COOLING POLYTROPIC SEQUENCES

I. Initial Model:
Consider a polytrope at the bar mode the neutral point, T/|W| = 0.138. The equilibrium model has (N_r,N_z) = (118,63) on a grid of size (128,64,64). (Note that the final model is on a grid of size (256,16,64). The simulations ran for 850,000 computational steps ~ 70 CIRPs.

The polytrope was cooled for a time long enough to allow it to reach the bar mode dynamic stability limit. The polytrope was given a low-amplitude random initial perturbation. The goal of the simulation to see if the Lebovitz expectation is realized.

II. Initial Model:

Consider an n=3/2,n'=0 polytrope with T/|W|=0.262. The polytropic constant K is then decreased exponentially. For these tests, we used smaller grids to allow a more thorough exploration of the (t_c,perturbation)-parameter space. We performed the following tests:
• Dependence on t_c

• Dependence on Initial Random Perturbation Amplitude

• Maclaurin Bar Perturbation

• Maclaurin Bar Perturbation: Amplitude Dependence

Slowly cooling polytropes with small imposed perturbations (random and bar-like) do not behave in a qualitatively different manner compared to the evolution of highly unstable equilibria in terms of the bar mode instability.