The structure of the central disk of NGC 1068: a clumpy disk model

NGC 1068 is one of the best studied Seyfert II galaxies, for which the blackhole mass has been determined from the Doppler velocities of water maser. We show that the standard $\alpha$-disk model of NGC 1068 gives disk mass between the radii of 0.65 pc and 1.1 pc (the region from which water maser emission is detected) to be about 7x10$^7$ M$_\odot$ (for $\alpha=0.1$), more than four times the blackhole mass, and a Toomre Q-parameter for the disk is $\sim$0.001. This disk is therefore highly self-gravitating and is subject to large-amplitude density fluctuations. We conclude that the standard $\alpha$-viscosity description for the structure of the accretion disk is invalid for NGC 1068. In this paper we develop a new model for the accretion disk. The disk is considered to be composed of gravitationally bound clumps; accretion in this clumped disk model arises because of gravitational interaction of clumps with each other and the dynamical frictional drag exerted on clumps from the stars in the central region of the galaxy. The clumped disk model provides a self-consistent description of the observations of NGC 1068. The computed temperature and density are within the allowed parameter range for water maser emission, and the rotational velocity in the disk falls off as $r^{-0.35}$.Comment: To appear in Ap

Memory-induced anomalous dynamics: emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model

We present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of behavior by simply changing parameter values. Furthermore, the model offers the great advantage of analytic tractability. Our model is non-Markovian in that the next jump of the walker is (probabilistically) determined by the history of past jumps. It also has elements of intermittency in that one possibility at each step is that the walker does not move at all. This rich encompassing scenario arising from a single model provides useful insights into the source of different types of asymptotic behavior