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--- culinary_services [2014/05/30 17:31]
parzuchowski created
+++ culinary_services [2014/06/05 14:59]
warren
@@ Line 1: / Line 1: @@
-We are Culinary Services.
+We are Culinary Services. \\
-We cook helium and hydrogen.
+\\
+Who ordered the extra side of <sup>44</sup>Ti?
+**GROUP MEMBERS**\\
+Alex Long (parameters)\\
+MacKenzie Warren (code)\\
+Nathan Parzuchowski (analysis)\\
+==== TOPIC ====
+Sensitivity studied of <sup>44</sup>Ti production in in core-collapse supernova environments.
+===Scientific Background===
+There are many uncertainties in our understanding of core-collapse supernovae, including the explosion mechanism and nucleosynthesis.  One way to gain insight into these phenomena is to study the nucleosynthesis of radioactive isotopes in the shock-heated material.  These isotopes, such as <sup>44</sup>Ti and <sup>56</sup>Ni, determine the features of the supernova light curve.  Observations of supernova remnants can be used to put bounds on the production of these isotopes.
+ {{ ::cassa.png?nolink&200 | Observation of Cassiopeia A.  Green shows <sup>44</sup>Ti distribution, blue is <sup>28</sup>Si, and the red shows the Fe distribution.  (From Grefenstette et al 2014)}}
+Using simulations, we can use these observations to gain insight into the supernova environment.  By matching observed abundances, we can gain insight into the environment in which this nucleosynthesis must have taken place and in turn, the details of the explosion mechanism.  However, most core-collapse supernova simulations do not include sufficiently large reaction networks to simulate this nucleosynthesis.
+If the shock heating is sufficient, the material will be in Nuclear Statistical Equilibrium (NSE).  The isotopic abundances will be set by the thermodynamic environment (i.e. temperature and density).
+===Simulations===
+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 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.
+Then you run the code, and it doesn't work. (nevermind, it does work.)
+===Results===
+**REFERENCES** \\
+[[http://iopscience.iop.org/0067-0049/191/1/66|Trends in 44Ti and 56Ni from Core-Collapse Supernovae (Magkotsios et al (2010))]]\\
+[[http://iopscience.iop.org/0004-637X/504/1/500|Nuclear Reactions Governing the Nucleosynthesis of 44Ti (The et al (1998))]]\\
+[[http://www.sciencedirect.com/science/article/pii/S1387647303002707|X-ray and gamma-ray observations of Cas A]]

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