Learning the Universe at High Redshifts: Impact of Accretion Modeling on Early Black Hole Growth
JWST discoveries of the earliest ($z \gtrsim 9$) supermassive black holes (BHs, $M_\bullet \gtrsim 10^6\,\rm{M}_\odot$) challenge the BH seeding and accretion models of most cosmological simulations. In this work, we compare early BH growth arising from three different accretion prescriptions characterized by distinct scalings between the accretion rate ($\dot{M}_{\rm \bullet}$) and the BH mass ($M_{\rm \bullet}$): the commonly used Bondi-Hoyle model ($\dot{M}_{\rm \bullet}\propto M_{\rm \bullet}^2$), and two free-fall models with shallower scalings ($\dot{M}_{\rm \bullet}\propto M_{\rm \bullet}^{1/2}$ and $M_{\rm \bullet}$). Bondi accretion tends to produce stronger runaway growth than the free-fall models when using heavy ($\sim10^5\,\rm{M}_\odot$) seeds in extreme environments owing to the steeper $M_\bullet$ scaling, but its sensitivity to the local gas sound speed makes it more susceptible to suppression from temperature increases due to AGN and stellar feedback. The free-fall models tend to produce stronger growth for lower-mass seeds ($\sim10^{3-4}\,\rm{M}_\odot$) in moderate environments as they are less dependent on the BH's mass to accrete effectively, however in this regime BH growth remains negligible for all accretion models in the presence of fiducial stellar feedback. Enhancing early BH growth via many BH-BH mergers disproportionately enhances subsequent accretion-driven growth for Bondi due to the steeper $M_{\rm \bullet}$ dependence. Our simulations can thus assemble BHs with masses of $\sim10^6-10^7~M_{\odot}$ at $z\gtrsim9$, as inferred by JWST, under two circumstances: 1) abundant heavy-seed formation that drives BH-BH mergers, or 2) Bondi accretion with weak feedback.