Stellar variability and rotation in Kepler planetary transit search data

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.This thesis is not currently available in ORA