Testing the locality of transport in self-gravitating accretion discs

Abstract

In this paper, we extend our previous analysis of the transport properties induced by gravitational instabilities in cooling, gaseous accretion discs to the case where the disc mass is comparable to the central object. In order to do so, we have performed global, three-dimensional smoothed particle hydrodynamics simulations of massive discs. These new simulations show a much more complex temporal evolution with respect to the less massive case. Whereas in the low disc mass case a self-regulated, marginally stable state (characterized by an approximately constant radial profile of the stability parameter Q) is easily established, in the high disc mass case we observe the development of an initial transient and subsequent settling down in a self-regulated state in some simulations, or a series or recurrent spiral episodes, with low azimuthal wave number m, in others. Accretion in this last case can therefore be a highly variable process. On the other hand, we find that the secular evolution of the disc is relatively slow. In fact, the time-average of the stress induced by selfgravity results in accretion time-scales much longer than the dynamical timescale, in contrast with previous isothermal simulations of massive accretion discs. We have also compared the resulting stress tensor with the expectations based on a local theory of transport, finding no significant evidence for global wave energy transport.

The Role of Gravitational Instabilities in the Feeding of Supermassive Black Holes

“…The issue of the nonlinear evolution of gravitational instabilities in gaseous discs has been studied in great detail over the last 10-15 years [13,[20][21][22][23][24][25]. As a result, despite the differences in the numerical methods adopted and in the setup used, a coherent picture of the overall dynamics is emerging.…”

“…Having clarified the main dependencies from the physical parameters, we may then establish the disc response in any particular system. Following this approach, a number of papers have considered the details of the process [13,21,24,25], extending the simulations to full 3D and considering thus global and potentially thick configurations, as a function of the main parameters of the system, such as the disc mass and thickness. Here, I will present a summary of the main results concerning the issue of fragmentation and self-regulation of the instability.…”

“…It should be noted that, in most of the simulations described here [13,20,21,24,25], the parameter β is taken to be a single-free parameter for each simulation, with no dependance on either time or position in the disc. This is certainly not realistic, as in fact the cooling time should and will depend on the local microphysics associated with the disc opacity and radiative properties.…”

Fragmentation favoured in discs around higher mass stars

“…The growth of the gravitational instability has two E-mail: cadman@roe.ac.uk basic outcomes. The disc will either settle into a long-lived (Hall et al 2019) quasi-steady state in which the instability acts to transport angular momentum (Paczynski 1978;Laughlin & Bodenheimer 1994;Lodato & Rice 2004), or it can become sufficiently unstable that it fragments to form bound objects, potentially of planetary mass (Boss 1997(Boss , 1998.…”

“…In particular we concentrate on the critical disc-to-star mass ratios for fragmentation. To approach this, 1D disc models for various stellar masses have been used to calculate the effective viscous-α values (Shakura & Sunyaev 1973;Lodato & Rice 2004) for a range of disc radii and accretion rates. It has then been determined for which disc-to-star mass ratios we expect the disc to be unstable against fragmentation, assuming that disc fragmentation can occur when α 0.1 (Gammie 2001;Rice, Lodato & Armitage 2005).…”