Neutron Star problem

A space for version controlling my computational code of the neutron star problem, with each folder corresponds to a certain state of the problem and our progress.

Fitting procedure

The code for fitting the parameters of the spin-dependent terms of the CDM3Yn interactions (with n=4,5,6,8) is in the folder Fit_CDM3Yn. A detailed documentation of the fitting method can be found at the Jupyter notebook Fitting procedure.ipynb. The data files d0D1.csv and d1D1.csv are the Brueckner-Hartree-Fock (BHF) result by Vidana et al, 2016, which are saved in 2 columns, corresponding to the nucleon number density n_b and the energy per baryon EA

In each folder CDM3Yn (with n=4, 5, 6, 8), there are 2 files of the form CDM3Yn_F1i.csv (with i=0, 1) and each of them is the "translated" BHF result in the form of n_b and F1i. There are also 2 files of the form CDM3Yn_F1i_pars.csv which contains the best-fit results of the parameters in concern, i.e. C, alpha, beta, gamma. This act of "translation" is done via the file src/EA_to_F. In case you want to recompile this file, run

cd src
make

Spin polarized nuclear matter

With all parameters of the form factor deduced from the Fitting procedure, each model is then calculated within the framework of Hartree-Fock (HF) with 4 different scenarios of the polarization's density-dependence, various configurations of the equation of states of asymmetric spin-polarized nuclear matter are recorded in the .csv files at the folder Spin_Polarized_NM/result, namely

• Baryon number density n_b,
• Energy per baryon E/A,
• Pressure P,
• Nuclear incompressibility K,
• Symmetry energy S,
• Symmetry pressure P_S, i.e. the pressure difference between pure neutron matter and symmetric nuclear matter,
• Spin symmetry energy W,
• Spin symmetry pressure P_W, i.e. the pressure difference between totally polarized and spin saturated nuclear matter.

Also, severals parameters of the EoS at saturation density n_b=0.17 are saved in the folder EoS_config, each is separated into the symmetry parameters from isospin (*_S.csv, calculated with symmetric NM) and spin (*_W.csv, calculated with spin-saturated NM). The informations presented are

• Spin polarization Delta or nuclear asymmetry delta,
• Nuclear incompressibility K,
• Symmetry coefficient J_S or J_W,
• Slope parameter L_S or L_W,
• Curvature paramter Ksym_S or Ksym_W.

Note that all quantities are given in the unit of MeV and fm. The detailed calculation code is stored in the src folder, while the figures generated from the notebook Density-dependent polarization nuclear matter.ipynb are stored in the folder fig. In order to rerun the HF calculation, go to the folder Spin_Polarized_NM and run the command

bash run.sh

Beta-stable neutron star matter

A simple neutron star matter model consisting of strongly interacting baryons (neutrons and protons) and leptons (electrons and muons) is described in detail in the folder Neutron_Star_Matter. As a results, many quantities are given, i.e.

• Number densities of consituent particles at every specific baryonic density n_b, dubbed as n_n, n_p, n_e and n_mu,
• Total energy density of the NS matter, along with the contributions from baryons, electrons and muons,
• Same as energy density for pressure.

To rerun the process with all CDM3Yn versions, a simple script is given,

bash run.sh

The total equations of states (neutron star core + crust) corresponding to each case is stored in the EoS_total folder and will be used for the GR calculation. In these files, only the baryonic number density n_b, energy density E and pressure P of the neutron star matter. Note that in this folder, E and P are saved in terms of g and cm. All figures are again generated from the notebook Beta-stable neutron star matter.ipynb and are stored in fig. All calculations are performed with 4 scenarios of polarization, i.e. A, B, C and D, based on the magnetic field distribution modelled by Fujisawa, 2014 and the polarization reaction with magnetic field made by Aguirre, 2011.

TOV calculation

In this part, everything is recorded in the folder TOV_Equation. With the equation of states obtained from the HF calculation, several relations, i.e. properties of the neutron star can be generated, namely

• Central baryonic density n_b,
• Central pressure Pc,
• Gravitational mass M in unit of solar mass,
• Radius R in km,
• Tidal Love numbers of order 2, 3, 4; where k, j_st and j_ir stand for the gravito-electric and gravito-magnetic (static and irrotational fluid) TLN,
• Dimensionless tidal deformability correspondingly, i.e. Lambda for gravito-electric and Sigma for gravito-magnetic.

In order to compute everything again, run the Bash/Zsh command

bash run.sh

All figures used in the paper are generated from the Jupyter notebook Neutron star properties.ipynb and are saved in the fig folder in categories.