Changes between Version 9 and Version 10 of u/erica/RadHydro
- Timestamp:
- 03/29/16 19:49:01 (9 years ago)
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u/erica/RadHydro
v9 v10 53 53 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($\kappa_R$)]]). 54 54 55 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) ,55 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): 56 56 57 57 [[latex($\frac{\partial E}{\partial t} \propto \nabla \cdot \nabla E + (4 \pi B - cE)$)]], 58 58 59 then, 59 then, E will decrease faster than it is increasing (confused by the sign in the diffusion term), which in this equation: 60 60 61 61 [[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)<0$)]] 62 62 63 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 63 64 65 [[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)>0$)]] 64 66 65 Eventually the material should become dense enough that is becomes optically thick to the radiation. Thus, despite the gas heating up through infall, it should no longer be adding these photons to the radiation field (for if it does, it will continue to cool given the equations are inverses of each other)...? We can imagine the 66 67 the material shouldn't be able to cool through radiation. 67 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? 68 68 69 69 ''' Radiation with a source '''