| 27 | Prediction: By 24 days, expect the diffusion wave to hit the boundary. Depending on the energy injection rate compared to the diffusion rate, the shape of the curve might be different. For instance, if energy injection rate (Er) >> diffusion rate (Dr), might expect the gaussian to be increasing in height as well as width. If Er = Dr, might expect the profile to be flat, as it grows in width. If Er << Dr, expect a gaussian that grows in width over time, but not height. |
| 28 | |
| 29 | Check: Make time curves of Erad(x), and check that the wave hits the boundary by t=24 days. |
| 30 | |
| 31 | |
| 32 | Prediction: The total thermal energy should increase like t^2^. This is because, |
| 33 | |
| 34 | [[latex($\frac{\partial e}{\partial t} = -\kappa_P \rho (4 \pi B - cE)$)]], where |
| 35 | |
| 36 | [[latex($cE = 4 \pi B + Lt$)]] (L is luminosity of FHSC) |
| 37 | |
| 38 | [[latex($\frac{\partial e}{\partial t} = \kappa_P \rho Lt$)]] |
| 39 | |
| 40 | [[latex($e \propto \kappa_P \rho L t^2$)]] (density doesn't change given t_diff << t_sc) |
| 41 | |
| 42 | Check: Make curve of e_total(t). |
| 43 | |
| 44 | |