Equation of State Generators illustration notebook

First import all of the package that will be used here.

import EOSgenerators.crust_EOS as crust
import EOSgenerators.fastRMF_EoS as fast
import EOSgenerators.RMF_EOS as RMF
import TOVsolver.main as main
import TOVsolver.EoS_import as EoS_import
from matplotlib import pyplot
import matplotlib.pyplot as plt
import TOVsolver.constant as constant
from itertools import repeat
import numpy as np
import math

Load crust EOS and prepare interface EOS

Define constants, and load the crust EOS into this notebook, since when we solve the equation of state to TOV equation, we need full scope of the equation of state. Here, crust eos file is ‘Tolos_crust_out.txt’, while we need to times G / c^2 for energy density and G / c^4 for pressure, to make MeV/fm3 to be a natural unit, that will be easier for treatment, no need worry about G and c.

Then just connect the crust part with the interface part(the part between core equation of state and crust) by a PolyInterpolate function

c = constant.c
G = constant.G
oneoverfm_MeV = constant.oneoverfm_MeV
Tolos_crust_out = np.loadtxt('Tolos_crust_out.txt', delimiter='  ')
eps_crust_T_out = Tolos_crust_out[:,3] * G / c**2
pres_crust_T_out = Tolos_crust_out[:,4] * G / c**4

eps_com, pres_com = crust.PolyInterpolate(eps_crust_T_out, pres_crust_T_out)

Defining the paramters

Defining the free prameters that we need to compute the equation of state, you could check our intro part of documentation or just check the original paper of us about details. Huang et al,2023

After defined the equation of state parameters, we could call the ‘compute_EOS’ function from RMF, to compute full core equation of state.

m_sig = (495.0)/oneoverfm_MeV
m_w = 3.96544
m_rho = 3.86662

g_sigma = math.sqrt(107.5751)
g_omega = math.sqrt(182.3949)
g_rho = math.sqrt(206.4260)

kappa = 3.09114168/197.33
lambda_0 = -0.00168015405
zeta = 0.024
Lambda_w = 0.045
theta = np.array([m_sig, m_w, m_rho, g_sigma, g_omega, g_rho, kappa, lambda_0, zeta, Lambda_w])
eps, pres = RMF.compute_EOS(eps_com, pres_com, theta)

Connecting Core and crust EOS

These two line can easily connect the Equation of state we computed for core part by setting the parameters and the crust equation of state, to a full equation of state that prepared for next step output

eps_total = np.array([*eps_com, *eps])
pres_total = np.array([*pres_com, *pres])

Here below is one of the possiblity, use our defined function, ‘OutputMR’ to compute out what the mass radius curve corresponding to this equation of state.

MR = main.OutputMR('',eps_total,pres_total).T

Mass Radius file will be generated and stored as  2-d array. The first column is Radius, second one is mass

fig, ax = plt.subplots(1,1, figsize=(9,6))
ax.plot(MR[0], MR[1],lw=2)
ax.set_ylabel(r'M [$M_{\odot}$]', fontsize=16)
ax.set_xlabel('R [km]', fontsize=16)
ax.set_xlim(8., 20.)
ax.set_ylim(0,3)
ax.tick_params(top=1,right=1, which='both', direction='in', labelsize=14)
ax.tick_params(top=1,right=1, which='both', direction='in', labelsize=14)
fig.tight_layout()
plt.show()