Cococubed.com Polytropic Stars
Home Astronomy Research    2025 Neutrinos From De-excitation    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    2025 AAS YouTube    2025 AAS Peer Review Workshops 2025 ASU Energy in Everyday Life 2025 MESA Classroom Other Stuff:    Bicycle Adventures    Illustrations    Presentations Contact: F.X.Timmes my one page vitae, full vitae, research statement, and teaching statement.	The code public_poly.tbz computes the structure of stars that are in hydrostatic equilibrium and obey a polytropic equation of state \begin{equation} P = K \rho^{\gamma} = K \rho^{1 + 1/n} \ . \label{eq1} \tag{1} \end{equation} The solution to the resulting Lane-Emden equation \begin{equation} \dfrac{d^2y}{dx^2} + \dfrac{2}{x} \dfrac{dy}{dx} + y^n = 0 \hskip 0.5in y(x=0)=1 \hskip 0.5in \left . \dfrac{dy}{dx}\right |_{x=0} = 0 \ , \label{eq2} \tag{2} \end{equation} where $x$ is a dimensionless radius and $y$ is a dimensionless density, is written out in dimensionless form and in physical units. Certain polytropic stars are related cold white dwarfs. Pathways in the PV-plane for a polytropic equation of state. Note γ ≡ 1 + 1/n = n for the golden ratio of n = Φ = 1.6180… Numerical solutions to the Lane-Emden equation. For n < 5, the solutions can be continued to negative y. Although not physical, such complex solutions exists and are useful for determining the values of x and dy/dx when y is zero. It's an exercise for the user to compare the computed surface values with other's tabulated values. Difference between the analytical and numerical solutions for n = 0, 1, and 5 for various integration accuracies. The larger n, the more extended the object. Other physical properties can be gleaned from the output files. It was a good day. Chicago. 2nd floor LASR. One in an impeccable brown suit and the other in blue overalls, white t-shirt, and Sear's DieHard steel-toe black shoes.
	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.