We present the effective temperatures (T-eff), metallicities, and colours in Sloan Digital Sky Survey (SDSS), Two Micron All Sky Survey, and Wide-field Infrared Survey Explorer filters, of a sample of 3834 late-K and early-M dwarfs selected from the SDSS Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectroscopic survey ASPCAP (APOGEE Stellar Parameters and Chemical Abundances Pipeline) catalogue. We confirm that ASPCAP T-eff values between 3550 < T-eff < 4200 K are accurate to similar to 100 K compared to interferometric T-eff values. In that same T-eff range, ASPCAP metallicities are accurate to 0.18 dex between -1.0 <[M/H]< 0.2. For these cool dwarfs, nearly every colour is sensitive to both T-eff and metallicity. Notably, we find that g - r is not a good indicator of metallicity for near-solar metallicity early-M dwarfs. We confirm that J - K-S colour is strongly dependent on metallicity, and find that W1 - W2 colour is a promising metallicity indicator. Comparison of the late-K and early-M dwarf colours, metallicities, and T-eff to those from three different model grids shows reasonable agreement in r - z and J - K-S colours, but poor agreement in u - g, g - r, and W1 - W2. Comparison of the metallicities of the KM dwarf sample to those from previous colour-metallicity relations reveals a lack of consensus in photometric metallicity indicators for late-K and early-M dwarfs. We also present empirical relations for T-eff as a function of r - z colour combined with either [M/H] or W1 - W2 colour, and for [M/H] as a function of r - z and W1 - W2 colour. These relations yield T-eff to similar to 100 K and [M/H] to similar to 0.18 dex precision with colours alone, for T-eff in the range of 3550-4200 K and [M/H] in the range of -0.5-0.2.

Recent photometric studies have revealed that surface spots that produce flux variations are present on virtually all L and T dwarfs. Their likely magnetic or dusty nature has been a much-debated problem, the resolution to which has been hindered by paucity of diagnostic multi-wavelength observations. To test for a correlation between magnetic activity and photometric variability, we searched for Ha emission among eight L3-T2 ultra-cool dwarfs with extensive previous photometric monitoring, some of which are known to be variable at 3.6 mu m or 4.5 mu m. We detected Ha only in the non-variable T2 dwarf 2MASS J12545393-0122474. The remaining seven objects do not show Ha emission, even though six of them are known to vary photometrically. Combining our results with those for 86 other L and T dwarfs from the literature show that the detection rate of Ha emission is very high (94%) for spectral types between L0 and L3.5 and much smaller (20%) for spectral types. >= L4, while the detection rate of photometric variability is approximately constant (30%-55%) from L0 to T8 dwarfs. We conclude that chromospheric activity, as evidenced by H alpha emission, and large-amplitude photometric variability are not correlated. Consequently, dust clouds are the dominant driver of the observed variability of ultra-cool dwarfs at spectral types, at least as early as L0.

We report the first detailed chemical abundance analysis of the exoplanet-hosting M-dwarf stars Kepler-138 and Kepler-186 from the analysis of high-resolution (R similar to 22,500) H-band spectra from the SDSS-IV-APOGEE survey. Chemical abundances of 13 elements-C, O, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, and Fe-are extracted from the APOGEE spectra of these early M-dwarfs via spectrum syntheses computed with an improved line list that takes into account H2O and FeH lines. This paper demonstrates that APOGEE spectra can be analyzed to determine detailed chemical compositions of M-dwarfs. Both exoplanet-hosting M-dwarfs display modest sub-solar metallicities: [Fe/H](Kepler-138) = -0.09 +/- 0.09 dex and [Fe/H](Kepler-186) = -0.08 +/- 0.10 dex. The measured metallicities resulting from this high-resolution analysis are found to be higher by similar to 0.1-0.2 dex than previous estimates from lower-resolution spectra. The C/O ratios obtained for the two planet-hosting stars are near-solar, with values of 0.55 +/- 0.10 for Kepler-138 and 0.52 +/- 0.12 for Kepler-186. Kepler-186 exhibits a marginally enhanced [Si/Fe] ratio.

Open clusters have been the focus of several exoplanet surveys, but only a few planets have so far been discovered. The Kepler spacecraft revealed an abundance of small planets around small cool stars, therefore, such cluster members are prime targets for exoplanet transit searches. Kepler's new mission, K2, is targeting several open clusters and star-forming regions around the ecliptic to search for transiting planets around their low-mass constituents. Here, we report the discovery of the first transiting planet in the intermediate-age (800 Myr) Beehive cluster (Praesepe). K2-95 is a faint (Kp = 15.5 mag) M3.0 +/- 0.5 dwarf from K2's Campaign 5 with an effective temperature of 3471 +/- 124 K, approximately solar metallicity and a radius of 0.402 +/- 0.050 R-circle dot. We detected a transiting planet with a radius of 3.47(-0.53)(+0.78)R(circle plus) and an orbital period of 10.134 days. We combined photometry, medium/high-resolution spectroscopy, adaptive optics/speckle imaging, and archival survey images to rule out any false-positive detection scenarios, validate the planet, and further characterize the system. The planet's radius is very unusual as M-dwarf field stars rarely have Neptune-sized transiting planets. The comparatively large radius of K2-95b is consistent with the other recently discovered cluster planets K2-25b (Hyades) and K2-33b (Upper Scorpius), indicating systematic differences in their evolutionary states or formation. These discoveries from K2 provide a snapshot of planet formation and evolution in cluster environments and thus make excellent laboratories to test differences between field-star and cluster planet populations.

Condensate clouds fundamentally impact the atmospheric structure and spectra of exoplanets and brown dwarfs, but the connections between surface gravity, cloud structure, dust in the upper atmosphere, and the red colors of some brown dwarfs remain poorly understood. Rotational modulations enable the study of different clouds in the same atmosphere, thereby providing a method to isolate the effects of clouds. Here, we present the discovery of high peak-to-peak amplitude (8%) rotational modulations in a low-gravity, extremely red (J-K-s = 2.55) L6 dwarf WISEP J004701.06+680352.1 (W0047). Using the Hubble Space Telescope (HST) time-resolved grism spectroscopy, we find a best-fit rotational period (13.20 +/- 0.14 hr) with a larger amplitude at 1.1 mu m than at 1.7 mu m. This is the third-largest near-infrared variability amplitude measured in a brown dwarf, demonstrating that large-amplitude variations are not limited to the L/T transition but are present in some extremely red L-type dwarfs. We report a tentative trend between the wavelength dependence of relative amplitude, possibly proxy for small dust grains lofted in the upper atmosphere, and the likelihood of large-amplitude variability. By assuming forsterite as a haze particle, we successfully explain the wavelength-dependent amplitude with submicron-sized haze particle sizes of around 0.4 mu m. W0047 links the earlier spectral and later spectral type brown dwarfs in which rotational modulations have been observed; the large amplitude variations in this object make this a benchmark brown dwarf for the study of cloud properties close to the L/T transition.

This dissertation presents the results of a study to (1) determine the census of the nearby southern M dwarf stellar population via three types of distances and (2) determine the multiplicity rate of nearby M dwarfs using two different search methodologies. The first part of this work reports three types of distance calculations (photographic, photometric, and trigonometric) for 1748 southern M dwarfs. Distances were estimated for 500 red dwarfs using photographic plate BRI magnitudes from SuperCOSMOS, while estimates were made for 667 stars using CCD VRI magnitudes. Both BRI and VRI were combined with 2MASS infrared JHK magnitudes. Distances for an additional 581 red dwarfs were derived from trigonometric parallaxes, 124 of which were measured for the first time during this work. For the second portion of this thesis, an all-sky sample of 1122 M dwarfs, known via trigonometric parallaxes to lie within 25 pc of the Sun, was surveyed for stellar companions at separations of 2" to 600". I-band images using primarily the CTIO/SMARTS 0.9m and the Lowell 42in telescopes were obtained in order to search these systems for companions at separations of 2" to 180". A complementary reconnaissance of wider companions to 600" was also done via blinking SuperCOSMOS BRI images. We find a stellar multiplicity fraction of 27.4 $\pm$ 1.3% for M dwarfs. Using this new gauge of M dwarf multiplicity near the end of the stellar main sequence, we calculate a multiplicity fraction of 30.1% for stellar systems of all types, implying that most systems are single. We find a peak in the separation distribution of the companions at 26 AU, i.e., distances on the scale of our Solar System, with a weak trend of smaller projected separations for lower mass primaries. A hint that M dwarf multiplicity may be a function of age/composition was revealed, with faster moving (and generally older) systems being multiple slightly less often. We calculate that at least 16% of M dwarf mass is made up of the stellar companions of multiple systems. Finally, we show that the mass function for M dwarfs increases to the end of the main sequence.

The aim of this dissertation is to address the topic of distinguishing very low mass stars from brown dwarfs through observational means. To that end, we seek to better characterize both populations and establish mechanisms that facilitate establishing an individual object's membership in either the very low mass star or the brown dwarf populations. The dissertation is composed of three separate observational studies. In the first study we report on our analysis of HST/NICMOS snapshot high resolution images of 255 stars in 201 systems within ~10 parsecs of the Sun. We establish magnitude and separation limits for which companions can be ruled out for each star in the sample, and then perform a comprehensive sensitivity and completeness analysis for the subsample of 138 M dwarfs in 126 systems. We calculate a multiplicity fraction of $0.0-0.0+3.5% for L companions to M dwarfs in the separation range of 5 to 70 AU, and $2.3-0.7+5.0% for L and T companions to M dwarfs in the separation range of 10 to 70 AU. Considering these results and results from several other studies, we argue that the so-called "brown dwarf desert" extends to binary systems with low mass primaries and is largely independent of primary mass, mass ratio, and separation. In the second study we construct a Hertzsprung-Russell diagram for the stellar/substellar boundary based on a sample of 63 objects ranging in spectral type from M6V to L4. We report new VRI photometry for 63 objects and new trigonometric parallaxes for 37 objects. We employ a novel SED fitting algorithm to determine effective temperatures, bolometric luminosities, and radii. We find evidence for the local minimum in the radius-temperature and radius-luminosity trends that may indicate the end of the stellar main sequence and the start of the brown dwarf sequence at $Teff ~2075K, log(L/Lsun) ~ -3.9, and (R/Rsun) ~ 0.086. The third study is a pilot study for future work and part of a long term search for astrometric binaries that have the potential to yield dynamical masses. We report the discovery of five new multiple systems and discuss their potential for determining dynamical masses: LHS 2071AB, GJ 1215 ABC, LTT 7434 AB, LHS 501 AC, and LHS 3738 AB.

We image 104 newly identified low-mass (mostly M-dwarf) pre-main sequence (PMS) members of nearby young moving groups (YMGs) with Magellan Adaptive Optics (MagAO) and identify 27 stellar binaries with instantaneous projected separation as small as 40 mas. Fifteen were previously unknown. The total number of multiple systems in this sample including spectroscopic and visual binaries from the literature is 36, giving a raw stellar multiplicity rate of at least 35(-4)(+5)% for this population. In the separation range of roughly 1-300 au in which infrared AO imaging is most sensitive, the raw multiplicity rate is at least 24(-4)(+5)% for binaries resolved by the MagAO infrared camera (Clio). The M-star subsample of 87 stars yields a raw multiplicity of at least 30(-4)(+5)% over all separations, 21(-4)(+5)% for secondary companions resolved by Clio from 1 to 300 au (23(-4)(+5)% for all known binaries in this separation range). A combined analysis with binaries discovered by the Search for Associations Containing Young stars shows that stellar multiplicity fraction as a function of mass over the range of 0.2 to 1.2M(circle dot) appears to be linearly flat, in contrast to the field, where multiplicity increases with mass. After bias corrections are applied, the multiplicity of low-mass YMG members (0.2-0.6M(circle dot)) is in excess of the field. The overall multiplicity fraction is also consistent with being constant in age and across YMGs, which suggests that multiplicity rates for this mass range are largely set by 10 Myr without appreciable evolution thereafter.

In this paper, we investigate the relation between disk mass and mass accretion rate to constrain the mechanism of angular momentum transport in protoplanetary disks. We find a correlation between dust disk mass and mass accretion rate in Chamaeleon I with a slope that is close to linear, similar to the one recently identified in Lupus. We investigate the effect of stellar mass and find that the intrinsic scatter around the best-fit M-dust-M star and M-acc-M star relations is uncorrelated. We simulate synthetic observations of an ensemble of evolving disks using a Monte Carlo approach and find that disks with a constant alpha viscosity can fit the observed relations between dust mass, mass accretion rate, and stellar mass but overpredict the strength of the correlation between disk mass and mass accretion rate when using standard initial conditions. We find two possible solutions. In the first one, the observed scatter in M-dust and M-acc is not primordial, but arises from additional physical processes or uncertainties in estimating the disk gas mass. Most likely grain growth and radial drift affect the observable dust mass, while variability on large timescales affects the mass accretion rates. In the second scenario, the observed scatter is primordial, but disks have not evolved substantially at the age of Lupus and Chamaeleon I owing to a low viscosity or a large initial disk radius. More accurate estimates of the disk mass and gas disk sizes in a large sample of protoplanetary disks, through either direct observations of the gas or spatially resolved multiwavelength observations of the dust with ALMA, are needed to discriminate between both scenarios or to constrain alternative angular momentum transport mechanisms such as MHD disk winds.

The K2 mission is targeting large numbers of nearby (d < 100 pc) GKM dwarfs selected from the SUPERBLINK proper motion survey (mu > 40 mas yr(-1), V < 20). Additionally, the mission is targeting low-mass, high proper motion stars associated with the local (d < 500 pc) Galactic halo population also selected from SUPERBLINK. K2 campaigns 0 through 8 monitored a total of 26,518 of these cool main-sequence stars. We used the auto-correlation function to search for fast rotators by identifying short-period photometric modulations in the K2 light curves. We identified 481 candidate fast rotators with rotation periods < 4 days that show light-curve modulations consistent with starspots. Their kinematics show low average transverse velocities, suggesting that they are part of the young disk population. A subset (13) of the fast rotators is found among those targets with colors and kinematics consistent with the local Galactic halo population and may represent stars spun up by tidal interactions in close binary systems. We further demonstrate that the M dwarf fast rotators selected from the K2 light curves are significantly more likely to have UV excess and discuss the potential of the K2 mission to identify new nearby young GKM dwarfs on the basis of their fast rotation rates. Finally, we discuss the possible use of local halo stars as fiducial, non-variable sources in the Kepler fields.