Observational and Timing Studies of Compact Binaries Containing Compact Objects and Evolved Stars

Compact binary stars are a cornerstone of and often the first step in exploring some of the most interesting processes in the Universe. These systems, which typically have orbital periods of less than a day, take on many different appearances and probe various points of stellar evolution. Some populations of binary stars are large and well studied, while others are smaller and therefore benefit from each new discovery and characterization of its class. It is only through complementary and comprehensive studies of the variety of binary types that we hope to gain a more cohesive picture of how these systems and their constituent parts evolve and give way to other interesting astrophysical phenomena. This thesis presents investigations of three different types of compact binaries. These studies assume complementary approaches to characterize stellar systems via observational, computational, and timing techniques, as well as to describe individual systems and their populations. Chapter 2 presents a case study of a B-type hot subdwarf (sdB) and the optical photometry and spectroscopy obtained to characterize it. The study of this system represents the first effort in a forthcoming series of papers aimed at increasing and better-characterizing the compact, binary-hot-subdwarf population. Chapter 3 describes an analysis of 45 previously classified white dwarf--main sequence (WDMS) binaries using high-resolution, near-infrared spectra from the Apache Point Galactic Evolution Experiment. This study not only added additional systems to the number of compact WDMS systems -- arguably the largest population of compact binaries that have undergone common-envelope evolution -- with derived orbital periods but it also pointed out potential alterations to the chemical composition of the MS companion during the common-envelope phase. Finally, Chapter 4 presents a new technique for achieving long-term timing solutions of redback (RB) millisecond pulsars. Owing to the erratic nature of the orbit and circumbinary material in these systems, previous studies could only track the rotation of the pulsar over baselines of a few years. By decoupling the pulsar's spin from its binary orbit, we show that RB spin parameters could be derived from almost 20 years of archival data.