Testing the locality of transport in self-gravitating accretion discs — II. The massive disc case

By G. Lodato, W. I. O. Astronomy, Cambridge, U. D. O. Physics, Astronomy, U. S. Andrews, S. Andrews, UK.. 2003

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In this paper, we extend our previous analysis (Paper I) 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 case of low disc mass a self-regulated, marginally stable state (characterized by an approximately constant radial profile of the stability parameter Q) is easily established, in the case of high disc mass 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 wavenumber 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 self-gravity results in accretion time-scales much longer than the dynamical time-scale, 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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/37c134894c0574a744213c9d8361f6d26b84a192

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THE TWO MODES OF GAS GIANT PLANET FORMATION (2009, background): “(1) When GIs are in a self-regulating phase, the effective Shakura & Sunyeaev (1973) α tends toward a few hundredths or less (e.g., Gammie 2001; Lodato & Rice 2004; Mejia et al. 2005; Boley et al. 2006), so the timescale for Σ and κ to change due to mass transport should be much larger than the…”
Gravitational Instabilities in Circumstellar Disks (2016, background): “…specific form of the cooling time, which in some cases is taken to be a constant (Mejia et al. 2005) while in other cases is taken to be proportional to the dynamical timescale as a function of radius, so that β = Ωtcool is kept constant (e.g., Gammie 2001; Lodato & Rice 2004; Lodato & Rice 2005).”
The properties of brown dwarfs and low-mass hydrogen-burning stars formed by disc fragmentation (2008, methodology): “The code uses time- dependent viscosity with parameters α⋆ = 0.1, β = 2α (Morris & Monaghan 1997) and a Balsara switch (Balsara 1995), so as to reduce artificial shear viscosity (Artymowicz & Lubow 1994; Lodato & Rice 2004; Rice, Lodato, & Armitage 2005).”
Rapid inward migration of planets formed by gravitational instability (2011, background): “The difference is probably due to our large disc mass (& 0.2M⋆) and large aspect ratio (h ∼ 0.1), which tend to foster global transport2 of angular momentum (e.g., Lodato & Rice 2004).”
THE FORMATION MECHANISM OF GAS GIANTS ON WIDE ORBITS (2009, positive): “The maximum-mass disks hold between 1/4 and 1/3 of the system mass and may undergo global gravitational instabilities that aid planet/planetesimal formation (e.g. Adams et al. 1989; Rice et al. 2004; Lodato & Rice 2005), which we examine in §5.”
Dynamics of Protoplanetary Disks (2010, background): “Lodato & Rice (2004, 2005) studied angular momentum transport in a model system composed of an isolated disk that cools everywhere on a time scale that is a fixed multiple of the local dynamical time.”
STRUCTURE AND EVOLUTION OF PRE-MAIN-SEQUENCE CIRCUMSTELLAR DISKS (2009, methodology): “1.5 the disk is gravitational unstable and develops spiral waves to transport angular momentum outward and mass inward (Lodato & Rice 2004).”
Investigating fragmentation conditions in self-gravitating accretion discs (2005, methodology): “2 S I M U L AT I O N R E S U LT S The simulations performed here are very similar to those of Rice et al. (2003a) and Lodato & Rice (2004, 2005).”
Systematic effects in measurement of black hole masses by emission-line reverberation of active galactic nuclei: Eddington ratio and inclination (2006, background): “The larger the gravitational instability, the larger the heating rate (cf. Lodato & Rice 2004).”
Global Models for the Evolution of Embedded, Accreting Protostellar Disks (2007, methodology): “Our third source is the global SPH simulations of Rice et al. (2003), Lodato & Rice (2004), and Lodato & Rice (2005), in which a cooling time∝ Ω−1 is imposed locally; these cover the entire parameter space in µ.”
How do massive black holes get their gas (2009, background): “…certain conditions, such local instabilities could instead produce small-scale, tightly wound spiral waves instead of leading to fragmentation (e.g. Lodato & Rice 2004; Rice, Lodato & Armitage 2005; Boley et al. 2006); however, this generally occurs when the cooling time is comparable to or larger…”
The impact of magnetic fields on single and binary star formation (2007, background): “Second, if a protostellar disc is gravitationally unstable(but not so strongly as to fragment), spiral density waves are likely to be the dominant angular momentum transport mechanism within the accretion disc (Lodato & Rice 2004, 2005; Fromang et al. 2004).”
Black hole mergers: can gas discs solve the ‘final parsec’ problem? (2009, background): “For longer cooling times,β & 3, the instability saturates at a finite amplitude and the disc displays a long-lived spiral structure (Lodato & Rice 2004, 2005).”
On planet formation in HL Tau (2015, background): “Massive discs should almost certainly show gravitationally instability and henc prominent and large scale spiral arms (e.g.Lodato & Rice 2004), as seen in the theoretical predictions for HL Tau made byGreaves et al. (2008).”
Neutrino-dominated accretion flows as the central engine of gamma-ray bursts (2017, background): “This mode may drive long-duration, violent explosions if the disk mass is large enough (e.g., Lodato & Rice 2005), which may give rise to SGRBs with extended emission (e.g., Liu et al. 2012b; Cao et al. 2014) or X-ray flares in LGRBs.”
Protoplanetary disc evolution and dispersal: the implications of X-ray photoevaporation (2010, background): “The failure to match the spread in accretion rates at early times 1Myr may not be surprising, since at early times the angular momentum transport mechanism may be dominated by self-gravity and accretion may be episodic (e.g. Lodato & Rice, 2005).”
Supermassive black hole formation during the assembly of pre-galactic discs (2006, background): “The prescription described above implies that at Q = Qc the disc provides no stress, while on the other hand, Lodato & Rice (2004, 2005) have shown that a Q = 1 disc is able to deliver a sizable stress.”
Characterization of exoplanets from their formation - II. The planetary mass-radius relationship (2012, background): “Later numerical simulations have rather found (e.g. Nelson et al. 1998; Lodato & Rice 2004) that with increasing disk mass, lower (global) modes do become more important than at lower disk masses, but that they have a mixed character involving various modes with m. 5.”