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culinary_services [2014/06/02 17:57] long |
culinary_services [2014/06/03 17:06] parzuchowski |
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Sensitivity studied of <sup>44</sup>Ti production in in core-collapse supernova environments. | Sensitivity studied of <sup>44</sup>Ti production in in core-collapse supernova environments. | ||
- | * [[Background|Scientific Background]] | + | **[[Scientific Background|Scientific Background]]** |
**Recipe** \\ | **Recipe** \\ | ||
Starting with a set parameter space of peak temperatures [T<sub>9</sub> = 4 - 7] and densities [$\rho$ = 10<sup>5</sup> - 10<sup>7</sup> g/cm<sup>3</sup>]. | Starting with a set parameter space of peak temperatures [T<sub>9</sub> = 4 - 7] and densities [$\rho$ = 10<sup>5</sup> - 10<sup>7</sup> g/cm<sup>3</sup>]. | ||
+ | |||
+ | We use analytic adiabatic freeze-out trajectories (Hoyle et al. 1964; Fowler & Hoyle 1964) which satisfy the differential equations: | ||
+ | |||
+ | \begin{equation} | ||
+ | \frac{dT}{dt} = \frac{-T}{3\tau} \hspace{1cm} \frac{d\rho}{dt} = -\frac{\rho}{\tau} | ||
+ | \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. | ||
+ | |||
+ | |||
**REFERENCES** \\ | **REFERENCES** \\ | ||
[[http://iopscience.iop.org/0067-0049/191/1/66|Trends in 44Ti and 56Ni from Core-Collapse Supernovae]] | [[http://iopscience.iop.org/0067-0049/191/1/66|Trends in 44Ti and 56Ni from Core-Collapse Supernovae]] |