Changes between Version 4 and Version 5 of u/erica/radtimescales


Ignore:
Timestamp:
03/29/16 15:16:08 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/radtimescales

    v4 v5  
    99[[latex($\boxed{t_{diff}\approx \frac{L^2}{c}\frac{\kappa_R \rho}{\lambda}}$)]]
    1010
    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 the radiative energy.
     11L 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.
    1212
    1313Offner et al '09 gives,
     
    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 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,
    2525
    26 [[latex($\boxed{t_{diff}\approx 15,000 ~s}$)]]
     26[[latex($\lambda=\frac{1}{R}$)]]
    2727
    28 or ~ 4hrs.
     28where
     29
     30[[latex($R=\frac{1}{L}\frac{E}{\kappa_R \rho E}$)]]
     31
     32and so I gather an estimate for lambda might be:
     33
     34[[latex($\lambda = L \kappa_R \rho $)]]
     35
     36which using our values gives:
     37
     38[[latex($\lambda=.002$)]]
     39
     40Using all of these values in the formula above for the diffusion time gives,
     41
     42[[latex($\boxed{t_{diff}\approx 7.5e+6 ~s}$)]]
     43
     44or ~ 86 days.
    2945
    3046
     
    3349[[latex($\boxed{t_{fs}=\frac{L}{c}\approx\frac{3e+17}{3e+10}=10^7 ~s}$)]]
    3450
    35 or 57 days. I am guessing lambda should be something much smaller than 1. Any estimates on lambda?
     51or 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?
    3652
    3753