polytrope EOS solver

Functions to compute polytrope Equation of state from given parameters.

EOSgenerators.Polytrope_EOS.compute_EOS(rhos, theta, rho_t_start=0.0012463097241917458, P_t_start=2.4572783742936653e-06)[source]

Calculate the pressure of a neutron star based on density using a piecewise polytropic equation of state (EOS).

This function computes the pressure (pres) as a function of density (rho) by applying different polytropic indices (gamma_1, gamma_2, …, gamma_n) within specified density thresholds (rho_t_start, rho_t_1, rho_t_2, …, rho_t_n-1). The EOS is defined in n distinct regions:

  • Low-density region: rho_t_start < rho <= rho_t_1

  • Intermediate-density region: rho_t_1 < rho <= rho_t_2, …, rho_t_k < rho <= rho_t_k+1, …, rho_t_n-2 < rho <= rho_t_n-1

  • High-density region: rho > rho_t_n-1

Parameters:

  • rho (array-like) – An array of density values (in cgs units) at which to calculate the pressure.

  • theta (array-like, length 2 * n - 1) –

    A list or tuple containing the EOS parameters in the following order:

    • gamma_1 (float): Polytropic index for the low-density region.

    • gamma_2 to gamma_2_n-1 (float): Polytropic index for the intermediate-density region.

    • gamma_n (float): Polytropic index for the high-density region.

    • rho_t_1 (float): Density threshold between the low and intermediate-density regions (in cgs units).

    • rho_t_2 to rho_t_n-2 (float): Density for the intermediate regions (in cgs units).

    • rho_t_n-1 (float): Density threshold between the intermediate and high-density regions (in cgs units).

  • rho_t_start (float) – Start point of the density for polytropic EOS

  • P_t_start (float) – Start point of the pressure for polytropic EOS

Returns:

pres – An array of pressure values (in cgs units) corresponding to the input density values.

Return type:

ndarray

EOSgenerators.Polytrope_EOS.fun_gamma_max(rho2, rho1, p1)[source]

Outputs the maximum gamma for given densities and pressure at both ends of a section of polytropic function. :param rho2: density at the end point. :type rho2: float :param rho1: density at the start point. :type rho1: float :param p1: pressure at the start point. :type p1: float

Returns:

the maximum gamma.

Return type:

gamma_max (float)