the_lumberjacks
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the_lumberjacks [2014/06/11 14:46] warren |
the_lumberjacks [2014/06/11 15:40] warren |
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| ===== Log ===== | ===== 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. | ||
| + | |||
| + | 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. | ||
| ===== References ===== | ===== References ===== | ||
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| * http://adsabs.harvard.edu/abs/2009A%26A...494..829P | * http://adsabs.harvard.edu/abs/2009A%26A...494..829P | ||
| * http://adsabs.harvard.edu/abs/2013JPhG...40a3201A | * http://adsabs.harvard.edu/abs/2013JPhG...40a3201A | ||
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the_lumberjacks.txt · Last modified: 2014/06/11 15:47 by warren
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