On the abundance of circumbinary planets
Circumbinary planets are bodies that orbit both components in a binary star system. This thesis focuses on transits of these planets, which with the aid of the Kepler space telescope have recently led to the discovery of several such objects. First, transit timing variations - departures from strict periodicity in the transit times - are studied. These arise from both the motion of the host stars and relatively rapid precession of the planet’s orbit. Limits on the maximum possible transit timing variation are derived, and tested against N-body simulations of simulated circumbinary systems. 
 
These limits are then utilised to form a search algorithm designed to find these planets in light curves, focusing on data from the WASP and Kepler observatories. This search algorithm uses an individual transit search to identify potential transit signatures, then forms periodograms allowing for the possible timing variations. It is used to identify several new candidate planets, as well as confirm detections of previously known circumbinary systems. In addition a number of interesting multiple stellar systems are identified including the as yet unexplained KIC2856960, which display multiple eclipses, significant tidal heating or rapid orbital evolution on the timescale of the 4 year Kepler observations. 
 
In 2013 unbiased stellar radii for the eclipsing binaries of the Kepler dataset were not available. A catalogue is produced, derived from spectral energy distribution fits to data from the KIS, HES and 2MASS surveys of the Kepler field, which gives temperatures for these stars accurate to⇠300K. These are then used to find calibrated stellar masses and radii. These parameters, in combination with the search algorithm, are used to study circumbinary planet rates of occurrence in the Kepler dataset. The known sample of eclipsing binaries is tested for detectability, and a Monte Carlo population synthesis used to find probability density functions for these rates. These are a function of the as yet unknown circumbinary planetary inclination distribution, and show that the rate of occurrence of circumbinary planets is consistent with that of single stars if these planets are in the majority coplanar with their host binaries. However, if they are more misaligned, to a degree greater than that implied by a 5# Gaussian distribution, their rate of occurrence becomes significantly higher. Furthermore, it is confirmed that planets of Jupiter size and greater occur less often in circumbinary configurations, and that circumbinary planets are preferentially found around binaries with periods longer than⇠7 days.