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Possible formation scenarios of supermassive black holes in the earlyuniverse include rapid growth from less massive seed black holes (BHs) viasuper-Eddington accretion or runaway mergers, yet both of these scenarios wouldrequire seed BHs to efficiently sink to and be trapped in the galactic centervia dynamical friction. This may not be true for their complicated dynamics inclumpy high-$z$ galaxies. In this work we study this "sinking problem" withstate-of-the-art high-resolution cosmological simulations, combined with bothdirect $N$-body integration of seed BH trajectories and post-processing ofrandomly generated test particles with a newly developed dynamical frictionestimator. We find that seed BHs less massive than $10^8\,M_\odot$ (i.e., allbut the already-supermassive seeds) cannot efficiently sink in typical high-$z$galaxies. We also discuss two possible solutions: dramatically increasing thenumber of seeds such that one seed can end up trapped in the galactic center bychance, or seed BHs being embedded in dense structures (e.g. star clusters)with effective masses above the mass threshold. We discuss the limitations ofboth solutions.

Seeds Don't Sink: Even Massive Black Hole "Seeds" Cannot Migrate to Galaxy Centers Efficiently