The recent space-based exoplanet transit searches, CoRoT and Kepler, have revolutionised the field of stellar variability. In this thesis I exploit the public Kepler data to characterise stellar variability, and study rotation periods. For the study of stellar variability it is a complicated but necessary process to remove instrumental systematics while maintaining intrinsic stellar signal. I was involved in the development of a new correction method for systematics, denoted ARC (Astrophysically Robust Correction). This method relies on the removal of a set of basis functions that are determined to be present in small amounts across many light curves. Using the first month of Kepler data, corrected with the ARC method, I studied the variability properties of main sequence stars as a function of fundamental stellar parameters. I find that the fraction of stars with variability greater than that of the Sun is 60%, and confirm the trend of increasing variability with decreasing effective temperatures. I show tentative evidence that the more active stars have lower proper motions and may be located closer to the galactic plane. I also investigate the frequency content of the variability, showing that there exist significant differences in the nature of variability between spectral types, with a trend towards longer periods at later spectral types. In order to exploit the full potential of the Kepler data for stellar rotation period measurement, I developed a novel method of period detection for use on star spot modulated light curves. Standard approaches to period detection are based on Fourier decomposition or least-squares fitting of sinusoidal models. However, typical stellar light curves are neither sinusoidal nor strictly periodic. Therefore, I developed an algorithm for period detection based on the autocorrelation function (ACF) of the light curve. Because the ACF measures only the degree of self-similarity of the light curve at a given time lag, the period remains detectable even when the amplitude and phase of the photometric modulation evolve significantly. I applied the ACF method for the sample of M-dwarfs observed during the first 10 months of the Kepler mission, and detected rotation periods in 1570, ranging from 0.37-69.7 days. The rotation period distribution is clearly bimodal, with peaks at ~19 and ~33 days, hinting at two distinct waves of star formation. These two peaks form two distinct sequences in period-temperature space, with the period decreasing with increasing temperature. In a natural continuation to this work I applied measured periods for 1000 stars in each of the F, G and K-dwarf sets observed by Kepler, and combined these with the M-dwarf results. The trend of increasing rotation period with increasing mass is clear throughout, as the observations fall along a wide by distinct sequence. Comparison to the rotational isochrones of Barnes (2007) show an overall agreement, although the dataset, which I believe is the largest set of rotation period measurements for main sequence stars, shows addition detail, not captured by the gyrochronology relations. This includes a dip in the rotation period distribution at ~0.6 M⊙ and a steep increase in period for the M-dwarfs. I also applied the ACF method to the Kepler exoplanet candidate host stars and used the results to search for evidence of tidal interaction between the star and planet. I show that for the majority of exoplanet host stars, spin-orbit interaction will not have affected the stellar rotation period, permitting the application of gyrochronology for age determination. A comparison of the host stars with a sample of field stars selected to match their temperature and magnitude distribution also indicates no significant difference in the period or amplitude distributions of the two sets. The only notable variation is the lack of planets around the very fast rotators across all spectral types.

During the last decade, the transit method has evolved to one of the most promising techniques in the search for extrasolar planets and the quest to find other earth-like worlds. In theory, the transit method is straight forward being based on the detection of an apparent dimming of the host star’s light due to an orbiting planet traversing in front of the observer. However, in practice, the detection of such light curve dips and their confident ascription to a planetary transit is heavily burdened by the presence of different sources of noise, the most prominent of which is probably the so called intrinsic stellar variability. Filtering out potential transit signals from background noise requires a well adjusted high-pass filter. In order to optimize such a filter, i.e. to achieve best separation between signal and noise, one typically requires access to benchmark datasets that exhibit the same light curve with and without obstructing noise. Several methods for simulating stellar variability have been proposed for the construction of such benchmark datasets. However, while such methods have been widely used in testing transit method detection algorithms in the past, it is not very well known how such simulations compare to real recorded light curves - a fact that might be contributed to the lack of large databases of stellar light curves for comparisons at that time. With the increasing amount of light curve data now available due to missions such as Kepler, I have here undertaken such a comparison of synthetic and real light curves for one particular method that simulates stellar variability based on scaled power spectra of the Sun’s flux variations. Conducting the respective comparison also in terms of estimated power spectra of real and simulated light curves, I have revealed that the two datasets exhibit substantial differences in average power, with the synthetic power spectra having generally a lower power and also lacking certain distinct power peaks present in the real light curves. The results of this study suggest that scaled power spectra of solar variability alone might be insufficient for light curve simulations and that more work will be required to understand the origin and relevance of the observed power peaks in order to improve on such light curve models.

A broad near-infrared photometric survey is conducted of 1678 stars in the direction of the $\rho$ Ophiuchi ($\rho$ Oph) star forming region using data from the 2MASS Calibration Database. The survey involves up to 1584 photometric measurements in the \emph{J}, \emph{H} and \emph{K$_{s}$} bands with an $\sim$1 day cadence spanning 2.5 years. Identified are 101 variable stars with $\Delta$\emph{K$_{s}$} band amplitudes from 0.044 to 2.31 mag and $\Delta$(\emph{J}-\emph{K$_{s}$}) color amplitudes ranging from 0.053 to 1.47 mag. Of the 72 $\rho$ Oph star cluster members, 79$\%$ are variable; in addition, 22 variable stars are identified as candidate members. The variability is categorized as periodic, long timescale, or irregular based on the \emph{K$_{s}$} time series morphology. The dominant variability mechanisms are assigned based on the correlation between the stellar color and single band variability. Periodic signals are found in 32 variable stars with periods between 0.49 to 92 days. The most common variability mechanism among these stars is rotational modulation of cool starspots. Periodic eclipse-like variability is identified in 6 stars with periods ranging from 3 to 8 days; in these cases the variability mechanism may be warped circumstellar material driven by a hot proto-Jupiter. Aperiodic, long time scale variability is identified in 31 stars with time series ranging from 64 to 790 days. The variability mechanism is split evenly between either variable extinction or mass accretion. The remaining 40 stars exhibit sporadic, aperiodic variability with no discernible time scale or variability mechanism. Interferometric images of the active giant $\lambda$ Andromedae ($\lambda$ And) were obtained for 27 epochs spanning November. 2007 to September, 2011. The \emph{H} band angular diameter and limb darkening coefficient of $\lambda$ And are 2.777 $\pm$ 0.027 mas and 0.241 $\pm$ 0.014, respectively. Starspot properties are extracted via a parametric model and an image reconstruction program. High fidelity images are obtained from the 2009, 2010, and 2011 data sets. Stellar rotation, consistent with the photometrically determined period, is traced via starspot motion in 2010 and 2011. The orientation of $\lambda$ And is fully characterized with a sky position angle and inclination angle of 23$\degree$ and 78$\degree$, respectively.

M dwarfs have been the subject of renewed interest as potential habitable planet hosts and have increasingly become the targets of planet detection surveys. Currently, however, the number of detections of transiting M dwarf planets remain low. The characterisation of M dwarf activity is an important consideration for such surveys, and provides constraints on the modelling of magnetically active low mass stars. Currently the spottedness of M dwarfs is not well understood owing to their intrinsic faintness and the lack of diagnostics for assessing starspot morphologies and distributions. The WFCAM Transit Survey (WTS) contains long term observations of M dwarfs in the near infra-red and presents an opportunity to study the long term variability of M dwarfs. The M dwarfs in the WTS are identified by use of colour-spectral type relations, and the periodically variable M dwarfs in the sample are detected using a Lomb-Scargle periodogram analysis. A total of 72 periodically variable M dwarfs are found with periods ranging from 0.16 to 90.33 days. The relations between the spectral subtypes, amplitudes and periods are studied and comparisons to earlier works studying M dwarf rotation are made. A number of examples of significant spot evolution are found, which exhibit complex light curve morphologies that vary in form and amplitude over periods of months to years. This provides an indication as to the nature of the spottedness of these stars. Simulations are performed to probe the connection between spot coverage, temperature and light curve amplitude. Using the results from these simulations, the spot coverage fractions of the WTS M dwarfs are estimated and they are found to be heavily spotted. Dynamic models with spots evolving at various average rates are used to explore how spot evolution can drive increased dispersion in the light curves, and to what extent this affects the detectability of periodicity by the method used. It is found that spot evolution can invoke significant noise in an M dwarf light curve, and in combination with photon noise, can in some instances inhibit the detection of a period. In reflection of the results, the relation between the light curve dispersion and spot coverage of the WTS M dwarfs is considered and it is found that more heavily spotted M dwarfs have intrinsically noisier light curves. The morphologies of the light curves produced by the simulations, and the manner in which they evolve, are qualitatively similar to the real M dwarfs in the WTS sample and indicate how models extrapolated from sunspot distributions can explain behaviour seen in active M dwarf light curves.