Neutron-Star-TOV-Solver

Computational Modeling of Neutron Stars

This repository contains the numerical framework developed for my undergraduate thesis at the Aristotle University of Thessaloniki. It solves the structure equations for compact objects and calculates tidal deformability for various Equations of State (EoS).

Features

• TOV Solver: Integration of the Tolman-Oppenheimer-Volkoff equations: $$\frac{dP}{dr} = -\frac{G}{r^2} \left( \rho + \frac{P}{c^2} \right) \left( M + \frac{4\pi r^3 P}{c^2} \right) \left( 1 - \frac{2GM}{c^2 r} \right)^{-1}$$
• Tidal Deformability: Calculation of the second tidal Love number $k_2$ and the dimensionless parameter $\Lambda$.
• EoS Support:
  • Purely Hadronic (DD2, etc.)
  • Hybrid stars (Maxwell construction)
  • Color-Flavor Locked (CFL) Quark matter using the MIT Bag Model.

Physical Background

The project investigates the effect of the QCD Cooper-pair gap ($\Delta$) and the bag constant ($B$) on the stability and maximum mass of neutron stars, comparing results with observational constraints from GW170817 and NICER.

Scientific Results & Visualizations

1. Mass-Radius Relations

The following plots illustrate the Mass-Radius sequences for different Equations of State (EoS) models being either purely hadronic or in the Color-Flavor Locked (CFL) phase . The shaded regions and markers represent observational constraints from NICER and GW170817.

Hadronic Stars	CFL Quark Stars

2. Hybrid Stars & Phase Transitions

Modeling the transition from hadronic matter to quark matter using Maxwell construction. The plot shows the hybrid branches under variating parameters and the effect of the transition on stellar configurations.

3. CFL Stability Window

Analysis of the thermodynamic stability of the Color-Flavor Locked phase relative to the nuclear binding energy ($930 , \text{MeV}$), showing the dependence on the Bag constant $B$ and the gap parameter $\Delta$. We identify these conditions under which pure quark stars can exist

Thesis

This repository is based on my undergraduate thesis: "Computational Modeling of Neutron Stars: Mass-Radius Relations and Tidal Deformability for Hadronic, Hybrid and CFL Quark Equations of State". You can find the full text in PDF format here.