| | 87 | Thus we have found the explicit form of the density perturbation. For [[latex($\lambda > \lambda_J$)]] , the density perturbation will be unstable and grow exponentially with time. For [[latex($\lambda < \lambda_J$)]], the density perturbation is oscillatory, and will travel through the medium as a sound wave. (Given this analytical expression, one can compute the growth rate explicitly with AstroBEAR. That is, by seeding the grid with this density perturbation with self gravity turned off, one can visualize this perturbation function over time. To test the code's self-gravity, one could seed the grid with the density perturbation without the exponential factor (i.e. only sinusoidal density perturbation), turn self-gravity on, and see if the density grows with a rate that matches that of the analytical solution.) |
