Black-hole seed

A black-hole seed is an early black hole from which a later massive black hole can grow by accretion and mergers.

For fixed radiative efficiency $\eta$, Eddington-limited accretion without mergers gives $M(t)=M_0{e}^{t/t_{\mathrm{Sal}}}$ with $t_{\mathrm{Sal}}=\eta {\sigma }_{T}c/[(1-\eta )4\pi G{m}_p]$. A specified final mass and growth interval therefore require $M_0\ge M_f{e}^{-\Delta t/t_{\mathrm{Sal}}}$. The retained factor $1-\eta$ distinguishes actual hole growth from rest-mass supply.

A Population III remnant seed forms when a massive metal-free star collapses, typically leaving a light seed of order $10$--$10^2{M}_{\odot }$ depending on stellar mass loss and pair-instability effects.

A runaway stellar-collision seed forms when mass segregation and repeated mergers in a dense young cluster create a very massive star that collapses to a black hole of roughly $10^2$--$10^4{M}_{\odot }$.

A direct-collapse black-hole seed forms when rapidly inflowing primordial gas avoids fragmentation, builds a supermassive star or quasistar, and collapses to a seed of roughly $10^4$--$10^6{M}_{\odot }$.