43 | | Imagine 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 will increase the radiative energy field, and thus act to 'cool' the gas (as Erad increases, e decreases). Is this right? Thinking of radiation as a source of cooling for optically thin gas...? |
| 43 | 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, |
| 44 | |
| 45 | [[latex($\frac{\partial E}{\partial t} \propto (4 \pi B - cE) > 0$)]] |
| 46 | |
| 47 | and thus act to 'cool' the gas (as Erad increases, e decreases): |
| 48 | |
| 49 | [[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)<0$)]] |
| 50 | |
| 51 | (Is this right? Thinking of radiation as a source of cooling for optically thin gas...? Seems natural..) |
| 52 | |
| 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 | |
| 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 | |
| 57 | [[latex($\frac{\partial E}{\partial t} \propto \nabla \cdot \nabla E + (4 \pi B - cE)$)]], |
| 58 | |
| 59 | then, |
| 60 | |
| 61 | [[latex($\frac{\partial \rho e}{\partial t} = -\kappa (4\pi B- cE)<0$)]] |
| 62 | |
| 63 | |