High-frequency gravitational wave transients from superradiance

Published 1 Apr 2026 in gr-qc | (2604.01407v2)

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.

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Summary

The paper demonstrates that ultralight boson clouds formed via superradiance around primordial black holes can emit persistent MHz–GHz gravitational wave signals.
The methodology combines analytic models and numerical simulations, employing Regge trajectories and occupation number evolution to map the optimal parameter space.
The study highlights significant experimental challenges and proposes novel detector templates and design improvements for high-frequency gravitational wave searches.

High-Frequency Gravitational Wave Transients from Superradiance: Comprehensive Review

Physical Mechanism and Parameter Space

The study analyzes gravitational wave (GW) emission in the MHz–GHz regime arising from ultralight bosons forming macroscopic clouds—gravitational atoms (GAs)—around rotating black holes (BHs) via superradiance. The essential control parameter is the gravitational fine-structure constant $\alpha = G M_{\rm BH} \mu$ , linking boson mass $\mu$ to the BH mass $M_{\rm BH}$ . Efficient superradiance and GW emission occur for $\alpha \sim 0.1$ –$0.3$, which, for boson masses $\mu \sim 10^{-8}$ – $10^{-5}$ eV, identifies primordial black holes (PBHs) in the mass range $M_{\rm BH} \sim 10^{-6}$ – $10^{-3} M_\odot$ as natural sites for GHz gravitational wave production.

Regge trajectories, defined by the minimum BH spin required for superradiance as a function of $\mu$ , $\mu$ 0, and mode $\mu$ 1, delineate the parameter region where clouds grow and extract rotational energy (Figure 1).

Figure 1: Regge trajectories showing the minimum black hole spin $\mu$ 2 required to sustain superradiant growth as a function of boson and black hole parameters for azimuthal modes $\mu$ 3; shaded regions represent active superradiance.

Cloud Formation, Growth, and Saturation

Macroscopic bosonic clouds form when superradiance is active, with occupation numbers reaching $\mu$ 4– $\mu$ 5. Instability rates are highly sensitive to $\mu$ 6 and are dominated by the lowest-angular-momentum ( $\mu$ 7) states. The growth timescale spans seconds to cosmological times, depending on $\mu$ 8, with sharp suppression outside the optimal range.

Cloud saturation via superradiant spin-down enables a maximum transfer of BH mass to the boson cloud, calculated to be approximately $\mu$ 9, in agreement with both analytic and numerical results.

Figure 2: Fractional BH mass transferred to each superradiant level, maximizing at $M_{\rm BH}$ 0 for dominant modes.

Bosenova (self-interaction-induced) collapse imposes an upper limit on the cloud occupation, but for QCD axion couplings this threshold does not constrain the bulk of the parameter space considered.

Gravitational Wave Emission Channels in Isolated Gravitational Atoms

Isolated GAs yield two GW channels:

Level Transitions: Quadrupole self-interactions between two populated states (excited and ground) drive quasi-monochromatic GW emission at the Bohr frequency $M_{\rm BH}$ 1.
Annihilation: Pairwise boson annihilation produces monochromatic GWs at $M_{\rm BH}$ 2.

The signals are quasi-monochromatic and, especially for annihilation, persist over timescales vastly exceeding experiment ring-up times, satisfying detectability prerequisites for resonant-cavity detectors.

Numerical results show level transitions yield peak GW strains $M_{\rm BH}$ 3 at 1 kpc, while annihilation can reach $M_{\rm BH}$ 4.

Figure 3: Time evolution of occupation numbers for excited and ground levels alongside the level-transition gravitational wave strain envelope.

Signal lifetimes are $M_{\rm BH}$ 5– $M_{\rm BH}$ 6 years for level transitions, and $M_{\rm BH}$ 7– $M_{\rm BH}$ 8 years for annihilation, rendering both highly coherent and persistent.

Figure 4: Time evolution of the cloud occupation number and corresponding annihilation strain envelope; annihilation persistently dominates after saturation.

Frequency-domain templates for both emission channels are provided, enabling direct comparison to detector sensitivities.

Gravitational Wave Signatures from Binary-Perturbed Gravitational Atoms

The presence of a binary companion induces tidal perturbations that trigger resonant level transitions via a Landau–Zener mechanism, resulting in transient GW bursts. The signal duration, peak frequency, strain amplitude, and spectral width are determined by the adiabaticity parameter $M_{\rm BH}$ 9, instability rates, and orbital parameters.

The characteristic strain for binary-driven transitions is orders of magnitude below the sensitivity floor of current experiments at astrophysically plausible distances and is only detectable for unrealistically small event separations.

Figure 5: Ratio $\alpha \sim 0.1$ 0 illustrates parameter space constraints for signal duration relative to merger time.

Peak transition frequencies for PBH–GA binaries naturally populate the ADMX GHz band only in the relevant PBH mass regime.

Figure 6: Peak transition frequency in PBH–GA binaries for different boson masses and couplings; shaded region identifies ADMX frequency scan range.

Waveforms, both time and frequency domain, are computed for benchmark configurations. The ring-up condition for cavity detection is universally satisfied for relevant parameter combinations, but strain amplitude is severely limiting.

Figure 7: Time-domain and frequency-domain amplitude for a benchmark PBH binary GA system located at $\alpha \sim 0.1$ 1 kpc.

Detailed comparison of GW strains with ADMX sensitivity curves confirms the significant gap in detectability.

Figure 8: GW characteristic strain $\alpha \sim 0.1$ 2 and ADMX minimum detectable strain $\alpha \sim 0.1$ 3 for binary GA systems; no overlap in relevant parameter space.

Event Rates and Detection Prospects

Merger rates for PBH binaries are computed from early universe formation models, primarily via the two-body channel, for dichromatic and double-lognormal mass functions. For ADMX-relevant binaries ( $\alpha \sim 0.1$ 4), event rates imply characteristic distances of $\alpha \sim 0.1$ 5 kpc for one event per year, whereas detection requires sources within $\alpha \sim 0.1$ 6 AU. Even optimistic PBH clustering fails to bridge the strain sensitivity gap.

Figure 9: Binary event distances for merger rates and mass functions; ADMX-relevant binaries merge at distances far from detector sensitivity thresholds.

Theoretical and Practical Implications

Theory: PBH–GA systems provide a rare, well-motivated astrophysical source for MHz–GHz GWs. The QCD axion mass window is uniquely accessible, and waveform templates enable direct applications to high-frequency GW searches.
Experiment: Detectability of isolated GA annihilation signals is more promising versus binary-induced bursts. The necessary improvements include strain sensitivity enhancements (factor $\alpha \sim 0.1$ 7), broader frequency coverage, and faster detector response times.
Constraints: Non-observation could set bounds on PBH abundance and boson properties; matched-filter searches using analytic templates could extend exclusion regions in parameter space.
Future Developments: Novel detector designs, larger volumes, stronger fields, lower temperatures, and extended integration times are imperative. Plasma haloscopes, LC circuits, and broadband acoustic resonators may yield complementary coverage.
Figure 10: Population evolution for superradiant states and corresponding gravitational strain due to annihilation; highlights regime transition from growth to persistent emission.

Figure 11: Event distance distribution in non-dichromatic (lognormal) PBH mass functions; characteristic distances remain above detection thresholds.

Conclusion

Superradiance around PBHs produces persistent and transient GW signals in the MHz–GHz range via bosonic clouds, with analytic and numerical characterization of both isolated and binary-perturbed systems. While theoretical models identify ideal conditions for strong signal generation, practical detection is limited by current instrument sensitivity and event rates. The templates and parameter mappings developed offer benchmarks for future high-frequency GW searches. Isolated GA annihilation signals are the priority target for near-term detection, while binary-induced bursts require advancements far beyond current capabilities. The systematic elucidation of the physical mechanism, parameter space, waveform properties, and event statistics provides a foundation for ongoing experimental and theoretical investigations into ultralight boson physics, PBH demographics, and high-frequency gravitational wave astronomy.

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