Spin misalignment of black hole binaries from young star clusters: implications for the origin of gravitational waves events

Recent studies indicate that the progenitors of merging black hole (BH) binaries from young star clusters can undergo a common envelope phase just like isolated binaries. If the stars emerge from the common envelope as naked cores, tidal interactions can efficiently synchronize their spins before they collapse into BHs. Contrary to the isolated case, these binary BHs can also undergo dynamical interactions with other BHs in the cluster before merging. The interactions can tilt the binary orbital plane, leading to spin-orbit misalignment. We estimate the spin properties of merging binary BHs undergoing this scenario by combining up-to-date binary population synthesis and accurate few-body simulations. We show that post-common envelope binary BHs are likely to undergo only a single encounter, due to the high binary recoil velocity and short coalescence times. Adopting conservative limits on the binary-single encounter rates, we obtain a local BH merger rate density of ${\sim } 6.6 {\, \rm yr}^{-1} \, \rm Gpc^{-3}$. Assuming low (≲0.2) natal BH spins, this scenario reproduces the trends in the distributions of effective spin χ_eff and precession parameters χ_p inferred from GWTC-2, including the peaks at (χ_eff, χ_p) ~ (0.1, 0.2) and the tail at negative χ_eff values.