Abstract
(ABRIDGED) We present a model in which the seeds of supermassive black holes form from the lowest angular momentum gas in proto-galaxies at high redshift. We show that this leads to a correlation between black hole masses and spheroid properties, as observed today. We assume that gas in early-forming, rare halos has a distribution of specific angular momentum similar to that expected for dark matter halos. This distribution has a significant low angular momentum tail which implies that every proto-galaxy should contain gas that ends up in a high-density disc. In halos more massive than a critical threshold of \~10^8Msun, the discs are gravitationally unstable, and experience an efficient Lin-Pringle viscosity that allows mass inflow. This process continues until the first massive stars disrupt the disc. Black holes are created with a characteristic mass of ~10^5 Msun, independent of the redshift of formation. This serves as a lower bound for black-hole masses in galaxies today. The comoving mass density of black hole seeds grows with time, and saturates when cosmic reionization stops gas cooling in these low-mass systems. By z~15, the comoving mass density becomes comparable to that inferred from observations, with room for appropriate additional luminous growth during a later quasar accretion phase. Hierarchical merging after z~15 naturally leads to a linear correlation between black-hole mass and stellar spheroid mass, with negligible black hole masses in disc-dominated galaxies.
Highlights
Detailed studies of gas and stellar kinematics near the centers of present-day galaxies have revealed that almost all galaxy spheroids host super-massive black holes, with masses Mbh = (106 − 109)M⊙, or ∼ 10−4 of the total stellar mass of their parent galaxies (e.g. Kormendy & Gebhardt 2001; Ferrarese & Merritt 2000; Magorrian et al 1998)
We presented a physical model for the production of massive seed black holes at high redshifts, with a characteristic mass ∼ 105M⊙
Massive seeds may help explain the existence of the supermassive black holes associated with luminous Active Galactic Nuclei (AGN) at z>∼ 6
Summary
The situation may get even worse at earlier times because the typical collapsing mass M⋆(a) is smaller in proportion to a high power of the expansion factor a ≡ (1 + z)−1 This implies that the ratio of the centrifugally supported size (∝ aM⋆(a)1/3) to the Schwarzschild radius (∝ M⋆(a) if the black hole mass is a constant fraction of the halo mass) increases dramatically at early times, unless the sites of black hole formation are rare haloes much more massive than M⋆(a). This line of argument indicates that the seed black holes originate from material at the very lowest end of the angular-momentum distribution within rare, massive haloes at high redshift.
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