Abstract Details
| Name: Mamta Gulati Affiliation: IISER-Mohali Conference ID: ASI2015_526 Title : A study of slow modes in Keplerian discs. Authors and Co-Authors : Dr. Tarun Deep Saini, Indian Institute of Science, Bangalore and Dr. S. Sridhar, Raman Research Institute, Bangalore. Abstract Type : Oral Abstract Category : Thesis Abstract : In this thesis we study slow modes for various astrophysically relevant discs. These modes are suspected to be the reason behind various structures observed in these discs, which inturn are correlated to the global properties of discs. We begin with a study of slow modes in hot, thin accretion discs where the self- gravity is not important. We show that the analysis reduces to a simple Sturm- Liouville type problem and for most physically interesting discs the modes appear to be counter-rotating w.r.t. the Keplerian flow. It is difficult to excite these modes since external forcing is expected to rotate along with the matter in the disc. We then analyze two coplanar counter-rotating discs which interact gravitationally through a softened potential. These discs mimic more complicated stellar discs, where the softening mimics velocity dispersions. We explore slow, azimuthal wave-number m=1, instabilities that make the initial axisymmetric system develop a growing, lopsided, precessing pattern. The problem is addressed both through WKB and integral eigenvalue problem. We next study the dynamics of counter-rotating discs by treating them more realistically as stellar discs in WKB limit. The eigenvalues are obtained for a single disc and equal counter-rotation. The single disc eigen-modes were found to be stable in agreement with the previous calculation by Tremaine; however, the difference is that this treatment is not based on any ad-hoc prescription for disc heat, but uses genuine stellar discs. Another difference is that stellar discs allow slow modes for m values. We discuss and compare the eigenvalues for m=1 and 2 eigenmodes. Then, focusing on non-local short- wavelength modes an integral eigenvalue problem is formulated for a single disc. It is shown using the local analysis that the eigenvalue equation yields the correct dispersion relation, thereby providing a check on the validity of this equation. We then numerically solve the eigen-equation for two disc profiles. We show that due to the symmetry of the kernel of the eigenvalue equation, all slow modes are stable. We also discuss trends in eigen-spectrum and eigen-functions due to variation in the velocity dispersion in the discs, and 'm' values. The modes appear to be qualitatively similar for the two discs analyzed; although the numerical value of pattern speed does depend on the disc profile. We conclude that slow m=1 modes are easier to excite through external perturbation and are thus more likely to be the source of slow time variation in astrophysical discs. |