Kepler-16: A Transiting Circumbinary Planet
Laurance R. Doyle, Joshua A. Carter, Daniel C. Fabrycky, Robert W. Slawson, Steve B. Howell, Joshua N. Winn, Jerome A. Orosz, Andrej Prsa, William F. Welsh, Samuel N. Quinn, David Latham, Guillermo Torres, Lars A. Buchhave, Geoffrey W. Marcy, Jonathan J. Fortney, Avi Shporer, Eric B. Ford, Jack J. Lissauer, Darin Ragozzine, Michael Rucker, Natalie Batalha, Jon M. Jenkins, William J. Borucki, David Koch, Christopher K. Middour, Jennifer R. Hall, Sean McCauliff, Michael N. Fanelli, Elisa V. Quintana, Matthew J. Holman, Douglas A. Caldwell, Martin Still, Robert P. Stefanik, Warren R. Brown, Gilbert A. Esquerdo, Sumin Tang, Gabor Furesz, John C. Geary, Perry Berlind, Michael L. Calkins, Donald R. Short, Jason H. Steffen, Dimitar Sasselov, Edward W. Dunham, William D. Cochran, Alan Boss, Michael R. Haas, Derek Buzasi, Debra Fischer
11 Kepler-16: A Transiting Circumbinary Planet
Laurance R. Doyle , Joshua A. Carter , Daniel C. Fabrycky , Robert W. Slawson , Steve B. Howell ,Joshua N. Winn , Jerome A. Orosz , Andrej Prˇsa , William F. Welsh , Samuel N. Quinn , DavidLatham , Guillermo Torres , Lars A. Buchhave
9, 10 , Geoffrey W. Marcy , Jonathan J. Fortney , AviShporer , Eric B. Ford , Jack J. Lissauer , Darin Ragozzine , Michael Rucker , Natalie Batalha ,Jon M. Jenkins , William J. Borucki , David Koch , Christopher K. Middour , Jennifer R. Hall ,Sean McCauliff , Michael N. Fanelli , Elisa V. Quintana , Matthew J. Holman , Douglas A.Caldwell , Martin Still , Robert P. Stefanik , Warren R. Brown , Gilbert A. Esquerdo , SuminTang , Gabor Furesz , John C. Geary , Perry Berlind , Michael L. Calkins , Donald R. Short ,Jason H. Steffen , Dimitar Sasselov , Edward W. Dunham , William D. Cochran , Alan Boss ,Michael R. Haas , Derek Buzasi , Debra Fischer Carl Sagan Center for the Study of Life in the Universe, SETI Institute, 189 Bernardo Avenue, Mountain View,CA 94043, USA, [email protected], [email protected], [email protected], [email protected],[email protected] Hubble Fellow, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138,USA, [email protected] Hubble Fellow, Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064,USA, [email protected] NASA Ames Research Center, Moffett Field, CA 94035, USA, [email protected],[email protected], [email protected], [email protected] Massachusetts Institute of Technology, Physics Department and Kavli Institute for Astrophysics and SpaceResearch, 77 Massachusetts Avenue, Cambridge, MA 02139, USA, [email protected] Astronomy Department, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-1221,[email protected], [email protected] Villanova University, Dept. of Astronomy and Astrophysics, 800 E Lancaster Ave, Villanova, PA 19085, USA,[email protected] Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA,[email protected], [email protected], [email protected], [email protected],[email protected], [email protected], [email protected], [email protected],[email protected], [email protected] Niels Bohr Institute, Copenhagen University, DK-2100 Copenhagen, Denmark, [email protected] Centre for Star and Planet Formation, Natural History Museum of Denmark, University of Copenhagen, DK-1350Copenhagen, Denmark Astronomy Department, University of California, Berkeley, CA, 94720, USA, [email protected] Department of Astronomy and Astrophysics, University of California, Santa Cruz, Santa Cruz, CA 95064,USA, [email protected] Las Cumbres Observatory Global Telescope Network, 6740 Cortona Drive, Suite 102, Santa Barbara, CA 93117, USA, Department of Physics, Broida Hall, University of California, Santa Barbara, CA 93106, USA, [email protected]
211 Bryant Space Science Center, Gainesville, FL 32611-2055, USA, [email protected] Physics Department, San Jose State University, San Jose, CA, 95192, USA, [email protected],[email protected] Orbital Sciences Corporation/NASA Ames Research Center, Moffett Field, CA 94035, USA,[email protected], [email protected], [email protected] Bay Area Environmental Research Inst./NASA Ames Research Center, Moffett Field, CA 94035, [email protected], [email protected] Konkoly Observatory, Konkoly ut 15-17, Budapest, H-1121, Hungary Fred Lawrence Whipple Observatory, Smithsonian Astrophysical Observatory, Amado, AZ 85645, USA,[email protected], [email protected] Mathematics Department, San Diego State University, 5500 Campanile Drive, San Diego, CA USA 92182,[email protected] Fermilab Center for Particle Astrophysics, P.O. Box 500, Batavia IL 60510, USA [email protected] Lowell Observatory, Flagstaff, AZ, 86001, USA, [email protected] McDonald Observatory, University of Texas at Austin, Austin, TX, 78712, USA, [email protected] Carnegie Institute of Washington, Washington, DC 20015 USA, [email protected] Eureka Scientific, Inc., 2452 Delmer Street Suite 100, Oakland, CA 94602, USA, [email protected] Department of Astronomy, Yale University, New Haven, CT 06511 USA, [email protected]
Submitted to
Science:
July 7, 2011Final revision submitted: August 16, 2011
Abstract
We report the detection of a planet whose orbit surrounds a pair of low-mass stars.Data from the Kepler spacecraft reveal transits of the planet across both stars, in addition tothe mutual eclipses of the stars, giving precise constraints on the absolute dimensions of allthree bodies. The planet is comparable to Saturn in mass and size, and is on a nearlycircular 229-day orbit around its two parent stars. The eclipsing stars are 20% and 69% asmassive as the sun, and have an eccentric 41-day orbit. The motions of all three bodies areconfined to within 0.5° of a single plane, suggesting that the planet formed within acircumbinary disk.
A planet with two suns is a familiar concept from science fiction. However, theevidence for the existence of circumbinary planets—those that orbit around both members ofa stellar binary—has been limited. A few good cases have been made for circumbinaryplanets based upon timing of stellar eclipses (see, e.g., refs. ), but in no previous case haveastronomers obtained direct evidence of a circumbinary planet by observing a planetarytransit (a miniature eclipse as the planet passes directly in front of a star). Detection of atransit greatly enhances confidence in the reality of the planet, and provides unusually preciseknowledge of its mass, radius, and orbital parameters ( ).Here we present the detection of a transiting circumbinary planet around a binary starsystem based on photometric data from the NASA Kepler spacecraft.
Kepler is a 0.95mspace telescope that monitors the optical brightness of about 155,000 stars within a fieldencompassing 105 square degrees in the constellations Cygnus and Lyra ( ).Star number 12644769 from the Kepler
Input Catalog was identified as an eclipsingbinary with a 41-day period, from the detection of its mutual eclipses ( ). Eclipses occurbecause the orbital plane of the stars is oriented nearly edge-on as viewed from Earth.During primary eclipses the larger star, denoted “A”, is partially eclipsed by the smaller star“B”, and the system flux declines by about 13%. During secondary eclipses B is completelyocculted by A, and the resulting drop in flux is only about 1.6% because B is relatively smalland has a lower surface brightness (Figure 1).This target drew further attention when three additional drops in brightness weredetected outside of the primary and secondary eclipses, separated by intervals of 230.3 and221.5 days ( ). These tertiary eclipses could not be attributed to the stars alone, andindicated the presence of a third body. The differing intervals between the tertiary eclipses are simply explained if the third body is in a circumbinary orbit, because stars A and B wouldbe in different positions in their mutual orbit each time the third body moved in front of them(
11, 12 ). In contrast, there would be no ready explanation for the shifting times of thetertiary eclipses if they were produced by a background star system or some other unrelatedevent. During tertiary eclipses the total light declines by 1.7%. Because this is larger thanthe 1.6% decline during secondary eclipses (when star B is completely concealed), thetertiary eclipses had to be transits of the third body across star A. This interpretation wassupported by the subsequent detection of weaker 0.1% quaternary eclipses, which wereconsistent with the passage of the third body across star B. The observed time of thisquaternary eclipse was used to predict two other times of quaternary eclipses that shouldhave been present in the data, and these two events were subsequently detected (Figure 1).Because the third body covers only 1.7% of the area of star A, which was determinedto be smaller than the Sun based on its broad band colors (10), the circumbinary body wassuspected to be either a planet, or a third star with grazing eclipses. Decisive evidence thatit is a planet came from investigation of the timing of the stellar eclipses. The primary andsecondary eclipse times were found to depart from strict periodicity by deviations of orderone minute. A third body causes timing variations in two ways. Firstly there is a light travel-time effect: the third body induces a periodic motion of the center of mass of the stellarbinary, causing periodic variations in the time required for the eclipse signals to reach theEarth (13, 14). Secondly there is a dynamical effect: the gravitational attraction of each starto the third body varies with time due to the changing positions of all three bodies, causingperturbations in the stars' orbital parameters and therefore in the eclipse times (15, 16). Botheffects depend on the mass of the third body. Therefore we could constrain the mass of thethird body by fitting the eclipse data with a numerical model of three-body gravitationalinteractions. This model, described below in detail, showed that the third body must be lessmassive than Jupiter.Hence, based on the depth of the tertiary eclipses, and on the magnitude of the eclipsetiming variations, the third body was shown to be a transiting circumbinary planet.The model was based on the premise that the three bodies move under the influenceof mutual Newtonian gravitational forces. For this purpose we modified the computer codethat was used to model the triple star system KOI-126 ( , SOM). The leading-orderrelativistic correction to the force law was included, although it proved to be unimportant.The bodies’ positions were calculated with a Bulirsch-Stoer algorithm and corrected for thefinite propagation speed of light across the system before comparing to the data. The loss oflight due to eclipses was calculated by assuming the disks of stars A and B to be circular,with a quadratic law describing the decline in intensity toward the limb ( ). We alsoallowed for an additional time-independent source of light to account for any possiblebackground stars within the Kepler photometric aperture. In practice this parameter wasfound to be consistent with zero, and bounded to be less than 1.3% of the total light of thesystem ( ). We fitted all of the photometric data within 6 hours of any eclipse or transit. Beforefitting, a linear trend was removed from each segment, to correct for the slow starspot-induced variations evident in Figure 1. A successful model had to be compatible with thetimings, durations, and depths of the primary and secondary stellar eclipses, as well as thetransits of the planet across both stars. The model also had to account for the slightdepartures from strict periodicity of the stellar eclipses. Furthermore, to pin down the stellarmasses and provide an absolute distance scale, we undertook spectroscopic observations totrack the radial velocity variations of star A (Figure 2, top panel).The model parameters were adjusted to fit the photometric and radial-velocity data(Table 1). Figures 1 and 2 show the very good match that was achieved between the modeland the data. Uncertainties in the parameters were determined with a Differential EvolutionMarkov Chain Monte Carlo simulation (
SOM).Due to the presence of uniquely three-body effects (namely, the shifts in eclipse timesand transit durations), the masses, radii, and orbital distances of this system are welldetermined in absolute units, and not just in relative units. The eclipse timing variations aredominated by the effects of dynamical perturbations, with light-time variations contributingonly at the level of one second. The third body’s dimensions are well within the planetaryregime, with a mass of 0.333 ± 0.016 and a radius of 0.7538 ± 0.0025 those of Jupiter.Following the convention of Ref. 22, we can denote the third body Kepler-16 (AB)-b, orsimply “b” when there is no ambiguity.Considering its bulk properties, the planet is reminiscent of Saturn but with a highermean density (0.964 g cm –3 , compared to the Saturnian density of 0.687 g cm –3 ). Thissuggests a greater degree of enrichment by heavy elements. With a mass and radius one canbegin to model a planet’s interior structure, which will depend on age because planets cooland contract with time. Usually the stellar age is used as a proxy for the planetary age, but inthis case the stellar age is not unambiguous. The primary star is a slow rotator (with a periodof about 35.1 days, judging from the out-of-eclipse variations), usually indicative of old age.In contrast, the level of starspot activity and chromospheric emission (Mt. Wilson S value =1.10) are indicative of youth. The spectroscopic determination of star A’s heavy-elementfraction ([m/H] = –0.3 ± ). This would imply a composition of approximately half gas(hydrogen and helium) and half heavy elements (presumably ice and rock). Saturn, bycontrast, is at least two-thirds gas by mass ( ).To investigate the long-term (secular) changes in the orbital parameters, and check onthe system’s stability, we integrated the best-fitting model forward in time by two millionyears. Within the context of our gravitational three-body model, secular variations occur ona timescale of about 40 years, without any significant excursions in orbital distance thatwould have led to instability. The planet’s orbital eccentricity reaches a maximum of about0.09. Likewise, the planet’s line-of-sight orbital inclination changes by 0.2°, which is largeenough that transits are only visible from Earth about 40% of the time (averaged over centuries). In particular, the planetary transits across star A should cease in early 2018, andreturn some time around 2042. The planetary transits across star B are already grazing, andare predicted to disappear for 35 years beginning in May 2014.The planet experiences swings in insolation due to the motion of the stars on shorttimescales, and due to secular changes in the planet’s orbit on long timescales. Thesevariations are likely to affect the temperature and structure of the planet’s atmosphere. Theplanet’s current equilibrium temperature, averaged over several orbits, is between 170 and200 K, assuming isotropic re-radiation of the stellar flux and a Bond albedo between 0.2-0.5(in the neighborhood of Saturn’s value of 0.34). Orbital motion of the stars and the planetare expected to produce seasonal temperature variations of around 30
K.The planetary orbit is aligned with the stellar orbit to within 0.4°. This extremecoplanarity suggests that the planet was formed along with the stars, within a circumbinaryprotoplanetary disk, as opposed to being captured from another system. Planetesimalformation around an eccentric binary is a theoretical challenge, because of the large collisionvelocities of particles that are stirred by the stellar binary ( ), although the detection ofdebris disks around close binaries has been interpreted as dust produced by collidingplanetesimals ( ). Subsequent stages of planet formation around binaries has been studiedtheoretically, both for terrestrial planets ( ) and gas giants ( ), but these and othertheoretical studies ( ) have lacked a well-specified circumbinary planetary system thatcould allow such a refinement of models.Finally, the stars themselves are worthy of attention, independently of the planet. It israre to measure the masses and radii of such small stars with such high precision, usinggeometrical and dynamical methods independent of stellar evolutionary models. Inparticular, Star B, with only 20% the mass of the Sun, is the smallest main-sequence star forwhich such precise mass and radius data are available ( ). The mass ratio of 0.29 is alsoamong the smallest known for binaries involving fully convective stars at the low-mass endof the main sequence ( ). With well-characterized low-mass stars, in addition to a transitingcircumbinary planet, this makes Kepler -16 a treasure for both exoplanetary and stellarastrophysical investigations.
References and Notes
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Stat. Comput ., 16, 239-249 (2006).39. The computations in this paper were run on the Odyssey cluster supported by the FASScience Division Research Computing Group at Harvard University.40. Eggleton, P., Kiseleva, L., Astroph. J., 455, 640-645 (1995).41. Holman, M.J. and Wiegert, P.A., Astron. J, 117, 621-628 (1999).42. NASA’s Science Mission Directorate provided funding for the
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Science Team. JAC and DCF acknowledge support for this workwas provided by NASA through Hubble Fellowship grants HF-51267.01-A and HF-51272.01-Aawarded by the Space Telescope Science Institute, which is operated by the Association ofUniversities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. JNW isgrateful for support from the NASA Origins program (NNX09AB33G). GF acknowledges thesupport of the Hungarian OTKA grant MB08C 81013. The Kepler data used in this analysis can bedownloaded from http://archive.stsci.edu/prepds/kepler_hlsp.
Figure 1.
Photometry of Kepler-16 . Top .—Photometric time series from the
Kepler spacecraft of star system
Kepler -16(KIC
Kepler magnitude = 11.762). Eachdata point is the relative brightness at a given time (in barycentric Julian days, BJD). The 1%variations on ~10-day timescales are likely due to starspots carried around by stellar rotation(a periodogram gives a rotation period of about 35 days). The sharp dips are eclipses,appearing as vertical lines in this 600-day plot. They are identified as primary (B-eclipses-A;blue), secondary (A-occults-B; brown), tertiary (b-transits-A; green) and quaternary (b-transits-B; red). Because of interruptions in
Kepler observing, data are missing from oneprimary eclipse at BJD 2,455,089, and one secondary eclipse at BJD 2,455,232. Note inparticular the shifting order of the tertiary (green) and quaternary (red) eclipses: the first andthird pairs begin with the tertiary eclipse, while the second pair leads with the quaternaryeclipse. This is because the stars’ orbital motion places them in different positions at eachinferior conjunction of the planet. The stars silhouette the planet as they move behind it.
Bottom .—Close-ups (narrower scales in time and relative flux) of representative examples ofeach type of eclipse, along with the best-fitting model (gray), with parameters from Table 1. Figure 2.
Radial-velocity variations, and perturbations of eclipse times . Top .—Observed radial-velocity variations of star A as a function of orbital phase, based onobservations with the TRES spectrograph and the Tillinghast 1.5m telescope at the Fred Lawrence Whipple Observatory on Mt. Hopkins, Arizona (SOM). Solid dots are the data,and the smooth curve is the best-fitting model. Although only the light from star A could bedetected in the spectra, the model for star B’s motion is also shown. Residuals from the bestmodel fits are given just below the radial velocity curve.
Middle and
Bottom panels .—Deviations of the stellar eclipse times from strict periodicity, asobserved (colored dots) and modeled (open diamonds). As noted previously, one primaryeclipse and one secondary eclipse were missed. The deviations are on the order of oneminute for both primary and secondary stellar eclipses. In the model, the effects ofdynamical perturbations are dominant, with light-time variations contributing only at thelevel of one second. If the third body were more massive than a planet (> 13 Jovian masses),the timing variations would have exceeded 30 minutes. This would have been off the scaleof the diagram shown here, and in contradiction with the observations. Figure 3:
Scale diagram of the
Kepler -16 system . The current orbits of the