Changes between Version 4 and Version 5 of u/johannjc/scratchpad22

Timestamp:

01/12/17 14:29:46 (8 years ago)

Author:

Jonathan

Comment:

—

u/johannjc/scratchpad22

@@ -65 +65 @@
 $e_{c,\Gamma} = \frac{\sigma}{\sigma_c} N_s \frac{F}{F_c}\frac{T_s}{E_s} = \frac{N_s}{E_s}$
 
+== Recombination Cooling ==
+In physical units we have
 
+$\frac{dE}{dt}=\Lambda kT T^{-.89} n_e n_{H+}$
 
+and in computational units we have
+
+$\frac{dE_c}{dt_c}=\Lambda_c T T^{-.89} n_{c,e} n_{c,H+}$
+
+and dividing the two gives us 
+
+$\Lambda_c = \Lambda \frac{k N_s^2 T_s}{E_s}$
+
+== Lyman Alpha Cooling ==
+
+In physical units we have 
+
+$\frac{dE}{dt}=\Lambda e^{-118348 K/T} n_e n_{H}$
+
+and in computational units we have
+
+$\frac{dE_c}{dt_c}=\Lambda_c e^{-118348 K/T} n_{c,e} n_{c,H}$
+
+and dividing the two gives us
+
+$\Lambda_c = \Lambda \frac{N_s^2 T_s}{E_s}$
 
 == Test problem ==
@@ -76 +100 @@
 $R_c=1.5\times 10^{10} cm$
 
-$F=2\times 10^{14} cm^{-2} s^{-1}$
+$F=2\times 10^{13} cm^{-2} s^{-1}$
 
 $T= 10^3 K$
 
+
 embedded in a lower density pressure balanced ambient with a density ratio 
 
-$\chi=1000$
+$\chi=100$
 
-
-With a cross section for photo-ionization of 6.3e-18 and our clump's column density of 9e18, we would expect the clump to be optically thick
+With a cross section for photo-ionization of 6.3e-18 and our clump's column density of 9e18, we would expect the tau=1 surface to be 5% of the way in towards the clump center.
 
 And with a flux of 2e13, we would expect photo-ionization of the column to take 5 days or so...