Collapse of a uniform sphere

t_{ff}=\sqrt{\frac{3 \pi}{32 G \rho}}$

The free fall time should be 1.5323

A single sink particle appears at approximately that time but then drifts from the center of the grid. This may be due to poor resolution (only based on the Jeans length)

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Artificial fragmentation will occur whenever the density violates the TrueLove criterion. However, the federrath criteria for forming sink particles requires more then just a single cell above the truelove criterion. The cell must be in the minimum of a local potential well, have converging flow from each direction, and the surrounding sphere with a radius of 4*dx where dx is the finest level resolution must also be a bound system. If the sphere of 4*dx is much larger then the collapsing condensation, then it can lead to problems since particles will likely not form although the jeans criterion will lead to artificial fragmentation. The only solution is to add more resolution…