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culinary_services [2014/06/06 14:06] long |
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===Simulations=== | ===Simulations=== | ||
+ | ==Parameter Space== | ||
We have chosen to do a parameter space study in peak temperature, density, and electron fraction, tarting 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>] for three values of the electron fraction [Y<sub>e</sub> = 0.45, 0.50, 0.55]. This parameter space roughly corresponds with the shock heated region in simulations of Cassiopeia A-like supernovae (Young & Fryer 2007). | We have chosen to do a parameter space study in peak temperature, density, and electron fraction, tarting 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>] for three values of the electron fraction [Y<sub>e</sub> = 0.45, 0.50, 0.55]. This parameter space roughly corresponds with the shock heated region in simulations of Cassiopeia A-like supernovae (Young & Fryer 2007). | ||
+ | ==Thermodynamic Trajectories== | ||
We use analytic adiabatic freeze-out trajectories (Hoyle et al. 1964; Fowler & Hoyle 1964) which satisfy the differential equations: | We use analytic adiabatic freeze-out trajectories (Hoyle et al. 1964; Fowler & Hoyle 1964) which satisfy the differential equations: | ||
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where $T_0$ and $\rho_0$ are the peak temperature and density in the supernova. | where $T_0$ and $\rho_0$ are the peak temperature and density in the supernova. | ||
+ | ==Reaction Network == | ||
We used the [[https://wikihost.nscl.msu.edu/talent/lib/exe/fetch.php?media=xnet_public.zip|XNet]] reaction network code. Our code included 447 isotopes ranging from hydrogen through germanium. We took the reaction rates from the [[https://groups.nscl.msu.edu/jina/reaclib/db/library.php?action=viewsnapshots|JINA Reaclib database]]. We set the threshold temperature for NSE to be 5 GK. | We used the [[https://wikihost.nscl.msu.edu/talent/lib/exe/fetch.php?media=xnet_public.zip|XNet]] reaction network code. Our code included 447 isotopes ranging from hydrogen through germanium. We took the reaction rates from the [[https://groups.nscl.msu.edu/jina/reaclib/db/library.php?action=viewsnapshots|JINA Reaclib database]]. We set the threshold temperature for NSE to be 5 GK. | ||
+ | |||
+ | ==Initial Abundances and Y$_{e}$== | ||
+ | For any given peak temperature and density, our initial composition was pure $^{28}$Si (therefore Y$_{e}$ = .5) In order to change the initial Y$_{e}$, we just added protons or neutrons to the initial composition according to the following equations: | ||
+ | |||
+ | \begin{equation} | ||
+ | X(^{28}Si) = 1 - \left | 2Y_{e} - 1 \right | \\ | ||
+ | X(p) = \left | 2Y_{e} - 1 \right | \hspace{1cm} X(n) = \left | 2Y_{e} - 1 \right | \\ | ||
+ | proton-rich \hspace{1cm} neutron-rich | ||
+ | \end{equation} | ||
Finally we looked at the mass fraction of several isotopes. In particular, $^{4}$He, $^{28}$Si, $^{44}$Ti, and $^{56}$Ni. We then compare our results to that of Magkotsios //et al// with in our parameter space. | Finally we looked at the mass fraction of several isotopes. In particular, $^{4}$He, $^{28}$Si, $^{44}$Ti, and $^{56}$Ni. We then compare our results to that of Magkotsios //et al// with in our parameter space. | ||
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===Results=== | ===Results=== | ||
- | ==$^{44}Ti== | + | ==$^{44}$Ti Production== |
- | {{ :44ti.png?nolink&800 }} | + | {{ :44ti.png?nolink&900 }} |
+ | |||
+ | ==$^{56}$Ni Production== | ||
+ | {{:56ni.png?nolink&900|}} | ||
**REFERENCES** \\ | **REFERENCES** \\ |