Changes between Version 15 and Version 16 of u/erica/radtimescales


Ignore:
Timestamp:
03/30/16 14:31:20 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/radtimescales

    v15 v16  
    7777If I assume the radiation output from the protostar (its accretion energy) is constant over time, I can kill the difference of E* on the LHS. This leaves,
    7878
    79 [[latex($ t = \frac{\triangle B(T)}{\kappa_P \rho c E_*}$)]]
     79[[latex($ t = \frac{4 \pi \triangle B(T)}{\kappa_P \rho c^2 E_*}$)]]
    8080
    8181Plugging in for B(T) puts this in terms of temperature:
     
    8383[[latex($ t = \frac{a(T_2^4-T_1^4)}{\kappa_P \rho c E_*}$)]]
    8484
    85 So the coupling time depends on the temperature difference you want to achieve, as well as the planck opacity, density, and radiation output from the protostar.
     85So the coupling time depends on the temperature difference you want to achieve, as well as the planck opacity, density, and radiation output from the protostar. Note, I may have made dropped a factor of 4pi/c in the case it isn't absorbed by 'a'.