An Application of Kerr Blackhole Fly-Wheel Model to Statistical Properties of QSOs/AGNs

The aim of this work is to demonstrate the properties of the magnetospheric model around Kerr blackholes (BHs), so-called the fly-wheel (rotation driven) model. The fly-wheel engine of the BH-accretion disk system is applied to the statistics of QSOs/AGNs. In the model, the central BH is assumed to be formed at $z \sim 10^2$ and obtains nearly maximum but finite rotation energy ($\sim$ extreme Kerr BH) at the formation stage. The inherently obtained rotation energy of the Kerr BH is released through an magnetohydrodynamic process. This model naturally leads finite lifetime of AGN activity. Nitta et al. (1991) clarified individual evolution of Kerr BH fly-wheel engine which is parametrized by BH mass, initial Kerr parameter, magnetic field near the horizon and a dimension-less small parameter. We impose a statistical model for the initial mass function (IMF) of ensemble of BHs by the Press-Schechter formalism. By the help of additional assumptions, we can discuss the evolution of the luminosity function and the spatial number density of QSOs/AGNs.