Exoplanet characterisation through transit timing variations
Keywords: transits
TTVs
Kepler
exoplanets
TESS

Transit Timing Variations (TTVs) arise in exoplanetary systems as a result of nonlinear perturbations from Keplerian orbits. Their presence provides a valuable tool for examining the characteristics and architectures of such systems and enable measurements of mass and eccentricity as well as the detection of new planets.
In this thesis, I start with the work presented in Kaye et al. (2022), taking an in-depth look at TOI- 270, a system of three transiting planets orbiting near 5:3 and 2:1 mean-motion resonances. Following an extensive observing campaign using 8 different space-based and ground-based observatories between 2018 and 2020, I report a clear detection of TTVs for planets c and d, with amplitudes of ∼10 minutes and a super-period of ∼3 years. When incorporating recently published constraints from radial velocity (RV) observations, we obtain precise masses and eccentricities for all three planets as well as significantly refine estimates of the radii and mean orbital periods of all three planets. Our findings imply an Earth-like rocky composition for the inner planet, and Earth-like cores with an additional He/H2O atmosphere for the outer two. TOI- 270 is now one of the best-constrained systems of small transiting planets, and it remains an excellent target for atmospheric characterisation.
After this in-depth look at TOI- 270, I then step out and take a broader look, presenting a catalogue of transiting exoplanetary systems discovered in Kepler or K2 data that were observed again by TESS (Kaye & Aigrain, paper in prep). I refine ephemerides and orbital parameters, as well as look for long-term non-linear trends in their transit times indicative of TTVs. In total, I reexamine 121 planets in 117 systems. Of these, 19 were known previously to show TTVs. I additionally find evidence for either periodic timing residuals or non-linear trends in the ephemerides of 24 systems for which variation was not previously detected. Of particular interest are Kepler-522 b, which shows TTVs of 20 minutes in amplitude, and K2-348, which contains of two Neptune-sized planets for which TESS data shows long-term second order trends. Many systems further experienced an improvement in their linear ephemerides by a factor of 2-10. I perform further analysis on a few of these interesting systems, fitting the TTVs of Kepler-522 b to reveal a potential non-transiting companion and assessing the limits of detecting tidal decay in several of Kepler and K2’s hot Jupiters.
I then present several case studies of systems in which TTV analysis complements the greater work of exoplanet discovery and characterisation. We start with a system of two transiting Neptune-sized planets around the bright, young M-dwarf AU Mic, presented in Zicher et al. (2022) and Wittrock et al. (2022). With data from a 1-year, intensive monitoring campaign of the system’s RV using 91 observations with the HARPS spectrograph, and use of a multidimensional Gaussian Process framework to model the stellar and planetary signals simultaneously, we arrived at mass estimates for both planets. I modeled TTVs for this system to show that these masses are consistent with the scatter in observed transit times and help guide future observations.
Finally, we discuss the role of TTVs in rounding out the discovery and validation of a two-planet system around a bright early G dwarf through the Planet Hunters TESS project (Eisner et al., 2021). Modelling of the transits combined with RV data from Nicholson et al. (in prep) yields periods for each planet that put them in 5:3 orbital resonance. Using the mass estimates from RV data I model TTVs and find reasonable agreement to the scatter seen in transit points. The potential to better characterise the system’s TTVs combined with the brightness of the host star and the strong likelihood of an extended H/He atmosphere on both planets, this system offers excellent prospects for atmospheric characterisation and comparative planetology.