Changes between Version 10 and Version 11 of u/erica/RadHydro

Timestamp:

03/29/16 20:00:53 (9 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/RadHydro

@@ -41 +41 @@
 ''' Jeans unstable gas ''' 
 
-Imagine now starting with a uniform, Jeans unstable gas mass. Initially it is in radiative equilibrium, but on a freefall timescale, the gas will begin to collapse -- becoming denser and hotter as it does (recall equation for internal energy has a gravitational energy term). This will lead to regions in the grid where 4piB>cE. This will increase the radiative energy field,
+Imagine now starting with a uniform, Jeans unstable gas mass. Initially it is in radiative equilibrium (as in previous section), but within a freefall time, the gas will begin to collapse -- becoming denser and hotter as it does (recall equation for internal energy has a gravitational energy term). This will lead to regions in the grid where 4piB>cE. This will increase the radiative energy field,
 
 [[latex($\frac{\partial E}{\partial t} \propto (4 \pi B - cE) > 0$)]]
 
-and thus act to 'cool' the gas (as Erad increases, e decreases):
+and thus act to 'cool' the gas:
 
 [[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)<0$)]]
 
-(Is this right? Thinking of radiation as a source of cooling for optically thin gas...? Seems natural..)
-
-Now in the next timestep this energy could either diffuse away, or stick around, depending on how optically thick the gas is (controlled by [[latex($\kappa_R$)]]).
+Now in the next timestep this radiative energy could either diffuse away, or stick around, depending on how optically thick the gas is (controlled by [[latex($\kappa_R$)]]).
 
 If the diffusion term is larger than the coupling term (which acts to increase Erad over the course of the infall by the conversion of gravitational energy into heat):  
@@ -57 +55 @@
 [[latex($\frac{\partial E}{\partial t} \propto \nabla \cdot \nabla E + (4 \pi B - cE)$)]],
 
-then, E will decrease faster than it is increasing (confused by the sign in the diffusion term), which in this equation:
+then, E will decrease faster than it is increasing (confused by the sign in the diffusion term), which implies:
 
 [[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)<0$)]]
 
-keeps the gas cooling. However, eventually the material should become dense enough that it becomes optically thick to the radiation. This should act to heat the gas up. In order to get
+i.e. the gas continues cooling. However, eventually the material should become dense enough that it becomes optically thick to the radiation, and the gas should begin to heat up. In order to get,
 
 [[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)>0$)]]
 
-means cE needs to get larger than 4piB. This can be achieved by the combined effect of increased BB radiation (through the compressional heating), ''in addition '' to slower diffusion. Thus, for this problem it seems that making [[latex($\kappa_R= \kappa_R (\rho)$)]] makes sense. In the early stages of collapse, the increased heat should be cooling through radiative losses. That is, the collapse should remain isothermal. However, after a certain point the collapse becomes adiabatic. This seems to be controllable through the diffusion term. I can't think of physical reasons why you might want to change [[latex($\kappa_p$)]]. In what situations would you want more or less coupling?
+cE needs to get larger than 4piB. This can be achieved by the combined effect of increased BB radiation (through the compressional heating), ''in addition '' to slower diffusion. Thus, for this problem it seems you would want [[latex($\kappa_R= \kappa_R (\rho)$)]], as that would control the scenario you want. That is, in the early stages of collapse, the increased heat due to infall should be cooling through radiative losses. I.e., the collapse should remain isothermal. However, after a certain point the collapse should become adiabatic. This seems to be controllable through the diffusion term. I can't think of physical reasons why you might want to change [[latex($\kappa_p$)]]. In what situations would you want more or less coupling?
 
 ''' Radiation with a source '''