| | 7 | By substituting for rho, we can turn this into the more physically intuitive condition: |
| | 8 | |
| | 9 | [[latex($\lambda_J \propto (Cs^2/G*M/r^3)^{1/2}$)]] |
| | 10 | |
| | 11 | Thus, for a given cloud of radius r, sound speed Cs, and mass M, we can compute a Jeans length, which is either less than r or greater than r. For a [[latex($\lambda_J$)]] < r, the cloud is gravitationally unstable. For the opposite, the cloud is gravitationally stable. |
| | 12 | |
| | 13 | Given the formulation of [[latex($\lambda_J (T, M, r)$)]] we can easily see how the Jeans length depends on the various quantities of interest for the BE problem. For instance, consider we hold M and T fixed and vary r. We see that decreasing r leads to a decrease in [[latex($\lambda_J$)]], which corresponds to making the sphere LESS stable. If we instead hold T and r fixed, but vary M, we see that an increase in M has the same effect. Thus we can think of the collapse in the various cases as occuring from either situation, either the r of the BE sphere shrinks or the M of the sphere increases, both of which can trigger collapse. We seem to be seeing different effects happening in the different simulations. |
| | 14 | |
| | 15 | Now, given it is likely a combination of these effects that are happening, and one in turn leads to the other, e.g. given the gravitational force is given by: |
| | 16 | |
