| 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 | |
