wiki:u/erica/radtimescales

Version 11 (modified by Erica Kaminski, 9 years ago) ( diff )

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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