RMF EOS solver

Functions to compute RMF Equation of state from given parameters.

EOSgenerators.RMF_EOS.Energy_density_Pressure(x, rho, theta, return_tag=False)[source]

Compute the pressure and energy density for the equation of state (EOS) based on the Relativistic Mean Field (RMF) model parameters,

Parameters:

  • x (array) – An array containing the initial values for sigma, omega, rho, and chemical potential, obtained from the initial_values function.

  • rho (float) – The central density at which the EOS computation begins.

  • theta (array) – An array of 10 parameters that define the RMF model in the Lagrangian.

  • return_tag (bool, optional) – If False (default), returns only the energy density and pressure. If True, returns additional EOS components.

Returns:

If return_tag is False:
energy_density (float): The energy density in natural units

(to convert to MeV.fm-3, divide by MeV.fm-3).

pressure (float): The pressure in natural units.

If return_tag is True:
numpy array: A 1D array representing EOS components:

  • EoS[0]: Number density in fm-3.

  • EoS[1]: Energy density in natural units.

  • EoS[2]: Pressure in natural units.

  • EoS[3]: Proton chemical potential in natural units.

  • EoS[4]: Neutron chemical potential in natural units.

  • EoS[5]: Electron chemical potential in natural units.

  • EoS[6]: Muon chemical potential in natural units.

  • EoS[7]: Proton fraction (dimensionless).

Return type:

tuple

EOSgenerators.RMF_EOS.compute_EOS(eps_crust, pres_crust, theta, return_tag=False)[source]

Generate core part equation of state, main function, from RMF model,

Parameters:

  • eps_crust (array) – the energy density of crust EoS in g.cm-3.

  • pres_crust (array) – the pressure from crust EoS model in dyn.cm-2.

  • theta (array) – An array representing the parameters used to determine a RMF model in the

  • case (Lagrangian. In this)

  • parameters. (the RMF model is defined by 10)

  • return_tag (bool, optional) – If False (default), returns only the energy density and pressure. If True, returns additional EOS components.

Returns:

energy_density (float): The energy density in natural units

(to convert to MeV.fm-3, divide by MeV.fm-3).

pressure (float): The pressure in natural units.

If return_tag is True:
numpy array: A 1D array representing EOS components:

  • EoS[0]: Number density in fm-3.

  • EoS[1]: Energy density in natural units.

  • EoS[2]: Pressure in natural units.

  • EoS[3]: Proton chemical potential in natural units.

  • EoS[4]: Neutron chemical potential in natural units.

  • EoS[5]: Electron chemical potential in natural units.

  • EoS[6]: Muon chemical potential in natural units.

  • EoS[7]: Proton fraction (dimensionless).

Return type:

If return_tag is False

EOSgenerators.RMF_EOS.fields_alpha(x, args)[source]

Iterate the sigma, omega, and rho fields for a given proton fraction and density.

Parameters:

  • x (array) – initial sqrt(sigma) sqrt(omega) and rho from initial_values function.

  • args (array) – parameters to determine a RMF model in Lagrangian; here, we have 12 parameters,

  • fraction (where the last parameters are the proton)

  • matter (For pure neutron)

Returns:

field equations which are then solved using the scipy root finding function.

Return type:

f (array)

EOSgenerators.RMF_EOS.functie(x, args)[source]

Iterates the the sigma, omega, rho term and chemical potential of electron and neutron at any given density,

Parameters:

  • x (array) – initial sigma omega rho and chemical potential from initial_values function

  • args (array) – parameters of a specific RMF model Lagrangian; here, we have 10 parameters.

Returns:

sigma term in the Lagrangian. omega (float): omega term in the Lagrangian. rho_03 (float): rho term in the Lagrangian. mu_n (float): chemical potential of neutron matter. mu_e (float): chemical potential of electron portion.

Return type:

sigma (float)

EOSgenerators.RMF_EOS.get_energy_pressure_alpha(x, rho, theta)[source]

Generate pressure and energy density at a given number density and proton fraction.

Parameters:

  • x (array) – An array that consists of the initial values of sqrt(sigma), sqrt(omega), and rho

  • function. (obtained from the initial_values)

  • rho (float) – The central density from which the computation of the equation of state begins.

  • theta (array) – An array representing the parameters used to determine a RMF model in the

  • case (Lagrangian. In this)

  • parameters (where the last)

  • parameters

  • fraction (is the proton)

Returns:

EOS ingredient, energy density in natural units. pressure (float): EOS ingredient, pressure in natural units.

Return type:

energy_density (float)

EOSgenerators.RMF_EOS.get_eos_alpha(theta, single_point=False)[source]

Generate EOS for a given alpha

Parameters:

  • theta (array) – An array representing the parameters used to determine a RMF model in the

  • case (Lagrangian. In this)

  • parameters (the RMF model is defined by 11)

  • last (where the)

  • fraction (defined the proton)

  • single_point (boolean) – Allows for the return of a single point of the EoS.

Returns:

EOS ingredient, density in fm-3. energy_density (array): EOS ingredient, energy density in natural units. pressure (array): EOS ingredient, pressure in natural units.

Return type:

rho (array)

EOSgenerators.RMF_EOS.initial_guess_alpha(rho, theta)[source]

Outputs the sigma, omega, rho field value

Parameters:

  • rho (float) – given nuclear density

  • theta (array) – parameters to determine an RMF model in Lagrangian, here there are 11 parameters,

  • fraction (where the last parameters are the proton)

Returns:

square root of the sigma term in the Lagrangian. math.sqrt(omega) (float): square root of the omega term in the Lagrangian. rho_03 (float): rho term in the Lagrangian.

Return type:

math.sqrt(sigma) (float)

EOSgenerators.RMF_EOS.initial_values(rho, theta)[source]

Outputs the the sigma, omega, rho term and chemical potential of electron and neutron at given initial density.

Parameters:

  • rho (float) – given nuclear density

  • theta (array) – parameters of determine a RMF model in Lagrangian; here, we have 10 parameters.

Returns:

sigma term in Lagrangian. omega (float): omega term in Lagrangian. rho_03 (float): rho term in Lagrangian. mu_n (float): chemical potential of neutron matter. mu_e (float): chemical potential of electron portion.

Return type:

sigma (float)