Hierarchical Gravitational Collapse

So I've started playing around with gravo-turbulence in 2D. I've tried using linear perturbations to the density within a clump, however the entire clump will collapse in the same time it takes for the local perturbations to grow. So we need a clump with small Jeans-unstable clumplets inside that have a much shorter free fall time. So I tried a density distribution where log(rho) had a flat power spectra. .

The clump density was 400 and the temperature was 10K giving an overall Jeans length of 1.1 pc and free fall time of 1.7 Myr.

Since the perturbations kept the pressure constant, the Temperature was proportional to . As a result, the free-fall time scales like and the Jeans length goes like

The perturbations had a flat spectra from k_min=4 to kmax=48 or from 6 pc to .5 pc. As a result, the local density enhancements had typical size scales of .5 pc (8 cells). Most of these had densities of at least 800 (twice the mean) with several having densities of 1600 and a few with densities of 3200. The ones with a density of 800 would be stable to collapse and those with a density of 1600 have Jeans lengths of .26 pc and could potentially collapse - although the timescales would be similar to the timescales for the global collapse. This is in fact what we see… Two particles form before the entire thing collapses.

So i modified the mean density to be 10, increased the power spectra slope to -2 and strengthened the perturbation. (Plot is now in log scale)

And here is the movie

Everything looks great until the particles form - then the whole thing expands. After some pondering - I realized that this was because the potential of the sink particles needs to be modified in 2D to represent the potential of sink cylinders. The potential goes like and the gravitational force goes like .

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Comments

1. Adam Frank -- 13 years ago

What do you mean you increases the slop to -1? e((1/P(x)) ?

Some comments: The collapse appears to result in 4 "stars" and a global expansion (explosion) which then hints at recollapse (real?).

2 of your stars form a binary while the others escape (real?)