The lowest-mass stars, known as M-dwarfs, form target samples for upcoming exoplanet searches, and together with lower-mass substellar objects known as brown dwarfs, are among prime targets for detailed study with high-contrast adaptive optics (AO) imaging and sub-millimeter interferometry. In this thesis, I describe results from three studies investigating the companion properties and environments of low-mass systems: (1) The 245-star M-dwarfs in Multiples (MinMs) Survey, a volume-limited survey of field M-dwarf companions within 15 pc, (2) the Taurus Boundary of Stellar/Substellar (TBOSS) Survey, an ongoing study of disk properties for low-mass members within the Taurus star-forming region, and (3) spectroscopy of a brown dwarf companion using the Gemini Planet Imager (GPI).

Direct imaging of M-dwarfs is a sensitive technique to identify low-mass companions over a wide range of orbital separation, and the high proper motion of nearby M-dwarfs eases confirmation of new multiple stars. Combining AO and wide-field imaging, the MinMs Survey provides new measurements of the companion star fraction (CSF), separation distribution, and mass ratio distribution for the nearest K7-M6 dwarfs. These results demonstrate the closer orbital separations (~6 AU) and lower frequency (~23% CSF) of M-dwarf binaries relative to higher-mass stars.

From the TBOSS project, I report 885µm Atacama Large Millimeter/sub-millimeter Array continuum measurements for 24 Taurus members spanning the stellar/substellar boundary (M4-M7.75). Observations of submillimeter emission from dust grains around the lowest-mass hosts show decreasing disk dust mass for decreasing host star mass, consistent with low frequencies of giant planets around M-dwarfs. Compared to the older stellar association of Upper Scorpius, Taurus disks have a factor of four higher mass in submillimeter-sized grains.

From the GPI Exoplanet Survey, I describe near-infrared spectroscopy of an unusually red companion orbiting inside the debris disk of an F5V star. As the second brown dwarf discovered within the innermost region of a debris disk, the properties of this system offer important dynamical constraints for companion-disk interaction and a useful benchmark for brown dwarf and giant planet atmospheric study.

I present a catalog of 1,794 stellar evolution models for solar-type and low-mass stars, which is intended to help characterize real host-stars of interest during the ongoing search for potentially habitable exoplanets. The main grid is composed of 904 tracks, for 0.5-1.2 M_sol at scaled metallicity values of 0.1-1.5 Z_sol and specific elemental abundance ratio values of 0.44-2.28 O/Fe_sol, 0.58-1.72 C/Fe_sol, 0.54-1.84 Mg/Fe_sol, and 0.5-2.0 Ne/Fe_sol. The catalog includes a small grid of late stage evolutionary tracks (25 models), as well as a grid of M-dwarf stars for 0.1-0.45 M_sol (856 models). The time-dependent habitable zone evolution is calculated for each track, and is strongly dependent on stellar mass, effective temperature, and luminosity parameterizations. I have also developed a subroutine for the stellar evolution code TYCHO that implements a minimalist coupled model for estimating changes in the stellar X-ray luminosity, mass loss, rotational velocity, and magnetic activity over time; to test the utility of the updated code, I created a small grid (9 models) for solar-mass stars, with variations in rotational velocity and scaled metallicity. Including this kind of information in the catalog will ultimately allow for a more robust consideration of the long-term conditions that orbiting planets may experience.

In order to gauge the true habitability potential of a given planetary system, it is extremely important to characterize the host-star's mass, specific chemical composition, and thus the timescale over which the star will evolve. It is also necessary to assess the likelihood that a planet found in the "instantaneous" habitable zone has actually had sufficient time to become "detectably" habitable. This catalog provides accurate stellar evolution predictions for a large collection of theoretical host-stars; the models are of particular utility in that they represent the real variation in stellar parameters that have been observed in nearby stars.

High-energy explosive phenomena, Gamma-Ray Bursts (GRBs) and Supernovae (SNe), provide unique laboratories to study extreme physics and potentially open up the new discovery window of Gravitational-wave astronomy.

Uncovering the intrinsic variability of GRBs constrains the size of the GRB emission region, and ejecta velocity, in turn provides hints on the nature of GRBs and their progenitors. We develop a novel method which ties together wavelet and structure-function analyses to measure, for the first time, the actual minimum variability timescale, Delta t_min, of GRB light curves. Implementing our technique to the largest sample of GRBs collected by Swift and Fermi instruments reveals that only less than 10% of GRBs exhibit evidence for variability on timescales below 2 ms. Investigation on various energy bands of the Gamma-ray Burst Monitor (GBM) onboard Fermi shows that the tightest constraints on progenitor radii derive from timescales obtained from the hardest energy channel of light curves (299--1000 keV). Our derivations for the minimum Lorentz factor, Gamma_min, and the minimum emission radius, R = 2c Gamma_min^2 Delta t_min / (1+z), find Gamma < 400 which imply typical emission radii R ~ 1 X 10^14 cm for long-duration GRBs and R ~ 3 X 10^13 cm for short-duration GRBs (sGRBs).

I present the Reionization and Transients InfraRed (RATIR) followup of LIGO/Virgo Gravitational-wave events especially for the G194575 trigger. I show that expanding our pipeline to search for either optical riZ or near-infrared YJH detections (3 or more bands)

should result in a false-alarm-rate ~1% (one candidate in the vast 100 deg^2 LIGO error region) and an efficiency ~90%.

I also present the results of a 5-year comprehensive SN search by the Palomar Transient Factory aimed to measure the SN rates in the local Luminous Infrared Galaxies. We find that the SN rate of the sample, 0.05 +/- 0.02 1/yr (per galaxy), is consistent with that expected from the theoretical prediction, 0.060 +/- 0.002 1/yr (per galaxy).

The field of exoplanet science has matured over the past two decades with over 3500 confirmed exoplanets. However, many fundamental questions regarding the composition, and formation mechanism remain unanswered. Atmospheres are a window into the properties of a planet, and spectroscopic studies can help resolve many of these questions. For the first part of my dissertation, I participated in two studies of the atmospheres of brown dwarfs to search for weather variations. To understand the evolution of weather on brown dwarfs we conducted a multi-epoch study monitoring four cool brown dwarfs to search for photometric variability. These cool brown dwarfs are predicted to have salt and sulfide clouds condensing in their upper atmosphere and we detected one high amplitude variable. Combining observations for all T5 and later brown dwarfs we note a possible correlation between variability and cloud opacity.

For the second half of my thesis, I focused on characterizing the atmospheres of directly imaged exoplanets. In the first study Hubble Space Telescope data on HR8799, in wavelengths unobservable from the ground, provide constraints on the presence of clouds in the outer planets. Next, I present research done in collaboration with the Gemini Planet Imager Exoplanet Survey (GPIES) team including an exploration of the instrument contrast against environmental parameters, and an examination of the environment of the planet in the HD 106906 system. By analyzing archival HST data and examining the near-infrared colors of HD 106906b, we conclude that the companion shows weak evidence of a circumplanetary dust disk or cloud. Finally, I measure the properties of the low mass directly imaged planet 51 Eridani b. We combined published J, H spectra with updated LP photometry, new K1, K2 spectra, and MS photometry. The new data confirms that the planet has redder than similar spectral type objects, which might be due to the planet still transitioning from to L-to-T. Model atmospheres indicate a cooler effective temperature best fit by a patchy cloud atmosphere making 51 Eri b an excellent candidate for future variability studies with the James Webb Space Telescope.

As the detection of planets become commonplace around our neighboring stars, scientists can now begin exploring their possible properties and habitability. Using statistical analysis I determine a true range of elemental compositions amongst local stars and how this variation could affect possible planetary systems. Through calculating and analyzing the variation in elemental abundances of nearby stars, the actual range in stellar abundances can be determined using statistical methods. This research emphasizes the diversity of stellar elemental abundances and how that could affect the environment from which planets form. An intrinsic variation has been found to exist for almost all of the elements studied by most abundance-finding groups. Specifically, this research determines abundances for a set of 458 F, G, and K stars from spectroscopic planet hunting surveys for 27 elements, including: C, O, Na, Mg, Al, Si, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Mo, Ba, La, Ce, Nd, Eu, and Hf. Abundances of the elements in many known exosolar planet host stars are calculated for the purpose investigating new ways to visualize how stellar abundances could affect planetary systems, planetary formation, and mineralogy. I explore the Mg/Si and C/O ratios as well as place these abundances on ternary diagrams with Fe. Lastly, I emphasize the unusual stellar abundance of τ Ceti. τ Ceti is measured to have 5 planets of Super-Earth masses orbiting in near habitable zone distances. Spectroscopic analysis finds that the Mg/Si ratio is extremely high (~2) for this star, which could lead to alterations in planetary properties. τ Ceti's low metallicity and oxygen abundance account for a change in the location of the traditional habitable zone, which helps clarify a new definition of habitable planets.

3D models of white dwarf collisions are used to assess the likelihood of double-degenerate mergers as progenitors for Type Ia supernovae (henceforth SNIa) and to identify observational signatures of double-degenerate collisions. Observations of individual SNIa, SNIa rates in different galaxy types, and double white dwarf binary systems suggest that mergers or collisions between two white dwarfs play a role in the overall SNIa population. Given the possibility of two progenitor systems (single-degenerate and double-degenerate), the sample of SNIa used in cosmological calcula- tions needs to be carefully examined. To improve calculations of cosmological parameters, the development of calibrated diagnostics for double-degenerate progenitor SNIa is essential. Head-on white dwarf collision simulations are used to provide an upper limit on the Ni-56 production in white dwarf collisions. In chapter II, I explore zero impact parameter collisions of white dwarfs using the Eulerian grid code FLASH. The initial 1D white dwarf profiles are created assuming hydrostatic equilibrium and a uniform composition of 50% C-12 and 50% O-16. The masses range from 0.64 to 0.81 solar masses and have an isothermal temperature of 10^7 K. I map these 1D models onto a 3D grid, where the dimensions of the grid are each eight times the white dwarf radius, and the dwarfs are initially placed four white dwarf radii apart (center to center). To provide insight into a larger range of physical possibilities, I also model non-zero impact parameter white dwarf collisions (Chapter III). Although head-on white dwarf collisions provide an upper limit on Ni-56 production, non-zero impact parameter collisions provide insight into a wider range of physical scenarios. The initial conditions (box size, initial separation, composition, and initial temperature) are identical to those used for the head-on collisions (Chapter II) for the same range of masses. For each mass pair- ing, collision simulations are carried out at impact parameters b=1 and b=2 (grazing). Finally, I will address future work to be performed (Chapter IV).

The only elements that were made in significant quantity during the Big Bang were hydrogen and helium, and to a lesser extent lithium. Depending on the initial mass of a star, it may eject some or all of the unique, newly formed elements into the interstellar medium. The enriched gas later collapses into new stars, which are able to form heavier elements due to the presence of the new elements. When we observe the abundances in a stellar regions, we are able to glean the astrophysical phenomena that occurred prior to its formation. I compile spectroscopic abundance data from 49 literature sources for 46 elements across 2836 stars in the solar neighborhood, within 150 pc of the Sun, to produce the Hypatia Catalog. I analyze the variability of the spread in abundance measurements reported for the same star by different surveys, the corresponding stellar atmosphere parameters adopted by various abundance determination methods, and the effect of normalizing all abundances to the same solar scale. The resulting abundance ratios [X/Fe] as a function of [Fe/H] are consistent with stellar nucleosynthetic processes and known Galactic thin-disk trends. I analyze the element abundances for 204 known exoplanet host-stars. In general, I find that exoplanet host-stars are not enriched more than the surrounding population of stars, with the exception of iron. I examine the stellar abundances with respect to both stellar and planetary physical properties, such as orbital period, eccentricity, planetary mass, stellar mass, and stellar color. My data confirms that exoplanet hosts are enriched in [Fe/H] but not in the refractory elements, per the self-enrichment theory for stellar composition. Lastly, I apply the Hypatia Catalog to the Catalog of Potentially Habitable Stellar Systems in order to investigate the abundances in the 1224 overlapping stars. By looking at stars similar to the Sun with respect to six bio-essential elements, I created maps that have located two ``habitability windows'' on the sky: (20.6hr, -4.8deg) and (22.6hr, -48.5deg). These windows may be of use in future targeted or beamed searches.