Project for ASTR7741

Fall Semester, 2003

Andy Rodriguez

Before proceeding to study this problem in a relatively simplistic fashion, you should be aware that some quite sophisticated models of rotating core collapse are already in the literature. Most notable is the series of articles reporting on simulations by a group at the Max Planck Institute (MPI) in Garching, Germany. Here is the URL of their home page:

From this page, you can click on their "Wave Catalog" page (www.mpa-garching.mpg.de/Hydro/RGRAV/wave.shtml) to see some of their published strain curves. You'll be trying to reproduce only the very earliest portion of these strain curves.

Part I: Free-fall Collapse of a Rotating (and nonrotating), n = 0 Spheroid

First, you need to generalize the free-fall collapse problem by (numerically) deriving the collapse solution for a freely falling (pressure-free) spheroid. You should set the problem up so that you can study both nonrotating and rotating spheroids. The solution to this problem has previously been published in three key papers:

• Lynden-Bell, D. 1962, Proc. Cambridge Phil. Soc., 50, 709
• Lin, C.C., Mestel, L. & Shu, F.H. 1965, ApJ, 142, 1431
• Hutchins, J.B., 1976, ApJ, 205, 103

Part II: Gravitational-Wave Strain Curve for Nonspherical Collapses

Once you have a numerical algorithm that follows the free-fall collapse of a uniform-density spheroid, you need to add to it a routine that calculates the two principal moments of inertia of the spheroid at various points during its collapse. The second time-derivative of these moments of inertia can then be used to determine the strain curve.

The only published work that I know comes close to providing this desired solution is the following paper by Thuan & Ostriker:

• Thuan, T.X. & Ostriker, J.P. 1974, ApJ, 191, L105