wiki:u/erica/radtimescales

Version 4 (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 has to do with gradient length scales of the 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 do not know what an appropriate is… can't find a reference to it in Offner's paper… So letting gives:

or ~ 4hrs.

That is a pretty quick diffusion time, considering the 'free streaming limit' gives:

or 57 days. I am guessing lambda should be something much smaller than 1. Any estimates on lambda?

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