This thesis contains the results of two investigations: one into the nature of stars with degenerate neutron cores and the other into the interpretation of the phenomenology of luminous low-mass X-ray binaries (LMXBs) displaying slowquasi-periodic oscillations (QPOs) in their X-ray flux.
A star with a degenerate neutron core would be a red giant or supergiant. In this thesis we investigate the structure of such a supergiant, particularly examiningthe energy production and seeking an identifying observational signature. This star is convective from near the photosphere down to the base of the envelope justoutside the degenerate core (radius 10 km). The star's luminosity comes from the rp-process in a convective burning region within 100 km of the base of the envelope. The convection brings fuel for therp-process into the burning region from throughout the envelope and deposits the products ofrp-burning back into the envelope, including the photosphere. After about 10^5 years, the abundances of Br, Rb, Y, and Nb at the surface of the star will be about 200 times greater than their solar abundances, and that of Mo, over 1000 times solar. A suitable observational signature would be the strong enhancement of absorption lines for these elements in the star's spectrum. As many as 10 of the nearest 100 redsupergiants (those within 5 kpc) could have neutron cores.
The other investigation concerns a model of rapid accretion onto an unmagnetized neutron star with radius somewhat less than 6GM/c^2. This model is applied to the phenomenology of a class of LMXBs displaying slow (∼ 6 Hz)QPOs in X-ray flux. These sources are highly luminous (approximately Eddington) and display what appears to be three modes ("branches") of accretion. In this model, at low accretion rates, the neutron star lies within the inner edge of the accretion disk, and matter is dripped onto the neutron star from the inner edge. As the accretion rate increases, the transition from the "horizontal branch"to the "normal branch" occurs when the disk thickens and its inner edge touches the star and forms a boundary layer. The formation of a boundary layer changes the structure of the inner disk and the spectral character of the escaping X-rays. The transition from the normal branch to the "flaring branch" occurs when the boundary layer covers the whole surface of the neutron star and radiation escapesprimarily through convective instabilities. This thesis presents an exploration of this model, with an emphasis on establishing the plausibility that a neutron star could indeed lie inside an accretion disk accreting at the observed rate and that a change of mass accretion rate could push the inner radius onto the surface of thestar.
