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A set of twenty late-type (K5-M5) stars were observed with the Herschel Space Observatory at 100 and 160 microns with the goal of searching for far-infrared excesses indicative of the presence of circumstellar disks. Out of this sample, four stars (TYC 7443-1102-1, TYC 9340-437-1, GJ 784 and GJ 707) have infrared excesses above their stellar photospheres at either 100 or 160 m or both. At 100 microns TYC 9340-437-1 is spatially resolved with a shape that suggests it is surrounded by a face-on disk. The 100 m excess flux associated with GJ 707 is marginal at around 3 . The excess flux associated with GJ 784 is most likely due to a background galaxy as the dust radius estimated from the spectral energy fit implies that any associated dust disk should have been resolved in the Herschel images but is not. TYC 7443-1102-1 has been observed with ALMA which resolves the emission at its location into two distinct sources making the Herschel excess most likely also due to a background galaxy. It is worth noting that this star is in the 23 Myr old β Pic association. With a disk luminosity on the order of 10−3 L*, this system is an ideal follow-up target for high-contrast imaging and ALMA.

Debris discs are an essential piece of planetary system architecture. These exo-asteroid belts and exo-Kuiper belts of stellar systems both comprise that which did not form into planets and are often indelibly marked by that which did. Observing and understanding them is necessary to understanding planetary systems as a whole. M-dwarf debris discs are one of the largest current unknowns within debris disc science. Past surveys have found vanishingly small, if not empty, detection rates among field populations. Only eight discs are currently published in the literature, only four have been resolved, and only the disc of AU Mic has been resolved both thermally and in scattered light. Whether or not M-dwarf discs are significantly less common than the discs of earlier types, or are significantly different in dust properties and planetesimal belt morphology to the discs of earlier types, are unresolved questions. In this thesis I present new resolved ALMA images of two M-dwarf debris discs never before observed at mm-wavelengths or thermally resolved. I also present the first ALMA survey searching for M-dwarf debris discs, identifying two new M-dwarf debris discs and presenting excellent opportunities for follow-up observation. I analyse the newly mm-resolved Fomalhaut C debris disc, now the latest type star to have a resolved debris disc, and find the ring to have a 880 μm flux of 0.9±0.1 mJy, a radius of 26.4±0.6 AU and a narrow full width at half maximum of at most 4.2 AU. I find a 3σ upper limit on the eccentricity of 0.14, neither confirming nor ruling out previous dynamical interactions with Fomalhaut A. Finally, I find that its radius is as expected from previous disc radius–host luminosity trends. I also analyse the newly mm-resolved GSC 07396-00759 debris disc, now the second Mdwarf star to be resolved both thermally and in scattered light, and find the ring to have a 880 μm flux of 1.84±0.22 mJy and a radius of 70.2±4.4 AU. I confirm the total intensity scattered light radius found by Sissa et al. [2018], which is significantly smaller than the radius derived from the polarimetric scattered light observations of Adam et al. [2021], implying complex behaviour in the scattering phase function. I do not recover the brightness asymmetry found in scattered light observations, nor evidence of an extended halo of dust grains, implying that these features observed in scattered light must be limited to the small grain dust and are likely the result of pressure forces acting on the disc, such as stellar wind pressure and interaction with the interstellar medium. Finally, I analyse ALMA observations of 33 M-dwarf systems in the β Pictoris Moving Group, the first such survey conducted with ALMA. I detect two sub-mm excesses that likely constitute new M-dwarf debris discs around GJ 2006 A and AT Mic A and model distributions of the disc fractional luminosities and temperatures. From the science sample of 36 M-dwarfs including AU Mic I find a disc detection rate of 4/36 or 11.1+7.4 -3.3% that rises to 23.1+8.3 -5.3% when adjusted for completeness and conclude that this detection rate is consistent with the detection rate of discs around G and K type stars and that M-dwarf discs are not less likely to host debris discs, but instead require longer wavelength and higher sensitivity observations than have previously been employed.

We present new ALMA Band 7 observations of the edge-on debris disc around the M1V star GSC 07396-00759. At ~20 Myr old and in the beta Pictoris Moving Group along with AU Mic, GSC 07396-00759 joins it in the handful of low mass M-dwarf discs to be resolved in the sub-mm. With previous VLT/SPHERE scattered light observations we present a multi-wavelength view of the dust distribution within the system under the effects of stellar wind forces. We find the mm dust grains to be well described by a Gaussian torus at 70 au with a FWHM of 48 au and we do not detect the presence of CO in the system. Our ALMA model radius is significantly smaller than the radius derived from polarimetric scattered light observations, implying complex behaviour in the scattering phase function. The brightness asymmetry in the disc observed in scattered light is not recovered in the ALMA observations, implying that the physical mechanism only affects smaller grain sizes. High resolution follow-up observations of the system would allow investigation into its unique dust features as well as provide a true coeval comparison for its smaller sibling AU Mic, singularly well observed amongst M-dwarfs systems.

Previous surveys in the far-infrared have found very few, if any, M-dwarf debris discs among their samples. It has been questioned whether M-dwarf discs are simply less common than earlier types, or whether the low detection rate derives from the wavelengths and sensitivities available to those studies. The highly sensitive, long wavelength Atacama Large Millimetre/submillimetre Array can shed light on the problem. This paper presents a survey of M-dwarf stars in the young and nearby Beta Pictoris Moving Group with ALMA at Band 7 (880\\,\\(\\mu\\)m). From the observational sample we detect two new sub-mm excesses that likely constitute unresolved debris discs around GJ\\,2006\\,A and AT\\,Mic\\,A and model distributions of the disc fractional luminosities and temperatures. From the science sample of 36 M-dwarfs including AU\\,Mic we find a disc detection rate of 4/36 or 11.1\\(^{+7.4}_{-3.3}\\)\\% that rises to 23.1\\(^{+8.3}_{-5.5}\\)\\% when adjusted for completeness. We conclude that this detection rate is consistent with the detection rate of discs around G and K type stars and that the disc properties are also likely consistent with earlier type stars. We additionally conclude that M-dwarf stars are not less likely to host debris discs, but instead their detection requires longer wavelength and higher sensitivity observations than have previously been employed.

A set of twenty late-type (K5-M5) stars were observed with the Herschel Space Observatory at 100 and 160 microns with the goal of searching for far-infrared excesses indicative of the presence of circumstellar disks. Out of this sample, four stars (TYC 7443-1102-1, TYC 9340-437-1, GJ 784 and GJ 707) have infrared excesses above their stellar photospheres at either 100 or 160 micron or both. At 100 microns TYC 9340-437-1 is spatially resolved with a shape that suggests it is surrounded by a face-on disk. The 100 micron excess flux associated with GJ 707 is marginal at around 3sigma. The excess flux associated with GJ 784 is most likely due to a background galaxy as the dust radius estimated from the spectral energy fit implies that any associated dust disk should have been resolved in the Herschel images but is not. TYC 7443-1102-1 has been observed with ALMA which resolves the emission at its location into two distinct sources making the Herschel excess most likely also due to a background galaxy. It is worth noting that this star is in the 23 Myr old beta Pic association. With a disk luminosity on the order of 10^-3 L*, this system is an ideal follow-up target for high-contrast imaging and ALMA.

Fomalhaut C (LP 876-10) is a low mass M4V star in the intriguing Fomalhaut triple system and, like Fomalhaut A, possesses a debris disc. It is one of very few nearby M-dwarfs known to host a debris disc and of these has by far the lowest stellar mass. We present new resolved observations of the debris disc around Fomalhaut C with the Atacama Large Millimetre Array which allow us to model its properties and investigate the system's unique history. The ring has a radius of 26 au and a narrow full width at half maximum of at most 4.2 au. We find a 3\\(\\sigma\\) upper limit on the eccentricity of 0.14, neither confirming nor ruling out previous dynamic interactions with Fomalhaut A that could have affected Fomalhaut C's disc. We detect no \\(^{12}\\)CO J=3-2 emission in the system and do not detect the disc in scattered light with HST/STIS or VLT/SPHERE. We find the original Herschel detection to be consistent with our ALMA model's radial size. We place the disc in the context of the wider debris disc population and find that its radius is as expected from previous disc radius-host luminosity trends. Higher signal-to-noise observations of the system would be required to further constrain the disc properties and provide further insight to the history of the Fomalhaut triple system as a whole.