Ph circumbinary final

draft version October 14, 2012

Planet Hunters: A Transiting Circumbinary Planet in a Quadruple Star System

Megan E. Schwamb1,2,17 , Jerome A. Orosz3 , Joshua A. Carter4,18 , William F. Welsh3 , Debra A.
Fischer5 , Guillermo Torres4 , Andrew W. Howard6 , Justin R. Crepp7,8 , William C. Keel9,10 , Chris
J. Lintott11,12 , Nathan A. Kaib13,19 , Dirk Terrell14 , Robert Gagliano15 , Kian J. Jek15 , Michael
Parrish12 , Arfon M. Smith12 , Stuart Lynn12 , Robert J. Simpson11 , Matthew J. Giguere5 , and
Kevin Schawinski1,2,16,20

megan.schwamb@yale.edu

ABSTRACT

1
Yale Center for Astronomy and Astrophysics, Yale University,P.O. Box 208121, New Haven, CT 06520, USA
2
Department of Physics, Yale University, New Haven, CT 06511, USA
3
Department of Astronomy, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-1221, USA
4
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
5
Department of Astronomy, Yale University, New Haven, CT 06511, USA
6
Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
7
Department of Astronomy, California Institute of Technology, 1200 E.California Blvd.,Pasadena, CA91125, USA
8
Department of Physics, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA
9
Department of Physics & Astronomy, 206 Gallalee Hall, 514 University Blvd., University of Alabama, Tuscaloosa,
AL 35487-034, USA
10
SARA Observatory, Dept. of Physics and Space Sciences, Florida Institute of Technology, Melbourne, FL 322901,
USA
11
Oxford Astrophysics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
12
Adler Planetarium, 1300 S. Lake Shore Drive, Chicago, IL 60605, USA
13
Northwestern University, 2131 Tech Drive, Evanston, IL, 60208, USA
14
Department of Space Studies, Southwest Research Institute, Boulder, Colorado 80302, USA
15
Planet Hunters
16
Institute for Astronomy, Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 16, CH-8093 Zurich,
Switzerland
17
NSF Astronomy and Astrophysics Postdoctoral Fellow
18
Hubble Fellow
19
CIERA Postdoctoral Fellow
20
Einstein Fellow

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We report the discovery and confirmation of a transiting circumbinary planet (PH1)
around KIC 4862625, an eclipsing binary in the Kepler field. The planet was discovered
by volunteers searching the first six Quarters of publicly available Kepler data as part
of the Planet Hunters citizen science project. Transits of the planet across the larger
and brighter of the eclipsing stars are detectable by visual inspection every ∼137 days,
with seven transits identified in Quarters 1-11. The physical and orbital parameters
of both the host stars and planet were obtained via a photometric-dynamical model,
simultaneously fitting both the measured radial velocities and the Kepler light curve of
KIC 4862625.The 6.18 ± 0.17 R⊕ planet orbits outside the 20-day orbit of an eclipsing
binary consisting of an F dwarf ( 1.734 ± 0.044 R , 1.528 ± 0.087 M ) and M dwarf
( 0.378 ± 0.023 R , 0.408 ± 0.024 M ). For the planet, we find an upper mass limit
of 169 M⊕ (0.531 Jupiter masses) at the 99.7% confidence level. With a radius and
mass less than that of Jupiter, PH1 is well within the planetary regime. Outside the
planet’s orbit, at ∼1000 AU, a previously unknown visual binary has been identified
that is bound to the planetary system, making this the first known case of a quadruple
star system with a transiting planet.

Subject headings: binaries-eclipsing—stars: individual(KIC 4862625)—planets and satel-
lites: detection—planets and satellites:general

1. Introduction

For the past three and a half years NASA’s Kepler spacecraft (Borucki et al. 2010) has mon-
itored, nearly continuously, over 160,000 stars looking for the signatures of transiting exoplanets.
The Kepler team has discovered more than 2300 planet candidates (Batalha et al. 2012), nearly
quadrupling the sample of known planets, in addition to identifying close to 2200 eclipsing binary
stars (Prˇa et al. 2011; Slawson et al. 2011). One of Kepler’s many successes has been the first
s
confirmed identification of transiting circumbinary planets, planets orbiting both stars in a binary
star system (Doyle et al. 2011; Welsh et al. 2012; Orosz et al. 2012a,b). Although planets have
previously been suspected to be orbiting both stars in a binary star system before Kepler (Bennett
et al. 1999; Deeg et al. 2008; Lee et al. 2009; Beuermann et al. 2012), the Kepler era ushered in
the first confirmed identification of such systems.

Identifying transiting exoplanets in binary star systems, on P-type (circumbinary) orbits where
the planet orbits around both stars, is difficult when using the automated transit search methods
and candidate validation processes employed by the Kepler team. The Transiting Planet Search
(TPS) (Tenenbaum et al. 2012; Jenkins et al. 2010b, 2002) pipeline and the candidate vetting
process were primarily designed to identify transiting planets around single stars (Batalha et al.
2012). Transits due to planets in binary star systems can easily be drowned out by the much
larger stellar eclipse signal and may even be superimposed on top of a primary or secondary eclipse

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escaping detection. What makes automatic detection challenging is the fact that the planet transits
in such systems are not necessarily constant in duration or repeated at regular intervals due to the
changing positions and velocities of the stars at each transit. Alternative detection techniques,
including visual inspection and the search for eclipse timing variations on the host stars due to
non-Keplerian three-body effects, are currently being employed to find planets in the nearly 750
eclipsing binary systems with orbital periods larger than 1 day. These efforts have proven successful
with the discovery of six transiting circumbinary planets in the Kepler field (Kepler-16b, Kepler-
34b, Kepler-35b, Kepler-38b, Kepler-47a, Kepler-47b; Doyle et al. 2011; Welsh et al. 2012; Orosz
et al. 2012a,b).

These multistar planetary systems are the extremes of planet formation and serve as the test
grounds for planetary accretion and evolution models that must be able to explain the existence of
planets in these dynamically challenging environments. Paardekooper et al. (2012) and Meschiari
(2012) are unable to simulate the creation of planetary cores at the distances the Kepler circumbi-
nary planets currently reside suggesting these planets formed further from their parent stars and
migrated inward to their present orbits. Models of circumbinary protoplanetary disk evolution by
Alexander (2012) predict that disks around close binaries with semimajor axes (a) less than 1 AU
live longer than those around single stars, but disk lifetimes decline as photoevaporation increases
at larger binary semimajor axes. As a result, they predict a dearth of circumbinary planets around
wide binaries with a > 10 AU and an abundance of circumbinary planets in stellar binaries with a <
1 AU. Bate et al. (2000) predict that circumstellar disks around binaries with a < 100 AU should
be coplanar to the orbit of the binary. Thus any planets formed from such a disk are expected
to all be aligned with the binary’s orbit. According to dynamical evolution models by Pierens &
Nelson (2008), Jupiter-mass planets on circumbinary orbits will be rare and difficult to find. In
their simulations, the Jupiter-mass bodies typically had a close encounter with the secondary star
during migration causing the planet to be subsequently ejected from the system or scattered out-
ward to the edge of the circumstellar disk. Therefore planets with masses equal to or less than that
of Saturn are predicted to be the most abundant in these types of planetary systems. By finding
more planets in multistar systems we can probe the environments these planets reside in and begin
to test and evaluate the predictions from these formation and dynamical evolution models.

We report here the discovery and characterization of a new transiting circumbinary planet,
orbiting a known Kepler eclipsing binary, via visual inspection of the first 16 months of publicly
released Kepler data by volunteers from the Planet Hunters citizen science project. This is Planet
Hunters’ first confirmed planet, and we subsequently refer to the planet as PH1’. The 6.18 ± 0.17
R⊕ planet orbits outside a 20-day period eclipsing binary. Beyond the orbit of PH1, a distant
visual binary located at a projected distance of ∼1000 AU is bound to the planetary system. This
is the first identification of a confirmed transiting planet orbiting in a quadruple star system. In
this Paper, we present the discovery, observational follow-up, and characterization of this hierar-
chical stellar-planetary system. Combining the Kepler photometric light curve and radial velocity
observations with a 3-body photometric-dynamical model, we constrain the physical and orbital

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properties of the planet and host stars.

2. Discovery

The Planet Hunters1 (Fischer et al. 2012; Schwamb et al. 2012) citizen science project uses
the power of human pattern recognition via the World Wide Web to identify transits in the Kepler
public data. Planet Hunters uses the Zooniverse2 platform, first described in (Lintott et al. 2008;
Smith et al. 2011), to present visitors to the Planet Hunters website with a randomly selected ∼30-
day light curve segment from one of Kepler’s ∼160,000 target stars. 5-10 independent volunteers
review each 30-day light curve segment and draw boxes directly on the web interface to mark the
locations of visible transits. For further details of the website and classification interface we refer
the reader to (Schwamb et al. 2012).

In addition to the main classification interface, the Planet Hunters website hosts an object-
oriented discussion and investigation tool known as ‘Planet Hunters Talk’ (referred to as ‘Talk’)3 .
Talk hosts forum-style message boards enabling volunteers to discuss and analyze interesting light
curves together. In addition each 30-day light curve presented on the Planet Hunters main classifi-
cation interface has a dedicated page on the Talk website where volunteers can write comments, add
searchable Twitter-like hash tags, and group similar light curves together. Volunteers are directed
to these pages through the main Planet Hunters website. Once a classification on the main interface
is complete, the volunteer is asked “Would you like to discuss this star?”. If the volunteer answers
‘yes’, he or she is directed to the light curve’s dedicated Talk page. From there a Planet Hunters
volunteer can also view all available public light curve data for that Kepler target presented as it
would be seen on the main Planet Hunters website, including the ability to zoom in both time and
brightness.

Talk was designed to aid in identifying objects of particular interest and unusual light curves
that are difficult to find via automatic detection algorithms and beyond the scope of the main
Planet Hunters classification interface. It also provides an avenue for communicating directly with
the Planet Hunters science team through the message boards and comments. From 2010 December
16 to 2012 June 9, in total, 69 percent of registered Planet Hunters participants have visited the
Talk site with 23 percent having contributed comments. In this time frame, an average of 116 and
a median of 72 Planet Hunters users visit Talk each day. In addition an average of 511 and median
of 329 comments discussing presented light curves are generated on Talk daily. We note that the
two planet candidates presented in Lintott et al. (2012) were first identified by the Planet Hunters

1
http://www.planethunters.org
2
http://www.zooniverse.org
3
http://talk.planethunters.org - The code is available under an open-source license at
https://github.com/zooniverse/Talk

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science team via the discussion of the light curves on the Talk message boards before a systematic
search of the Q2 light curves had been completed.

On 2011 May 11, coauthor Kian Jek posted on Talk highlighting the light curve of eclipsing
binary KIC 12644769, identifying additional transits due to a possible third body. Slawson et al.
(2011) had already noted the additional transit features, and the system subsequently turned out
to be Kepler-16, the first circumbinary discovered in the Kepler field (Doyle et al. 2011). After the
announced discovery of Kepler-16b, the Planet Hunters science team posted links to the Talk pages
for the entire Slawson et al. (2011) eclipsing binary list encouraging volunteers to examine these
eclipsing binary light curves and perform their own search for additional transits due to an orbiting
planet. During visual inspection of the light curve for detached eclipsing binary KIC 4862625,
coauthor Robert Gagliano spotted two transit-like features in Quarters 2 and 4 (see Figure 1)
separated by ∼137 days, and on 2012 March 2 highlighted this light curve on the Talk forums as a
potential circumbinary. At the time only Quarters 1-4 (∼310 days of science data) were available
on Planet Hunters website, but Quarters 1-6 were publicly available. On 2012 March 3, Kian Jek,
examined the Quarter 5 and 6 light curves, obtained from the Kepler Mission Archive4 hosted by
the Mikulski Archive for Space Telescopes (MAST5 ), identifying a third transit with similar depth
in Quarter 5 occurring roughly 137 days after the Quarter 4 transit. These additional transit events
in Quarters 1-5 as well as others subsequent Quarters were also independently identified by Kostov
et al.(2012) in a separate and concurrent analysis of the Kepler public data. After examining the
reported column pixel centroids in the FITS files for a shift during in and out of transit that may
indicate contamination from a faint background eclipsing binary, Kian Jek noted the presence of
this third transit in a Talk discussion thread6 and notified the Planet Hunters science team of the
potential discovery of a circumbinary planet.

3. Kepler Light Curve

There are two types of Kepler light curves provided in MAST: Pre-Search Data Conditioning
(PDC) and Simple Aperture Photometry (SAP). The PDC correction optimizes the light curve for
detection for planet transits as well as removing systematic effects and long-term trends, but also
makes some assumption for stellar variability and attempts to remove that signal. The SAP light
curve is the summed flux in the target aperture with no further corrections. For further specifics
of the Kepler data processing and data products we refer the reader to Jenkins et al. (2010b,a);
Christiansen et al. (2011), and Smith et al. (2012). We note that the original discovery on the Planet
Hunters website was using the PDC-corrected light curve, but for the remainder of the analysis

4
http://archive.stsci.edu/kepler
5
http://archive.stsci.edu
6
http://talk.planethunters.org/discussions/DPH1014m5m?group id=SPH10052872

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presented here, we choose to use the SAP light curves in order to preserve the stellar variability
and the eclipse signals, performing our own detrending and removal of instrumental systematics
for each individual Quarter of Kepler observations.

The normalized light curve for KIC 4862625, for Quarters 1-11 is shown in Figure 2. The
Kepler Input Catalog7 (KIC, Brown et al. 2011). reports a magnitude of 13.72 for the eclipsing
binary in the broad Kepler filter (Kp). We will refer to the brighter more massive star as ‘Aa’ and
use ‘Ab’ to denote the fainter lower-mass stellar companion in the eclipsing binary. These two stars
have an orbital period of 20.000214 days on an eccentric orbit with an eccentricity of 0.24181 as
reported by Slawson et al. (2011). In the Kepler light curve the depth of the primary eclipses are
∼1.3%, and the depth of the secondary eclipses are only slightly deeper than the planet transit at
∼0.11%. Three transits of PH1 crossing Aa are visible in Quarters 2, 4, and 5, the data publicly
available at the time of discovery, with another four identified in Quarters 7, 8,10, and 11. No
transits across Ab were identified. Initial modeling of the light curve to remove brightness changes
due to stellar variability found that the three transits in Quarters 2,4, and 5 had similar depths
(∼0.1%) consistent with the third body transiting being planetary in size, ∼2.8 R⊕ assuming a
primary (Aa) stellar radius of 0.804 R as reported in the KIC (Brown et al. 2011).

One of the largest sources of false positives for Kepler planet candidates are blended faint
background eclipsing binaries, but this would require a chance sky alignment of two eclipsing binary
systems along the line of sight. This scenario, though highly unlikely, cannot be completely ruled
out by statistical arguments alone. If the transiting body truly is orbiting both stars in the binary,
the exact timing and the duration of the planet transits should vary due to the changing positions
and velocities of the stars at each transit (e.g Deeg et al. 1998; Doyle et al. 2000, 2011; Welsh et al.
2012; Orosz et al. 2012a,b). A transit function is fit individually to each of the seven transits to
measure the transit times and widths. The measured transit midpoints are reported in Table 1.
The mean period is 135.648 days. We note all times and ephemerides in our analysis are using
Barycentric Julian Dates in Barycentric Dynamical Time, which we will refer to as BJD. Observed
(O) minus Calculated (C) offsets and durations for the seven transits are plotted in Figure 3. O-C
amplitudes as high as ± 1 day are observed and the transit durations are varying with the binary
orbital phase, confirming this body is indeed orbiting stars Aa and Ab and the transit features are
not due to a blended background eclipsing binary or any other astrophysical false positive.

Furthermore, the tidal field of the planet may cause nonlinear timing variations in the eclipsing
binary, but the zeroth order effect is a period difference between primary and secondary eclipses,
as had been observed the for Kepler-16b, Kepler-34b, and Kepler-35b systems (Doyle et al. 2011;
Welsh et al. 2012). Primary and secondary eclipse timings were estimated by fitting a low-order
cubic Hermite polynomial (for details see Steffen et al. 2011; Welsh et al. 2012) to each individual
eclipse in the normalized Quarters 1-11 light curve. The measured primary and secondary eclipse
midpoints for KIC 4862625 are reported in Table 2. The best fitting linear primary and secondary

7
http://archive.stsci.edu/Kepler/Kepler fov/search.php

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eclipse ephemerides are: T0 = -52.18091 ± 0.00018 (BJD - 2455,000) with a period P = 20.0002498
± 0.0000064 days for the primary eclipse and T0 = -44.3252 ± 0.0016 (BJD - 2455,000) with
P = 20.000244 ± 0.000056 days for the secondary eclipse. The difference between the primary
and secondary periods is 0.50 ± 4.87 seconds. The timings of the stellar eclipses are measured
and compared to the that expected from the best-fit eclipse ephemerides. The O-C offsets for the
primary and secondary stellar eclipses are plotted in Figure 4. No discernible timing variation signal
in either the primary or secondary eclipses were found. The planet may not be massive enough
to gravitationally perturb the stellar orbits significantly over the timescale of the observations, as
is the case for the Kepler-38 and Kepler-47 systems (Orosz et al. 2012a,b). Without detectable
perturbations on the stellar orbits, we will only be able to place an upper limit on the mass of PH1
when the light curve and radial velocity observations are combined in the photometric-dynamical
model fit as described in Section 7.

4. Flux Contamination

The Kepler pixel scale is 4 per pixel, with a typical photometric aperture radius of 6 (Jenkins
et al. 2010a). With such a wide aperture, stellar contamination and photometric blends are a
concern when analyzing the Kepler photometry of target stars. Adding linearly, the contribution
of extra light decreases the observed transit and eclipse depths. Accurately estimating the size
of the transiting planet requires knowledge of the additional flux contributors to the Kepler light
curve for KIC 4862625. A search of the KIC found that two nearest sources are KIC 4862611 and
KIC 4862601 located 8.68 and 11.8 respectively from KIC 4862625 (Brown et al. 2011). With
Kepler magnitudes of 18.052 and 18.256 respectively, these two stars would not be completely in
the Kepler photometric aperture and at most would contribute less than a percent of total flux in
the light curve.

Faint companions closer than a few arcseconds to the Kepler target may not be found in
the KIC or 2MASS catalog (Skrutskie et al. 2006; Brown et al. 2011). To better constrain the
presence of additional stars not listed in the KIC that may be contaminating the Kepler aperture,
we obtained near-infrared adaptive optics (AO) observations using the NIRC2 imager behind the
natural guide-star (NGS) AO system on the Keck II telescope (Ghez et al. 2008). K (1.948-2.299
µm) imaging was taken on 2012 May 29 UT with NIRC2 in the narrow camera setting, yielding
a 10x10 field-of-view with a pixel scale of 9.9 mas per pixel. We used a 9-point dither pattern
with a 2- offset between each position. At each nod, 60s integrations were taken, resulting in a
total integration time on target of 540s. The raw frames were dark and background subtracted,
flat fielded. Bad and hot pixels were interpolated over. The reduced frames were then combined
into a single image. Visual inspection revealed two nearby stars: a source 0.702 southwest of KIC
4862625 approximately 5 times fainter than the target star and a much fainter source ∼3 away
to the southwest. From this point forward, we refer to these sources as the 0.7 contaminator
and the 3 contaminator respectively. Both stars are well within the photometric aperture of KIC

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4862625. The Kepler data analysis pipeline would not account for the flux contribution from these
contaminating stars.

In order to estimate the light curve dilution due to the brighter 0.7 contaminator, we obtained
further observations with NIRC2 NGS AO in Ks (1.991-2.302 µm) and J (1.166-1.330 µm) filters on
2012 June 7 UT in the same observing setup. The images were reduced in the same manner as on
the first night but with a 3 offset between nods. J images were taken with an integration time of
90s exposures at each nod. The Ks imaging consisted of 60s at each nod. A total integration time
of 810s in J and 540s in Ks respectively was achieved. There were intermittent high cirrus clouds
during those observations, and therefore we were only able to obtain relative J and Ks photometry.
Figure 5 presents the reduced Ks AO image for the 0.7 contaminator and the primary KIC target.
Using aperture photometry, we measure δKs = 1.67± 0.03 and δJ = 1.89 ± 0.04 mag difference.

We adopt the method developed by Howell et al. (2012) to extrapolate to the broad band Kepler
filter (Kp) using J and Ks colors. The measured relative J and Ks colors were combined with the
reported 2MASS photometric magnitudes (J=12.714, K=12.394) to obtain the true apparent Ks
and J magnitudes for both KIC 4862625 and the 0.7 contaminator. The 2MASS colors are a
summation of all three identified sources. The 3 contaminator is too faint in AO observations
to measure an accurate relative magnitude, but contributes at most at the percent level to the
infrared colors. Therefore, we chose to assume KIC 4862625 and the 0.7 contaminator are the
only contributions to the reported 2MASS colors. The KIC reports Kp= 13.71 mag for KIC
4862625. Using the filter transforms determined by Howell et al. (2012) we find a Kp magnitude of
13.79 for KIC 4862625 and 16.10 for the 0.7 contaminator is the Kepler target is a dwarf star. If it
is a giant, we estimate a Kp magnitude of 13.77 for KIC 4862625 and 16.21 for the faint companion.
Thus the 0.7 contaminator contributes 11-12% of the light in the light curve for KIC 4862625.

It is not surprising that we find a source less than 1 from KIC 4862625. Adams et al. (2012)
find that 20% of the Kepler candidates observed with adaptive optics have a close companion
within 2 , and Lillo-Box et al. (2012)report similar findings with 17% of their sample of Kepler
candidates examined had at least one contaminating source within 3 of the Kepler target. Using
the KIC stellar parameters and the expected galactic extinction, KIC 4862625 is approximately 1
kpc away, thus the projected distance between the binary and the 0.7 contaminator is ∼1000 AU.
Although gravitationally bound multistellar systems exist with such separations, we would need
measurements of the proper motions of both the binary (Aa and Ab) and the 0.7 contaminator
to confirm association. From the NGS AO observations alone, we cannot determine if the 0.7
contaminator is bound to the system. The time separation of our observations is insufficient to
measure proper motions, but the radial velocity observations (discussed in Section 5), find this
source has a systemic velocity consistent with that of the eclipsing binary. In addition the AO
observations reveal the 0.7 source is itself a binary. We further discuss the properties of this third
stellar component in detail in Section 6.

In order to estimate the brightness of the 3 contaminator and to quantify the contributions

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of additional faint stars 2-6 from KIC 4862625, we use R-band optical imaging from the remote
SARA 1m telescope on Kitt Peak. We obtained a series of 60 60s exposures on 2012 July 18 UT,
keeping individual exposures short so that all stars of interest remained in the linear count regime.
The co-added SARA image is presented in Figure 6. We used both elliptical model fitting and
PSF subtraction (from a similarly bright star without bright neighbors) to remove the wings of
the bright-star profile. Slight irregularities in the PSF shape made the subtraction of a scaled PSF
more successful. We estimate errors based on the scatter of photometry in independent fits from 6
10-exposure averages of the data. The photometric zero point was established from 20 nearby KIC
stars brighter than r=17.5, using photometry from Brown et al. (2011),ignoring the small color
term in transforming from R to Kepler bands. The image quality was 1.5 FWHM, well sampled
with 0.38 pixels. Measurements used apertures of 4-pixel (1.5 ). We estimate an R magnitude of
18.73 ± 0.05 for the 3 contaminator, providing 1% of the flux measured in the Kepler aperture. We
also identify an additional faint source located northeast of KIC 4862625. This star is 20.65 ± 0.09
R magnitude, much fainter than the 3 contaminator and contributes well less than a percent flux
dilution in the Kepler light curve. Any additional sources present within the Kepler photometric
aperture are fainter than 21st magnitude and will have negligible impact on the Kepler light curve
for KIC 4862625.

The dominant sources of additional flux to KIC 4862625’s light curve are the 0.7 and 3
contaminators. Combining the contributions from both stars, we assume 12-13% flux contamination
to the Kepler photometric aperture. Accounting for the dilution of the transit, the flux drop caused
by the planet now corrected to be 0.1%. We account for this additional light when modeling the
light curve and assessing PH1’s properties (discussed in Section 7). In Section 9.3, we revise this
estimate assuming the stellar properties obtained from the photometric-dynamical model and stellar
evolution models.

5. Radial Velocity Observations

Radial velocities were obtained with the HIgh Resolution Echelle Spectrometer (HIRES) (Vogt
et al. 1994) on the Keck I telescope on Mauna Kea, Hawaii from 2012 April 1- August 4. We
note that the time baseline and precision of these radial velocity measurements are insufficient to
constrain the mass of PH1 and only characterize the properties of the close binary (Aa and Ab).
These observations were taken with the standard setup used by the California Planet Survey (CPS)
(Howard et al. 2010; Chubak et al. 2012) with a typical resolution of R ∼55,000 covering 3642 to
7990 ˚. All Keck observations were taken with the C2 decker, except for the first observation,
A
which was taken with the B5 decker. The observations were reduced using a standard reduction
and extraction pipeline developed for the CPS (Howard et al. 2010; Chubak et al. 2012) and then
corrected for cosmic rays.

The radial velocities were measured using the spectral line broadening function (BF) technique
(Rucinski 1992). This method lends itself particularly well to double lined spectroscopic binaries

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where the radial velocity difference between the stars is on the order of the resolution of the spectral
observation or for high rotation stars where there is significant broadening of the spectral lines.
To compute the broadening functions, a spectrum of a slowly rotating single star is required as a
reference template. A single template spectra was used in the BF analysis for all the radial velocity
observations of KIC 4862625. The HIRES spectrum of HD 169830, an F7V star, taken on 2012
April 1 UT was used for this purpose in the BF analysis. The radial velocity of the template star
was assumed to be -17.4 km s−1 . The analysis returns a BF defined over a velocity range for each
set of spectral lines present in the observation. For each component, the respective broadening
function is fit to a aanalytic broadening kernel and the peak value is taken as the measured radial
velocity. A barycentric correction is applied to each of the obtained velocities and the contribution
of the template radial velocity is removed to obtain the true Doppler shifts for each component
identified in the BF analysis.

HIRES spectra are split on three CCD chips: blue (3642.9-4794.5 ˚), middle (4976.6-6421.4 ˚),
A A
and red (6543.2-7989.8 ˚). The BF analysis is applied separately to the spectra obtained on each
A
chip. The majority of HIRES observations were taken with the iodine cell in, which introduces the
iodine spectra superimposed on the stellar spectra on the middle chip. We find the HIRES spectra
are double-lined with two BFs: one with a narrow width and a second much broader function. Due
to the presence of the second velocity component, we chose to restrict ourselves to the blue chip
to measure radial velocities because the iodine lines made it more difficult to fit the BFs on the
middle chip, and the BFs on the red chip were weaker than those obtained on the blue chip. A
representative sample of the BFs obtained from the blue chip is plotted in Figure 7.

Table 3 lists the measured radial velocities and uncertainties for both BFs, and Figure 8a plots
the radial velocities obtained from both the wide and narrow BFs. A two component model was
used for all observations except for observations 9 and 12, which due to a nearly full moon, required
an additional third component in order to account for the contribution from sky line emission. The
peak velocity of the wide component varies as a function of the binary orbital period and is the
contribution from KIC 4862625. The narrow component is due to another source and is unchanging
with a nearly constant radial velocity over the 5 month time baseline of the HIRES observations.
The C2 decker is 14.0 long and 0.861 wide. The B5 decker is the same width but only 3.5 long.
For all observations the HIRES slit was aligned East-West on the sky. Located at a position angle
of 123 degrees East of North, the 0.7 contaminator contributes light into the HIRES slit at the
∼10% level, and thus is the additional narrow component identified in the BF analysis.

The radial velocities were fit with the Eclipsing Light Curve (ELC) code (Orosz & Hauschildt
2000). Although the spectra are double-lined the close binary (Aa and Ab) is a single-lined spec-
troscopic binary (SB1). Star Ab is too faint to be detected in the radial velocity observations,
and therefore we do not directly obtain the independent masses of Aa and Ab from the HIRES
observations alone. The ELC modeling ignores the gravitational effects of the planet and assumes
a two-body system. The ELC modeling cannot constrain the mass of the binary. Instead with the
radial velocity observations, the ELC fits for the binary’s (Aa and Ab) eccentricity (e), inclina-

– 11 –

tion (i), orbital period (P), time of conjunction (Tconj ), argument of periastron (w), radial velocity
semi-amplitude (KA ). The Kepler light curve was used in the fit to force a consistent binary orbital
phase and eccentricity. The best-fit parameters are reported in Table 4. The resulting radial veloc-
ity model and radial velocity residuals are plotted in Figure 8a. The radial velocity measurement
error for KIC 4862625 was scaled by a factor of 11.2 to produce a reduced χ2 of 1 for the model
fit. We note the 0.7 contaminator has a mean radial velocity (19.12 ± 0.49 km s−1 ) very close to
that of the systemic velocity obtained for the eclipsing binary, 17.82 ± 0.03 km s−1 .

The ELC fit for KIC 4862625 is poor with 1-2 km s−1 residuals for the best-fit solution. With
the CPS observing setup, HIRES is aligned such that that ThAr lines across the echelle format
fall on the same CCD pixels, to sub-pixel precision such that the obtained HIRES spectra have
the same wavelength solution, accurate to about a pixel (1.4 km s−1 ). The HIRES wavelength
solution zeropoint and dispersion varies within a 1 pixel between observations within a single night
and on separate nights, which is on the order of 1 km s−1 . We do not correct for this effect in
the BF analysis and this is thus the largest source of uncertainty in our velocity measurements.
Subtracting the mean radial velocity of the 0.7 contaminator from its measured values, we find
that the residuals are directly correlated with the ELC fit residuals for KIC 4862625 (see Figure
9). If we assume the 0.7 contaminator has a constant radial velocity, we can use it to correct for
the instrumental systematics in each observation’s wavelength solution. We apply the narrow BF
velocity residual as a linear offset to correct each of the radial velocities measured for KIC 4862625.

With the offset-corrected radial velocity observations, the ELC fit is significantly improved
with typical residuals of 0.5 km s−1 or smaller. The radial velocity measurement error for KIC
4862625 was scaled by only a factor of 4.63 to produce a reduced χ2 of 1. Table 5 lists the offset
corrected radial velocities for KIC 4862625, and the model parameters are reported in Table 4.The
ELC model fit model and residuals for the revised KIC 4862625 radial velocities are plotted in
Figure 8b. Overplotted on Figure 8b are the radial velocities of the narrow BF component, the 0.7
contaminator, also corrected by the same instrumental offset applied to the KIC 4862625 values.

With the correction, the systemic radial velocity of KIC 4862625 is found to be 18.18 ± 0.03
km s−1 . The average velocity of the 0.7 contaminator (19.12 ± 0.49 km s−1 ) is within the 2-
σ uncertainty of the binary’s systemic radial velocity. Within measurement uncertainty the 0.7
contaminator has the same radial velocity as the systemic velocity of KIC 4862625. Even before the
offset corrections for the radial velocity values, the measured systemic velocity of the binary was
17.82 ± 0.03 km s−1 , within 3-σ of the mean radial velocity of the 0.7 contaminator. Given that
velocity dispersion of random field stars in the Galaxy is between 20 and 60 km s−1 (e.g. Wielen
1977), the radial velocity of the 0.7 contaminator matches the systemic velocity of KIC 4862625.
At such large separations (∼ 1000 AU), the barycentric motion in such a wide binary would be
negligible and bound stars would have the same proper motions and systemic radial velocities. This
criterion has been used to identify wide binary star systems (e.g. Tokovinin 1997; Pribulla et al.
2009), and we adopt it here. Thus Aa, Ab, and the 0.7 contaminator are common radial velocity
stars and therefore associated. We note that follow-up observations to measure the common proper

– 12 –

motion or orbital acceleration of these stars in the future could solidly confirm their association.
Thus, the third source, the 0.7 contaminator, is bound to the eclipsing binary (Aa and Ab) in a
hierarchical architecture. We further discuss the implications in Section 6.

6. Additional Stellar Companions

The radial velocity observations strongly indicate that the 0.7 contaminator (located at
roughly ∼1000 AU from KIC 4862625) is likely associated with the eclipsing binary (Aa and Ab)
in a wide binary. Further inspection of the AO observations reveals that the 0.7 contaminator
is itself a visible double. The point-spread function (PSF) of the 0.7 contaminator is elongated
compared to the circular PSF of KIC 4862625 (see Figure 10). The one-dimensional full width-half
maximum (FWHM) in the vertical direction is almost exactly twice as wide as the primary (KIC
4862625). This was observed on both nights of AO observations. Thus, the 0.7 contaminator is
itself a wide visual binary, making the KIC 4862625 system a quadruple star system, and the first
identified to host a planet.

The AO observations barely resolve the outer star system, which we will label ‘Ba’ and ‘Bb’.
Our rough estimate of the AO Ks -band brightness difference of 1.0 ± 1.0 mag. Both Ba and Bb
contribute flux to the Keck spectra with nearly equal brightness. Both stars contribute to the second
broadening function identified in the Keck spectra and both have the systemic radial velocity of
Aa and Ab. Thus, Ba and Bb are associated with the close binary (Aa and Ab) and are bound
gravitationally to the system. We are unable to ascertain an accurate projected separation between
the two stars, but we estimate that it must be less than 0.04 ( < ∼40 AU). In Section 9.3, using
stellar evolution models. we estimate the spectral type of Ba and Bb and more accurately estimate
both their projected separation and their projected distance to KIC 4862625.

This quadruple stellar system is configured as a close eclipsing binary (Aa and Ab) and a wide
binary (Ba and Bb) arranged with a projected distance between the two binaries that is larger
than the physical separation between the individual stars in the binary components. This is not
an atypical stellar architecture; Tokovinin (2001) and Correia et al. (2006) identify nearly half of
their sample of quadruple systems in such a two pair hierarchical structure. The two binary pairs
are only weakly bound to each other. Interactions with passing stars and molecular clouds can
dynamically disrupt and ionize wide binaries with separations on the order of 1000 AU (Heisler
& Tremaine 1986; Jiang & Tremaine 2010). Kaib et al (2012) find for two star wide binaries,
after 10 gigayears 90% of systems with semimajor axes greater than 3000 AU are ionized. Those
with smaller semimajor axes survive much longer. We expect the results to be similar for two
-pair hierarchical systems, and thus expect such stellar systems separated by a few thousand AU
to survive for 10 gigayears or longer. Thus the presence of the additional Ba and Bb does not
significantly constrain the age of the planetary system.

With the radial velocity observations we can only ascertain that the visual binary is gravita-

– 13 –

tionally bound to stars Aa and Ab. With only one epoch of adaptive optics observations we do not
have a sufficient time baseline, to measure their motion on sky, and accurately determine their orbit
around Aa and Ab. Future adaptive optics observations may be able to measure a proper motion
and constrain the orbits of the visual binary. Orbital integrations with MERCURY (Chambers
1999) of Ba and Bb assuming circular orbits with semimajor axes of 1000 AU around Aa and Ab
find that on timescales of gigayears, there is little effect from the distant binary on the planet’s
orbit and the eclipsing binary’s (Aa and Ab) orbits. This is consistent with the results of Kaib
et al (2012) who that only for wide-binary systems with semimajor axes less than 10E3 AU, is
eccentricity pumping observed in the planet’s orbit, thus the effect from Ba and Bb on the planet
is negligible.

7. Photometric-Dynamical Model

To constrain the orbital and physical properties of the stars and planet, we employ a ‘photometric-
dynamical’ model, as has been applied to the previously discovered Kepler transiting circumbinary
planets (Doyle et al. 2011; Welsh et al. 2012; Orosz et al. 2012a,b) fitting the combined radial
velocity observations and Kepler light curve data. In this model, the two host stars (Aa and Ab)
and the planet interact according to Newtonian gravity. The effects of the wide binary (Ba and
Bb) are not observable in the Kepler data, and thus were not included in our dynamical model.
The initial coordinates of the three bodies (Aa, Ab, and the planet) are specified at a particu-
lar time (in this case t0 = 2,454,970 BJD) and their positions at any other time are calculated
via numerical integration. Positions are calculated at the times of the Kepler observations and
used as inputs to produce a light curve model. The light curve model presumes spherical planet
and stars with radial brightness profiles specified according to a quadratic limb darkening law
(I(µ) = I0 (1 − uAa (1 − µ) − vAa (1 − µ)2 )).

In previous applications of the photometric-dynamical paradigm, the eclipses of the stellar
binary and the transit events due to the planet(s) were modeled self-consistently. The goodness-
of-fit metric, for the best-fitting model, describing the eclipsing stellar binary data alone (i.e.,
considering just the data at primary and secondary stellar eclipses) was verified to be acceptable
in isolation from the planetary events in these cases. As we will describe in more detail below, the
joint photometric-dynamical fit to both stellar and planetary eclipse events (and the subsequent
parameter posterior calculation via Markov Chain Monte Carlo simulation) indicated a solution
for the stellar events that was marginally unsatisfactory. In detail, the joint fit yielded parameters
describing the stellar eclipse data that were 1 − 2σ departures from those same parameters when
fitting the eclipsing binary data alone. In particular, this bias appears to affect the bulk parameter
estimates of the stars at the ∼2-σ level. This error is barely perceptible (by eye) in the photometric
residuals and only weakly significant in the resulting parameter posteriors; however, the bias is
statistically clear. We posit that the failure of the model to adequately describe the data is due
to either missing mass components (e.g., a fourth body), an overly simplified treatment of the

– 14 –

light curve noise (e.g., correlated noise may be corrupting information gleaned from the planetary
transits) and/or deterministic light curve features that could not be clearly modeled in this analysis
(spot crossing during transits). We argue below, after describing our model and analyses, that the
latter two options are more likely than invoking a fourth body given the significance of the anomaly.

The photometric-dynamical model describing all eclipse events has 23 parameters. All pa-
rameters have uniform priors (over open intervals unless otherwise specified). Eleven parameters
describe the Jacobian coordinates of the stellar binary and the binary comprised of the center-of-
mass of the stellar binary and the planet. These eleven parameters are osculating Keplerian terms
(one set for each ‘binary’) that are slowly varying in time: a period, two linearly-independent pa-
rameters involving the eccentricities and arguments of periastron, a sky-plane inclination, a time
of conjunction and longitude of the ascending node. Only one nodal angle need be specified as
the absolute nodal longitude (relative to North) cannot be determined from the data; we fix the
longitude of the stellar binary to zero. We encode the eccentricity and argument of periastron of
the stellar binary as components of a vectorial eccentricity: eA = [eA sin ωA , eA cos ωA ]. Those for
√ √
the binary including the planet involve a square-root in the amplitudes ([ eb sin ωb , eb cos ωb ]) to
simplify the specification of uniform priors in eb and ωb . In addition to the coordinates, we must
specify the masses of all three bodies. We do so by specifying the mass of star Aa (times the
gravitational constant), GMAa , and then ratios of MAa : q = MAb /MAa and qp = Mb /MAa - both
of which have positive priors. We parameterize the density of star Aa – this quantity is directly
measurable from the light curve when the mass ratio q is constrained by the planetary events.
Six more parameters describe the eclipse and transit light curve: the radius ratios of stars and
planet, RAb /RAa , Rb /RAa , the contaminating flux in the Kepler bandpass relative to that of star
Aa, FX /FAa , the flux of star Ab to Aa, FAb /FAa , and two limb darkening parameters of star Aa,
uAa and vAa . The limb darkening parameters were restricted to physically plausible values with
the linear constraints 0 < uAa < 1, uAa + vAa < 1. The limb darkening coefficients of the secondary
star had a negligible affect of the overall fit and were fixed to uAb = 0.6, vAb = 0.1. The width of
the assumed normal, uncorrelated noise of the photometric data was also fitted (σLC ). Finally, we
specify the offset of the radial velocity data and a radial velocity jitter term, added in quadrature
to the formal radial velocity errors.

Only data within 1 day of either a stellar eclipse or planetary transit were considered. This
corresponds to 5302 cadences of data at primary or secondary eclipse and 521 cadences of data
near planetary transit (some of these cadences appear in both data sets as transits occur in close
proximity to eclipses, at times). These data were initially corrected for a cubic trend in time
excluding the eclipse events. After an initial photometric-dynamical fit, this cubic fit was repeated,
this time including all data after having divided out this best-fitting model for the eclipses. The
level of the out-of-eclipse flux is determined inline prior to the computation of the likelihood (given
below). In other words, for a given parameter set p, we divide out the eclipse model then determine
the mean of the residuals and divide through by this value prior to computing the likelihood. This
linear parameter is weakly correlated with the remaining parameters and trivially marginalized

– 15 –

over.

The likelihood of a given parameter set p was specified as
 
NRV
−1 (∆FiLC )2 2 2 −1/2 (∆Vj )2
L(p) ∝ σLC exp − 2 × σj + σRV exp −  (1)
i
2σLC j
2 2
2 σj + σRV

(FX /FAa − 0.12)2
× exp −
2(0.02)2

where ∆FiLC is the ith photometric data residual, σLC is the width parameter describing the
photometric noise of the long cadence data, ∆Vj is the jth radial velocity residual, σj is the
uncertainty in the jth radial velocity measurement and σRV is the stellar jitter term added in
quadrature with the σj . The final product in the second line of the above equation enforces a
Gaussian prior on the contamination of FX /FAa = 0.12 ± 0.02, appropriate given the discussion in
Section 4.

We first performed a fit to the combined eclipse and planetary transit data (hereafter the ‘joint
solution’) and determined credible intervals in the above parameters using a Differential Evolution
Markov Chain Monte Carlo algorithm (DE-MCMC; ted Braak 2008). In detail, we generated a
population of 100 Markov chains in an overdispersed region covering the final posterior and evolved
through 19,000 generations until the chains showed adequate convergence according to the standard
metrics. These chains were concatenated after removing a portion of ‘burn-in.’ Results from this
analysis, in the form of medians and 68% credible intervals, are reported in the first data column
of Table 6.

Investigating the parameters from the joint solution, we see that the contamination term is 2σ
lower than the expectation (even with a Gaussian prior enforced). It is not expected that the stellar
binary eclipse data alone would be sufficient to measure or constrain the level of contamination –
this drew further investigation. We isolated the data involving the stellar eclipses alone (hereafter
’EB-only’) and repeated our analysis (with the same model). We fixed the planetary mass ratio
to zero and varied only those parameters relevant to modeling the eclipsing binary (light curve
and RV data). In particular, we fixed all osculating Keplerian elements of the planetary binary
and the mass ratio of the stellar binary to those found from the joint solution. Fifty chains were
evolved through 25,000 generations in the DE-MCMC. The results of this EB-only analysis are
provided in the second data column of Table 6. Without any information on the stellar mass ratio
from the timings of the planetary events, we were unable to provide absolute dimensions to the
stars or planet; instead, we report standard measured quantities from the analysis of an eclipsing,
single-lined spectroscopic binary (SB1). This analysis shows, as was expected, that the EB-only
analysis has no preference in contamination – its marginalized posterior reflects the prior. The
remaining EB-only parameters, which are correlated with this contamination level, are also 1 − 2σ
biased relative to the joint solution equivalent parameters as a consequence. The EB-only solution
was only weakly preferred over the joint solution with ∆χ2 ≈ 30 when considering just the data

– 16 –

involving the stellar eclipses, the radial velocity data and the contamination prior (see below for
further details).

We suspected that our inability to accurately model the planetary events was driving the
bias in contamination. To investigate this, we completed a third analysis by fixing the best-fitting
solution for the eclipsing stellar SB1 (from the EB-only analysis above) and fitting for the planetary
binary orbit and the stellar mass ratio considering only data involving the planetary events. In
practice, this involved fixing the 11 osculating elements of the stellar binary, the normalized lengths
RAa /a, RAb /RAa , flux ratios, limb darkening coefficients and the mass function as determined from
the best-fitting EB-only model. Forty chains were evolved through 64,000 generations. The results
of this analysis are reported in the final data column of Table 6. In addition to those parameters
directly measured from this analysis (the osculating elements of the planetary binary, the stellar
mass ratio and the planetary radius ratio) we report parameter posteriors (daggered values in
Table 6) assuming the independence of EB-only and planetary, EB-fixed solutions. For example,
the mass of star Aa is determined assuming the mass function determined in the EB-only analysis
and the mass ratio in the planetary, EB-fixed analysis are independent (simple propagation of errors
renders our resulting hybrid posterior).

We compared the best-fitting solutions from the three analyses to help elucidate the nature
of the anomaly. First, we adopted the value of σLC = 203.157 ppm as derived from the EB-only
analysis. We assert that the model describing the stellar eclipses is less sensitive to potential
correlated noise sources (stochastic sources or from spot-crossings, for example), as the eclipse
events are approximately identical at each epoch (outside of insignificant timing anomalies due to
the planet), and provides a more robust measure of the uncorrelated noise component. We note that
this value of σLC is within 12% of the root-mean-square of the best-fit EB-only residuals. Having
adopted this width, we compute the traditional χ2 statistic for the various contributions to the
likelihood. The difference in χ2 between the joint solution and the EB-only solution considering
only the radial velocity is negligible. For the 5302 cadences involving only the stellar eclipses
we find χ2 = 5314.36 and χ2 = 5290.02 for the joint and EB-only (or EB-fixed, planetary)
EB EB
solutions, respectively. The eclipsing binary solution has 5290 degrees of freedom (after having
excluded parameters relating to the RV data, the planet, the planet orbit and stellar mass ratio)
which suggests the EB-only solution is marginally preferred over that from the joint solution. When
considering the 521 cadences associated with planetary transits alone, we find χ2 L = 478.367 and
P
χ2 L = 520.572, for the joint and EB-fixed, planetary solutions, respectively. The model for the
P
planetary events alone has 512 degrees of freedom. Despite the preference for the lower χ2 L from the
P
joint solution (which accounts for the overall lower χ2 of the joint solution despite the contamination
prior and the worse-fitting EB solution), the χ2 L of the EB-fixed solution is acceptable (with a 38%
P
probability of having a χ2 larger than 520.572). Given this and our confidence in our estimation
EB
of the contamination prior, we conclude that the preferred EB-only solutions, tabulated in the final
two columns of Table 6 provide the most accurate assessment of the system parameters. We adopt,
however, the limit on the mass of the planet from the joint analysis.

– 17 –

8. ELC Model Fit

The ELC modeling can be used as an independent check on the binary properties derived
from the photometric-dynamical modeling effort. The ELC ignores the gravitational effects of the
planet, which in this case are negligible over the duration of the Kepler light curves. Because Ab
is too faint to be observed in the HIRES spectrum, ELC cannot obtain an independent mass for
Aa and Ab or the absolute radii of Aa and Ab. Combining the radial velocity observations and the
Kepler light curve, the ELC fits for binary’s (Aa and Ab) eccentricity (e), inclination (i), orbital
Period (P), time of conjunction (Tconj ), argument of perihelion (w), radial velocity semi-amplitude
(KA ). the fractional radii of Aa and Ab (RAa /a and RAb /a), flux contamination, the binary
temperature ratio (TAb /TAa ), and limb darkening parameters for star Aa (uAa and vAa ) assuming
the same quadratic limb darkening law identical to that used in the photometric-dynamical model
(as described above in Section 7). Table 8 lists the physical and orbital parameters for Aa and Ab
obtained from the ELC fit. The ELC-derived values are consistent with those obtained from the
photometric-dynamical modeling ’EB only’ solution (see Table 6) within the 1 − σ uncertainties.
Thus we are confident in the physical and orbital parameters derived in the ’fixed EB’ solution for
PH1 and its host stars.

9. Stellar Properties

In the following section, we further discuss and explore the stellar properties of all four stars
in the hierarchical system. The resulting best-fitting parameters and their uncertainties for Aa
and Ab from the photometric-dynamical model are summarized in Table 6. Derived physical and
orbital parameters for Aa and Ab are listed in Table 7 for the fixed EB’ solution. The primary star
(Aa) is an F dwarf ( 1.734 ± 0.044 R , 1.528 ± 0.087 M ) and Ab is M dwarf (0.378 ± 0.023 R ,
0.408 ± 0.024 M ). Using HIRES spectroscopic observations we further constrain the properties
of the primary star in the eclipsing binary (Aa). With stellar evolution models, we estimate the
ages and properties of the planet host stars (Aa and Ab) and the visual binary (Ba and Bb).

9.1. High Resolution Spectroscopy

To refine the physical properties of star Aa, the HIRES spectrum from 2012 August 4 UT,
was fit with Spectroscopy Made Easy (SME) (Valenti & Piskunov 1996; Valenti & Fischer 2005).
Modeling the stellar parameters with specific gravity remaining fixed at the value obtained from
the photometric-dynamical model, log(g)=4.14, the SME analysis finds: Tef f =6407 ± 150 K,
vsini=32.6 ± 2.0 km s−1 , and [Fe/H]= +0.21 ± 0.08 for Aa. Although Ba and Bb will have a
∼10% flux contribution to the spectrum, the high rotational velocity, which produces a significant
broadening of the spectral lines, will be the largest source of uncertainty and constraint on the
precision of the best-fit SME stellar parameters. The temperature estimate is consistent with that

– 18 –

of an F star. Combining the SME temperature estimate of Aa with the ELC binary temperature
ratio (TAb /TAa ), we find Ab has a temperature of 3561 ± 150 K.

9.2. Stellar evolution modeling

Combining the results from SME, ELC, and the photometric-dynamical modeling, our deter-
mination of the masses, radii, and temperatures of both stars in the eclipsing binary (Aa and Ab),
in addition to our knowledge of the metallicity of the system, permit a more stringent comparison
with models of stellar evolution with fewer free parameters than if the composition were unknown
(see, e.g., Andersen 1991; Torres et al. 2010). This test is particularly interesting for the low-mass
secondary. Relatively few systems containing M dwarfs with precise (and accurate) determinations
are available, and these stars have shown significant disagreements with theory in the sense that
they tend to be larger and cooler than predicted (Ribas 2003; Torres & Ribas 2002; L´pez-Morales
o
& Ribas 2005; Morales et al. 2009; Torres 2012)

Figure 11 compares the measured properties of the Aa star in the Teff –log g plane with models
from the Y2 (Yonsei-Yale) series (Yi et al. 2001). An evolutionary track (solid line) is shown for
the measured mass and metallicity of the star, with the 1-σ uncertainty in the location of the track
coming from the observational errors being represented by the shaded area (dark gray reflecting
the mass error only, and light gray including also the uncertainty in the metallicity). Isochrones
are indicated with dotted lines for ages from 1 to 13 Gyr. There is good simultaneous agreement
with the mass, radius, and temperature of the Aa within the uncertainties, for an age of roughly 2
Gyr, according to these models.

In Figure 12 we present another comparison using models from the Dartmouth series (Dotter
et al. 2008), in which the physical ingredients (including the equation of state and the non-gray
boundary conditions between the interior and the atmosphere) are more realistic for stars signif-
icantly below 1 M . With the reasonable assumption that the composition is the same for the
two objects, there is again satisfactory agreement between the models and the observations in the
mass–radius diagram shown in the top panel, also for Ab. The age we infer based on the primary
properties is 1–2 Gyr, similar to the previous estimate. The predicted flux ratio between the stars
in the Kp band is 0.0011, according to these models, which is not far from our measurement based
on the photometric-dynamical model (Table 6). The mass–temperature diagram in the lower panel
of Figure 12 indicates that the temperatures of both stars are consistent with predictions, given
our uncertainties, and again suggest an age near 2 Gyr.

The results for the Ab go against what has usually been found for other low-mass stars in
eclipsing binaries. Most previous studies have shown that M dwarfs in such systems are typically
“inflated” by up to 10% or so, and have their temperatures suppressed by up to about 5%. This
is believed to be due to magnetic activity, as most of those systems are close binaries in which
the stars are tidally synchronized and are rotating rapidly. This enhances their activity, which is

– 19 –

usually manifested by modulations in the light curve produced by spots, X-ray emission, and other
phenomena, and leads to the observed effects (e.g., Mullan & MacDonald 2001; Chabrier et al.
2007). For the PH1 system we find, on the other hand, that the size of the Ab is consistent with
theoretical expectations, and so is its temperature. Unfortunately we have no information on the
activity level of the Ab, which is some 700 times fainter than the primary.

The current precision of the measurements is about 6% in the masses and 3–6% in the radii
of the stars in PH1, while the temperatures are only good to about 150 K, mostly limited by the
rotationally broadened spectral lines of the primary. Additional spectroscopic observations and
further data from Kepler should help to reduce some of these uncertainties, providing for an even
more stringent test of models.

9.3. Photometric deconvolution

An additional estimate of the contamination level in the Kp band is possible using available
multi-color photometry for the system and the stellar evolution models. The photometric measure-
ments in the KIC, as well as the near-infrared magnitudes from 2MASS, contain significant light
from four stars: the two components of the eclipsing binary, and those of the 0.7 contaminator.
We assume here that the 3 contaminator is angularly separated enough that these magnitudes
are unaffected. With the additional assumption that the four stars are physically associated (see
Section 6), we carried out a deconvolution of all the magnitude measurements using fluxes from a
model isochrone, for which we adopted a 2-Gyr Dartmouth model that provides a good fit to the
properties of the eclipsing pair (Aa and Ab)(Sect. 9.2). Note that those properties (in particular the
radii and temperatures of the eclipsing components) depend to some extent on the level of contam-
ination adopted in the photometric-dynamical modeling of the Kepler light curve, so we proceeded
by iterations between the photometric deconvolution described below, the photometric-dynamical
modeling, and the model isochrone fitting.

To deconvolve the combined light of the four stars (SDSS griz, 2MASS JHKs , and the cus-
tom D51 magnitude from the KIC) we fixed the masses of components Aa and Ab to their values
obtained from the photometric-dynamical model, which sets their fluxes in all passbands from the
isochrone. We then added the masses of Ba and Bb as free parameters, along with the distance
modulus and reddening, and performed a grid search on those four variables to find the best match
between the predicted and measured values of the combined light. Appropriate reddening correc-
tions were applied to each passband. To constrain the masses of stars Ba and Bb we additionally
used our measurement of the brightness difference of their combined light relative to Aa and Ab,
from our AO measurements (∆J = 1.89±0.04, ∆Ks = 1.67±0.03). As a further constraint to allow
a distinction between Ba and Bb we used a rough estimate of the Ks -band brightness difference
between those stars from the AO image, of 1.0 ± 1.0 mag.

We obtained a good fit to all photometric measurements to well within twice their uncertainties,

– 20 –

in most cases, and estimates for the masses of stars Ba and Bb of ∼0.99 M and ∼0.51 M ,
corresponding approximately to spectral types G2 and M2. The fitted distance modulus corresponds
to a distance of about 1500 pc. The combined apparent brightness of Ba and Bb in the Kepler band
amounts to 10.5± 2.5% of the light of Aa and Ab. From its measured brightness of R = 18.73± 0.05
the 3 companion contributes an additional 1%. This is consistent with our initial estimates of
contamination presented in Section 4 and assumed in our photometric-dynamical modeling. Our
distance estimate along with the angular separation of the Ba and Bb binary from the target
translates to a linear separation of about 1000 AU. Stars Ba and Bb are separated by roughly 60
AU.

9.4. Stellar variability

In addition to the eclipses and transits, the Kepler light curve exhibits low-amplitude variability
on a timescale of a few days. With KIC 4862625 providing ∼90% of the flux in the light curve,
we attribute this variability to Aa. To further analyze this modulation, we mildly detrended the
light curve by omitting the eclipses and removing low-frequency power by using a polynomial or a
wide Savitzy-Golay filter (50 cadences on each side). Outliers greater than 4-σ from the mean were
omitted. A Fourier analysis revealed a strong signal with a period of 2.6397 ± 0.0014 days; this
period is consistent with an autocorrelation analysis. The periodicity is present in all Quarters,
and was confirmed by phase folding each Quarter. The amplitude is on average 300 ± 60 ppm,
though its amplitude is noticeably diminished in Quarters 10 and 11. We note that no correction
for contamination has been applied in this amplitude estimate.

In stellar binaries, spin-orbit alignment is expected to be the first to occur. Next is synchro-
nization of the rotation of the two stars with the orbital motion. Orbital circularization is predicted
to be the last to occur (see Mazeh 2008 and references within). If we assume the modulation is
caused by a long-lived cluster of starspots on the primary star (Aa), the periodicity is then the
rotation period of the star. Using the radius of the star derived from the photometric-dynamical
model and the inclination of the binary, a predicted projected rotation velocity of v sin i = 33.2 ±
0.9 km s−1 is derived, is consistent with the observed value (vsini=32.6 ± 2.0 km s−1 ) obtained
from the SME analysis. This agreement lends credence to the hypothesis that starspot modulation
is the source of the periodicity, that the stellar radius is correct, and that the spin axis of the star
is mostly aligned with the orbital axis of the binary. It follows that that the stellar spin is very far
from being tidally locked into a pseudosynchronous spin state; a period of 15.5 days is expected
using the formulation of Hut (1981). This implies the binary (Aa and Ab) is a relatively young
system with an age less than approximately 9 Gyrs consistent with the findings from the stellar
evolution modeling in Section 9.2.

We note that we cannot rule out a γ-Doradus type stellar oscillation as the source of the
2.64 day modulation. This alternative hypothesis is attractive because of the sinusoidal shape of
the modulation and long-duration stability of the modulation (in amplitude and phase), but the

– 21 –

change in amplitude in Quarters 10 and 11 and the excellent agreement with the expected rotation
period from Vrot sin i make the starspot hypothesis more attractive. The primary eclipse fits do
not show correlated residuals indicative of a starspot crossing, so the starspot hypothesis cannot
be unambiguously confirmed as was done in the case of Kepler-47 (Orosz et al. 2012b).

10. Planet Properties

Derived physical and orbital parameters for the transiting planet, PH1, are listed in Table
7. The best-fit radius for PH1 is 6.18 ± 0.17 R⊕ . Without eclipse timing variations on the host
stars (Aa and Ab), the photometric-dynamical model can only place an upper limit on the mass of
the planet. At the 99.7% confidence level, planet’s mass must be less than 169 M⊕ (0.531 Jupiter
masses). With a sub-Jupiter mass and radius, the transiting body is well within the planetary
regime, making PH1 Planet Hunters’ first confirmed planet.

Figure 13 shows schematic diagrams of the stellar and planetary orbits. Assuming Aa is the
dominant source of insolation, neglecting the small impact of Ab on the surface temperature, we
estimate the equilibrium temperature for PH1. Assuming a Bond albedo of 0.3 (similar to that
of Neptune) and emissivity of 0.9, we estimate a minimum and maximum attainable equilibrium
temperatures for PH1. We find a minimum temperature of 524K and a maximum at 613 K. Thus,
PH1 is too hot to be in the habitable zone. Although PH1 is a gas giant planet, even if there is
a possibility of rocky moons orbiting the body, their surfaces would be too hot for liquid water to
exist.

The individual planet transits and the best-fitting model are plotted in Figure 14. All seven
transits of PH1 were across star Aa. With a mutual inclination of 2.619 ± 0.057◦ , the projected
orbits of PH1 and Ab could overlap, but the planet would only transit the face of the Ab near
quadratures, making this a rare event. If there is a chance alignment where PH1 does transit
across Ab, due to the much fainter magnitude of Ab, the total transit signal-to-noise of that event
would be below the Kepler point-point noise of 203 ppm. Thus transits across Ab would be at too
a low signal-to-noise to be identified in the light curve.

The derived upper mass limit of 169 M⊕ is the mass required to perturb the orbits of the Aa
and Ab such that it would induce eclipse timing variations, and therefore likely to be much higher
than the true mass of the planet. Using the radius-mass relationship derived from Lissauer et al.
(2011) and (Kane & Gelino 2012, private communication), we find a more reasonable mass range
for PH1 lies is somewhere around 20-50 M⊕ or 0.08 - 0.14 Jupiter masses. As noted by Orosz
et al. (2012b), all transiting circumbinary planets, including PH1, are Saturn-sized or smaller. This
trend may support the Pierens & Nelson (2008) prediction that Jupiter-mass circumbinary planets
should be rare due to being ejected or scattered out to the edge of circumstellar disk, but this
result is far from confirmed. The detection biases have yet to be characterized for any of the
circumbinary searches, as is the case for sPlanet Hunters as well. PH1 was found serendipitously,

– 22 –

and a systematic search of the Kepler eclipsing binaries has yet to be performed.

11. Orbital Stability and Formation

Following the analytic approximation given by Holman & Wiegert (1999), the critical orbital
period and radius in this binary below which the planet’s orbit could experience an instability is
respectively 107 days and 0.55 AU. Like the previously discovered Kepler circumbinary planets,
with a best-fit orbital period of 138.317 days and semimajor axis of 0.652 AU, the orbit of PH1 is
very close to the edge of stability, being only 29% above the critical period and only 18.6% larger
than the critical orbital radius. Orbital integrations using MERCURY (Chambers 1999) of the
system using best-fit physical and orbital parameters for Aa, Ab, and PH1 (neglecting the effects
of Ba and Bb), confirm that the system is indeed stable on gigayear time scales.

With the long-term stability of the PH1 system, the existence of the planet has implications
for formation scenarios of the stellar system and other multistellar systems. Fragmentation and
n-body dynamical interactions have been proposed as mechanisms for the formation of stellar
systems composed of 3 or more stars. The existence of PH1 itself suggests that there has been little
interaction of the outer binary (Ba and Bb) with the inner eclipsing binary (Aa and Ab). Any
dynamical close encounters between (Aa and Ab) and an additional star early on in its formation
would have perturbed the surrounding circumbinary disk, likely obliterating the planetesimal disk
and preventing accreting planetary cores from forming. Thus Ba and Bb have likely not had a
close encounter with Aa and Ab. The existence of PH1 suggests rather than N-body interactions,
fragmentation in the molecular cloud is the likely scenario for the formation of the four-star system,
preserving the planetesimal disk around Aa and Ab to grow PH1.

12. Conclusions

In this paper we have characterized the properties of the first confirmed planet in the Kepler
field found by Planet Hunters citizen science project. PH1 is a new circumbinary planet orbiting an
eclipsing binary (KIC 4862625) in a hierarchical quadruple star system. From follow-up observations
and analysis of the planetary system we conclude the following:

1. PH1 is a 6.18 ± 0.17 R⊕ planet on a 138.317+0.40 day orbit. At the 99.7% confidence level,
−0.027
we place an upper limit mass of 169 R⊕ (0.531 Jupiter masses).

2. PH1’s host stars are an eclipsing binary (Aa and Ab) with a 20.0002468 ± 0.0000044day
period. Aa is a 1.734± 0.044 R and 1.528 ± 0.087 M F dwarf. Ab is a 0.378 ± 0.023 R
and 0.408 ± 0.024 M M dwarf.

3. Adaptive optic observations reveal an additional pair of stars in a visual binary (Ba and Bb)
contaminating the Kepler photometric aperture, likely composed of a G2 and a M2 stars, at a

– 23 –

projected distance of sim1000 AU. Radial velocity observations confirm the pair is associated
and bound to the planetary system.

4. We estimate the age of the planetary system based on stellar evolution models of Aa and Ab
at ∼2 Gyrs.

The frequency and range of orbital configurations for circumbinary and other multistar plane-
tary systems has yet to be fully explored, but with this seventh confirmed transiting circumbinary
planets, we are moving closer to probing this parameter space. These planetary systems provide
new boundary conditions for planet formation This ever increasing sample of dynamically extreme
planetary systems will serve as unique and vital tests of proposed planetesimal formation models
and core accretion theories (Bate et al. 2000; Pierens & Nelson 2008; Paardekooper et al. 2012;
Meschiari 2012; Alexander 2012). PH1 was found serendipitously by Planet Hunters volunteers
examining the light curves of the known Kepler eclipsing binaries. The discovery of PH1 highlights
the potential of visual inspection through crowd sourcing to identify planet transits in eclipsing
multistar systems, where the primary and secondary eclipses of host stars make detection challeng-
ing compared to planets with single host stars. In particular, Planet Hunters may exploit a niche
identifying circumbinary planetary systems where the planet is not sufficiently massive to produce
measurable eclipse timing variations that would be identifiable via automatic detection algorithms.

Acknowledgements

The data presented in this paper are the result of the efforts of the Planet Hunters volunteers,
without whom this work would not have been possible. Their contributions are individually ac-
knowledged at http://www.planethunters.org/authors. We also acknowledge the following list of
individuals who flagged one or more of the transit events on Talk discussed in this paper before or
after discovery of the planet: Hans Martin Schwengeler, Dr. Johann Sejpka, and Arvin Joseff Tan.

MES is supported by a National Science Foundation(NSF) Astronomy and Astrophysics Post-
doctoral Fellowship under award AST-1003258 and in part by an American Philosophical Society
Franklin Grant. JAO and WFW acknowledge support from the Kepler Participating Scientist
Program via NASA grant NNX12AD23G and the NSF via grant AST-1109928. JAC acknowledges
NASA support through Hubble Fellowship grants, awarded by STScI, operated by AURA. DAF
acknowledges funding support from Yale University and support from the NASA Supplemental
Outreach Award, 10-OUTRCH.210-0001. GT also acknowledges support from NSF through grant
AST-1007992. CJL acknowledges support from The Leverhulme Trust. KS acknowledges support
from a NASA Einstein Postdoctoral Fellowship grant number PF9-00069, issued by the Chandra
X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for
and on behalf of NASA under contract NAS8-03060. The Planet Hunters ‘Talk’ discussion tool
used was developed at the Adler Planetarium with support from the NSF CDI grant: DRL-0941610.

The data presented herein were partly obtained at the W. M. Keck Observatory, which is op-

– 24 –

erated as a scientific partnership among the California Institute of Technology, the University of
California, and the National Aeronautics and Space Administration. The Observatory was made
possible by the generous financial support of the W. M. Keck Foundation. We thank the observers
from the California Planet Survey collaboration for their efforts. We thank Mike Brown and Emily
Schaller for their assistance in obtaining NGS AO observations. We thank Tom Barclay, Gibor
Basri,Luke Dones, Hans Kjeldsen, and Hal Levison for useful discussions.

This paper includes data collected by the Kepler spacecraft, and we gratefully acknowledge the
entire Kepler mission team’s efforts in obtaining and providing the light curves used in this anal-
ysis. Funding for the Kepler mission is provided by the NASA Science Mission directorate. The
publicly released Kepler light curves were obtained from the Mikulski Archive for Space Telescopes
(MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., un-
der NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA
Office of Space Science via grant NNX09AF08G and by other grants and contracts.

Facilities: Kepler Keck:I Keck:II SARA

f

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Table 1: Measured transit times for PH1
Quarter Transit Midpoint 1-σ Uncertainty
(BJD- 2455000) (Minutes)
2 70.80674 8.94
4 207.44916 9.00
5 344.11218 6.14
7 479.98746 8.89
8 613.17869 9.04
10 749.20260 6.49
11 885.91042 8.94

Table 2:: Measured primary and secondary eclipse times for
KIC 4862625

Orbital Primary Eclipse Secondary Eclipse
Cycle Midpoint Uncertainty Midpoint Uncertainty
(BJD- 2455000) (minutes) (BJD- 2455000) (minutes)
1 -32.18064 0.889 -24.32048 7.736
2 -12.18029 0.889 -4.31919 6.602
3 7.82051 0.889 — —
4 27.82051 0.876 35.67367 8.872
5 47.81987 0.967 55.68321 8.682
6 67.82051 0.903 75.66013 7.454
7 87.82091 1.032 95.68077 8.493
8 107.82066 0.850 115.67901 7.169
9 127.82052 0.863 135.67771 5.848
10 147.82173 0.993 — —
11 167.82246 0.850 175.67458 6.885
12 187.82161 0.876 195.67849 6.791
13 207.82279 1.229 215.67642 7.169
14 227.82271 0.889 235.67813 6.696
15 247.82347 0.889 255.67295 7.358
16 267.82365 0.876 295.68469 7.074
17 287.82313 0.889 315.66953 7.839
19 327.82365 0.902 335.67685 6.885
20 347.82402 0.889 355.68154 7.764
21 367.82395 0.902 375.67816 7.35804
22 387.82389 0.889 395.68198 6.980
23 407.82594 0.902 415.68345 6.885
Continued on Next Page. . .

– 29 –

Table 2 – Continued

Orbital Primary Eclipse Secondary Eclipse
Cycle Midpoint Uncertainty Midpoint Uncertainty
(BJD- 2455000) (minutes) (BJD- 2455000) (minutes)
24 427.82464 0.876 435.68501 6.980
25 447.82520 0.915 455.67885 6.980
26 467.82607 0.889 475.68108 7.169
27 487.82642 0.889 495.67777 7.641
28 507.82580 0.941 515.67622 7.930
29 527.82476 1.006 535.68698 7.074
30 547.82560 0.889 — —
31 — — 575.68315 7.454
32 587.82759 0.889 — —
33 607.82824 1.006 615.67919 6.696
34 627.82612 0.876 655.69609 7.925
35 647.82747 0.876 675.69147 7.650
36 667.82816 0.889 695.68003 7.263
37 687.82937 0.889 715.67600 7.454
39 727.82918 0.993 735.68862 7.547
40 747.82850 1.006 755.68434 6.980
41 767.82945 0.876 775.68358 7.263
42 787.83000 0.967 795.67857 8.211
43 807.82964 0.889 815.68275 6.980
44 827.83067 0.902 835.68385 7.265
45 847.82987 0.902 855.68746 6.696
46 867.82980 0.876 875.68666 8.114
47 887.83118 0.902 895.68856 7.547
48 907.83190 0.889 915.68830 6.696
49 927.83150 0.915 — —

– 30 –

Table 3: Measured Radial Velocities
Broad BF Narrow BF
Observation UT Date BJD-2455000 Radial σRV Radial σRV # of
# Velocity (km s−1 ) Velocity (km s−1 ) BFs
(km s−1 ) (km s−1 ) Fit
1 2012 April 1 1019.1136730 34.647 0.111 18.935 0.189 2
2 2012 May 26 1073.9616350 -0.050 0.186 19.299 0.256 2
3 2012 May 28 1076.0832280 19.503 0.126 19.963 0.218 2
4 2012 June 19 1098.0375080 32.848 0.176 20.736 0.367 2
5 2012 June 19 1098.1085180 32.989 0.153 22.249 0.290 2
6 2012 June 20 1099.0462140 31.941 0.116 16.303 0.333 2
7 2012 June 20 1099.0574410 31.925 0.094 16.722 0.176 2
8 2012 July 1 1110.0675670 2.359 0.140 20.088 0.133 2
9 2012 July 2 1111.0639150 -4.437 0.143 17.350 0.262 3
10 2012 July 3 1112.0969640 -8.515 0.153 16.860 0.268 2
11 2012 July 4 1113.0660410 -5.516 0.275 19.300 0.394 2
12 2012 August 4 1144.0612020 30.766 0.133 20.612 0.196 3

Table 4: Preliminary ELC Radial Velocity Fit Parameters for KIC 4862625
Parameter Uncorrected Radial Velocities Corrected Radial Velocities
KA (km s −1 ) 21.490± 0.480 21.185 ± 0.205
P (days) 20.0002514 ± 0.0000056 20.0002489 ± 0.0000051
Tconj (BJD- 2455000) -32.18068 ± 0.00010 -32.18068 ± 0.00099
ecos(w) -0.16739 ± 0.00006 -0.16763 ± 0.00010
esin(w) -0.14622± 0.00093 -0.13363± 0.00482
e 0.2223 ± 0.0010 0.2144 ± 0.0029
w (degrees) 221.14± 0.19 218.56 ± 1.04

– 31 –

Table 5: Corrected Radial Velocities for KIC 4862625
Observation UT Date BJD-2455000 Radial Velocity σRV
# (km s−1 ) (km s−1 )
1 2012 April 1 1019.1136730 34.746 0.111
2 2012 May 26 1073.9616350 -0.314 0.186
3 2012 May 28 1076.0832280 18.575 0.126
4 2012 June 19 1098.0375080 31.146 0.176
5 2012 June 19 1098.1085180 29.775 0.153
6 2012 June 20 1099.0462140 34.672 0.116
7 2012 June 20 1099.0574410 34.237 0.094
8 2012 July 1 1110.0675670 1.306 0.140
9 2012 July 2 1111.0639150 -2.752 0.143
10 2012 July 3 1112.0969640 -6.340 0.153
11 2012 July 4 1113.0660410 -5.782 0.275
12 2012 August 4 1144.0612020 29.189 0.132

Table 6:: Model parameters for PH1. The reference epoch
is t0 =2,454,970 (BJD). † - parameter median and credible
intervals determined from a combination of EB-only and EB-
fixed, planetary solutions.

Parameter Name Joint Solution EB only Planet only (EB Fixed)
Mass parameters
Mass of Star Aa, MAa (M ) 1.384 ± 0.079 – 1.528 ± 0.087†
Mass Ratio, MAb /MAa 0.2794 ± 0.0051 – 0.2663+0.0033
−0.0023
Mass of Star Ab, MAb (M ) 0.386 ± 0.018 – 0.408 ± 0.024†
Planet Mass Ratio, Mb /MAa (99.7% conf.) < 0.000357 0 (fixed) 0 (fixed)
Planet Mass, Mb (M⊕ , 99.7% conf.) < 169. – –
Radius Parameters
Normalized Radius, RAa /aA 0.04690 ± 0.00041 0.04490 ± 0.00064 0.04516 (fixed)
Radius of Star Aa, RAa (R ) 1.759 ± 0.030 – 1.734 ± 0.044†

– 32 –
Radius Ratio, RAb /RAa 0.240+0.020
−0.015 0.219 ± 0.014 0.215 (fixed)
Radius of Star Ab, RAb (R ) 0.422+0.038
−0.029 – 0.378 ± 0.023†
Planet Radius Ratio, Rb /RAa 0.03222 ± 0.00045 – 0.03268 ± 0.00032
Planet Radius, Rb (R⊕ ) 6.18 ± 0.14 – 6.18 ± 0.17†
Planetary Orbit
Period, Pb (days) 138.506+0.107
−0.092 – 138.317+0.040
−0.027
√
Eccentricity Parameter, eb cos(ωb ) 0.228+0.012
−0.014 – 0.2519+0.0044
−0.0060
√
Eccentricity Parameter, eb sin(ωb ) −0.044+0.034
−0.023 – −0.0824+0.0061
−0.0044
Bary. Transit Time, tb (BJD-2,454,900) 174.71 ± 0.11 – 174.490+0.052
−0.036
Sky-plane Inclination, ib (deg) 90.022+0.072
−0.061 – 90.050 ± 0.053
Relative Nodal Angle, ∆Ω (deg) 0.89 ± 0.16 – 0.89 ± 0.14
Stellar Orbit
Period, PA (days) 20.000214+0.000025
−0.000043 20.0002468 ± 0.0000044 20.00024678 (fixed)
Eccentricity Parameter, eA cos(ωA ) −0.16773+0.00021
−0.00018 −0.16747 ± 0.00037 −0.16750 (fixed)
Eccentricity Parameter, eA sin(ωA ) −0.1291 ± 0.0084 −0.141 ± 0.015 −0.1393 (fixed)
Continued on Next Page. . .

Primary Eclipse Time, tA (BJD-2,454,900) 67.81776 ± 0.00015 67.81797 ± 0.00016 67.81798 (fixed)
Sky-plane inclination, iA (deg) 87.360+0.063
−0.072 87.592 ± 0.053 87.58 (fixed)
Light Parameters
Linear Limb Darkening Parameter, uAa 0.27 ± 0.15 0.31+0.29
−0.21 0.32 (fixed)
Quadratic Limb Darkening Parameter, vAa 0.08 ± 0.18 0.17+0.21
−0.28 0.17 (fixed)
Stellar Flux Ratio, FAb /FAa ×100) 0.1533+0.0142
−0.0099 0.1414+0.0040
−0.0036 0.1405 (fixed)
Contamination, FX /FAa (×100) 7.5 ± 1.9 11.8 ± 1.9 12. (fixed)
Radial Velocity (RV) Parameters
RV Semi-amplitude, KAa (km/s) 20.69 ± 0.31 20.56 ± 0.33 –
Mass Function, f (MAa , MAb ) (M ) 0.01836 ± 0.00082 0.01802 ± 0.00089 0.01807 (fixed)
RV Jitter (km/s) 0.80+0.28
−0.17 0.81+0.27
−0.18 –
Table 6:: Model parameters for PH1 system. The reference
epoch is t0 =2,454,970 (BJD). † - parameter median and
credible intervals determined from a combination of EB-only

– 33 –
and EB-fixed, planetary solutions.

– 34 –

Table 7: Derived planet and binary parameters from photometric-dynamical model fit. Reference
epoch is t0 =2454970 (BJD) .
Stellar (Aa & Ab) Bulk parameters
Density of Star Aa, ρAa (g/cm3 ) 0.2542 ± 0.0076 – 0.293 ± 0.013†
Density of Star Ab, ρAb (g/cm3 ) 5.1 ± 1.2 – 7.5+1.4 †
−1.3
Gravity of Star Aa, log(gAa ) (cgs) 4.089 ± 0.014 – 4.144 ± 0.014†
Gravity of Star Ab, log(gAb ) (cgs) 4.772+0.061
−0.071 – 4.892 ± 0.057†
Stellar (Aa & Ab) Orbital Properties
Semimajor axis , aA (AU) 0.1744 ± 0.0031 – 0.1797 ± 0.0035†
Eccentricity, eA 0.2117 ± 0.0051 0.2188 ± 0.0094 0.2179 (fixed)
Argument of Periastron ωA (deg) 217.6 ± 1.9 220.1+2.9
−3.2 219.7504 (fixed)
Planet Orbital Properties
Semimajor axis ab (AU) 0.634 ± 0.011 – 0.652 ± 0.012†
Eccentricity of Planetary Orbit, eb 0.0539 ± 0.0081 – 0.0702+0.0029
−0.0039
Argument of Periastron, ωb (deg) 348.0+6.7
−5.0 – 341.88+0.97
−0.70
Mutual Inclinationa , I(deg) 2.814 ± 0.073 – 2.619 ± 0.057

a
Stellar to planetary orbit mutual inclination: The mutual inclination is the angle between the orbital planes of the
binary and the planet, and is defined as cos I = sin iA sin ib cos ∆Ω + cos iA cos ib . † - parameter median and credible
intervals determined from a combination of EB-only and EB-fixed, planetary solutions.

– 35 –

Table 8. Parameters from full ELC Model

Parameter Best fit

KA (km s−1 ) 21.179 ± 0.162
e 0.2165 ± 0.0013
ω (deg) 219.30 ± 0.45
RAa /a 0.04489 ± 0.00007
RAb /a 0.00938 ± 0.00008
Teff,Ab /Teff,Aa 0.5557 ± 0.0062
i (deg) 87.612 ± 0.004
uA a 0.208 ± 0.020
vA a 0.293 ± 0.0249
P (days) 20.0002490 ± 0.0000049
Tconj (BJD-2455000) -32.18064 ± 0.00203
Contamination 0.109 ± 0.012

Note. — Note: Subscript “Aa” denotes the
primary star, subscript “Ab” the secondary star
in the eclipsing binary KIC4862625 .

– 36 –

Fig. 1.— Planetary transits in addition to binary-star eclipses identiﬁed by Planet Hunters volun-
teers in KIC 4862625 as viewed in the Planet Hunters interface.

– 37 –

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11
Normalized Flux

Time (BJD-2455000)
Q2 Q4 Q5 Q7 Q8 Q10 Q11
Normalized Flux

Time (BJD-2455000)
Fig. 2.— Top: Normalized Kepler light curve for KIC 4862625 for Quarters 1-11 Bottom: Individual
transits of the planet across star Aa identiﬁed in Quarters 1-11. In Quarter 4 (Q4), the planet transit
occurs just before a primary eclipse.

– 38 –

a)

O-C (hours)

Time (BJD-2455000)

b)
O-C (hours)

Binary orbital phase
c)
Transit duration (hours)

Binary orbital phase

Fig. 3.— O-C offsets and transit durations for the circumbinary planet. a) O-C offsets measured
for the planet transits versus time. The 1-σ error bars are plotted. With uncertainties on the
transit times on the order of ∼5 minutes, the error bars are smaller than the size of the symbol.
b) O-C offsets measured for the planet transits versus binary orbital phase. The 1-σ error bars
are plotted. With uncertainties on the transit times on the order of ∼5 minutes, the error bars
are smaller than the size of the symbol. c) Transit duration as a function of binary orbital phase.
Transits near secondary eclipse φ = 0.39 are wider than those close to primary eclipse φ = 0.0

O-C (minutes) – 39 –

Time (BJD-2455000)
Fig. 4.— O-C oﬀsets measured for the primary and secondary (red in the online version) eclipses
of KIC 4862625.

– 40 –

N

E

0.5"

Fig. 5.— NGS AO Ks image of KIC 4862625 and the 0.7 contaminator located 0.702 away from
the primary Kepler target.

– 41 –

Fig. 6.— SARA 0.9m stacked image of KIC 4862625 and surrounding stars. The inner circle (light
blue in the online version) has a radius of 6 and the outer circle (red in the online version) has a
radius of 10 centered on KIC 4862625.

– 42 –

Observation 1 Observation 2
=0.57 =0.31
Correlation

Observation 3 Observation 7
=0.42 =0.57

Lag (km s-1)
Fig. 7.— The Broadening functions and the analytic broadening kernel ﬁts (solid line for the
sum, dotted lines for each component separately) for a subset of the Keck HIRES radial velocity
observations taken at diﬀerent binary orbital phases (φ).

– 43 –

Uncorrected Radial Velocities
a)
km s-1 Radial Velocity (km s-1)

Phase (P =20.000251025, T0=54967.8195)

Corrected Radial Velocities
b)
km s-1 Radial Velocity (km s-1)

Phase (P =20.000251025, T0=54967.8195)
Fig. 8.— a) Top: Uncorrected radial velocities obtained for KIC 4862625 and ELC fit to the light
curve and radial velocity observations. Bottom: The residuals of the ELC fit. b) Top: Offset-
corrected radial velocities obtained for KIC 4862625 and improved ELC fit to the light curve and
radial velocity observations. Bottom: The residuals of the ELC fit. - In both plots: The filled
dots are the measurements for KIC 4862625. The circles are the radial velocities of thenarrow
broadening function component, the 0.7 contaminator. Solid line (red in online version) is the
best-fitting ELC solution.

0.7’’ Contaminator residuals (km s-1) – 44 –

KIC 4862625 residuals (km s-1)
Fig. 9.— Radial velocity residuals for KIC 4862625 versus the radial velocities residuals of the
narrow broadening function component, the 0.7 contaminator before applying the oﬀset-correction.
The plotted line (red in the online version) is the 1 to 1 correlation in primary and companion radial
velocity residuals.

– 45 –

0.7’’ Contaminator KIC 4862625
Row

Column Column
Fig. 10.— Contour plot of the 0.7 contaminator (starting at 1049.404 counts) and KIC 4862625
(starting at 3940.448 counts) from the stacked NGS AO NIRC2 Ks observations. Contour intervals
are 300 counts in both plots.

– 46 –

Fig. 11.— Stellar evolution models from the Y2 (Yonsei-Yale) series by Yi et al. (2001) compared
against the measurements for the Aa. The solid line represents an evolutionary track for the
measured mass (MAa = 1.528 ± 0.087 M ) and metallicity ([Fe/H] = +0.21 ± 0.08), and the dotted
lines are 1–13 Gyr isochrones (left to right) in steps of 1 Gyr. The uncertainty in the location of
the track that comes from the observational errors is shown by the shaded area. The darker area
reﬂects the mass error, and the lighter area includes also the uncertainty in the metallicity.

– 47 –

Fig. 12.— Mass, radius, and eﬀective temperatures for Aa and Ab compared against 1–13 Gyr
model isochrones from the Dartmouth series by Dotter et al. (2008), for the measured metallicity
of the system ([Fe/H] = +0.21 ± 0.08). The solid line corresponds to a 2 Gyr isochrone, for
reference. (Top) Mass–radius diagram showing good agreement for both stars (Aa and Ab) for an
age between 1 and 2 Gyr; (Bottom) Mass–temperature diagram again showing that the models
match our estimated temperatures, within the errors.

– 48 –

PH1 0.5 AU

Aa

Ab

To Earth
b

Ab b
Aa
Fig. 13.— Orbital conﬁguration of the PH1 system for the reference epoch, t0 =2,454,970
(BJD).The inner close binary (primary star Aa and the secondary star Ab) and the planet (la-
beled b) are shown. The outer visual binary (Ba and Bb) is not depicted. Top: A scaled, face-on
view of the orbits. On this scale the stars and the planet are too small to be seen, and their
positions are represented by the boxes. Bottom: The region between the vertical lines in the top
diagram is shown on an expanded scale with an orientation corresponding to what would be seen
from Earth.

– 49 –

Q2 Q4 Q5 Q7
x1000 Normalized Flux

Q8 Q10 Q11
x1000 Normalized Flux

Time (BJD-2455000)
Fig. 14.— Photometric-dynamical model ﬁt to individual planet transits. In Quarter 4 (Q4) , the
planet transit occurs just before a primary eclipse.

Ph circumbinary final

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