Modeling and searching for a stochastic gravitational-wave background from ultralight vector bosons

Ultralight bosons, which are predicted in a variety of beyond-Standard-Model scenarios as dark-matter candidates, can trigger the superradiant instability around spinning black holes. This gives rise to oscillating boson condensates then dissipate through emission nearly monochromatic gravitational waves. Such systems promising sources for current and future gravitational-wave detectors. In this work, we consider minimally-coupled, massive vector produce significantly stronger signal compared scalar case. We adopt recently obtained numerical results flux, astrophysical models hole populations that include both isolated holes binary merger remnants, compute study detail stochastic background emitted by these sources. Using Bayesian framework, search such using data from first second observing runs Advanced LIGO. find no evidence signal. Therefore, allow us constrain minimally coupled fields with masses range $0.8\times10^{-13}\mathrm{eV}\leq m_b\leq 6.0\times10^{-13}\mathrm{eV}$ at 95% credibility, assuming optimistically dimensionless spin distribution population is uniform $[0,1]$. With more pessimistic assumptions, narrower $m_b\approx 10^{-13}\mathrm{eV}$ still be excluded long upper end $\gtrsim 0.2$.