Probability Distribution of Primordial Angular Momentum and Formation of Massive Black Holes

Details Probability Distribution of Primordial Angular Momentum and Formation of Massive Black Holes Probability Distribution of Primordial Angular Momentum and Formation of Massive Black Holes

1994-05-26

arxiv.org/abs/astro-ph/9405057v1

Prog.Theor.Phys.92:961-974,1994

Astronomy and Astrophysics

Astrophysics

21 pages and 6 figures, uuencoded compressed postscript, KUNS 1266

Scientific paper

10.1143/PTP.92.961

We consider the joint probability distribution function for the mass contrast and angular momentum of over-density regions on the proto- galactic scale and investigate the formation of massive black holes at redshift $z\gsim10$. We estimate the growth rate of the angular momentum by the linear perturbation theory and the decay rate by the Compton drag and apply the Press-Schechter theory to obtain the formation rate of massive black holes, assuming the full reionization of the universe at $z=z_{ion}\gg 10$. We find the correlation between the mass contrast and angular momentum vanishes in the linear theory. However, application of the Press-Schechter theory introduces a correlation between the mass contrast and angular momentum of bound objects. Using thus obtained probability distribution, we calculate the mass fraction of black holes with $M\sim10^6-10^8M_{\odot}$ in the universe. We find that it crucially depends on the reionization epoch $z_{ion}$. Specifically, for the standard CDM power spectrum with the COBE normalization, the condition $z_{ion}\gsim 500$ must be satisfied to reproduce the observed number density of QSOs.

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