Searching for Circumbinary Planets in K2 Data

Emma Lewis and Nicole Bañales, Swarthmore CollegeMarcus Hughes, Williams College

Advisor: Eric Jensen, Swarthmore College

Abstract

We present a method for searching K2 lightcurves for transiting planets around eclipsingbinary host stars using period detection tools. We search the K2 data from each campaignfor eclipsing binaries and remove the signal of the binary to allow us to detect fainter, longerperiod signals such as those of planetary transits. Methods for the removal of the binary starsignal include clipping out primary and secondary binary eclipses, as well as normalizing thedata to the moving median of the light curve folded on the binary period. We then analyze theresultant light curve with planet detection software developed by D. Foreman-Mackey et al.By injecting artificial planet transits into our eclipsing binary light curves, we constrained theeffectiveness of our detection with respect to planet period and planet-star radius ratio.

IntroductionThe Kepler Space Telescope has been an extremely fruitful source of exoplanet discoveries since

its launch in 2009, discovering about 1500 planets and 4000 planet candidates in its mission to char-acterize the abundance of Earth-sized and larger planets in our galaxy1. After the failure of two ofthe spacecraft’s four reaction wheels in 2013, the mission was relaunched as K2, which exhibitedprecision worse than Kepler’s original photometric precision due to pointing drift and the periodicthruster firings used to correct that drift (Howell et al. 2014). Nevertheless, the mission’s obser-vational precision of about 30 ppm remains much better than that of ground-based observatories.Due to the changes in the nature of the K2 data from the introduction of thruster firing-generatednoise, new methods of data reduction were needed in order to allow the light curves to be searchedfor smaller signals such as those of planetary transits (Howell et al. 2014).

A small number of planets orbiting binary star systems, i.e. circumbinary planets, have beendiscovered, namely Kepler-16b, Kepler-34b, Kepler-35b, and Kepler-38b (Doyle et al. 2011; Welshet al. 2012; Orosz et al. 2012). However, these discoveries represent a very small sample, andprovide little insight as to the parameter distributions of circumbinary planets as a whole. Anyfurther circumbinary planet discovery will therefore be extremely scientifically valuable.

We are additionally motivated by the higher probability that a planet orbiting a known eclipsingbinary would be observable from our point of view. The orbital plane of an eclipsing binary isclosely aligned with our line of sight. Theoretical models indicate that a circumbinary planet’splane of orbit is also often closely aligned with the plane of orbit of the binary stars (Foucart & Lai2013), increasing the probability that a circumbinary planet would also transit one or more of thebinary stars along our line of sight, allowing the planet to be detected through aperture photometry.

1Numbers taken from exoplanets.org.

For these reasons, we look to refine the existing planet detection methods to be better suitedtowards the detection of circumbinary planets, and to use these methods to search K2 data forcircumbinary planets.

Selection of eclipsing binariesKepler’s K2 mission provides access to 22,000 lightcurves from campaign 1 and 13,399 lightcurves

from campaign 2, which each provide the flux over time of a single star in the telescope’s field ofview. In order to find eclipsing binary candidates, we first used the box-least squares (BLS) methodto detect periodic signals (Kovács et al. 2002). Light curves were then checked for three criteria.We first confirmed that the periodic signal detected by the BLS method was under 30 days, as anylonger periodic signals would restrict planetary periods to a length of time longer than each cam-paign’s time duration of approximately 72 days (Artymowicz & Lubow 1994). We then confirmedthat the periodic signal detected corresponded to a dip in the star’s flux instead of a peak, as transitsof eclipsing binaries reduce the total observable flux from the pair of stars. Finally, we confirmedthat the strength of the period signal was above a certain threshold. The lightcurves which metthese criteria were compiled into a list of about six hundred EB candidates for each campaign.Using an interactive tool we wrote, we manually confirmed that the shape of each lightcurve re-sembled that of an EB and confirmed the lightcurves’ period, central time of the primary eclipse,phase width of the primary and secondary eclipses, and phase separation between the eclipses.

Fig. 1.— Lightcurves of an eclipsing binary star found in this project. The left figure shows the raw datafrom Kepler. The right picture shows the lightcurve folded on its strongest periodic signal, clearly displayingthe binary star’s primary and secondary eclipses.

Non-eclipsing-binary light curves

While our main purpose is to categorize EBs so that we can attempt to detect circumbinaryplanets, we also explored other light curves that had unexpected or intriguing features. One char-acteristic of particular interest involved regular primary dips with a particular period and smallersecondary-like dips with their own particular period that would occur along with the larger dips.Some of these light curves also contained eclipsing binaries with their own primary and secondaryeclipses. We speculate that some are due to spot variations on the observed star and have found thatsome of these stars are listed as T Tauri stars or young stellar objects in the SIMBAD database.

Furthermore, some of these stars are located near Upper Scorpius, a nearby star-forming region(Preibisch & Mamajek 2008). While we did not further explore these lightcurves, this would be aviable future project.

Masking the eclipsing binary periodSince the EB periodic signal overpowers the smaller planet signal, it must be masked to recover

the less strong planet period. We developed two slightly different methods of circumbinary planetdetection, and tested their detection efficiencies by injecting false planets into our candidate EBlightcurves and assessing the recovery rates of these planets. Our two best methods of EB periodmasking were clipping the EB eclipse signals out entirely, and dividing the data by the movingmedian of the data folded on the period of the EB.

Fig. 2.— Eclipsing binary lightcurve, folded on the detected period of the binary star, with the eclipseshighlighted. The highlighted eclipses were removed from the lightcurve to allow us to detect the periodsignal of an injected planetary transit.

Eclipse-clipping

We used the lightcurves’ eclipse timings and eclipse widths to remove eclipse signals via clip-ping, i.e. removing any in-transit data from the lightcurve. After removing datapoints in the por-tions of the light curves that represented binary eclipses, we saw a significant improvement in ourability to recover fainter periodic signals and planets in our injection tests. However, in removingdatapoints, we could be removing planet transits that overlap with the binary eclipse as well. Notall the binary eclipses are cleanly bounded, meaning that these remnants of the EB signal can causefurther period detection analysis to still detect the EB period as the strongest periodic signal.

Moving medial EB removal

Simply removing the portion of the light curve associated with the eclipses was somewhat suc-cessful but left a large fraction (approximately 89%) of injected planets undetected. After clippingout the binary eclipses, the EB period was often still present in the data, as out-of-eclipse datasometimes also contained periodic variation on the period of the binary eclipses, as can be seenin Figure 1. Using the confirmed EB period, we fitted the folded lightcurve with a moving me-

Fig. 3.— The unfolded lightcurve of the example binary above, before (left) and after (right) binary eclipsesare removed. In the clipped lightcurve, the transits of the injected fake planet can be seen.

dian with a window size of five data points. This model was then divided from the light curve tominimize periodic signals corresponding to the period of the eclipsing binary.

Fig. 4.— The unfolded lightcurve of a binary star with an injected sequence of fake planetary transits. Thefigure on the left shows the lightcurve without any modification after injection, and the figure on the rightshows the same lightcurve divided by the moving median of the data folded over the EB period. The movingmedian division clearly shows the planetary transits, while they are hidden before the division.

Search for circumbinary planetsThe K2 mission is plagued with more systematics than the original Kepler mission was because

it slowly rolls as it is observing and requires thruster firings to correct for pointing drift every 6hours. Foreman-Mackey et al. (2015) proposed simultaneously fitting a box-model transit and thesystematics caused by thruster firings using principal components analysis, because this methodprovides more correct results than first trying to correct for systematics and then discover planets.We are using this method to recover planets in the clipped light curves. We looked at the toptwenty-five periods recovered and examined light curves folded on this period for any prominentperiodic signal closely matching the shape of a planetary transit.

Determining detection efficiencyPast studies have asserted that in order to use data about the parameters of confirmed planets

to characterize the attributes of real planetary populations, researchers must address the effects ofdetection bias on the distribution of observed planetary properties (Foreman-Mackey et al. 2014).Planet surveys conducted using transit detection methods are particularly sensitive to planets thatare large compared to their host star or stars, therefore producing deeper, more visible transits,and planets that are close to their host stars, and therefore will transit the stars more frequently.Previous characterizations of detection efficiency in Kepler data, using code off of which we baseour own code, have been performed (Foreman-Mackey et al. 2015). However, due to the largechanges we made to the light curves in order to remove the periodic signal of the EB, and due tothe potentially obscuring effects of the EB’s eclipses, we decided it was necessary to create newmeasurements of detection efficiency for our altered process.

Detection efficiency was characterized for our code through injection trials, in which artificialplanetary transit light curves, created with parameters chosen randomly from specific distributions,were injected into K2 light curves known to be those of eclipsing binaries. These altered lightcurves were run through the circumbinary planet detection code, and success rates were plottedagainst various 2D projections of the parameter space of the planetary system. This approach waspreviously used by Foreman-Mackey et al. (2015) in their characterizations of detection efficiency.

Parameter distributions of injected planets

The distributions of parameters of the injected systems were chosen to create realistic relation-ships in the data, and to allow even characterization of detection efficiency for parameters of whichthe true distribution was not known, such as planetary radius and planetary orbital period.

Flat distributions were chosen for parameters that planet surveys aim to characterize, in order toallow an even mapping of detection efficiency across these parameters, which will allow for moreaccurate assertions about the distributions of these parameters in planetary populations later on.The variables for which we chose flat distributions were impact parameter, transit time, and orbitalperiod. However, in systems for which the orbital period generated was smaller than theoreticalconstraints on dynamically stable circumbinary planets would allow, (i.e. less than about 2.8 timesthe EB period, derived from planet formation constraints on the semimajor axis; Artymowicz &Lubow 1994), the orbital period was regenerated until it was above this threshold. This results in aperiod distribution that is close to flat, but which tapers down slightly in the shorter-period regionsdue to the lower chance of very short orbital periods being allowed by our criteria. Accordingly,very short-period areas of the planetary space have slightly less accurate detection efficiencies.

We also generated flat distributions of stellar mass (which was linked to stellar radius by anempirical mass-radius relationship for main sequence stars), as including exceptionally large starsin our data introduced an overabundance of systems with a low ratio between planet radius andstellar radius. As we wanted to characterize the detection efficiency of our code with respect tothis ratio, which directly controls the depth of the planetary transit, we chose to generate planetradius by randomly choosing a planet-star radius ratio value, and then computing planet radius asa fraction of stellar radius.

Injection process

Once these parameters were chosen, light curves were generated for each set of system parame-ters using transit formulas from Mandel & Agol (2002), via code from Ian Crossfield2, implement-ing quadratic limb-darkening with limb-darkening coefficients mirroring those of a Sun-like star(Sing 2010).

These model light curves were multiplied into K2 light curves of eclipsing binaries, which werethen processed according to our two different EB signal removal processes, and sent through ourplanetary detection code. After removing the signal of the EB as described above, for each system,we checked if any of the top 25 peaks in the periodogram (the periods for which there was thestrongest periodic signal) was within 0.1 days of the injected period value. If this was true, thedetection was recorded as a success. It should be noted that there is significant difference betweenthis definition of success and the criteria used when looking through the real data to find planets.When the raw EB data were searched for planets, the data were folded on the 25 periods with thestrongest period signal and searched by eye for transit-shaped events. Compared to our method oflooking at the real data, our method for assessing success within the injection trials is likely moresensitive, and so detection efficiency results are possibly higher than the real values for our methodof looking at actual K2 data.

Detection efficiency results

Detection efficiency was determined with respect to various parameters for both of our twomasking processes, EB eclipse clipping and moving median division, as well as for the controlcase in which nothing was done to remove the influence of the eclipsing binary signal. Theseresults were determined for the same set of 3,000 modified light curves.

For the control case, we ran the injected light curves through our code with no modification afterthe injection of the planet, leaving the signal of the eclipsing binary in the light curve. Recoveryrates for the control case were very low (Figure 5). Situations when the planetary signal wasactually recovered, when examined, were largely cases in which the injected planetary transit wasdeeper than the eclipsing binary transits.

For the clipping process, we found an overall average detection efficiency of about 11% for ourdataset. The efficiency as a function of orbital period and the ratio of the planet radius and thestar radius is shown in the left panel of Figure 6. Within this projection of the parameter space,our code was most efficient for systems with low periods and with high planet radius to star radiusratios. It is noticeable in the diagram that the first ‘column’ of the efficiency map, correspondingto systems with a period of under about 12 days, has a lower efficiency in low-radius-ratio regionsthan does the next ‘column’, which represents systems with a period of about 12 to 24 days. Thiscould perhaps be explained by the fact that only a small number of the original EB light curveshad small enough periods for the generated planetary periods to fall within this range, leaving thecharacterization of efficiency on the left-hand side of the graph more susceptible to statistical noise.

For the moving median process, we found an overall average detection efficiency of about 20%

2Code accessible at http://www.astro.ucla.edu/~ianc/files/transit.py, retrieved June 19 2015.

Fig. 5.— The detection efficiency of our planet-finding code, as a function of orbital period (x-axis) and theratio between planet radius and star radius (y-axis), for the control case in which the signal of the eclipsingbinary was not removed or masked in any way.

for the same dataset. The efficiency as a function of orbital period and the ratio of the planet radiusand the star radius is shown in the right panel of Figure 6. As before, our code was most efficientin low-period and high planet-to-star radius ratio areas of the parameter space, however, it wassignificantly more successful than the clipping process.

Future plansWe plan to continue to process K2 mission data as more campaigns are released by the Kepler

team. We also intend to make the success criteria for finding a planet candidate in real K2 data andfor finding injected planets in our detection efficiency trials more similar, so that we can use ourefficiency models and the results of our planet search to establish constraints on the populations ofcircumbinary planets.

We thank the NSF, Swarthmore College, Howard Hughes Medical Institute, and Keck NortheastAstronomy Consortium for their generous funding. We would also like to thank the Kepler SpaceTelescope team for providing the data used in this study, as well as Ian Crossfield for code used ingenerating model transits. This research has made use of the SIMBAD database, operated at CDS,Strasbourg, France, and of NASA’s Astrophysics Data System.

Fig. 6.— The detection efficiency of our planet-finding code as a function of orbital period (x-axis) and theratio of planet radius to stellar radius (y-axis). The diagram on the left shows results for the light curveswhich had datapoints within the timeframe of the binary eclipses completely removed. The diagram on theright shows results for the light curves which were folded on the period of the eclipsing binary, and thendivided by their moving median.

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