Adiabatic Temperature Gradient
White Dwarfs


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Contact: F.X.Timmes
my one page vitae,
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The tool contained in adiabatic_white_dwarf.tar.xz generates models of white dwarfs in hydrostatic equilibrium with an adiabatic temperature gradient for a general stellar equation of state. Such a model can be useful, for example, during the simmering phase of a white dwarf supernova progenitor. Starting from a given central density $\rho_c$, central temperature $T_c$, composition, and background temperature of the white dwarf $T_b$, this tool integrates the relevant equations of stellar structure \begin{equation} \begin{split} \frac{dr}{dm} & = \frac{3}{4 \pi r^2 \rho} \\ \frac{dP}{dm} & = \frac{dP}{dr} \frac{dr}{dm} = - \frac{G m \rho}{r^2} \frac{dr}{dm}\\ \frac{dT}{dm} & = \frac{dP}{dm} \ \frac{T}{P} \ \left ( \frac{\partial \ln T}{\partial \ln P} \right )_{\rm ad}\\ \frac{d\epsilon}{dm} & = q_{\rm eff} \ N_A \ \left ( \frac{1}{2} \ Y_{\rm 12}^2 \ \rho \ \lambda_{\rm 1212} \right ) \end{split} \label{eq1} \tag{1} \end{equation} where $r$ is the distance, $m$ is the mass, $P$ is the pressure, $N_A$ is the Avogadro number, $\lambda_{\rm 1212}$ is the C12+C12 reaction rate, and $q_{\rm eff}$ is the effective Q-value of the C12+C12 reaction (see Chamulak et al 2008 equation 6). Here are some examples with $T_b = 3 \times 10^8$ K. One can check the output files that the entropy is indeed constant in the adiabatic region ;)




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