Tag: James Imamura

Searching for Simpler Models of Astrophysical Pattern Formation

Presenter: Eryn Cangi

Co-Presenters: Daniel Abrams

Faculty Mentor: Daniel Abrams, James Imamura

Presentation Type: Poster 6

Primary Research Area: Science

Major: Physics

Funding Source: REU, National Science Foundation and Northwestern University, $4500

In astrophysics, it is easy to solve problems relating two objects, such as two stars in a binary star or a planet and its moon. Systems of more than three bodies are both unsolvable analytically (“by hand”) and require large amounts of computation time to simulate, scaling with the square of the number of objects. Thus, astrophysical synchronization, in which orbital periods of objects converge, is well understood for systems of two or three objects but largely unexplored for systems of many objects. We investigate the possibility of using mathematical models of nonlinear oscillations (in which objects that oscillate in some way change their frequency in a non-constant fashion) in lieu of Newtonian gravitation to understand how systems of astronomical objects form larger structures. In particular, we use methods drawn from the study of the Kuramoto model, a model which has been used to describe synchronization in systems containing many similar objects, such as the blinking of fireflies or people marching across a bridge. With modification, this model can produce either strong synchronization (one synchronized group) or partial synchronization (two or more groups of synchronized objects form). This partial synchronization may be suggestive of astronomical systems. As an example, we developed a model for N small objects orbiting a massive planet and in MATLAB. Preliminary models show promise that this approach will yield new insight into astronomical synchronization across a range of length scales.

The Effect of Large Circumstellar Disks on the Formation of Short Orbital Period Binary Star Systems

Presenter(s): Carl Ranney − Physics

Faculty Mentor(s): James Imamura

Poster 36

Research Area: Physical Science

The purpose of this research is to determine the validity of the fission model of short orbital period binary star formation. The fission model describes the process in which a protostar with large angular velocities splits into two bodies in orbit around a common center of mass. The fission model is one of the three major models currently under investigation by the wider astrophysical community as possible sources for the formation of short orbital period binary star systems. While fission has not received much attention in the last two decades due to results found in large scale numerical simulations, the advances in computational power now available allow much more complex simulations that show promise in solving this problem. Rather than looking at single stars, we are simulating the evolution of a rotating protostar with a large circumstellar disk that is approaching a reverse Roche limit, where the mass of the disk starts to pull the protostar apart. By including this large disk in our calculations, we find that the prospects for fission is greatly enhanced. We are using the computer code Chymera in Aciss and Talapas, the University of Oregon high-performance computing clusters in our study to simulate the fluid dynamics of this system. Chymera includes many nonlinear instabilities which were not widely known or where undiscovered during the period when the last major simulations of the fission model were attempted. With the combination of these two factors, our research has provided valuable insight into previously unexplored aspects of the complex system.

Equilibrium Solutions for 2-Dimensional Nonaxisymmetric Disks

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 .