Changes between Version 25 and Version 26 of u/erica/radtimescales

Timestamp:

04/04/16 14:53:39 (9 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/radtimescales

@@ -155 +155 @@
 
 
-Compare this time to the 'free streaming limit':
+Compare this time to the light crossing time:
 
 [[latex($\boxed{t_{fs}=\frac{L}{c}\approx\frac{1.5e+17}{3e+10}= 57 ~days}$)]]   
@@ -193 +193 @@
 
 
-[[latex($t_{diff}\approx \frac{L^2}{c}\frac{\kappa_R \rho}{\lambda}$)]]
-
-[[latex($t_{diff}\approx $)]]
+[[latex($t_{diff}\approx \frac{r^2}{c}\frac{\kappa_R \rho}{\lambda}$)]]
+
+Note this can be rewritten as,
+
+[[latex($t_{diff}\approx \frac{r}{c}\frac{r}{l}\lambda^{-1}$)]]
+
+The first factor is the light-crossing time:
+
+[[latex($t_{light} = \frac{r}{c} = 8 ~days $)]]
+
+The second factor is the ratio of the box radius to the mean free path. We set this to = 1 in our derivation above:
+
+[[latex($\frac{r}{l} = 1$)]]
+
+And the last factor is inverse lambda. Again, we constrained this in our derivation:
+
+[[latex($\lambda^{-l} \approx 3$)]]
+
+Taken together, in the '''optically thick limit, when r=l''':
+
+[[latex($t_{diff}\approx 3~ t_{light}$)]]
+
+So for a simulation with these parameters, expect a diffusion wave to cross the grid in '''24 days''':
+
+[[latex($\boxed{t_{diff}\approx 24 ~days}$)]]
+
 
 = Coupling time estimate =
@@ -228 +251 @@
 So the coupling time depends on the temperature difference you want to achieve, as well as the planck opacity, density, and radiation output from the protostar. Note, I may have made dropped a factor of 4pi/c in the case it isn't absorbed by 'a'.
 
-''' Crossing time '''
+''' Sound crossing time '''
 
 The time it takes a sound wave to travel from the center of the prestellar core, to the outer edge is: