Compact Objects and their Stability

Wrishik Naskar

Department of Physics, Indian Institute of Technology Kanpur, Kalyanpur, Kanpur, Uttar Pradesh - 208017

Professor Dipankar Bhattacharya

Department of Astrophysics, Inter-University Centre for Astronomy and Astrophysics, Pune, Maharashtra - 411007

ABSTRACT

This project deals with the physics of compact objects, mainly white dwarfs and neutron stars, objects which are born when normal stars die, i.e., when most of their nuclear fuel is consumed. Unlike normal stars, they can't support themselves against gravitational collapse by generating thermal pressure, since they do not burn nuclear fuel. Instead, white dwarfs are supported by the pressure of degenerate electron gas, while neutron stars are supported largely by degenerate neutron gas pressure, even though they have further complications. We take the above into account, and analyse the stability of compact star configurations using the regular hydrostatic equilibrium equations, taking the effect of General Relativity into account, i.e. we use the Tolman-Oppenheimer-Volkoff (TOV) equation. In hydrostatic equilibrium, we balance the pressure gradient with the force of gravity, and along with this, we use different equations of state for different stellar configurations. The problem is then reduced to a system of two differential equations, which we solve using 4th Order Runge Kutta method with adaptive step size, on C++, over a wide range of central or core densities. We obtain relations between the stellar mass and radius, as well as between stellar mass and central density, and plot the values using Origin graph plotting software. We then analyse the graphs, from which we infer the stability of white dwarf and neutron star configurations. We compare our results with those in existing literature.

Keywords: Compact Objects, Hydrostatic Equilibrium, Equation of State, White Dwarfs, Neutron Stars