Bosenova collapse of axion cloud around a rotating black hole

TL;DR

This work investigates nonlinear dynamics of ultralight axions around rapidly spinning black holes, modeling the axion as a sine-Gordon field in Kerr spacetime. Using a new 3D code with ZAMO-based coordinates, the authors reveal that nonlinear self-interactions can trigger a bosenova-like collapse of the axion cloud, accompanied by generation of the (ℓ,m)=(1,−1) mode and substantial mode mixing that alters energy and angular-momentum fluxes. An effective nonrelativistic theory based on a Gaussian wavepacket reproduces the onset of collapse as a phase-transition in the potential, with distinct behavior for small vs large α_g (e.g., α_g≈0.1 vs α_g≈0.4). The results indicate that saturation by nonlinearities is unlikely in some regimes and that bosenovae could have observational consequences, including possible gravitational-wave bursts, depending on the axion decay constant $f_a$ and BH parameters.

Abstract

Motivated by possible existence of stringy axions with ultralight mass, we study the behavior of an axion field around a rapidly rotating black hole (BH) obeying the sine-Gordon equation by numerical simulations. Due to superradiant instability, the axion field extracts the rotational energy of the BH and the nonlinear self-interaction becomes important as the field grows larger. We present clear numerical evidences that the nonlinear effect leads to a collapse of the axion cloud and a subsequent explosive phenomena, which is analogous to the "bosenova" observed in experiments of Bose-Einstein condensate. The criterion for the onset of the bosenova collapse is given. We also discuss the reason why the bosenova happens by constructing an effective theory of a wavepacket model under the nonrelativistic approximation.

Figures (18)

• Figure 1: The potential $V(\omega,r_*)$ (in the unit $M=1$) in Eq. \ref{['WKB-equation']} for a quasibound state of the Klein-Gordon field for situation $a/M=0.99$ and $\alpha_g:=M\mu=0.4$ (solid line). The horizontal dotted line indicates the value of $\omega^2$. Here, the imaginary part is ignored. There are four domains I, II, III, and IV, depending on the relation between $V$ and $\omega^2$, and the quasibound state is formed in region III. Due to the tunneling effect, the waves gradually fall into the region I. Because the energy of waves takes a negative value in region I under the superradiant condition, the field in region III is amplified.
• Figure 2: A snapshot for the contours of the Klein-Gordon field $\varphi$ of the $(\ell,m)=(1,1)$ mode of the quasibound state in the case of $a/M=0.99$ and $\alpha_g:=M\mu=0.4$ in the equatorial plane $\theta=\pi/2$ (left panel) and in the $(\rho, z)$-plane (right panel). Here, $\rho:=r\sin\theta$ and $z:=r\cos\theta$, and the $(\rho, z)$-plane is drawn for the azimuthal angle $\phi = \pi/5$ and $(6/5)\pi$ so that the plane crosses the peak of the field.
• Figure 3: The relation between the grid size $\Delta r_*$ (with unit $M=1$) and the numerical error evaluated at $t=12.5M$. The error decreases as $\Delta r_*$ is increased, and the slope of the curve is $\simeq 5$. This reflects our combined fourth- and sixth-order scheme.
• Figure 4: The values of total energy and angular momentum normalized by the initial values, $E(t)/E(0)$ and $J(t)/J(0)$, as functions of time (the solid line and the dashed line, respectively). Deviation from unity indicates the amount of numerical error. The error is less than $0.04\%$ at $t/M=1000$.
• Figure 5: The peak value $\varphi_{\rm peak}$ of the field $\varphi$ (upper panel) and its location $r_*^{\rm (peak)}$ with respect to the tortoise coordinate (lower panel) as functions of time observed in simulation (A) [i.e., $\varphi_{\rm peak}(0)=0.6$]. The peak location moves back and forth periodically. When the peak location becomes close to the horizon, the value of $\varphi_{\rm peak}$ becomes larger.