We present an equatorial (± 30◦ Decl.) sample of all known single (within 4′′) mid M-dwarfs (M2.5V-M8.0V) extending out to 10 pc. For this sample of 58 stars, we provide photometry, low dispersion optical (6000−9000 ̊A) spectra from which spectral types are determined, Hα equivalent widths, and gravity sensitive NaI indices. For 45 of these 58 stars, strict limits are placed on the presence of companions, based on precise infrared radial velocities. Our spectroscopic results indicate that on average, we rule out the existence of companions with masses of 1.5 MJUP or greater in 10 day orbital periods around slowly rotating (vsini < 6.5 km s−1) M-dwarfs. Similarly, strict limits are placed on the presence of companions to 53 out of the 58 stars with astrometry. Our astrometric results show that, on average, we rule out the presence of companions with masses greater than 9 MJUP with an orbital period of 8 years. These results establish these stars as the nearest set of single mid M-dwarfs. Two additional stars, GJ 867B and LHS 1610, were initially included in this program, but later discovered to be spectroscopic binaries (SB). The binary GJ 867BD is a wide (24.5') companion to the M2 dwarf GJ 867AC. With this discovery, the GJ 867 system (d =8.82 ± 0.08 pc) becomes one of only four quadruple systems with in 10 pc of the Sun and the only among these with all M-dwarf (or cooler components). To measure how the rotational velocities vary with spectral type, we assembled a list of all known single (within 3′′) mid M-dwarfs that have trigonometric parallaxes within 25 pc and reside between −30◦ and +65◦ Decl from the RECONS sample. From this list of 402 stars, only 169 stars have previously reported vsini values. We obtained spectroscopic measurements for an additional 75 stars. Of those, 17 have vsini values above our detection threshold of 3 km s−1. Our data are consistent with the trend of more low mass M-dwarfs having high projected rotational velocity values than high mass M-dwarfs.

In this work, we investigate the presence of stellar companions around hot Jupiter systems using data sets from the Clio and VISAO instruments on the Magellan Telescope. We observed eighteen targets of which eleven have known spin-orbit obliquity measurements. We detected eleven candidate companions of which five are new discoveries, five involved the validation and confirmation of previous studies, and one candidate proved to be a background star not bound to the transiting planet system. Out of eleven systems with known spin-orbit obliquity, seven systems have candidate companions. Due to the size of the sample, we could not find any correlation between the spin-orbit obliquity and the presence of a stellar companion. As future work, we will do follow up observations on the targets with candidate companions. We will increase our sample to one hundred systems to investigate if there is a correlation between spin-orbit obliquity and the presence of a distant stellar companion.

Until the last decade or so, our entire knowledge of planets around Sun-like stars consisted of those in our own Solar System. This is no longer the case. Over 200 planets have been discovered through radial velocity surveys and photometric studies, both of which depend on observing the planet's effects on its host star. Much of our knowledge of the planets orbiting these stars is uncertain, based on assumptions about the stars' masses and the planets' orbital inclinations. This dissertation is comprised of two main sections. The first involves measuring the angular diameters for a sample of exoplanet host stars using Georgia State University's CHARA Array in order to learn more about the nature of these stars. These direct angular measurements are not dependent on the exoplanet systems' inclinations or the masses of the stars. Improved angular diameters lead to linear diameters when combined with HIPPARCOS parallax measurements, which in turn tell us of the stars' ages and masses. Of the 82 exoplanet systems observable with the CHARA Array, 31 host stars were observed and stellar angular diameters were measured for 26 systems. In the special case of an exoplanet system with a transiting planet, this direct measurement of the star's angular diameter leads to a direct measurement of the planet's diameter, when the planet-to-star-radii ratio is known from photometric studies. This was done for HD 189733. The star's angular diameter is 0.377 +/- 0.024 mas, which produces a stellar linear radius of 0.779 +/- 0.052 R_Sun and a planetary diameter of 1.19 +/- 0.08 R_Jupiter. The second part of this project involved the inspection of the exoplanet systems for stellar companions masquerading as planets. From radial velocity studies alone, it is impossible to distinguish between a planet in a high-inclination orbit and a low-mass stellar companion in a low-inclination orbit. Using the CHARA Array, it was possible to rule out certain secondary spectral types for each exoplanet system observed by studying the errors in the diameter fit and searching for separated fringe packets. While no definitive stellar companions were found, two expolanet systems, upsilon Andromedae and rho Coronae Borealis, exhibited behavior that were not consistent with the host star being a simple limb-darkened disk.

Over the past half century, multiplicity studies have provided a foundation for the theories of stellar formation and evolution through understanding how likely it is that stars form alone or with companions. If spectroscopic orbits are combined with techniques that can determine visual orbits, we can access the most fundamental parameter of stellar evolution, stellar mass. This dissertation is composed of two main sections. The first involves the investigation of the seminal multiplicity study of Duquennoy & Mayor (1991b) which has been the ``gold standard" for solar-type stars for nearly 20 years. Improvements in technology in the intervening years have improved the measurement accuracy for radial velocities and distances on which the study was based. Using Georgia State University's CHARA Array to search the systems in Duquennoy & Mayor's multiplicity survey for overlooked companions along with a literature search covering regimes unreachable by the CHARA Array, we have found that more than 40% of the Duquennoy & Mayor's sample was further than originally believed and the uncorrected multiplicity percentages change from 57:38:4:1:0% (single:double:triple:quad:quint%) to 48:42.5:7.5:1:1% with the discoveries of multiple previously undiscovered companions. The second part of this project describes the application of separated fringe packets for resolving the astrometric position of secondaries with small angular separations on long-baseline optical interferometers. The longest baselines of the CHARA Array allow access to a previously inaccessible range of separations compared with other techniques (<40 milliarcseconds) and the ability to very accurately angularly resolve a large number of single- and double-lined spectroscopic binaries. Combining astrometric and spectroscopic orbits provides assumption-free stellar masses and using the CHARA Array allows access to many previously unreachable systems available for high-accuracy mass determinations. We report the first angular separation measurements of seven spectroscopic binary systems, five additional separated fringe packet detections, ten systems with probably overlapping fringe packets, four systems with new data on pre-existing orbits, one completely new visual orbit for a SB2 system previously unresolved, and the detection of two previously unknown companions.