Changes between Version 9 and Version 10 of u/erica/radtimescales


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Timestamp:
03/29/16 15:31:15 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/radtimescales

    v9 v10  
    2222|| [[latex($\kappa_R$)]]|| .23 ||
    2323
    24 (For L, the radiation is leaving from the center of the volume, so is going approximately 1 half the length). I am not completely sure on [[latex($\lambda$)]], but from Offner's paper,
     24(For L, the radiation is leaving from the center of the volume, so is going approximately 1 half the length). I am not completely sure on [[latex($\lambda$)]], but from Offner's paper it should have units of,
    2525
    26 [[latex($\lambda=\frac{1}{R}$)]]
     26[[latex($\lambda=\frac{1}{R^2}$)]]
    2727
    2828where R has units of:
     
    3232and so I gather an estimate for lambda might be:
    3333
    34 [[latex($\lambda = L \kappa_R \rho $)]]
     34[[latex($\lambda = (L \kappa_R \rho)^2 $)]]
    3535
    3636which using our values gives:
    3737
    38 [[latex($\lambda=.002$)]]
     38[[latex($\lambda=4e-6$)]]
    3939
    4040Using all of these values in the formula above for the diffusion time gives,
    4141
    42 [[latex($\boxed{t_{diff}\approx 7.5e+6 ~s}$)]]
     42[[latex($\boxed{t_{diff}\approx 3.75e+9 ~s}$)]]
    4343
    44 or ~86 days.
     44or ~118 years.
    4545
     46I am not sure on this because lambda is not well constrained, and you can get very different estimates based on what you choose lambda to be (i.e tdiff = .5 day when lambda =1, tdiff=87 days when lambda = .002, etc).
    4647
    47 That is a pretty quick diffusion time, considering the 'free streaming limit' gives:
     48Compare this time to the 'free streaming limit':
    4849
    4950[[latex($\boxed{t_{fs}=\frac{L}{c}\approx\frac{1.5e+17}{3e+10}=.5e+7 ~s}$)]]