This document describes a method for searching Kepler K2 lightcurves for transiting planets orbiting eclipsing binary star systems (circumbinary planets). The researchers search K2 data to identify eclipsing binaries, then remove the binary signal to search for planetary transits. They test two methods for removing the binary signal: clipping eclipses, and dividing by the moving median. Detection efficiency is determined by injecting artificial planets and measuring recovery rates with respect to planet parameters. Moving median removal yields a higher detection efficiency of around 20% compared to 11% for eclipse clipping.

1. Searching for Circumbinary Planets in K2 Data
Emma Lewis and Nicole Bañales, Swarthmore College
Marcus Hughes, Williams College
Advisor: Eric Jensen, Swarthmore College
Abstract
We present a method for searching K2 lightcurves for transiting planets around eclipsing
binary host stars using period detection tools. We search the K2 data from each campaign
for eclipsing binaries and remove the signal of the binary to allow us to detect fainter, longer
period signals such as those of planetary transits. Methods for the removal of the binary star
signal include clipping out primary and secondary binary eclipses, as well as normalizing the
data to the moving median of the light curve folded on the binary period. We then analyze the
resultant 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 the
effectiveness of our detection with respect to planet period and planet-star radius ratio.
Introduction
The 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 of
the spacecraft’s four reaction wheels in 2013, the mission was relaunched as K2, which exhibited
precision worse than Kepler’s original photometric precision due to pointing drift and the periodic
thruster 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-generated
noise, new methods of data reduction were needed in order to allow the light curves to be searched
for 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 been
discovered, namely Kepler-16b, Kepler-34b, Kepler-35b, and Kepler-38b (Doyle et al. 2011; Welsh
et al. 2012; Orosz et al. 2012). However, these discoveries represent a very small sample, and
provide little insight as to the parameter distributions of circumbinary planets as a whole. Any
further circumbinary planet discovery will therefore be extremely scientifically valuable.
We are additionally motivated by the higher probability that a planet orbiting a known eclipsing
binary would be observable from our point of view. The orbital plane of an eclipsing binary is
closely aligned with our line of sight. Theoretical models indicate that a circumbinary planet’s
plane of orbit is also often closely aligned with the plane of orbit of the binary stars (Foucart & Lai
2013), increasing the probability that a circumbinary planet would also transit one or more of the
binary stars along our line of sight, allowing the planet to be detected through aperture photometry.
1Numbers taken from exoplanets.org.

2. For these reasons, we look to refine the existing planet detection methods to be better suited
towards the detection of circumbinary planets, and to use these methods to search K2 data for
circumbinary planets.
Selection of eclipsing binaries
Kepler’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 of
view. In order to find eclipsing binary candidates, we first used the box-least squares (BLS) method
to 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 any
longer 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 confirmed
that the periodic signal detected corresponded to a dip in the star’s flux instead of a peak, as transits
of eclipsing binaries reduce the total observable flux from the pair of stars. Finally, we confirmed
that the strength of the period signal was above a certain threshold. The lightcurves which met
these 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 data
from Kepler. The right picture shows the lightcurve folded on its strongest periodic signal, clearly displaying
the 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 circumbinary
planets, 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 smaller
secondary-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 secondary
eclipses. We speculate that some are due to spot variations on the observed star and have found that
some of these stars are listed as T Tauri stars or young stellar objects in the SIMBAD database.

3. 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 a
viable future project.
Masking the eclipsing binary period
Since 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 planet
detection, and tested their detection efficiencies by injecting false planets into our candidate EB
lightcurves and assessing the recovery rates of these planets. Our two best methods of EB period
masking were clipping the EB eclipse signals out entirely, and dividing the data by the moving
median 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 eclipses
highlighted. The highlighted eclipses were removed from the lightcurve to allow us to detect the period
signal 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 our
ability to recover fainter periodic signals and planets in our injection tests. However, in removing
datapoints, we could be removing planet transits that overlap with the binary eclipse as well. Not
all the binary eclipses are cleanly bounded, meaning that these remnants of the EB signal can cause
further 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 clipping
out the binary eclipses, the EB period was often still present in the data, as out-of-eclipse data
sometimes also contained periodic variation on the period of the binary eclipses, as can be seen
in Figure 1. Using the confirmed EB period, we fitted the folded lightcurve with a moving me-

4. Fig. 3.— The unfolded lightcurve of the example binary above, before (left) and after (right) binary eclipses
are 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 to
minimize 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. The
figure on the left shows the lightcurve without any modification after injection, and the figure on the right
shows the same lightcurve divided by the moving median of the data folded over the EB period. The moving
median division clearly shows the planetary transits, while they are hidden before the division.
Search for circumbinary planets
The 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 6
hours. Foreman-Mackey et al. (2015) proposed simultaneously fitting a box-model transit and the
systematics caused by thruster firings using principal components analysis, because this method
provides 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 top
twenty-five periods recovered and examined light curves folded on this period for any prominent
periodic signal closely matching the shape of a planetary transit.

5. Determining detection efficiency
Past 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 of
detection 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 that
are 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 base
our own code, have been performed (Foreman-Mackey et al. 2015). However, due to the large
changes we made to the light curves in order to remove the periodic signal of the EB, and due to
the potentially obscuring effects of the EB’s eclipses, we decided it was necessary to create new
measurements of detection efficiency for our altered process.
Detection efficiency was characterized for our code through injection trials, in which artificial
planetary 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 light
curves were run through the circumbinary planet detection code, and success rates were plotted
against various 2D projections of the parameter space of the planetary system. This approach was
previously 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 which
the 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 to
allow an even mapping of detection efficiency across these parameters, which will allow for more
accurate 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 orbital
period. However, in systems for which the orbital period generated was smaller than theoretical
constraints on dynamically stable circumbinary planets would allow, (i.e. less than about 2.8 times
the 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 a
period distribution that is close to flat, but which tapers down slightly in the shorter-period regions
due 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 an
empirical mass-radius relationship for main sequence stars), as including exceptionally large stars
in our data introduced an overabundance of systems with a low ratio between planet radius and
stellar radius. As we wanted to characterize the detection efficiency of our code with respect to
this ratio, which directly controls the depth of the planetary transit, we chose to generate planet
radius by randomly choosing a planet-star radius ratio value, and then computing planet radius as
a fraction of stellar radius.

6. 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 were
then processed according to our two different EB signal removal processes, and sent through our
planetary 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 the
strongest periodic signal) was within 0.1 days of the injected period value. If this was true, the
detection was recorded as a success. It should be noted that there is significant difference between
this 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 the
strongest period signal and searched by eye for transit-shaped events. Compared to our method of
looking at the real data, our method for assessing success within the injection trials is likely more
sensitive, and so detection efficiency results are possibly higher than the real values for our method
of looking at actual K2 data.
Detection efficiency results
Detection efficiency was determined with respect to various parameters for both of our two
masking processes, EB eclipse clipping and moving median division, as well as for the control
case in which nothing was done to remove the influence of the eclipsing binary signal. These
results 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 after
the injection of the planet, leaving the signal of the eclipsing binary in the light curve. Recovery
rates for the control case were very low (Figure 5). Situations when the planetary signal was
actually recovered, when examined, were largely cases in which the injected planetary transit was
deeper than the eclipsing binary transits.
For the clipping process, we found an overall average detection efficiency of about 11% for our
dataset. The efficiency as a function of orbital period and the ratio of the planet radius and the
star 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 radius
ratios. It is noticeable in the diagram that the first ‘column’ of the efficiency map, corresponding
to systems with a period of under about 12 days, has a lower efficiency in low-radius-ratio regions
than does the next ‘column’, which represents systems with a period of about 12 to 24 days. This
could perhaps be explained by the fact that only a small number of the original EB light curves
had small enough periods for the generated planetary periods to fall within this range, leaving the
characterization 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.

7. Fig. 5.— The detection efficiency of our planet-finding code, as a function of orbital period (x-axis) and the
ratio between planet radius and star radius (y-axis), for the control case in which the signal of the eclipsing
binary 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 radius
and the star radius is shown in the right panel of Figure 6. As before, our code was most efficient
in low-period and high planet-to-star radius ratio areas of the parameter space, however, it was
significantly more successful than the clipping process.
Future plans
We 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 and
for finding injected planets in our detection efficiency trials more similar, so that we can use our
efficiency models and the results of our planet search to establish constraints on the populations of
circumbinary planets.
We thank the NSF, Swarthmore College, Howard Hughes Medical Institute, and Keck Northeast
Astronomy Consortium for their generous funding. We would also like to thank the Kepler Space
Telescope team for providing the data used in this study, as well as Ian Crossfield for code used in
generating model transits. This research has made use of the SIMBAD database, operated at CDS,
Strasbourg, France, and of NASA’s Astrophysics Data System.

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