Changes between Version 1 and Version 2 of u/erica/radtimescales

Timestamp:

03/29/16 14:54:34 (9 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/radtimescales

@@ -7 +7 @@
 We get:
 
-[[latex($t_{diff}\approx \frac{L^2}{c}\frac{\kappa_R \rho}{\lambda}$)]]
+[[latex($\boxed{t_{diff}\approx \frac{L^2}{c}\frac{\kappa_R \rho}{\lambda}}$)]]
 
 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 dimensional parameter that has to do with gradient length scales of the radiative energy. 
@@ -15 +15 @@
 [[latex($\kappa_R=.23 \frac{cm^2}{g}$)]]
 
-for T=10 K gas.  
+for T=10 K gas. Assuming our system is a protostellar core, we have L~.1 pc, rho~1 solar mass/L^3^. In cgs these parameters work out to be:
 
+|| c || 3e+10 ||
+|| [[latex($\rho$)]] || 6.5e-20 ||
+|| L || 1/2*3.08e+17 || 
+|| [[latex($\kappa_R$)]]|| .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 [[latex($\lambda$)]] is... can't find a reference to it in Offner's paper... So letting [[latex($\lambda = 1$)]] gives:
+
+[[latex($\boxed{t_{diff}\approx 15,000 ~s}$)]]
+
+or ~ 4hrs. 
+
+
+That is a pretty quick diffusion time, considering the 'free streaming limit' gives:
+
+ 
+
+
+  
+