Changes between Version 2 and Version 3 of u/u/erica/BEAnalysis


Ignore:
Timestamp:
05/28/13 13:46:38 (11 years ago)
Author:
Erica Kaminski
Comment:

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  • u/u/erica/BEAnalysis

    v2 v3  
    11= Jeans Analysis =
    22
    3 A uniform cloud of gas will collapse under gravity if its gravitational timescale is shorter than its thermal timescale. That is, if the freefall time of the gas, [[latex($t_{ff} ~ 1/(G\rho)^{1/2}$)]] is less than the time it would take for sound waves to attempt to equilibrate the matter distribution, or the sound-crossing time, [[latex($t_{sc}=R/C_s$)]], where R is the radius of the cloud and Cs is its sound speed.
     3A uniform cloud of gas will collapse under gravity if its gravitational timescale (the freefall time, [[latex($t_{ff}$)]]) is shorter than its thermal timescale (sound crossing time, [[latex($t_{sc}$)]]). That is, if [[latex($t_{ff} \propto 1/(G\rho)^{1/2}$)]] is less than [[latex($t_{sc}=R/C_s$)]], where R is the radius of the cloud and Cs is its sound speed, a cloud is unstable to collapse. Setting these equal and solving for r gives an estimate of the Jeans length,
     4
     5  [[latex($\lambda_J \propto (Cs^2/G\rho)^{1/2}$)]]
    46
    57= The problem =