Formation of over-massive black holes in high-redshift disk galaxies via globular cluster accretion

Recent observations with the James Webb Space Telescope (JWST) have suggested the existence of over-massive black holes (OMBHs) in high-redshift galaxies. In this paper, we propose a new mechanism for the formation of OMBHs, based on the accretion of globular clusters (GCs) in compact disk galaxies. We derive the conditions under which OMBHs can form, focusing on key parameters such as halo mass, redshift, and halo spin parameter. Our results show that at redshift $z = 10$, a halo with mass $10^{11}~M_{\odot}$ and a spin parameter of $\sim 0.02$ can form a black hole of $2.3 \times 10^{8}~M_{\odot}$ through GC migration and accretion via tidal disruption events (TDEs). The resulting black hole-to-stellar mass ratio can reach $\sim 0.1$, corresponding to the fraction of GC mass accreted onto the black hole. This mechanism thus provides a plausible explanation for the OMBHs observed by JWST. Furthermore, by combining our model with the halo mass function and the spin-parameter distribution, we construct black hole mass functions that reproduce the number densities of the massive BH candidates UHZ1 and GHZ9 at $z \approx 10$, as well as the abundances of BHs with masses $\gtrsim 10^{8}~\rm{M_\odot}$ at $z \approx 5$ inferred from JWST observations. However, our model overpredicts the abundance of BHs with masses $ < 10^{8}~\rm{M_\odot}$, suggesting that moderately massive, inactive BHs are more frequent.