytic expressions for the time- and frequency-domain strain from transition and annihilation channels, emphasizing their narrow-band structure. For binaries, we model resonantly driven level transitions using the Landau--Zener formalism and compute the resulting transient signals. We find that, while binary-driven transitions generically yield signals with durations compatible with detector response times, their characteristic strain lies well below the sensitivity of current experiments at astrophysically plausible distances, and event rates further suppress detectability by requiring sources at unrealistically small separations. We quantify the improvements in sensitivity, bandwidth, and response needed to render these signals observable, and identify gravitational-atom systems around primordial black holes as a theoretically well-motivated target for future high-frequency gravitational-wave searches.

Figures (13)

• Figure 1: Regge trajectories showing the minimum black hole spin $a_*$ required to sustain superradiant growth as a function of boson and black hole parameters, for azimuthal modes $m = 1, 2, 3, 4$. Shaded regions indicate parameter space where superradiance is active. (a) Superradiance threshold as a function of boson mass $\mu$ for fixed $m = 1$ and varying black hole mass $M$. (b) Threshold as a function of $\mu$ for fixed $M = 10^{-6}\ M_\odot$ and varying $m$. (c) Threshold as a function of $M_{\rm BH}$ for fixed boson mass $\mu = 10^{-3}\ \mathrm{eV}$ and varying $m$. (d) Threshold as a function of the gravitational coupling $\alpha = M\mu$ for fixed $M = 10^{-6}\ M_\odot$ and varying $m$.
• Figure 2: (a) Estimates of superradiance lifetime $\tau = \Gamma^{-1}$ as a function of $\alpha$ and azimuthal quantum number $\ell = m$ for a $10^{-6}\,M_\odot$ BH. Solid lines show $a = 0.99$, dashed lines show $a = 0.90$. (b) Superradiance rate $\Gamma_{\rm SR}$ as a function of $\alpha$ for the same parameter space. Superradiance continues until $m\Omega_{\rm H} \geq \omega$ is violated through spin extraction via the superradiant cloud.
• Figure 3: Time evolution of the occupation numbers $N_{\{6,4,4\}}$ and $N_{\{5,4,4\}}$ alongside the corresponding gravitational-wave strain envelope $h(t)$ (dashed), computed for $\mu_a = 10^{-4}\,\text{eV}$, $M_{\rm BH} = 10^{-6}\,M_\odot$, $\alpha = 0.75$, and a source distance of $d = 1\,\text{kpc}$. At early times both states grow independently under superradiance (Eqs. \ref{['eq:dNg_indep']}--\ref{['eq:dNe_indep']}). Once $N_e$ is large enough, the gravitational self-interaction coupling $\Gamma_t N_g N_e$ (Eq. \ref{['eq:Gamma_t']}) begins to dominate the excited-state dynamics, and a net flux of bosons cascades into the lower state, emitting a nearly monochromatic gravitational wave analogous to stimulated emission in atomic physics. The transition frequency $\omega_{\rm tr} = 526.4\,\text{MHz}$ lies within the ADMX scan band. The peak strain reflects a specific benchmark configuration and is not representative of the maximal transition strain, which can reach $\sim 10^{-23}$ for more favorable parameters.
• Figure 4: Fractional BH mass transferred to each superradiant level, $M_c/(M_{\rm BH}-M_c)$, as a function of time for states with $n = m+1$, $\ell = m$, and $m = 1$--$6$, computed at $M_{\rm BH} = 6\times10^{-7}\,M_\odot$, $\mu_a = 5\times10^{-5}\,\text{eV}$, $\alpha = 0.22$. The $\{2,1,1\}$ level (darkest) reaches its saturation first and at the largest fractional mass. The maximum extracted mass for the most efficient state is $10.81\%$, in excellent agreement with the analytic upper bound of $10.8\%$ derived in Ref. Tomaselli:2024 for $\alpha \approx 0.2$ and $a_* \to 1$. Higher-$m$ levels saturate later and accumulate correspondingly smaller clouds, as their slower growth is overtaken by the already-saturated lower levels.
• Figure 5: Time evolution of the cloud occupation number $N(t)$ (solid) and the corresponding annihilation strain envelope $h_{0,\rm ann}(t)$ (dashed), computed for $\mu_a = 2\times10^{-7}\,\text{eV}$, $M_{\rm BH} = 4.5\times10^{-4}\,M_\odot$, $\alpha = 0.43$, and $d = 1\,\text{kpc}$. The occupation number grows during the superradiant phase (left portion of the curve) until it saturates at $N_{\rm max}$, after which $N(t)$ decays as $[1 + \Gamma_a N_{\rm max}\,t]^{-1}$ (Eq. \ref{['eq:N_ann']}) as boson pairs annihilate into gravitons. The corresponding strain peaks at $h_{0,\rm ann}^{\rm max} \approx 10^{-22}$ and decays on a timescale $\tau_{\rm ann} = (\Gamma_a N_{\rm max})^{-1}$ that can exceed the Hubble time, making the signal effectively monochromatic and persistent for any observation campaign. The annihilation frequency $\omega_{\rm ann}/(2\pi) \approx 96\,\text{MHz}$ is within the ADMX scan band.