| 30 | | And we see that as [[latex($R\rightarrow 0$)]], [[latex($\lambda\rightarrow \frac{1}{3}$)]] |
| | 30 | == Optically thick limit == |
| | 31 | |
| | 32 | And we see that as [[latex($R\rightarrow 0$)]], [[latex($\lambda\rightarrow \frac{1}{3}$)]]. How to interpret this? R is essentially the ratio of the optical depth [[latex($\tau=1/\kappa$)]], to the radiation's scale height, [[latex($L^{-1}=\frac{\nabla E}{E}$)]]. |
| | 33 | |
| | 34 | Thus, as [[latex($R\rightarrow 0$)]], we have that [[latex($\frac{\tau}{L}\rightarrow 0$)]] - i.e. radiation travels infinitesmally small distances before it is absorbed or scattered - and thus, we are in the optically thick regime. |
| | 35 | |
| | 36 | The rad diffusion equation then becomes, |
| | 37 | |
| | 38 | [[latex($\frac{\partial E}{\partial t} = \nabla \cdot (\frac{1}{3}\frac{c}{\kappa_R \rho} \nabla E)$)]] |
| | 39 | |
| | 40 | which is equation 6.59 in Drake's book. |
| | 41 | |
| | 42 | == Free streaming limit == |
