Building Polytropic Structure Files

This appendix describes the build_poly executable, which creates polytropic structure files for use with GYRE.


In addition to GYRE’s general pre-requisites (see the Installation chapter), build_poly needs a thread-safe version of the ODEPACK ordinary differential integrator library. This library is shipped with version 20.3.2 (and more recent) of the MESA SDK.

On Linux and MacOS platforms, this library is bundled together with all of the other pre-requisites in the Madison Software Development Kit (SDK), which can be downloaded from the MESA SDK homepage. Using this SDK is strongly recommended.

It does this by solving the Lane-Emden equation

\[\frac{1}{\xi^{2}} \deriv{}{\xi} \left( \xi^{2} \deriv{\Theta}{\xi} \right) = - \Theta^{\npoly}\]

for constant polytropic index \(\npoly\). Here, the dependent variable \(\Theta\) represents the local density \(\rho\) via

\[\Theta = \left( \frac{\rho}{\rho_{\rm c} \right)^{1/\npoly},\]

where \(\rho_{\rm c}\) is the central density; and the independent variable :math:`Theta` is related to the radial coordinate \(r\) via

\[\frac{r}{R} = \frac{\xi}{\xi_{1}},\]

where \(R\) and \(\xi_{1}\) are the surface values of \(r\) and \(\xi\), respectively. The Lane-Emden is solved subject to the boundary conditions

\[\theta(0) = 1, \qquad \theta(\xi_{1}) = 0\]