Equations of State for White Dwarfs

Abstract

This thesis is about deriving a few equations of state for white dwarfs below the regime of neutron drip. White dwarfs - also called degenerate dwarfs, composed mostly of electron-degenerate matter - are luminous and the color of the light they are emitting is white, hence their name. Because of the relatively enormous density, the gravitational potential of a white dwarf causes a collapse. White dwarfs are classified as compact objects, meaning that their life begins when a star dies, and are therefore considered as one possibility of a final stage of stellar evolution since they are considered static over the lifetime of the Universe. Star death is a point where the most of its nuclear fuel has been consumed. After the birth, white dwarfs are slowly cooling, radiating away their residual thermal energy. White dwarfs resist the gravitational collapse with electron degeneracy pressure. The temperature of white dwarfs is much higher than that of normal stars. These properties, together with exceedingly small size, are characteristic of white dwarfs. Cooling of white dwarfs offers information of solid state physics in a new setting - the circumstances of an original star can not be built up in a laboratory. Also, it would not be possible to realize the distance, which includes many advantages in sketching timescales and fundamental interactions by observation. More over, the evolution and the equation of state of white dwarfs provide us with more understanding of matter and physics describing the Universe. In this study, the equation of state for white dwarf matter is derived first by treating the matter as ideal Fermi gas, then including also electrostatic forces and considering the effects of inverse β-decay. We conclude with an overview of the equation of gravitational potential energy arising from hydrostatic equilibrium. The accuracy of the equation of state was concluded to depend on which interactions and phenomenon are included in the consideration. On the other hand, choosing the white dwarf model for an application depends significantly on the density of the matter, as well. The equations of state of ideal Fermi gas, with Coulomb correction and with the inverse β-decay correction were concluded to be accurate enough to provide a quantitatively adequate description of the phenomenon.