Transit timing analysis of the hot Jupiters WASP-43b and WASP-46b and the super Earth GJ1214b Mathias Polfliet Promotors: Michaël Gillon, Maarten Baes 1 Abstract Transit timing analysis is proving to be a promising method to detect new planetary partners in systems which already have known transiting planets, particularly in the orbital resonances of the system. In these resonances we might be able to detect Earth-mass objects well below the current detection and even theoretical (due to stellar variability) thresholds of the radial velocity method. We present four new transits for WASP-46b, four new transits for WASP-43b and eight new transits for GJ1214b observed with the robotic telescope TRAPPIST located at ESO La Silla Observatory, Chile. Modelling the data was done using several Markov Chain Monte Carlo (MCMC) simulations of the new transits with old data and a collection of transit timings for GJ1214b from published papers. For the hot Jupiters this lead to a general increase in accuracy for the physical parameters of the system (for the mass and period we found: 2.034±0.052 MJup and 0.81347460±0.00000048 days and 2.03±0.13 MJup and 1.4303723±0.0000011 days for WASP-43b and WASP-46b respectively). For GJ1214b this was not the case given the limited photometric precision of TRAPPIST. The additional timings however allowed us to constrain the period to 1.580404695±0.000000084 days and the RMS of the TTVs to 16 seconds. We investigated given systems for Transit Timing Variations (TTVs) and variations in the other transit parameters and found no significant (3sv) deviations. Based on the RMS of the TTVs we designed a tool using the MERCURY package. In doing so we were able to exclude super-Earth massed planets in the resonances for the hot Jupiters, WASP-43b and WASP-46b and down to a tenth of an Earth mass for GJ1214b. 2 If I have seen further it is by standing on the shoulders of giants 3 Acknowledgments I would like to thank the university of Ghent and Maarten Baes to make this thesis possible and for the provided education over the past few years. My gratitude goes out to the university of Liège and the people working there for their hospitality. I wish to thank Sandrine Sohy for her help regarding all sorts of computational issues and Brice-Olivier Demory for the helpful discussions about TTVs and the development of my program. Most of all I would like to thank Michaël Gillon for his continuous support and help during the course of this thesis and his readiness to aid me when I required it. 4 Contents 1 Other Worlds 6 1.1 Radial velocity............................................6 1.2 Transiting exoplanets........................................ 12 1.3 Exoplanets: The global picture.................................. 18 2 Transit Timing Variations 21 2.1 Introduction............................................. 21 2.2 Inner planet............................................. 22 2.3 Non-resonant outer planet..................................... 23 2.4 Resonant planet........................................... 24 2.5 Analytic approach.......................................... 24 2.6 Exomoon............................................... 26 2.7 Other TTV signals.......................................... 27 3 Observations and data reduction 29 3.1 Data description........................................... 29 3.2 Data analysis............................................. 29 3.3 TTV simulator............................................ 34 4 Results and discussion 36 4.1 WASP-43b.............................................. 36 4.2 WASP-46b.............................................. 42 4.3 GJ1214b................................................ 47 5 Conclusion 54 5 Introduction In this work, we will use our extensive data sets to determine precisely the parameters of the transiting systems WASP-43, WASP-46 and GJ1214. We will compare our results to the ones presented in these system’s discovery papers Hellier et al.[2011], Anderson et al.[2012] and Charbonneau et al.[2009]. Additionally, we will investigate the given exoplanets further to reveal possible planetary partners us- ing the method of Transit Timing Variations (TTVs). TTVs are a promising method to detect planets down to several Earth masses for systems which already have known transiting planets, particularly in the orbital resonances of the system. We look for deviations in the transit timings that would be caused by an additional body orbiting the star. To achieve this we have created a program using the MERCURY package. The program is designed to exclude possible partners based on the RMS of the signal we find using the Markov Chain Monte Carlo simulations. Observations are made primarily by the TRAPPIST telescope. We present four new transits for WASP-46b, four new transits for WASP-43b and eight new transits for GJ1214b. in chapter 1, I will give an overview of the exoplanet findings and of the com- plementarity of the so-called transit and RV methods for studying exoplanets in details. In chapter 2 I describe the TTV method. The method we use to reduce, analyze and interpret the data are presented in chapter 3. Eventually we will present our results in chapter 4 and our conclusion in chapter 5. 1 Other Worlds To date more than 750 exoplanets in little over 600 planetary systems are know and a fraction of them have been characterized using numerous techniques [Schneider et al., 2011]. This new branch of astron- omy has literally boomed since the first discoveries in the nineties, as can be seen in Figure 1. Figure 2 shows that in recent years, we have begun to reach the precision to detect earth-like planets. The most successful detection techniques are the radial velocity and transit methods, but other techniques have also demonstrated their efficiency: microlensing, pulsar timing, direct imaging ... Going through all of these techniques is out of the scope of this thesis, and we will only discuss below the two most relevant techniques for our work, i.e. radial velocity and transits. Afterwards we will discuss some of the most important results in the field of exoplanetology. 1.1 Radial velocity Introduction It was already thought in the 1950s that the reflex stellar velocity for an edge-on orbit could be around 2 km s−1 for a planet ten times the mass of Jupiter [Struve, 1952]. The field of exoplanetary science had to wait, however, until 1989 for the first claimed discovery of an exoplanet [Latham et al., 1989]. The −1 planet with minimal mass of 11 MJup and a period of 84 days had a velocity amplitude of 600 m s . With a precision of 400 m s−1 hundreds of measurements were required to achieve a decent Signal to Noise Ratio (SNR). The object was named HD 114762 b after the star it orbits and has been considered to be a brown dwarf since the uncertainty in the inclination of the system (see below). Four years later the spectrograph ELODIE was used with a precision of 13 m s−1 to detect a Jupiter-like planet around 51 Pegasi with a reflex motion of 59± 3 m s−1 and a period of 4.23 days (see figure 3 taken from Mayor and Queloz[1995]). Among the scientific community there remained some skepti- cism regarding the nature of the source of this signal for two reasons. First of all there wasn’t a single 6 Figure 1: Histogram displaying the number of peer-reviewed exoplanetary discoveries per year Figure 2: Plot displaying the (line of sight) mass of exoplanetary discoveries per year 7 planetary formation theory that predicted the existence of such objects so close to their host star. Gas gi- ants can’t form so close to the star since there is not enough mass in the inner part of the protoplanetary disk, let alone enough hydrogen. And thus planetary physics underwent a revolution by introducing the concept of inward migration caused by gravitational interaction between the protoplanet and the surrounding gaseous disk (Goldreich and Tremaine[1979], Ward[1997], Tanaka et al.[2002], Tanaka and Ward[2004]). It is worth mentioning that the notion of inward migration had already been pro- posed in 1979 by Goldreich and Tremaine but remained unnoticed by the planetary community until the discovery of 51 Peg b. Secondly since we only measure the radial veloc- ity, one cannot determine the true mass as will be shown later. All of this lead to the suggestion that the signal could be caused by a non-resolved binary or a object in the gray zone between star and planet, the so-called brown dwarfs. These ob- jects are not massive enough to start Hydrogen- 1 fusion (the object would need a mass of 75- 80 Jupiter masses), but would only support deu- terium fusion (13 Jupiter masses) in their cores. The eventual confirmation of the planet-like na- ture of the objects came when the eleventh gas giant that was discovered using radial velocity measurements, HD 209458b, also yielded a tran- sit feature detected by ground-based photometry at the exact time predicted by the radial veloc- ity data (see figure 4 taken from Charbonneau et al.[2000]). The discovery removed all skepti- Figure 3: Original phased radial velocity diagram for 51 cism and confirmed that the wobble observed by peg b the radial velocity was indeed caused by a planet. Observing a transit feature meant that one could measure the inclination of the system and determine the true mass of the planetary companion instead of the minimal mass. Since then many more planets have been discovered and radial velocity remains the technique with the most discoveries after its name. The state-of-the-art instrument in this field is the HARPS spectrograph [Mayor et al., 2003] that can achieve radial velocity precisions of a few dozens of cm/s−1 on bright and quiet stars. Among its achievements is the detection of Gl581e, which is one of the lightest exoplanets known at the moment with a mass of 1.7 ± 0.2 Earth masses[Mayor et al., 2009].