The aim of this thesis is to use a cross-match between WISE, 2MASS and SDSS to identify a large sample of M dwarfs. Through the careful characterisation and quality control of these M dwarfs I aim to identify rare systems (i.e. unresolved UCD companions, young M dwarfs, late M dwarfs and M dwarfs with common proper motion companions). Locating ultracool companions to M dwarfs is important for constraining low-mass formation models, the measurement of substellar dynamical masses and radii, and for testing ultracool evolutionary models. This is done by using an optimised method for identifying M dwarfs which may have unresolved ultracool companions. To do this I construct a catalogue of 440 694 M dwarf candidates, from WISE, 2MASS and SDSS, based on optical- and near-infrared colours and reduced proper motion. With strict reddening, photometric and quality constraints I isolate a sub-sample of 36 898 M dwarfs and search for possible mid-infrared M dwarf + ultracool dwarf candidates by comparing M dwarfs which have similar optical/near-infrared colours (chosen for their sensitivity to effective temperature and metallicity). I present 1 082 M dwarf + ultracool dwarf candidates for follow-up. Using simulated ultracool dwarf companions to M dwarfs, I estimate that the occurrence of unresolved ultracool companions amongst my M dwarf + ultracool dwarf candidates should be at least four times the average for my full M dwarf catalogue. I discuss yields of candidates based on my simulations. The possible contamination and bias from misidentified M dwarfs is then discussed, from chance alignments with other M dwarfs and UCDs, from chance alignments with giant stars, from chance alignments with galaxies, and from blended systems (via visual inspection). I then use optical spectra from LAMOST to spectral type a subset of my M dwarf + ultracool dwarf candidates. These candidates need confirming as true M dwarf + ultracool dwarf systems thus I present a new method I developed to use low resolution near-infrared spectra which relies on two colour similar objects (one an excess candidate, one not) having very similar spectra. A spectral difference of these two colour similar objects should leave the signature of a UCD in the residual of their differences, which I look for using the difference in two spectral bands designed to identify UCD spectral features. I then present the methods used to identify other rare systems from my full M dwarf catalogue. Young M dwarfs were identified by measuring equivalent widths of Hα from the LAMOST spectra, and by measuring rotation periods from Kepler 2 light curves. I identify late M dwarfs photometrically (using reduced proper motion and colour cuts) and spectroscopically (using the LAMOST spectra with spectral indices from the literature). Also I present common proper motion analysis aimed at finding Tycho-2 primaries for my M dwarfs and look for physically separated M dwarf + M dwarf pairs (internally within my full M dwarf catalogue).

A number of substellar companions to evolved cool stars have now been reported. Cool giants are distinct from their progenitor main-sequence low-mass stars in a number of ways. First, the mass loss rates of cool giant stars are orders of magnitude greater than for the late-type main-sequence stars. Secondly, on the cool side of the Linsky–Haisch ‘dividing line’, K and M giant stars are not X-ray sources, although they do show evidence for chromospheres. As a result, cool star winds are largely neutral for those spectral types, suggesting that planetary or brown dwarf magnetospheres will not be effective in standing off the stellar wind. In this case, one expects the formation of a bow shock morphology at the companion, deep inside its magnetosphere. We explore radio emissions from substellar companions to giant stars using (a) the radiometric Bode's law and (b) a model for a bow shock morphology. Stars that are X-ray emitters likely have fully ionized winds, and the radio emission can be at the milli-Jansky level in favourable conditions. Non-coronal giant stars produce only micro-Jansky level emissions when adjusted for low-level ionizations. If the largely neutral flow penetrates the magnetosphere, a bow shock results that can be strong enough to ionize hydrogen. The incoherent cyclotron emission is sub-micro-Jansky. However, the long wavelength radio emission of Solar system objects is dominated by the cyclotron maser instability (CMI) mechanism. Our study leads to the following two observational prospects. First, for coronal giant stars that have ionized winds, application of the radiometic Bode's law indicates that long wavelength emission from substellar companions to giant stars may be detectable or nearly detectable with existing facilities. Secondly, for the non-coronal giant stars that have neutral winds, the resultant bow shock may act as a ‘feeder’ of electrons that is well embedded in the companion's magnetosphere. Incoherent cyclotron emissions are far too faint to be detectable, even with next generation facilities; however, much brighter flux densities may be achievable when CMI is considered.