Version 11 (modified by 9 years ago) ( diff ) | ,
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Diffusion time estimate
Starting from:
We get:
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.
Offner et al '09 gives,
for T=10 K gas. Assuming our system is a protostellar core, we have L~.1 pc, rho~1 solar mass/L3. In cgs these parameters work out to be:
c | 3e+10 |
6.5e-20 | |
L | ½*3.08e+17 |
.23 |
(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
, but from Offner's paper it should have units of,
where R has units of:
and so I gather an estimate for lambda might be:
which using our values gives:
Using all of these values in the formula above for the diffusion time gives,
or ~118 years.
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 = 4 hours when lambda =1, tdiff=87 days when lambda = .002, etc).
Compare this time to the 'free streaming limit':
or 57 days.
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