Journey to the M_BH -sigma relation: the fate of low mass black holes in the Universe

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In this paper, we explore the establishment and evolution of the empirical correlation between black hole mass and velocity dispersion with redshift.

• We track the growth and accretion history of massive black holes starting from high redshift using two seeding models:(i) Population III remnants, and (ii) massive seeds from direct gas collapse.
• Although the seeds do not initially satisfy the $M_{\rm BH} - \sigma$ relation, the correlation is established and maintained at all times if self-regulating accretion episodes are associated with major mergers.
• The massive end of the $M_{\rm BH} - \sigma$ relation is established early, and lower mass MBHs migrate over time.