Presenter(s): Daniel Sellers—Physics
Faculty Mentor(s): James Imamura
Session 5: To the Moon and Back—Relativity Matters
In this study we seek equilibrium solutions for compressible, self-gravitating, 2-dimensional nonaxisymmetric disks . Such structures arise in binary star systems and other systems where tidal forces arise such as in the Earth-moon system . These disks are governed by a Scalar Momentum Equation (SME) and a partial differential equation describing hydrodynamic flow within the disk (Stream Function Equation) . We solve these equations using a self-consistent field approach . At each iterative step, the Stream Function and gravitational potential are approximated at all grid points using Guass-Seidel iteration . These quantities, taken with the SME and appropriate boundary conditions are used to find an updated guess for the density distribution .
Guass-Seidel algorithms are applied to the relevant partial differential equations which have been discretized using a finite central-differencing technique . These solvers are implemented in python and verified using analytical solutions for simple cases, such as axisymmetric disks with uniform density . We find that our solvers converge to the analytical solutions over many iterations .
Parameters for the overall equilibrium solutions are taken from Andalib’s 1998 Dissertation focused on 2-D self-gravitating systems . Present work is focused on reproducing some of the presented solutions as both a check on our equilibrium solutions and as a starting point for further research .