Black Hole Superradiance of Interacting Multi-Field

Abstract

We investigate black hole superradiance evolution of the interacting multiple fields. We consider a model of two scalar fields interacting with a cubic coupling, and study the superradiant evolution of the cloud. We demonstrate that superradiance is typically suppressed when the superradiant field couples to another field, even with a very weak coupling strength. This implies that the constraints on dark particles derived from single-field analyses can be revised in the presence of interactions. Moreover, we find that the multi-field superradiant evolution and its corresponding observational signatures can be different across parameter spaces, which makes black hole superradiance an even more powerful probe of the dark sector in particle physics.

Figures (13)

• Figure 1: Eigenfrequencies of bound states with $n \ell m$ being $211$ (in black) and $322$ (in red). The upper and lower plots show the real and imaginary parts of the eigenfrequencies respectively. The solid lines are given by Eqs. \ref{['eq:real_freq']} and \ref{['eq:imag_freq']}, while the dashed lines show the resultes obtained from numerical calculation.
• Figure 2: Parameter space of two non-interacting fields. Without loss of generality, we assume $\psi_{211}$ to be the fastest growing mode, which excludes the white regime. Representative examples of the evolution in some regions are shown in Fig. \ref{['fig:ff_evo']}, while the boundaries and the superradiant evolution of each region are described in Sec. \ref{['sec:singlese']}. In particular, we find that superradiant growth of $\psi_{211}$ might be affected by $\varphi$, as which may accelerate black hole spin down, causing $\psi_{211}$ depletes prematurely.
• Figure 3: Presentative examples of non-interacting two-field superradiant evolution. The upper panel shows the evolution of occupation numbers in the region of corresponding color in Fig. \ref{['fig:ff_para']}, while the lower panel shows the evolution of black hole spin. In the left example, $\varphi_{211}$ and $\varphi_{322}$ cannot grow sufficiently become the black hole spin drops quickly due to the superradiant growth of $\psi_{211}$. In the middle example, $\psi_{211}$, $\varphi_{211}$, $\psi_{322}$ and $\varphi_{322}$ undergo efficient superradiant growth one after another and dominate the black hole spin in sequence. In the right example, the superradiant growth of $\varphi_{211}$ is suppressed by that of $\psi_{211}$, while $\varphi_{322}$ and $\psi_{322}$ can still grow in order after $\psi_{211}$ saturates.
• Figure 4: Possible channels involved in Eqs. \ref{['eq:eomm']}. The left diagram corresponds to the s-channel described by Eqs. \ref{['eq:scpsit']} and \ref{['eq:scphit']}, while the middle and right diagrams correspond to the t- and u-channels described by Eqs. \ref{['tu_channel']}.
• Figure 5: Numerical results of integrals \ref{['Ib']}, \ref{['Ie']}, and \ref{['Ir']}. In practice, we have to impose a cut-off $n_{\rm max}$ for the summation in Eq. \ref{['dwB']}. Given the left plot, we expect the summation converges well when $n_{\rm max} > 8$ for $q<5$.