Changes between Version 8 and Version 9 of u/erica/JeansInstability
- Timestamp:
- 06/21/13 11:50:35 (11 years ago)
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u/erica/JeansInstability
v8 v9 45 45 [[latex($\rho_1 = \cos(kx)e^{^+ _-\omega t}$)]] 46 46 47 Thus, the perturbation takes on a form that is oscillatory in x and exponential in time. To get the critical length scale (aka Jeans length) for the oscillations, we write the oscillatory condition 47 Thus, the perturbation takes on a form that is oscillatory in x and exponential in time. 48 49 = The Jeans Length = 50 51 To get the critical length scale (aka Jeans length) for the oscillations, we write the oscillatory condition 48 52 49 53 [[latex($C_s^2 k^2 > 4 \pi G \rho_0$)]] … … 58 62 59 63 60 64 = Unstable Modes = 61 65 62 66 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. … … 87 91 [[latex($\tau = \frac{1}{\Gamma}$)]] 88 92 93 = High lambda limit, i.e. pressure-less collapse, i.e. uniform collapse = 94 89 95
