Changes between Version 9 and Version 10 of u/erica/radtimescales
- Timestamp:
- 03/29/16 15:31:15 (9 years ago)
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u/erica/radtimescales
v9 v10 22 22 || [[latex($\kappa_R$)]]|| .23 || 23 23 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, 25 25 26 [[latex($\lambda=\frac{1}{R }$)]]26 [[latex($\lambda=\frac{1}{R^2}$)]] 27 27 28 28 where R has units of: … … 32 32 and so I gather an estimate for lambda might be: 33 33 34 [[latex($\lambda = L \kappa_R \rho$)]]34 [[latex($\lambda = (L \kappa_R \rho)^2 $)]] 35 35 36 36 which using our values gives: 37 37 38 [[latex($\lambda= .002$)]]38 [[latex($\lambda=4e-6$)]] 39 39 40 40 Using all of these values in the formula above for the diffusion time gives, 41 41 42 [[latex($\boxed{t_{diff}\approx 7.5e+6~s}$)]]42 [[latex($\boxed{t_{diff}\approx 3.75e+9 ~s}$)]] 43 43 44 or ~ 86 days.44 or ~118 years. 45 45 46 I am not sure on this because lambda is not well constrained, and you can get very different estimates based on what you choose lambda to be (i.e tdiff = .5 day when lambda =1, tdiff=87 days when lambda = .002, etc). 46 47 47 That is a pretty quick diffusion time, considering the 'free streaming limit' gives:48 Compare this time to the 'free streaming limit': 48 49 49 50 [[latex($\boxed{t_{fs}=\frac{L}{c}\approx\frac{1.5e+17}{3e+10}=.5e+7 ~s}$)]]