X-ray binaries are excellent test beds for studies of high-energy accretion flows and the properties of compact objects. Neutron star (NS) low-mass X-ray binaries (LMXBs) vary in brightness by almost 8 orders of magnitude and are hosts to diverse accretion flows, transporting varying amounts of energy and mass toward the central NS, as well as expelling significant mass from the binary. This thesis aims to shed light on the accretion flow properties across the mass and luminosity scale, with particular emphasis on constraining the matter accreted on the neutron star surface and the resulting heating, which has important implications for measurements of the NS mass and radius. We have utilized X-ray instruments with substantially different sensitivities in flux and resolving power, each suited to our focused study of the accretion flows in a particular luminosity regime.

In our study of the accretion disk wind in GX 13+1, we analyzed the Chandra High-Energy Transmission Grating spectrum of the NS binary accreting near its Eddington limit. We found multiple plasmas with different ionization states and velocities produce the observed absorption complex, in contrast to previous analyses that only found one absorption zone. The accretion disk wind expels mass from the disk at a rate comparable to the accretion onto the NS, and is consistent with a Compton-heated outflow, the driving mechanism likely behind all accretion disk winds in NS LMXBs and, possibly, all BH LXMBs. Frequent monitoring with the Swift X-Ray Telescope allowed us to observe SAX J1750.8-2900 in the relatively short-lived transition between outburst and quiescence. We found its X-ray spectrum softens towards lower luminosities, which can either be due to a radiatively-inefficient accretion flow or an increasing contribution of the boundary layer emission as the source's flux decreases. This work contributes to the establishment of spectral softening as a common property of the accretion flow in NS LMXBs between outburst and quiescence. We also found the transition does not produce significant NS heating.

In our studies of NS LMXB quiescent emission, we utilized an XMM-Newton observation of Cen X-4 while the source was at its brightest quiescent luminosity ever recorded. We found the first evidence of multi-temperature thermal emission in a non-pulsing quiescent NS. We have interpreted the hotter of the two thermal components as a potential hotspot on the NS surface, indicative of a magnetically channeled accretion flow and motivation for further studies into NS heating in quiescence. Finally, we present the results from a recent XMM observation of the extremely faint system SAX J1810.8-2609. We find that the thermal component is consistent with a cooling NS radiating heat from nuclear reactions activated during outburst. We also present a revised estimate of the time-averaged mass accretion rate based on a more detailed outburst history and a range of outburst properties, finding the outburst history is in agreement with the quiescent thermal luminosity and discounting assertions of enhanced cooling mechanisms in the NS of SAX .11810.8-2609. (Copies available exclusively from MIT Libraries, libraries.mit.edu/docs - docs mit.edu).