Companions to M-Dwarfs: Statistics and Habitability in New Dimensions

Abstract

Stellar binaries and their ubiquity have implications for a variety of astrophysics. Their configurations hold clues to the formation and dynamical histories of stars and planets. The most common type of binary systems may well be those consisting of M-dwarf stars, whose multiplicity statistics has traditionally been less well-constrained. Recent growing interest in exoplanets has mobilized bountiful observing resources to M-dwarfs, now deemed to be among the most favourable and accessible planet hosts. Using data originally intended for exoplanet studies, the first part of this thesis employs classical as well as novel techniques to characterize individual M-dwarf binaries systems and their ensemble statistics in a variety of unfamiliar regimes and environments. Very tight binaries can manifest as eclipsing systems in transiting planet surveys. Among the sample of field M-dwarf targets monitored by {\emph{Kepler}}, I detect 12 eclipsing binaries from light curve analysis. To translate these detections into a short-period binarity measurement for the M-dwarfs, I develop a variant of the exoplanet occurrence rate calculation formalism to define a ‘number of stars per star’ metric. The analysis implies that an M-dwarf has on average 0.11 M-dwarf companions within a 90-day orbit ($\sim 0.4$ AU). Finally, I derive a period distribution for the close binaries using parametric fits and non-parametric estimators. Adaptive optics imaging can visually resolve nearby binaries down to $\sim$few AU. From a survey of local young moving groups with the Magellan Adaptive Optics system that was originally intended to look for giant planets, I present the detection of 27 visual companions ($0\farcs04$ -- 4$\farcs$0: 1 -- 300 AU) to pre-main sequence K/M-dwarfs. I perform astrometric and photometric measurements, from which I determine the masses and physical separations of components in each system. I find the overall binarity rate for the M-dwarf subsample to be at least $30^{+5}_{-4}\%$. In concert with data from the literature, I compute the first multiplicity statistics that span M- to F-dwarfs in moving groups aged between 10 to 100 Myr. The results display no evidence of evolution during this age range, while the flat multiplicity rate with mass is in mild tension with the trend in the field. Gravitational microlensing using satellites in conjunction with ground-based surveys have enabled us to reliably measure properties of planets and stellar binaries across Galactic distances. I present the discovery of OGLE-2014-BLG-0962, a lensing event that was observed by both ground-based observatories and the {\emph{Spitzer}} satellite. Joint modelling measures a microlensing parallax and concludes that the lens system is a mid-M+M binary deep in the Galactic bulge. I compile a sample of similarly well-characterized events from the ongoing {\emph{Spitzer}} microlensing campaign. With this sample, I test Galactic models in the Bayesian framework that is commonly used to infer lens properties in the absence of parallax, validating their accuracy on the whole. Finally, I propose that space-based gravitational microlensing may be used to measure relative M-dwarf binary fractions across the Galaxy. With the realization that planets are on the whole abundant throughout the Galaxy, one naturally wonders whether some of them may also be home to biology. The prospect of finding extraterretrial life has spurred much discussion on what it means for a planet to be habitable, how to identify such alien worlds and to estimate their prevalence. To assess a given planet's potential to host life, many factors need to be considered, including the innate properties of the planet, its surroundings (the immediate as well as the broader environmental context), and its history. The second part of this thesis explores topics related to refining and applying several subtle points in the notion of habitability via theoretical as well as observational approaches. The dependence of planet demographics on the Galactic environment is one of the relevant unknowns in habitability considerations. By extending the scope of exoplanet science in the distance dimension, microlensing provides an avenue to investigate this variable. The {\emph{Spitzer}} campaign is a pathfinding mission intended to provide a preliminary assessment of the Galactic distribution of planets. In the aforementioned work, I also illustrate the methodology of studying the variation in planet occurrence frequency as a function of Galactic location using the {\emph{Spitzer}} sample, which at the time contained 4 planet systems and 8 binaries. I show that the distance distribution of this ensemble exhibits a significant excess halfway to the Galactic centre, though selection effects need to be better understood. As the campaign runs its course, new planet detections will enlarge the sample and enable a veritable planet occurrence analysis to confirm this tentative finding. Microlensing also expands the search space of exoplanets in orbital separation, being sensitive to planets around the snowline as well as those without host stars. As a technique, microlensing is uniquely capable of detecting free-floating planets and placing constraints on their population. This can help to inform planet formation theories and the prevalence of dynamical instability in planetary systems -- an important input in evaluating the longevity of habitability. I use data from K2's Campaign 9 to characterize two free-floating planet candidates, OGLE-2016-BLG-0813 and OGLE-2016-BLG-1231, using the principle of satellite microlensing. Preliminary analysis indicates that the objects are substellar, mostly likely isolated brown dwarfs. I describe the challenges of extracting robust K2 photometry from extremely crowded bulge fields, and issues that must be surmounted before the conclusions can be finalized. A planet's climate is in large part controlled by its orbital and rotational evolution. For example, the spin axial tilt, i.e., obliquity of a planet governs its seasons and atmospheric circulation patterns. If the obliquity angle also varies at large amplitudes over time, which can be caused by resonant interactions with other planets in the system, the long-term impact on climate stability can be destructive and severe. While observing the spin axis orientation of a planet is beyond current technological capabilities, its dynamics can be theoretically modelled given information on the system's orbital architecture. Here I study the spin axis dynamics of two habitable zone planets: Kepler-62f and Kepler-186f. Both are hosted by K/M-dwarf stars in multi-planet systems. I use numerical and analytical methods to characterize their obliquity variability in a large parameter space, including rotation period and the presence of moons. Assuming our current understandings of the systems are complete, I find that the two planets should have low obliquity variations except in fine-tuned conditions, such as at small ranges of high ($> 60^\circ$) obliquity values. However, even small deviations from coplanarity (e.g. mutual inclinations $\sim 3^\circ$) could trigger oscillations up to $\sim 20^\circ$ in peak-to-peak amplitude. Undetected planetary companions and/or the existence of a satellite could either stabilize or destabilize obliquities at a variety of values.