Viscosity prescription for gravitationally unstable accretion disks

Abstract

Gravitationally unstable accretion disks emerge in a variety of astrophysical contexts - giant planet formation, FU Orioni outbursts, feeding of AGNs, and the origin of Pop III stars. When a gravitationally unstable disk is unable to cool rapidly it settles into a quasi-stationary, fluctuating gravitoturbulent state, in which its Toomre Q remains close to a constant value Q_0~1. Here we develop an analytical formalism describing the evolution of such a disk, which is based on the assumptions of Q=Q_0 and local thermal equilibrium. Our approach works in the presence of additional sources of angular momentum transport (e.g. MRI), as well as external irradiation. Thermal balance dictates a unique value of the gravitoturbulent stress α_{gt} driving disk evolution, which is a function of the local surface density and angular frequency. We compare this approach with other commonly used gravitoturbulent viscosity prescriptions, which specify the explicit dependence of stress α_{gt} on Toomre Q in an ad hoc fashion, and identify the ones that provide consistent results. We nevertheless argue that our Q=Q_0 approach is more flexible, robust, and straightforward, and should be given preference in applications. We illustrate this with a couple of analytical calculations - locations of the snow line and of the outer edge of the dead zone in a gravitoturbulent protoplanetary disk - which clearly show the simplicity and versatility of the Q=Q_0 approach.

11 pages, 5 figures, submitted to ApJ

References in corpus (7)

• The Formation of Population III Binaries from Cosmological Initial Conditions
• Starbursts near supermassive black holes: young stars in the Galactic Center, and gravitational waves in LISA band
• Characterising the Gravitational Instability in Cooling Accretion Discs
• Global Models for the Evolution of Embedded, Accreting Protostellar Disks
• Properties of gravitoturbulent accretion disks
• New composite models of partially ionized protoplanetary disks
• Star Formation in Quasar Disk

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