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culinary_services [2014/06/03 16:14] parzuchowski |
culinary_services [2014/06/03 17:06] parzuchowski |
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\begin{equation} | \begin{equation} | ||
- | \frac{dT}{dt} = \frac{-T}{3\tau} | + | \frac{dT}{dt} = \frac{-T}{3\tau} \hspace{1cm} \frac{d\rho}{dt} = -\frac{\rho}{\tau} |
\end{equation} | \end{equation} | ||
+ | Where $\tau$ is some static free-fall timescale. | ||
+ | This **obviously** leads to: | ||
+ | |||
+ | \begin{equation} | ||
+ | T(t) = T_0 exp(-t/3\tau) \hspace{1cm} \rho (t) = \rho_0 exp(-t/\tau) | ||
+ | \end{equation} | ||
+ | where $T_0$ and $\rho_0$ are the peak temperature and density in the supernova. | ||