Universal transition diagram from dormant to actively accreting supermassive black holes

The vast majority of supermassive black holes (SMBHs) in the local universe exhibit levels of activity much lower than those expected from gas supplying rates onto the galactic nuclei, and only a small fraction of silent SMBHs can turn into active galactic nuclei. Revisiting observational data of very nearby SMBHs whose gravitational spheres of influence are spatially reached by the Chandra X-ray satellite, we find that the level of BH activity drastically increases from the quiescent phase when the inflow rate outside of the BH influence radius is higher than 0.1% of the Eddington accretion rate. We also show that the relation between the nuclear luminosity and gas accretion rate from the BH influence radius measured from X-ray observations is well described by the universal state transition of accreting SMBHs, as predicted by recent hydrodynamical simulations with radiative cooling and BH feedback. After the state transition, young massive stars should form naturally in the nucleus, as observed in the case of the nearest SMBH, Sagittarius A$^\ast$, which is currently quiescent but was recently active.Comment: 9 pages (main text), 2 figures, 1 table, accepted for publication in Ap

A model structure on the category of small categories for coverings

We define a new model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant objects in the model structure coincide with groupoids, and the fibrant replacement is the groupoidification.Comment: 16 page

Asymptotics of the densities of the first passage time distributions for Bessel diffusions

This paper concerns the first passage times of Bessel processes to a point on the positive real line. We are interested in the case when the process starts at a position on its right and compute the densities of the distributions of the passage time to obtain the asymptotic forms of them as time tends to infinity that are valid uniformly for the starting position.Comment: 25pages, To appear in Trans. Amer. Math. Soc. 367 (2015), no. 4, 2719-274