Simulations of Nonaxisymmetric Instability in a Rotating Star: A Comparison Between Eulerian and Smooth Particle Hydrodynamics

We have carried out 3-D numerical simulations of the dynamical bar instability in a rotating star and the resulting gravitational radiation using both an Eulerian code written in cylindrical coordinates and a smooth particle hydrodynamics (SPH) code. The star is modeled initially as a polytrope with index $n=3\mathrm{/}2$ and $T_{\mathrm{r}\mathrm{o}\mathrm{t}}\mathrm{/}\mathrm{\mid }W\mathrm{\mid }\approx 0.30$, where $T_{\mathrm{r}\mathrm{o}\mathrm{t}}$ is the rotational kinetic energy and $\mathrm{\mid }W\mathrm{\mid }$ is the gravitational potential energy. In both codes the gravitational field is purely Newtonian, and the gravitational radiation is calculated in the quadrupole approximation. We have run 3 simulations with the Eulerian code, varying the number of angular zones and the treatment of the boundary between the star and the vacuum. Using the SPH code we did 7 runs, varying the number of particles, the artificial viscosity, and the type of initial model. We compare the growth rate and rotation speed of the bar, the mass and angular momentum distributions, and the gravitational radiation quantities. We highlight the successes and difficulties of both methods, and make suggestions for future improvements.