We have followed up the three Y0 dwarfs WISEPA J041022.71+150248.5, WISEPA J173835.53+273258.9 and WISEPC J205628.90+145953.3 using the United Kingdom Infrared Telescope Wide Field Camera. We find parallaxes that are more consistent and accurate than previously published values. We estimate absolute magnitudes in photometric passbands from Y to W3 and find them to be consistent between the three Y0 dwarfs indicating that the inherent cosmic absolute magnitude spread of these objects is small. We examine the Mauna Kea Observatory system J magnitudes over the 4 yr time line and find small but significant monotonic variations. Finally, we estimate physical parameters from a comparison of spectra and parallax to equilibrium and non-equilibrium models finding values consistent with solar metallicity, an effective temperature of 450-475 K and log g of 4.0-4.5.

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In this thesis I present the spectroscopic analysis of a large sample of L and T dwarfs, in order to constrain the sub-stellar initial mass function and formation history. The main points I tried to address are the development of a better spectral type to distance calibration and of a better spectral type to effective temperature calibration, and the identification of a statistically complete sample of brown dwarf to be used to measure the luminosity function, and therefore to constrain the initial mass function and formation history. To achieve the first goal I conducted the spectroscopic follow-up of brown dwarfs from the PARallaxes of Southern Extremely Cool objects (PARSEC) program. This is a large astrometric campaign to measure the parallaxes and proper motions of 120 L and T dwarfs in the southern hemisphere. I combined the astrometric results with the near infra-red spectra I obtained using the Ohio State Infra-Red Imager/Spectrometer (OSIRIS) on the Southern Astrophysical Research telescope (SOAR). That allowed me to investigate the nature of some unresolved binaries and common proper motion companion in the sample, as well as sub-dwarfs candidates, and potential members of young moving groups. Combining the spectra with the astrometric information and the available photometry I derived the bolometric luminosity and effective temperature for the targets, and determined a new polynomial conversion between spectral type and effective temperature of a brown dwarfs. This is a fundamental step to compare the results of empirical observations to numerical simulations of the sub-stellar luminosity function. Once refined the type to temperature calibration, I measured the luminosity function. In order to do so my collaborators and I have selected a sample of 250 brown dwarfs candidates from the United Kingdom Deep Infra-red Sky Survey (UKIDSS) Large Area Survey (LAS) and followed them up with the echelle spectrograph X-shooter on the Very Large Telescope. I present in this thesis the results of the observations of 196 of the brown dwarfs candidates. Using the X-shooter spectra I determined their spectral types, and I identified a number of unresolved binary candidates and peculiar objects. One of the peculiar objects in the sample, ULAS J222711 004547, turned out to be the reddest brown dwarf observed so far, and I therefore proceeded to analyse further its spectrum. Applying a de-reddening technique to its spectrum suggests that the most likely reason for its redness is an excess of dust in its photosphere, and that can account for the differences seen between objects of similar spectral type. By comparing the results of the spectroscopic campaign to numerical simulations, I found that it is currently impossible to constrain robustly the initial mass function and formation history of sub-stellar objects, because of our limited knowledge of the binary fraction among brown dwarfs. The sample of binary candidates identified in this thesis can be used to place a better constraint on the binary fraction, but in order to do that the candidates need to be followed-up via high resolution imaging or radial velocity monitoring to confirm their binary nature.

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.

I present the development of two near infrared proper motion pipelines for high resolution near infrared data from UKIDSS and the VISTA VVV survey. The UKIDSS pipeline is capable of accuracies of order 5-10 mas yr⁻¹ for bright sources with the largest epoch baselines (~ 8 years). The VVV pipeline reaches 1-2 mas yr⁻¹ proper motion precision at the bright end and parallax measurements at ~ 1 mas precision. It will be possible to improve upon the VVV astrometric precision due to increases in data volume and further pipeline development. I have used the proper motion pipelines to generate three near infrared proper motion catalogues of the UKIDSS LAS and GPS and the VVV survey. The LAS proper motion catalogue covers 1500 deg2 at high Galactic latitudes and contains approximately 15 million sources with two J band epochs. The GPS proper motion catalogue covers 1500 deg2 of the northern Galactic plane and contains approximately 400 million sources with two K band epochs. The VVV proper motion catalogue covers 560 deg2 of the Galactic bulge and disc and contains approximately 200 million sources with between 50 and 150 Ks band epochs. I have also produced a preliminary 5σ parallax catalogue containing 3403 VVV sources. The LAS and GPS proper motion catalogues have been used by myself and other authors to identify and study many new examples of high proper motion stars, brown dwarfs, ul-tracool dwarf benchmark candidates, cool white dwarfs, substellar subdwarfs and nearby sources within < 25 pc. These catalogues remain far from fully exploited and will be a useful resource for future research by the astronomical community. Exploitation of the VVV proper motion catalogue is still in its infancy, yet it has already generated large numbers of new high proper motion sources. These include new brown dwarf candi-dates, important benchmark objects, and nearby sources which have previously avoided detection. Parallax results from the VVV pipeline will be useful to improve low mass star/ultracool dwarf luminosity functions, significantly increasing the numbers of brown dwarfs with known parallaxes and illustrates how general purpose multi-epoch wide area surveys can generate parallaxes. Finally, I discuss the long term usefulness of such catalogues in the Gaia era and how they might be exploited in the future.