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JeansInstability

-              v6
+              v7
 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.
+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.
+[[latex($\omega ^2 = -(4 \pi G \rho_0 - C_s^2 k^2) \Rightarrow$)]]
+[[latex($\omega = ^+_- [-4 \pi G \rho_0(1-\frac{C_s^2 k^2}{4 \pi G \rho_0})]^{1/2} \Rightarrow$)]]
+[[latex($\omega = ^+ _- i[4 \pi G \rho_0 (1 - \frac{C_s^2 k^2}{4 \pi G \rho_0})]^{1/2} \Rightarrow$)]]
+[[latex($\omega = ^+ _- i[4 \pi G \rho_0 (1 - \frac{\lambda_J ^2}{\lambda^2})]^{1/2}$)]]
+Taking the positive root and plugging into [[latex($\rho_1$)]], we see
+[[latex($\rho_1 =$)]]