Compact Stars

Stars are formed in gas and dust clouds with a non-uniform matter distribution. The compact stars, such as white dwarfs and neutron stars, are past the phase of having fusion processes in their interior. The pressure withstanding gravitational contraction comes from the Pauli exclusion principle. Due to the high density, the electrons or neutrons are so tightly packed that the degeneracy energy, a consequence of the fact that two fermions cannot be in the same single-particle state, is the dominating term. Because of this, we can use the Fermi gas equation of state for electrons and neutrons for white dwarfs and neutron stars respectively. The compact stars can be approximated by having a temperature T = 0. It isn’t actually zero, but it is a good approximation, because the energy of the highest occupied energy level is of a much larger magnitude than the thermal energy. Hence the fermions are in the ground state of the manyparticle system. The density is then on the form ρ = f(p), where f(p) is an arbitrary function of the pressure. We have used 2 different models: ? ρ is a constant ? ρ is polytropic A defining property of compact stars is their large densities. White dwarfs have densities of the order ρ ∼ 1010kg/m3, whereas neutron stars have ρ ∼ 1018kg/m3, i.e. nuclear densities. The densities for neutron stars demand the use of general relativity. Due to this, we have calculated radii and masses using the TOV-equations which incorporates general relativity. Measurements conducted by the Wilkinson Microwave Anisotropy Probe indicate that the universe consists of approximately 4% ordinary matter, 23% dark matter and 73% dark energy. The leading theory for the dark energy is a cosmological constant, a homogenous vacuum density throughout the universe. This theory can be incorporated into the TOV-equations. We have solved this form of the TOV-equations both analytically (ρ is constant) and numerically (ρ is polytropic). This has not been done previously.