The most massive black holes observed in the Universe weigh up to βΌ1010Mββ, nearly independent of redshift. Reaching these
final masses likely required copious accretion and several major mergers.
Employing a dynamical approach, that rests on the role played by a new,
relevant physical scale - the transition radius - we provide a theoretical
calculation of the maximum mass achievable by a black hole seed that forms in
an isolated halo, one that scarcely merged. Incorporating effects at the
transition radius and their impact on the evolution of accretion in isolated
haloes we are able to obtain new limits for permitted growth. We find that
large black hole seeds (Mβββ³104Mββ)
hosted in small isolated halos (Mhββ²109Mββ)
accreting with relatively small radiative efficiencies (Ο΅β²0.1) grow optimally in these circumstances. Moreover, we show that the
standard MβββΟ relation observed at zβΌ0 cannot be
established in isolated halos at high-z, but requires the occurrence of
mergers. Since the average limiting mass of black holes formed at zβ³10 is in the range 104β6Mββ, we expect to observe them
in local galaxies as intermediate-mass black holes, when hosted in the rare
haloes that experienced only minor or no merging events. Such ancient black
holes, formed in isolation with subsequent scant growth, could survive, almost
unchanged, until present.Comment: Accepted for publication in ApJ Letter