Changes between Version 6 and Version 7 of u/erica/JeansInstability
 Timestamp:
 06/21/13 11:37:52 (11 years ago)
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u/erica/JeansInstability
v6 v7 60 60 61 61 62 What we'd like to do now is determine, for which frequencies is the perturbation ''unstable'' (exponentially growing) , and for what frequencies is the perturbation ''stable'' (exponentially decaying). In order to determine this we can rewrite [[latex($\omega$)]] into a more intuitive form.62 What we'd like to do now is determine, for which frequencies is the perturbation ''unstable'' (exponentially growing). In order to determine this we can rewrite [[latex($\omega$)]] into a more intuitive form. 63 63 64 [[latex($\omega ^2 = (4 \pi G \rho_0  C_s^2 k^2) \Rightarrow$)]] 65 66 [[latex($\omega = ^+_ [4 \pi G \rho_0(1\frac{C_s^2 k^2}{4 \pi G \rho_0})]^{1/2} \Rightarrow$)]] 67 68 [[latex($\omega = ^+ _ i[4 \pi G \rho_0 (1  \frac{C_s^2 k^2}{4 \pi G \rho_0})]^{1/2} \Rightarrow$)]] 69 70 [[latex($\omega = ^+ _ i[4 \pi G \rho_0 (1  \frac{\lambda_J ^2}{\lambda^2})]^{1/2}$)]] 71 72 Taking the positive root and plugging into [[latex($\rho_1$)]], we see 73 74 [[latex($\rho_1 =$)]] 64 75 65 76