Changes between Version 4 and Version 5 of u/erica/radtimescales
- Timestamp:
- 03/29/16 15:16:08 (9 years ago)
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u/erica/radtimescales
v4 v5 9 9 [[latex($\boxed{t_{diff}\approx \frac{L^2}{c}\frac{\kappa_R \rho}{\lambda}}$)]] 10 10 11 L is the size of our system, c is speed of light, kappa_R is the rosseland specific mean opacity, rho is density of the system, and lamba is a dimensionless parameter that has to do with gradient length scales of theradiative energy.11 L is the size of our system, c is speed of light, kappa_R is the rosseland specific mean opacity, rho is density of the system, and lamba is a dimensionless parameter that seems to do with the length scale of gradients in radiative energy. 12 12 13 13 Offner et al '09 gives, … … 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 do not know what an appropriate [[latex($\lambda$)]] is... can't find a reference to it in Offner's paper... So letting [[latex($\lambda = 1$)]] gives: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, 25 25 26 [[latex($\ boxed{t_{diff}\approx 15,000 ~s}$)]]26 [[latex($\lambda=\frac{1}{R}$)]] 27 27 28 or ~ 4hrs. 28 where 29 30 [[latex($R=\frac{1}{L}\frac{E}{\kappa_R \rho E}$)]] 31 32 and so I gather an estimate for lambda might be: 33 34 [[latex($\lambda = L \kappa_R \rho $)]] 35 36 which using our values gives: 37 38 [[latex($\lambda=.002$)]] 39 40 Using all of these values in the formula above for the diffusion time gives, 41 42 [[latex($\boxed{t_{diff}\approx 7.5e+6 ~s}$)]] 43 44 or ~ 86 days. 29 45 30 46 … … 33 49 [[latex($\boxed{t_{fs}=\frac{L}{c}\approx\frac{3e+17}{3e+10}=10^7 ~s}$)]] 34 50 35 or 57 days. I am guessing lambda should be something much smaller than 1. Any estimates on lambda?51 or 57 days. I am guessing lambda should be something much smaller than 1. From offner's paper, it seems lambda may be interpreted as 1/R. Any estimates on lambda? 36 52 37 53