Changes between Version 9 and Version 10 of u/erica/RadHydro


Ignore:
Timestamp:
03/29/16 19:49:01 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/RadHydro

    v9 v10  
    5353Now in the next timestep this energy could either diffuse away, or stick around, depending on how optically thick the gas is (controlled by [[latex($\kappa_R$)]]).
    5454
    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), 
     55If 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): 
    5656
    5757[[latex($\frac{\partial E}{\partial t} \propto \nabla \cdot \nabla E + (4 \pi B - cE)$)]],
    5858
    59 then,
     59then, E will decrease faster than it is increasing (confused by the sign in the diffusion term), which in this equation:
    6060
    6161[[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)<0$)]]
    6262
     63keeps 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
    6364
     65[[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)>0$)]]
    6466
    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.
     67means 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?
    6868
    6969''' Radiation with a source '''