William McClymont, Sandro Tacchella, Xihan Ji, Rahul Kannan, Roberto Maiolino, Charlotte Simmonds, Aaron Smith, Ewald Puchwein, Enrico Garaldi, Mark Vogelsberger, Francesco D'Eugenio, Laura Keating, Xuejian Shen, Bartolomeo Trefoloni, Oliver Zier

JWST has revealed the apparent evolution of the black hole (BH)-stellar mass ($M_\mathrm{BH}$-$M_\rm{\ast}$) relation in the early Universe, while remaining consistent the BH-dynamical mass ($M_\mathrm{BH}$-$M_\mathrm{dyn}$) relation. We predict BH masses for $z>3$ galaxies in the high-resolution THESAN-ZOOM simulations by assuming the $M_\mathrm{BH}$-$M_\mathrm{dyn}$ relation is fundamental. Even without live BH modelling, our approach reproduces the JWST-observed $M_\mathrm{BH}$ distribution, including overmassive BHs relative to the local $M_\mathrm{BH}$-$M_\mathrm{\ast}$ relation. We find that $M_\mathrm{BH}/M_\mathrm{\ast}$ declines with $M_\mathrm{\ast}$, evolving from $\sim$0.1 at $M_\mathrm{\ast}=10^6\,\mathrm{M_\odot}$ to $\sim$0.01 at $M_\mathrm{\ast}=10^{10.5}\,\mathrm{M_\odot}$. This trend reflects the dark matter ($f_\mathrm{DM}$) and gas fractions ($f_\mathrm{gas}$), which decrease with $M_\mathrm{\ast}$ but show little redshift evolution down to $z=3$, resulting in small $M_\mathrm{\ast}/M_\mathrm{dyn}$ ratios and thus overmassive BHs in low-mass galaxies. We use $\texttt{Prospector}$-derived stellar masses and star-formation rates to infer $f_\mathrm{gas}$ across 48,022 galaxies in JADES at $3<z<9$, finding excellent agreement with our simulation. Our results demonstrate that overmassive BHs would naturally result from a fundamental $M_\mathrm{BH}$-$M_\mathrm{dyn}$ relation and be typical of the gas-rich, dark matter-dominated nature of low-mass, high-redshift galaxies. Such overmassive, rapidly growing BHs may strongly influence the earliest stages of galaxy formation.