Self-similar Evolution of Self-Gravitating Viscous Accretion Discs

Abstract

A new one-dimensional, dynamical model is proposed for geometrically thin, self-gravitating viscous accretion discs. The vertically integrated equations are simplified using the slow accretion limit and the monopole approximation with a time-dependent central point mass to account for self-gravity and accretion. It is shown that the system of partial differential equations can be reduced to a single non-linear advection diffusion equation which describes the time evolution of angular velocity. In order to solve the equation three different turbulent viscosity prescriptions are considered. It is shown that for these parametrizations the differential equation allows for similarity transformations depending only on a single non-dimensional parameter. A detailed analysis of the similarity solutions reveals that this parameter is the initial power law exponent of the angular velocity distribution at large radii. The radial dependence of the self-similar solutions is in most cases given by broken power laws. At small radii the rotation law always becomes Keplerian with respect to the current central point mass. In the outer regions the power law exponent of the rotation law deviates from the Keplerian value and approaches asymptotically the value determined by the initial condition. It is shown that accretion discs with flatter rotation laws at large radii yield higher accretion rates. The methods are applied to self-gravitating accretion discs in active galactic nuclei. Fully self-gravitating discs are found to evolve faster than nearly Keplerian discs. The implications on supermassive black hole formation and Quasar evolution are discussed.

arXiv commentAccepted for publication in MNRAS

References in corpus (21)

• Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks
• Protoplanetary Disk Structures in Ophiuchus
• The locality of transport in self-gravitating accretion discs
• On the Dynamical Foundations of Alpha Disks
• The effect of cooling on the global stability of self-gravitating protoplanetary discs
• VLBI Imaging of Water Maser Emission from the Nuclear Torus of NGC 1068
• Testing the locality of transport in self-gravitating accretion discs - II. The massive disc case
• Characterising the Gravitational Instability in Cooling Accretion Discs
• The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks III. Simulations with Radiative Cooling and Realistic Opacities
• The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks II. Extended Simulations with Varied Cooling Rates
• Non-Keplerian rotation in the nucleus of NGC 1068: evidence for a massive accretion disk?
• Evidence for a Geometrically Thick Self-Gravitating Accretion Disk in NGC 3079
• Time-dependent models of the structure and evolution of self-gravitating protoplanetary discs
• The Cool Accretion Disk in ESO 243-49 HLX-1: Further Evidence of an Intermediate Mass Black Hole
• The Nature of Angular Momentum Transport in Radiative Self-Gravitating Protostellar Discs
• Self-Similar Collapse of a Self-Gravitating Viscous Disk
• Self-regulated Accretion Disks
• AGN disks and black holes on the weighting scales
• Viscous accretion of a polytropic self-gravitating disk in the presence of wind
• A Gravitational Instability-Driven Viscosity in Self-Gravitating Accretion Disks
• Self-Similar Evolutionary Solutions of Self-Gravitating, Polytropic $\beta$-Viscous Disks

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