Convective overstability in accretion disks: 3D linear analysis and nonlinear saturation

Recently, Klahr & Hubbard (2014) claimed that a hydrodynamical linear overstability exists in protoplanetary disks, powered by buoyancy in the presence of thermal relaxation. We analyse this claim, confirming it through rigorous compressible linear analysis. We model the system numerically, reproducing the linear growth rate for all cases studied. We also study the saturated properties of the overstability in the shearing box, finding that the saturated state produces finite amplitude fluctuations strong enough to trigger the subcritical baroclinic instability. Saturation leads to a fast burst of enstrophy in the box, and a large-scale vortex develops in the course of the next $\approx$100 orbits. The amount of angular momentum transport achieved is of the order of $\alpha \approx 10^{-3}$, as in compressible SBI models. For the first time, a self-sustained 3D vortex is produced from linear amplitude perturbation of a quiescent base state.Comment: 7 pages, 4 figures. ApJ, accepte

Damage spreading in the Bak-Sneppen model: Sensitivity to the initial conditions and equilibration dynamics

The short-time and long-time dynamics of the Bak-Sneppen model of biological evolution are investigated using the damage spreading technique. By defining a proper Hamming distance measure, we are able to make it exhibits an initial power-law growth which, for finite size systems, is followed by a decay towards equilibrium. In this sense, the dynamics of self-organized critical states is shown to be similar to the one observed at the usual critical point of continuous phase-transitions and at the onset of chaos of non-linear low-dimensional dynamical maps. The transient, pre-asymptotic and asymptotic exponential relaxation of the Hamming distance between two initially uncorrelated equilibrium configurations is also shown to be fitted within a single mathematical framework. A connection with nonextensive statistical mechanics is exhibited.Comment: 6 pages, 4 figs, revised version, accepted for publication in Int.J.Mod.Phys.C 14 (2003

Pebble trapping backreaction does not destroy vortices

The formation of planets remains one of the most challenging problems of contemporary astrophysics. Starting with micron-sized dust grains, coagulation models predict growth up to centimeter (pebbles), but growth beyond this size is difficult because of fragmentation and drift. Ways to bypass this problem have focused on inhomogeneities in the flow, be that zonal flows, streaming instability, or vortices. Because vortices are in equilibrium between the Coriolis and the pressure force, the pressureless grains will orbit along a vortex streamline experiencing a drag force. This is a very effective mechanism to concentrate pebbles as also seen in numerical simulations and possibly in ALMA observations. Yet, a high pebble load is dangerous for the vortex, and we showed that in two-dimensional simulations the backreaction eventually leads to vortex disruption. We investigate whether the same happens in three dimensions. We perform 3D simulations with pebbles in a local box finding that, although the pebbles disturb the vortex around the midplane, the column does not get destroyed. This result is important because, based on the previous 2D result suggesting complete disruption, the vortex interpretation of ALMA observations has been called into question. We show instead that the vortex behaves like a Taylor column, and the pebbles as obstacles to the flow. Pebble accumulation in the center of the vortices proceeds to roughly the same concentration as in the control run without backreaction.Comment: AAS research note; 3 pages, 1 figur

On the connection between the magneto-elliptic and magneto-rotational instabilities

It has been recently suggested that the magneto-rotational instability (MRI) is a limiting case of the magneto-elliptic instability (MEI). This limit is obtained for horizontal modes in the presence of rotation and an external vertical magnetic field, when the aspect ratio of the elliptic streamlines tends to infinite. In this paper we unveil the link between these previously unconnected mechanisms, explaining both the MEI and the MRI as different manifestations of the same Magneto-Elliptic-Rotational Instability (MERI). The growth rates are found and the influence of the magnetic and rotational effects is explained, in particular the effect of the magnetic field on the range of negative Rossby numbers at which the horizontal instability is excited. Furthermore, we show how the horizontal rotational MEI in the rotating shear flow limit links to the MRI by the use of the local shearing box model, typically used in the study of accretion discs. In such limit the growth rates of the two instability types coincide for any power-type background angular velocity radial profile with negative exponent corresponding to the value of the Rossby number of the rotating shear flow. The MRI requirement for instability is that the background angular velocity profile is a decreasing function of the distance from the centre of the disk which corresponds to the horizontal rotational MEI requirement of negative Rossby numbers. Finally a physical interpretation of the horizontal instability, based on a balance between the strain, the Lorentz force and the Coriolis force is given.Comment: 15 pages, 3 figures. Accepted for publication in the Journal of Fluid Mechanic