Neutron stars for undergraduates

Abstract

Calculating the structure of white dwarf and neutron stars would be a suitable topic for an undergraduate thesis or an advanced special topics or independent study course. The subject is rich in many different areas of physics accessible to a junior or senior physics major, ranging from thermodynamics to quantum statistics to nuclear physics to special and general relativity. The computations for solving the coupled structure differential equations (both Newtonian and general relativistic) can be done using a symbolic computational package, such as Mathematica. In doing so, the student will develop computational skills and learn how to deal with dimensions. Along the way he or she will also have learned some of the physics of equations of state and of degenerate stars.

Equilibrium and stability of thin spherical shells in Newtonian and relativistic gravity

“…(A useful introduction to neutron stars can be found in Ref. [4].) The sequence is calculated on the basis of the relativistic structure equations (see, for example, Chapter 24 of Ref.…”

Order-of-magnitude physics of neutron stars

“…3 See [27] for an accessible discussion on how to implement this procedure. 4 The readers are invited to convince themselves that this is not possible for any other functional form P (ρ).…”

“…In this way, we intend to give a first introduction to neutron stars, transmitting a "feeling" for their properties and the physical basis of these. We do not aim at a comprehensive, detailed, or rigorous discussion, which can be found in various excellent textbooks, such as references [26,12,15], and review articles like [20], complemented by introductory articles aimed at undergraduate students, such as [27,24]. Section 2 describes how quantum mechanics (through the Heisenberg uncertainty principle), together with the competition between kinetic and interaction energies, sets the main properties of atoms and nuclei and the density of condensed matter around us.…”

Cold atom quantum simulator for dilute neutron matter

“…Let M (r) = r 0 4πr 2 ρ(r)dr be the total mass up to the radius r and let ρ(r)dSdr be the mass in the minute region dr. A stable star without collapse must exhibit a force balance between the pressure of the particles and the gravitational force F = − GM (r) r 2 ρ(r)dSdr at all positions. 50 This condition is given by…”