Gravitational radiation from an axion cloud around a black hole: Superradiant phase

Abstract: Motivated by possible existence of string axions with ultralight masses, we study gravitational radiation from an axion cloud around a rotating black hole (BH). The axion cloud extracts the rotation energy of the BH by superradiant instability, while it loses energy through the emission of gravitational waves (GWs). In this paper, GWs are treated as perturbations on a fixed background spacetime to derive the energy emission rate. We give an analytic approximate formula for the case where axion's Compton wavelength is much larger than the BH radius, and then, present numerical results without approximation. The energy loss rate of the axion cloud through the GW emission turns out to be smaller than the energy gain rate of the axion cloud by superradiant instability until nonlinear self-interactions of axions become important. In particular, an axion bosenova must happen at the last stage of superradiant instability.

Gravitational Radiation from an Axion Cloud Around a Black Hole: Superradiant Phase

The paper in focus presents a comprehensive analysis of gravitational wave (GW) emissions from an axion cloud formed around rotating black holes via superradiant instability. Originating from potential ultralight string axions, this research merges analytical methods with numerical simulations to offer insights into both fundamental physics and possible astrophysical observations.

Superradiant Instability of Axion Fields

Axions are hypothetical particles often tied to multiplicative dimensions in string theory. These fields can gain energy from rotating black holes through superradiant instability, where the axion cloud's rotational energy extraction surpasses its energy loss via GW emissions. Calculating the energy gain rates, the authors establish conditions under which the axion cloud continues to grow before nonlinear effects like bosenova collapse become pertinent.

Analytical Approximation for GW Radiation

For scenarios where the axion's Compton wavelength significantly exceeds the black hole radius, an analytical approximation in flat spacetime is utilized. This simplifies the problem into a gravitational atomic model analogous to hydrogen atoms, allowing for derivations of GW emission rates. The results indicate the emission rate scales with $M\mu$ raised to a power dependent on particle parameters, illustrating that GW emissions in this regime do not significantly impede axion cloud growth.

Numerical Analysis in Kerr Spacetime

The paper extends its treatment to general Kerr spacetimes, where numerical methods are applied to account for complex interactions and high-energy effects. For axion modes characterized by various angular and azimuthal quantum numbers, GW emission rates are systematically calculated. The numerical analysis reveals a diminishing GW emission rate with increased $M\mu$, corroborating analytical predictions while accounting for relativistic influences.

Implications and Future Work

This research underscores the feasibility of axion cloud formation through superradiance and the likely occurrence of a bosenova collapse. The negligible GW emission impact during axion cloud growth opens avenues to explore detectable signals from bosenova events. The conceptual framework may further apply to scenarios where multiple axion modes are involved, promising richer and more complex GW signatures. These findings advocate for continued efforts in uncovering novel astrophysical phenomena and refining gravitational wave detectors to confirm theoretical predictions.

The paper establishes significant groundwork for exploring gravitational interactions at the intersection of cosmic phenomena and quantum-scale physics, aligning with endeavors to characterize potential constituents of dark matter within our universe.