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--- the_lumberjacks [2014/06/11 14:37]
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   * **Parameter: MacKenzie Warren**
-===== Goals =====
+===== Goal =====
-  *  Use an analytic formulation of the neutrino driven wind environment in core-collapse supernova to determine the conditions for the r-process. Calculate, using the reaction network X-Net, abundance patterns for various values of the electron fraction and compare the robustness of the r-process in this environment.
+Explore the sensitivity of r-process abundances to electron fraction in the neutrino driven winds of a core-collapse supernova.
 ===== Scientific Background =====
-  *
+Although we observe robust r-process abundances even in low metallicity environments, the exact site of the r-process is still unclear.  Proposed sites include tidally ejected material in neutron star mergers and the neutrino driven winds of core-collapse supernovae.  However, due to uncertainties in the nuclear physics and conditions of the astrophysical environments, the exact site is still unclear.
-===== Links =====
+The neutrino driven winds of core-collapse supernovae provide a promising site for the r-process.  Core-collapse supernovae occur early enough in the universe to explain the observed r-process abundances in metal-poor halo stars.  However, the electron fraction (and thus the neutron abundance) is set by the details of the neutrino physics, which is still poorly understood.  By exploring the sensitivity of the r-process to the electron fraction, we can explore the likelihood of an r-process in the neutrino driven winds independent of the details of the neutrino transport.
-  * Thermodynamic Trajectories
-    * http://adsabs.harvard.edu/abs/2009A%26A...494..829P
-  * Literature
-    * http://adsabs.harvard.edu/abs/2013JPhG...40a3201A
 ===== Log =====
-We used the thermodynamic trajectories described in Panov & Janka (2009) to describe the evolution of the neutrino driven winds in core-collapse supernovae.  The free parameters in these trajectories are the initial temperatures and densities as well as the electron fraction.
+We used the thermodynamic trajectories described in Panov & Janka (2009) to describe the evolution of the neutrino driven winds in core-collapse supernovae.  Panov & Janka describe the material expansion using a piecewise analytic expansion.  The initial expansion is taken to be homologous, which results in an exponential decline of the density and temperature,
+\begin{equation}
+\rho(t) = \rho_{init} exp(-3 t/\tau_{dyn})
+\end{equation}
+\begin{equation}
+T_{9} (t) = T_{9}^{init} exp(-t/\tau_{dyn})
+\end{equation}
+where $\rho_{init}$ and $T_{9}^{init}$ are the initial density and temperature (in units of $10^{9}$K).  The dynamical timescale $\tau_{dyn}$ was taken to be 15ms.
-===== Other Resources =====
+The deceleration by the reverse shock alter the density and temperature evolution from the previously assumed homologous behavior.  We assume that the deceleration occurs at time $t_{0} = 60$ms and the density and temperature reach values $\rho_{0}$ and $T_{0}$ after the shock.  The density and temperature decline less steeply than the previous exponential behavior,
+\begin{equation}
+\rho(t) = \rho_{0} \left(\frac{t}{t_{0}}\right)^{-2}
+\end{equation}
+\begin{equation}
+T(t) = T_{0} \left(\frac{t}{t_{0}}\right)^{-2/3}
+\end{equation}
-  *
+The free parameters in these trajectories are the initial temperatures and densities as well as the electron fraction.  The initial temperature of 37Gk and initial density of $1\times 10^{9}$ g/cm${^3}$. The electron fraction was given values of 0.42, 0.44, 0.46, 0.48, and 0.50.
+We started the network calculation when the temperature reached 10GK.  This is a safe approximation since above this temperature, the material will be in Nuclear Statistical Equilibrium and the evolution of the abundances will not be set by the thermal history.  We used a network of 4510 isotopes, ranging from free nucleons to fermium (Z=100).
+===== References =====
+    * http://adsabs.harvard.edu/abs/2009A%26A...494..829P
+    * http://adsabs.harvard.edu/abs/2013JPhG...40a3201A

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