Black Hole Superradiance Signatures of Ultralight Vectors

TL;DR

This work analyzes gravitationally coupled ultralight vector bosons around rotating black holes, deriving leading-order spin-1 superradiance growth rates in the non-relativistic regime and showing that vector bound states can grow much faster than their scalar counterparts. It translates these growth rates into observable consequences, including rapid BH spin-down constrained by X-ray binary and SMBH spin measurements, and predicted gravitational-wave signals from vector cloud annihilations (and, to a lesser extent, transitions) detectable by Advanced LIGO and future detectors. The paper provides robust mass exclusions for vectors in the ranges $5\times 10^{-14}$ eV $< \mu < 2\times 10^{-11}$ eV (stellar BHs) and $6\times 10^{-20}$ eV $< \mu < 2\times 10^{-17}$ eV (SMBHs), and outlines statistical and all-sky GW search strategies to probe vector SR across astrophysical BH populations. By highlighting the distinct SR scaling and gravitational-wave signatures of vectors versus scalars, the work offers practical paths to identify or constrain ultralight vector bosons with current GW data and future observatories.

Abstract

The process of superradiance can extract angular momentum and energy from astrophysical black holes (BHs) to populate gravitationally-bound states with an exponentially large number of light bosons. We analytically calculate superradiant growth rates for vectors around rotating BHs in the regime where the vector Compton wavelength is much larger than the BH size. Spin-1 bound states have superradiance times as short as a second around stellar BHs, growing up to a thou- sand times faster than their spin-0 counterparts. The fast rates allow us to use measurements of rapidly spinning BHs in X-ray binaries to exclude a wide range of masses for weakly-coupled spin-1 particles, $5 \times 10^{-14} - 2 \times 10^{-11}$ eV; lighter masses in the range $6 \times 10^{-20} - 2 \times 10^{-17}$ eV start to be constrained by supermassive BH spin measurements at a lower level of confidence. We also explore routes to detection of new vector particles possible with the advent of gravitational wave (GW) astronomy. The LIGO-Virgo collaboration could discover hints of a new light vector particle in statistical analyses of masses and spins of merging BHs. Vector annihilations source continuous monochromatic gravitational radiation which could be observed by current GW observatories. At design sensitivity, Advanced LIGO may measure up to thousands of annihilation signals from within the Milky Way, while hundreds of BHs born in binary mergers across the observable universe may superradiate vector bound states and become new beacons of monochromatic gravitational waves.

Figures (12)

• Figure 1: The $A_i$ field at a moment in time for the lowest-radial-overtone $j=1$, $m=1$ hydrogenic bound states, with $\ell=0,1,2$ from top to bottom. The size and color of an arrow correspond to the magnitude of $A_i$ at that point. The change in the field over time corresponds to rotating each figure about its vertical axis, with angular frequency $\omega \simeq \mu$.
• Figure 2: Analytic approximations to superradiance rates for the fastest-growing vector bound states, at each value $m$ of angular momentum about the BH spin axis, for a Kerr BH with $a_* = 0.99$ (upper solid curves). The black data points are full numerical results from East:2017mrj. For the highest superradiance rate, including the subleading correction to bound state energy found in East:2017mrj improves the fit to numerical results at high $\alpha$ (dashed green curve). The lower red curves show the numerical results Dolan:2007mj (dotted) and analytic approximation (dashed) for the superradiance rate of the fastest-growing scalar bound state. The top axis shows the BH mass corresponding to a given $\alpha$ for vector mass $\mu = 10^{-12} \text{~eV}$. The right-hand axis shows the growth e-folding time in seconds, again for $\mu = 10^{-12} \text{~eV}$. The curve for the $\ell = 0$, $j = m = 1$ mode is the full leading-$\alpha$ rate, along with higher-order corrections from $m \Omega_H - \omega$ terms (see Appendix \ref{['ap:rates']}). The curves for the $\ell,j,m = 1,2,2$ and $\ell,j,m = 2,3,3$ modes show the sub-component of the superradiance rates due to Poynting flux through the BH horizon. These are underestimates of the full leading-$\alpha$ rates (Appendix \ref{['ap:rates']}), but have the correct scaling in the $\alpha \ll 1$ limit.
• Figure 3: Effect of superradiance on a BH due to a vector (bold) or scalar (dotted) with mass $\mu=10^{-12}$ eV. Shaded regions above the lines correspond to BH parameters that result in spin-down within a typical binary lifetime $\Gamma_m > \frac{1}{\tau_{bh}}\log N_m$, shown for $\tau_{\text{bh}} = 5 \times 10^{6}$ years, for levels with total angular momentum $j=1$ to $j=4$. We also show an example evolution in the spin-mass plane of a $20M_{\odot}$ BH with initial spin $a_{*}=0.9$. The dashed lines correspond to the superradiance boundaries for each $m$ value.
• Figure 4: The areas above the curves correspond to initial BH parameters affected by superradiance within $5\times 10^{6}$ years, in the presence of a vector with mass $\mu=10^{-11}\text{~eV}$. The data points are stellar BH measurements with $2\sigma$ errors. We use the five with the highest spin measurements (listed in Table \ref{['tab:stellar']}) to constrain vector masses --- BH parameters above the curves, such as the two fastest-spinning BHs in this Figure, rule out a given vector mass.
• Figure 5: Left: Constraints on mass of vectors derived from quickly-rotating supermassive BHs (at $90\%$ confidence). Only the $j=1$ level is used to set a constraint. Right: Constraints on mass of vectors derived from quickly-rotating stellar-mass BHs (at $2\sigma$). Each rectangle corresponds to a $j$-level which sets a constraint, starting with $j=1$ on the left. The gray bands account for theoretical uncertainty in the superradiance rates; the right and left edges of these bands are set by superradiance rates $\frac{1}{2}\times$ and $2\times$ the analytic value, respectively.