Stellar ages and stellar rotation
Keywords: Gaussian processes
Star spots
Kepler
Probabilistic
Stellar ages
Bayesian
Statistics
Signal processing
Stars
Stellar rotation
Flicker
Exoplanets

Stellar ages will play a big role in the next generation of astronomy. Useful to exoplaneteers and galactic archaeologists alike, this relatively under-exploited stellar property is currently limited by the precision of dating techniques. The work presented in this thesis contributes incrementally to a greater understanding of rotation period decay in Main Sequence (MS) stars as a proxy for stellar age. Inferring stellar ages from rotation periods, 'gyrochronology', is the only dating method with the potential to provide ages for stars on the hundreds-of-thousands scale. Unfortunately however, it suffers from being poorly calibrated as the sample of cool, MS stars with precise ages is extremely sparse. Using light curves of spotted, rotating, MS, FGK stars with asteroseismic ages from the Kepler spacecraft, I attempted to recalibrate the relation between rotation period, colour and age. I demonstrate that the simple, 'straight line' gyrochronology relations used in the past are unable to explain the new asteroseismic sample. Questions are raised about the power of gyrochronology---does it accurately predict ages for old stars? To fully answer this question, it will be necessary to exploit new data from the K2 (the repurposed Kepler mission). K2 has observed (and is still observing) several open clusters and asteroseismic field stars which may provide new insight into stellar rotational evolution. Unfortunately, systematic features in K2 light curves produced by Kepler's reduced pointing precision inhibit the detection of astrophysical signals in the data. These systematic features can be removed by modelling and subtracting them from the time series, 'detrending', but this process can remove some signals and can even inject noise. For this reason I developed a method for detecting periodic signals in K2 light curves without detrending: the Systematics-Insensitive Periodogram (SIP). This method is particularly useful for red giant asteroseismology. Precise ages can be inferred for oscillating red giants using the SIP and will be useful for galactic archaeology and open cluster age inference. In the next chapter of this thesis I return to the problem of stellar rotation period inference. Current methods for rotation period inference can produce inaccurate, imprecise periods with poorly approximated uncertainties and often without uncertainties altogether. I present a new method for inferring precise, accurate, probabilistic rotation periods with accurate uncertainties using Gaussian processes.
Although expensive to compute, this method is ideal for applying to individual targets. I hope to continue to develop this method and apply it to a large ensemble light curves from Kepler and other photometric surveys in the future. Star spots and acoustic (p-mode) oscillations are not the only mechanisms that produce variability in dwarfs and giants. A combination of asteroseismic pulsations and granulation on the stellar surface produces variability on short timescales. It has been shown that the amplitude of this short-term variability, called 'flicker' is strongly correlated with both surface gravity and stellar density (Bastien et al., 2013, Bastien et al., 2016, Kipping et al., 2014). However, there is substantial additional scatter in these relations that is not accounted for by the observational uncertainties. I provide a new calibration of these relations which models this level of additional, astrophysical variance using hierarchical probabilistic inference. In the final chapter of this thesis I explore rotation period recovery with the Large Synoptic Survey Telescope (LSST). With its ten year baseline, LSST light curves will be sensitive to long rotation periods which are characteristic of old and low-mass stars. If the rotation periods of such stars can be measured from LSST light curves, it may be possible to improve the gyrochronology relations. We find that LSST is most sensitive to rotation periods between 10 and 20 days. Its sensitivity falls at short periods due to the sparsity of its sampling and at longer periods due to the lower amplitudes of variability and smaller apparent magnitudes of slow rotators.