Cococubed.com Adiabatic Temperature Gradient White Dwarfs
Home Astronomy Research    Radiative Opacity    2024 Neutrino Emission from Stars    2023 White Dwarfs & 12C(α,γ)16O    2023 MESA VI    2022 Earendel, A Highly Magnified Star    2022 Black Hole Mass Spectrum    2021 Skye Equation of State    2021 White Dwarf Pulsations & 22Ne    Software Instruments      Stellar equation of states      EOS with ionization      EOS for supernovae      Chemical potentials      Stellar atmospheres      Voigt Function      Jeans escape      Polytropic stars      Cold white dwarfs      Adiabatic white dwarfs      Cold neutron stars      Stellar opacities      Neutrino energy loss rates      Ephemeris routines      Fermi-Dirac functions      Polyhedra volume      Plane - cube intersection      Coating an ellipsoid      Nuclear reaction networks      Nuclear statistical equilibrium      Laminar deflagrations      CJ detonations      ZND detonations      Fitting to conic sections      Unusual linear algebra      Derivatives on uneven grids      Pentadiagonal solver      Quadratics, Cubics, Quartics      Supernova light curves      Exact Riemann solutions      1D PPM hydrodynamics      Hydrodynamic test cases      Galactic chemical evolution      Universal two-body problem      Circular and elliptical 3 body      The pendulum      Phyllotaxis      MESA      MESA-Web      FLASH      Zingale's software      Brown's dStar      GR1D code      Iliadis' STARLIB database      Herwig's NuGRID      Meyer's NetNuc AAS Journals    2024 AAS YouTube    2024 AAS Peer Review Workshops 2024 ASU Energy in Everyday Life 2024 MESA Classroom Outreach and Education Materials Other Stuff:    Bicycle Adventures    Illustrations    Presentations Contact: F.X.Timmes my one page vitae, full vitae, research statement, and teaching statement.	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 ;)
	Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.