Dynamics of perturbation modes in protoplanetary discs : new effects of self-gravity and velocity shear
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Date
27/06/2011Author
Mamatsashvili, George
Metadata
Abstract
Protoplanetary discs, composed of gas and dust, usually surround young stellar objects and
serve two main purposes: they determine the accretion of matter onto the central object and
also represent sites of planet formation. The accretion proceeds through the transport of angular
momentum outwards allowing the disc matter to fall towards the centre. A mechanism
responsible for the transport can be turbulence, waves or other coherent structures originating
from various instabilities in discs that could, in addition, play a role in the planet formation
process. For an understanding of these instabilities, it is necessary to study perturbation dynamics
in differentially rotating, or sheared media. Thus, this thesis focuses on new aspects
in the perturbation dynamics in non-magnetised protoplanetary discs that arise due to their
self-gravity and velocity shear associated with the disc’s differential rotation. The analysis is
carried out in the framework of the widely employed local shearing box approximation. We
start with 2D discs and then move on to 3D ones.
In 2D discs, there are two basic perturbation types/modes – spiral density waves and
vortices – that are responsible for angular momentum transport and that can also contribute
to accelerating planet formation. First, in the linear regime, we demonstrate that the vortical
mode undergoes large growth due to self-gravity and in this process generates density waves
via shear-induced linear mode coupling phenomenon. This is noteworthy, because commonly
only density waves are considered in self-gravitating discs. Then we investigate vortex dynamics
in the non-linear regime under the influence of self-gravity by means of numerical
simulations. It is shown that vortices are no longer well-organised and long-lived structures,
unlike those occurring in non-self-gravitating discs. They undergo recurring phases (lasting
for a few disc rotation periods) of formation, growth and eventual destruction. We also
discuss the dust trapping capability of such transient vortices.
Perturbation dynamics in 3D vertically stratified discs is richer, as there are more mode
types. We first consider non-axisymmetric modes in non-self-gravitating discs and then only
axisymmetric modes in the more complicated case when self-gravity is present. Specifically,
in non-self-gravitating discs with superadiabatic vertical stratification, motivated by the recent
results on the transport properties of incompressible convection, we show that when
compressibility is taken into account, the non-axisymmetric convective mode excites density
waves via the same shear-induced linear mode coupling mechanism mentioned above. These
generated density waves transport angular momentum outwards in the trailing phase, and
we suggest that they may aid and enhance the transport due solely to convection in the
non-linear regime, where the latter becomes outward.
In the final part of the thesis, we carry out a linear analysis of axisymmetric vertical normal
modes in stratified self-gravitating discs. Although axisymmetric modes do not display
shear-induced couplings, their analysis provides insight into how gravitational instabilities
develop in the 3D case and their onset criterion. We examine how the structure of dispersion
curves and eigenfunctions of 3D modes are influenced by self-gravity, which mode first
becomes gravitationally unstable and thus determines the onset criterion and nature of the
gravitational instability in stratified discs. We also contrast the more exact instability criterion
obtained with our 3D model with that of density waves in 2D discs. Based on these
findings, we discuss the origin of 3D behaviour of perturbations involving noticeable disc
surface distortions, as seen in some numerical simulations of self-gravitating discs.