An Analysis of Noise in the CoRoT Data by Aaron Sampson Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2010 © Massachusetts Institute of Technology 2010. All rights reserved. '/ Author............... ------- .- ..---...-v-----f ----- Department of Physics May 17, 2010 Certified by............ .... ..... ... ... .< . ... .. Sara Seager Associate Professor of Physics Thesis Supervisor Accepted by ................... ............... ................ Professor David E. Pritchard Senior Thesis Coordinator, Department of Physics OF TECHNOLOGY ARCHIVES AUG 13 2010 LIBRARIES 2 An Analysis of Noise in the CoRoT Data by Aaron Sampson Submitted to the Department of Physics on May 17, 2010, in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics Abstract In this thesis, publically available data from the French/ESA satellite mission CoRoT, designed to seek out extrasolar planets, was analyzed using MATLAB. CoRoT at- tempts to observe the transits of these planets accross their parent stars. CoRoT occupies an orbit which periodically carries it through the Van Allen Belts, resulting in a a very high level of high outliers in the flux data. Known systematics and out- liers were removed from the data and the remaining scatter was evaluated using the median of abolute deviations from the median (MAD), a measure of scatter which is robust to outliers. The level of scatter (evaluated with MAD) present in this data is indicative of the lower limits on the size of planets detectable by CoRoT or a similar satellite. The MAD for CoRoT stars is correlated with the magnitude. The brightest stars observed by CoRoT display scatter of approximately 0.02 percent, while the median value for all stars is 0.16 percent. Thesis Supervisor: Sara Seager Title: Associate Professor of Physics 4 Acknowledgments I would like to thank everyone who helped me with this work, in particular Sukrit Ranjan and Lisa Messeri, with whom I worked on the early stages of the project. Thank you also to Dr. Suzanne Aigrain, who was extremely helpful in explaining the CoRoT mission, how the data is reported, and her techniques for analyzing the data. Thank you also to Elizabeth Adams for her help with understanding and calculating transit properties. Above all, I would like to thank Professor Sara Seager for her help and advice throughout the project. From its early stages of the analysis to the writing of this thesis, her insight has be critical to its completion. 6 Contents 1 Introduction 11 2 Noise Reduction Methods 15 2.1 CoRoT D ata .. .. .. .. .. ... ... ... .. .. 15 2.2 Corrections ........ ................................ 16 2.3 Identifying and removing Systematics . 17 2.4 Evaluating Scatter ............................ 18 3 Results 21 3.1 CoRoT Light Curves and Corrections ............ ...... 21 3.2 Scatter .......... ......................... 22 3.3 Calculating Transit Properties ......... ............ 24 3.4 Limits on Detection ............. 25 4 Relation to Other Missions 27 A Figures 31 B MATLAB Code 37 B.1 Read Light Curve ................... .......... 37 B.2 Apply Corrections ........... ............ ...... 42 B.3 Save Corrections ................... .......... 49 B.4 Save MAD, Magnitude ..... ............. 51 8 List of Figures A-1 This light curve is typical of CoRoT data before the application of any corrections. There are a very large number of very high outliers, a pronounced linear trend (upward, in this case, indicating pointing drift allowed more light into the area designated for the star) and low outliers over one portion of the observing run. .. .. .. .. .. .. 32 A-2 After the application of the correction techniques described in Section2, the CoRoT lightcurves exhibit significantly reduced outliers and have had any linear trend removed. The lower - outliers associated with entry or exit from the earths shadow (and loss of accuracy) are still apparent toward the end of the lightcurve. .. .. .. .. .. .. .. 32 A-3 Scatter is plotted against R magnitude here for stars observed dur- ing the fist short run designated as Chromatic, meaning that they are bright enough to have their flux reported in three separate color channels, red, green, and blue. The R magnitude is reported to only one decimal place for stars in teh short run. Scatter for this data set ranges from approximately 0.0003 to 0.002, with a positive correlation between magnitude and scatter. Scatter here is the median of absolute deviations from the median. .. .. ... .. .. .. ... .. .. .. 33 A-4 Plotted here is the scatter (MAD) versus R magnitude for the Monochro- matic stars from the short run, those stars too dim to have their flux reported in separate color channels. The MAD values in the same range as the chromatic set, and higher for the dimmest stars. .. .. 33 A-5 Equivalent scatter-magnitude plots were made for the first long (150 day) run data sets. The magnitude of these stars is reported with greater precision, with four decimal places in the FITS header, and the correlation between magnitude and scatter is apparent. .. .. .. 34 A-6 Scatter (MAD) is plotted against R magnitude for Chromatic stars observed during the first long observing run. The plot is a clear corre- lation between magnitude and scatter for these stars. .. .. .. 34 A-7 The blue curve above represents the relationship between the planet/star radius ratio and transit depth. Also plotted here and below are the transit depths of various planet/star pairs and the limits on transit depth imposed by CoRoT-level noise. .. .. .. .. .. .. .. .. 35 A-8 More transit depths are shown here, for the Earth and sun and CoRoT- 7 b, both of which are on the same order of magnitude as the lowest threshhold of detectability imposed by the scatter in CoRoT light curves. 35 A-9 Here, a quadratic fit to the scatter/magnitude plot from the long run monochromatic stars is shown along with transit depths for various planet/star pairs, showing which types of planets could be detectable at which m agnitudes. .. .. .. .. .. .. .. .. 36 Chapter 1 Introduction In recent years, there have been an abundance of newly discovered extrasolar planets- planets which orbit stars other than our own. Detecting these planets beyond the boundaries of our solar system requires highly precise and careful measurements of the stars around which these previously unseen objects orbit. One of the best methods for detecting these planets is observing their transit across their parent stars. As the planets orbit their stars, they will sometimes pass directly between the star and observers on earth, thereby blocking part of the light coming from that star. Although most known extrasolar planets known have been discovered by other methods, transit observation it is a method which holds great potential, especially for discovering small, earthlike planets. Measuring transits for these planets of greatest interest is especially challenging, however, because the change in light from the star is very small. It is therefore of great interest to determine the noise limits on detecting such planets through this method. Exoplanet transits can actually provide a great deal of information. Precise mea- surements can reveal both primary (planet passing in front of star) and secondary eclipses (planet passing behind star) as well as the smaller differences in incident flux when the illuminated side of the planet is visible (before or after a secondary transit) versus when the dark side is visible (near the primary transit) [10]. The difficulty in discovering planets via observation of transits arises in large part from the fact that the star-planet system needs to be oriented quite precisely in order for the two distant bodies to align as viewed from Earth. In fact, for those most interesting extrasolar planets, Earth-sized bodies occupying a habitable zone around their parent stars, the probability of observing the system in proper alignment for a transit is around 0.5 percent [6]. CoRoT (COnvection ROtation and planetary Transits) is a satellite mission ad- ministered by the French and European Space Agencies (CNES and ESA). Launched via Soyuz rocket on December 27, 2006 from Baikonur Cosmodrome in Kazakhstan, the mission has two purposes. In addition to searching for extrasolar planets, CoRoT performs asteroseismology measurements, studying the pulsation of stars. Seeking out exoplanet transits and studying asteroseismology both require measuring (very carefully and precisely) the intensity of light received from stars over periods of time. The needs of these dual missions are, however, somewhat different. The added dif- ficulty comes from the fact that in order to be sure a planet is observed while it is transiting, observations must be carried out throughout the planets entire orbital period. For a planet like Earth, the orbital period would be on the order of one year, necessitating a similarly long session of observing. So, while the detection of transits requires observing stars for as long as possible to maximize the probability of find- ing the star-planet system in the proper alignment, asteroseismology requires only relatively short periods of observation. For this reason, CoRoT alternates between long and short runs of data collection-a compromise between its dual missions. The short runs are 20 days in duration, and the long runs are 150 days. The publicly available data from CoRoT is therefore released by run. The satellite also alternates pointing in two opposite directions, reversing directions every six months to avoid the sun, which would otherwise come too close to its field of view. These two ten-degree radius patches of sky are known as the two "eyes of CoRoT" and all observations will be made within these areas, both of which lie in the galactic plane, one of which is pointed toward the center of the galaxy, one of which is pointed toward the outer edge [7]. The instruments on board CoRoT reflect the nature of its mission. CoRoT consists of an afocal telescope, housed in a baffle designed to block reflected sunlight from the Earth.