Constraints on the ultralight scalar boson from Advanced LIGO and Advanced Virgo's first three observing runs using the stochastic gravitational-wave background

Ultralight bosons are promising dark matter candidates and can trigger superradiant instabilities of spinning black holes (BHs), resulting in long-lived rotating "bosonic clouds" around the BHs and dissipating their energy through the emission of monochromatic gravitational waves (GWs). We focus on the scalar bosons minimally coupled with both isolated stellar-origin BHs (SBH) and their binary merger remnants, and perform Bayesian data analysis to search for the stochastic GW background from all the unstable modes that can trigger the superradiant instabilities using the data of Advanced LIGO and Advanced Virgo's first three observing runs. We find no evidence for such signal, and hence rule out the scalar bosons within the mass range $[1.5, 16]\times10^{-13}$ eV, $[1.9, 8.3]\times10^{-13}$ eV and $[1.3, 17]\times10^{-13}$ eV at $95\%$ confidence level for isolated SBHs having a uniform dimensionless spin distribution in $[0,1]$, $[0,0.5]$ and $[0.5,1]$, respectively.

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