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Register a new userOn the angular momentum transport due to vertical convection in accretion discs
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The mechanism of angular momentum transport in accretion discs has long been debated. Although the magnetorotational instability appears to be a promising process, poorly ionized regions of accretion discs may not undergo this instability. In this letter, we revisit the possibility of transporting angular momentum by turbulent thermal convection. Using high-resolution spectral methods, we show that strongly turbulent convection can drive outward angular momentum transport at a rate that is, under certain conditions, compatible with observations of discs. We find however that the angular momentum transport is always much weaker than the vertical heat transport. These results indicate that convection might be another way to explain global disc evolution, provided that a sufficiently unstable vertical temperature profile can be maintained.
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The structure of accretion curtain flows arising from magnetically disrupted discs is considered. It is shown that a sub-Alfvenic, magnetically channelled flow is consistent with matching the magnetic field across the curtain base. It is shown that some angular momentum is necessarily fed back into the disc, and this reduces the accretion torque acting on the star. The sonic point coordinates are found and a critical rotation rate results below which the sonic point merges with the curtain flow base so, for such stellar rotation rates, little or no thermal assistance is required for material to make the transition to a supersonic flow.
Gravitational instability (GI) controls the dynamics of young massive protoplanetary discs. Apart from facilitating gas accretion on to the central protostar, it must also impact on the process of planet formation: directly through fragmentation, and indirectly through the turbulent concentration of small solids. To understand the latter process, it is essential to determine the dust dynamics in such a turbulent flow. For that purpose, we conduct a series of 3D shearing box simulations of coupled gas and dust, including the gass self-gravity and scanning a range of Stokes numbers, from 0.001 to ~0.2. First, we show that the vertical settling of dust in the midplane is significantly impeded by gravitoturbulence, with the dust scale-height roughly 0.6 times the gas scale height for centimetre grains. This is a result of the strong vertical diffusion issuing from (a) small-scale inertial-wave turbulence feeding off the GI spiral waves and (b) the larger-scale vertical circulations that naturally accompany the spirals. Second, we show that at R=50 AU concentration events involving sub-metre particles and yielding order 1 dust to gas ratios are rare and last for less than an orbit. Moreover, dust concentration is less efficient in 3D than in 2D simulations. We conclude that GI is not especially prone to the turbulent accumulation of dust grains. Finally, the large dust scale-height measured in simulations could be, in the future, compared with that of edge-on discs seen by ALMA, thus aiding detection and characterisation of GI in real systems.
(Abridged) We analyse the stability and evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are power-law functions of cylindrical radius. We employ two different hydrodynamic codes to perform 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the viscosity. We present a stability analysis of the problem that we use to interpret the simulation results. We find that disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of modes with wavenumber ratios |k_R/k_Z| >> 1 when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time scale. These discs are subject to the Goldreich-Schubert-Fricke (GSF) or `vertical shear linear instability. Development of the instability involves excitation of vertical breathing and corrugation modes in the disc, with the corrugation modes in particular being a feature of the nonlinear saturated state. Instability operates when the dimensionless disc kinematic viscosity nu < 10^{-6} (Reynolds numbers Re>H c_s/nu > 2500). In 3D the instability generates a quasi-turbulent flow, and the Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches alpha ~ 6 x 10^{-4} by the end of the simulation. The vertical shear instability in disc models which include realistic thermal physics has yet to be examined. Should it occur, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance.
The source of viscosity in astrophysical accretion flows is still a hotly debated issue. We investigate the contribution of convective turbulence to the total viscosity in a self-consistent approach, where the strength of convection is determined from the vertical disc structure itself. Additional sources of viscosity are parametrized by a beta-viscosity prescription, which also allows an investigation of self-gravitating effects. In the context of accretion discs around stellar mass and intermediate mass black holes, we conclude that convection alone cannot account for the total viscosity in the disc, but significantly adds to it. For accretion rates up to 10% of the Eddington rate, we find that differential rotation provides a sufficiently large underlying viscosity. For higher accretion rates, further support is needed in the inner disc region, which can be provided by an MRI-induced viscosity. We briefly discuss the interplay of MRI, convection and differential rotation. We conduct a detailed parameter study of the effects of central masses and accretion rates on the disc models and find that the threshold value of the supporting viscosity is determined mostly by the Eddington ratio with only little influence from the central black hole mass.
The vertical shear instability (VSI) is a robust phenomenon in irradiated protoplanetary disks (PPDs). While there is extensive literature on the VSI in the hydrodynamic limit, PPDs are expected to be magnetized and their extremely low ionization fractions imply that non-ideal magneto-hydrodynamic (MHD) effects should be properly considered. To this end, we present linear analyses of the VSI in magnetized disks with Ohmic resistivity. We primarily consider toroidal magnetic fields, which are likely to dominate the field geometry in PPDs. We perform vertically global and radially local analyses to capture characteristic VSI modes with extended vertical structures. To focus on the effect of magnetism, we use a locally isothermal equation of state. We find that magnetism provides a stabilizing effect to dampen the VSI, with surface modes, rather than body modes, being the first to vanish with increasing magnetization. Subdued VSI modes can be revived by Ohmic resistivity, where sufficient magnetic diffusion overcome magnetic stabilization, and hydrodynamic results are recovered. We also briefly consider poloidal fields to account for the magnetorotational instability (MRI), which may develop towards surface layers in the outer parts of PPDs. The MRI grows efficiently at small radial wavenumbers, in contrast to the VSI. When resistivity is considered, we find the VSI dominates over the MRI for Ohmic Els{a}sser numbers $lesssim 0.09$ at plasma beta parameter $beta_Z sim 10^4$.
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