Solve TOV Equation

Function to solve the TOV equation from EOS equation of state given by user.

TOVsolver.solver_code.TOV_def(r, y, inveos, ad_index)[source]

Right-hand side of the TOV + tidal ODE system.

Parameters:

  • r (float) – raius as integrate varible

  • y (psudo-varible) – containing pressure, mass, h and b as intergarte varibles

  • equation (to solve out the TOV)

  • inveos – the invert of the eos, pressure and energy density relation to integrate

  • interpolate. (and)

Returns:

Derivatives [dP/dr, dm/dr, dh/dr, df/dr].

Return type:

numpy.ndarray

TOVsolver.solver_code.m1_from_mc_m2(mc, m2)[source]

a function that feed back the companion star mass from GW event measurement.

Parameters:

  • mc (float) – chrip mass of a GW event, unit in solar mass.

  • m2 (float or numpy array) – the determined mass for one of the star, this is computed from sampling of EoS.

Returns:

the companion star mass in solar mass.

Return type:

m1 (array)

TOVsolver.solver_code.solveTOV(center_rho, Pmin, eos, inveos, max_radius=3e+19)[source]

Solve the Tolman-Oppenheimer-Volkoff (TOV) equation to determine the structure of a neutron star

This function numerically integrates the TOV equations from the center outward to find the mass and radius of a neutron star with a given central density and equation of state. The integration uses an adaptive step size method to ensure numerical stability, especially near the surface where pressure gradients become steep.

Parameters:

  • center_rho (float) – The central energy density of the neutron star in unit.g_cm_3

  • Pmin (float) – Minimum pressure threshold that defines the star’s surface, in unit.G / unit.c**4

  • eos (function) – Function mapping energy density to pressure (ρ → P) Takes energy density in unit.G / unit.c**2, returns pressure in unit.G / unit.c**4

  • inveos (function) – Inverse equation of state, function mapping pressure to energy density (P → ρ)

  • max_radius (float, optional) – Safety parameter to prevent runaway integration in case the star’s surface is not properly detected. Defaults to 30e5*unit.cm

Returns:

(mass_Msun, radius_km)

Mass is in solar masses; radius is in kilometers.

Return type:

tuple[float, float]

Notes

  • Integration begins at a small non-zero radius (r = 1e-18 * unit.cm) to avoid the coordinate singularity at r=0

  • Initial pressure is calculated using a Taylor expansion around r=0 since the TOV equation has an indeterminate form (0/0) at the origin

  • We use adaptive step sizing for numerical stability

  • Multiple stopping conditions ensure robustness against EoS-related numerical issues

TOVsolver.solver_code.solveTOV_tidal(center_rho, energy_density, pressure, max_radius=3e+19)[source]

Solve TOV equation from given Equation of state in the neutron star core density range

Parameters:

  • center_rho (array) – This is the energy density here is fixed in main that is np.logspace(14.3, 15.6, 50)

  • energy_density (array) – Desity array of the neutron star EoS, in MeV/fm^{-3}. Notice here for simiplicity, we omitted G/c**4 magnitude, so (value in MeV/fm^{-3})*G/c**4, could convert to the energy density we are using, please check the Test_EOS.csv to double check the order of magnitude.

  • pressure (array) – Pressure array of neutron star EoS, also in nautral unit with MeV/fm^{-3}, still please check the Test_EOS.csv, the conversion is (value in dyn/cm3)*G/c**4.

Returns:

(mass_Msun, radius_km, tidal_deformability)

Tidal deformability is dimensionless.

Return type:

tuple[float, float, float]

TOVsolver.solver_code.tidal_deformability(y2, Mns, Rns)[source]

Compute Tidal deformability from y2, neutron star mass and raius

Parameters:

  • y2 (array) – midiate varrible that computing tidal

  • Mns (array) – neutron star mass in g/cm3

  • Rns (array) – neutron star radius in cm.

Returns:

neutron star tidal deformability with unit-less.

Return type:

tidal_def (array)