In the shadows of giants : a tomographic method for analysing the orbits of transiting exoplanets

The radial velocity anomaly which affects spectroscopic observations of stars undergoing transit by a companion body is known as the Rossiter-McLaughlin effect. This effect can be used to measure the obliquities of the orbits of transiting planets. In this thesis I present a tomographic method for analysing the effect, which manifests itself in stellar spectral line-profiles. I implement this method on seven systems known to host transiting planets, and some systems with early-type host stars, for which the transit events have not yet been shown to be the result of planetary companions. Despite being well-suited to examining systems with early-type, rapidly-rotating host stars which have a more pronounced Rossiter-McLaughlin effect, I find the tomographic method is able to produce reasonable results for the system parameters of planets orbiting relatively slowly-rotating stars. I show that the method provides a significant increase in the accuracy of determinations of the stellar rotation rate and is able to better constrain values for the transit impact parameter. Though I do not confirm the existence of any new planets around early-type stars, I do use the tomographic method to reject one candidate as a stellar eclipsing binary system, and also reveal that one of the candidate host stars is a non-radial pulsator. I show that the method is able to examine systems involving stars with a range of spectral types and rotation rates