Kepler-20: A Sun-like Star with Three Sub-Neptune Exoplanets and Two Earth-size Candidates
Thomas N. Gautier III, David Charbonneau, Jason F. Rowe, Geoffrey W. Marcy, Howard Isaacson, Guillermo Torres, Francois Fressin, Leslie A. Rogers, Jean-Michel Désert, Lars A. Buchhave, David W. Latham, Samuel N. Quinn, David R. Ciardi, Daniel C. Fabrycky, Eric B. Ford, Ronald L. Gilliland, Lucianne M. Walkowicz, Stephen T. Bryson, William D. Cochran, Michael Endl, Debra A. Fischer, Steve B. Howel, Elliott P. Horch, Thomas Barclay, Natalie Batalha, William J. Borucki, Jessie L. Christiansen, John C. Geary, Christopher E. Henze, Matthew J. Holman, Khadeejah Ibrahim, Jon M. Jenkins, Karen Kinemuchi, David G. Koch, Jack J. Lissauer, Dwight T. Sanderfer, Dimitar D. Sasselov, Sara Seager, Kathryn Silverio, Jeffrey C. Smith, Martin Still, Martin C. Stumpe, Peter Tenenbaum, Jeffrey Van Cleve
aa r X i v : . [ a s t r o - ph . E P ] F e b Kepler-20: A Sun-like Star with Three Sub-Neptune Exoplanetsand Two Earth-size Candidates
Thomas N. Gautier III , David Charbonneau , Jason F. Rowe , Geoffrey W. Marcy ,Howard Isaacson , Guillermo Torres , Francois Fressin , Leslie A. Rogers , Jean-MichelD´esert , Lars A. Buchhave , , David W. Latham , Samuel N. Quinn , David R. Ciardi ,Daniel C. Fabrycky , Eric B. Ford , Ronald L. Gilliland , Lucianne M. Walkowicz ,Stephen T. Bryson , William D. Cochran , Michael Endl , Debra A. Fischer , Steve B.Howell , Elliott P. Horch , Thomas Barclay Natalie Batalha , William J. Borucki ,Jessie L. Christiansen , John C. Geary , Christopher E. Henze , Matthew J. Holman ,Khadeejah Ibrahim , Jon M. Jenkins , Karen Kinemuchi , David G. Koch , Jack J.Lissauer , Dwight T. Sanderfer , Dimitar D. Sasselov , Sara Seager , Kathryn Silverio ,Jeffrey C. Smith , Martin Still , Martin C. Stumpe , Peter Tenenbaum , Jeffrey VanCleve ABSTRACT
We present the discovery of the Kepler-20 planetary system, which we ini-tially identified through the detection of five distinct periodic transit signalsin the
Kepler light curve of the host star 2MASSJ19104752+4220194. Fromhigh-resolution spectroscopy of the star, we find a stellar effective temperature T eff = 5455 ±
100 K, a metallicity of [Fe/H]= 0 . ± .
04, and a surface grav-ity of log g = 4 . ± .
1. We combine these estimates with an estimate of thestellar density derived from the transit light curves to deduce a stellar mass of M ⋆ = 0 . ± . M ⊙ and a stellar radius of R ⋆ = 0 . +0 . − . R ⊙ . For threeof the transit signals, we demonstrate that our results strongly disfavor the pos-sibility that these result from astrophysical false positives. We accomplish this Jet Propulsion Laboratory/California Institute of Technology, Pasadena, CA 91109;[email protected] Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 NASA Ames Research Center, Moffett Field, CA 94035 Department of Astronomy, University of California, Berkeley, CA 94720 Massachusetts Institute of Technology, Cambridge, MA 02139 Niels Bohr Institute, University of Copenhagen, DK-2100, Copenhagen, Denmark Centre for Star and Planet Formation, Natural History Museum of Denmark, University of Copenhagen,DK-1350, Copenhagen, Denmark NASA Exoplanet Science Institute/California Institute of Technology, Pasadena, CA 91125 Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 Astronomy Department, University of Florida, Gainesville, FL 32111 Department of Astronomy, 525 Davey Lab, The Pennsylvania State University, University Park, PA16802 Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 McDonald Observatory, The University of Texas at Austin, Austin, TX 78712 Department of Astronomy, Yale University, New Haven, CT 06511 Department of Physics, Southern Connecticut State University, New Haven, CT 06515 Bay Area Environmental Research Institute/NASA Ames Research Center, Moffett Field, CA 94035 Department of Physics and Astronomy, San Jose State University, San Jose, CA 95192 SETI Institute/NASA Ames Research Center, Moffett Field, CA 94035 × (Kepler-20b), 1 × (Kepler-20c), and 1 . × (Kepler-20d), sufficient to validate these objects as planetary companions. ForKepler-20c and Kepler-20d, the blend scenario is independently disfavored bythe achromaticity of the transit: From Spitzer data gathered at 4.5 µ m, we in-fer a ratio of the planetary to stellar radii of 0 . ± .
015 (Kepler-20c) and0 . ± .
011 (Kepler-20d), consistent with each of the depths measured in the
Kepler optical bandpass. We determine the orbital periods and physical radii ofthe three confirmed planets to be 3 .
70 d and 1 . +0 . − . R ⊕ for Kepler-20b, 10 .
85 dand 3 . +0 . − . R ⊕ for Kepler-20c, and 77 .
61 d and 2 . +0 . − . R ⊕ for Kepler-20d.From multi-epoch radial velocities, we determine the masses of Kepler-20b andKepler-20c to be 8 . ± . M ⊕ and 16 . ± . M ⊕ , respectively, and we place anupper limit on the mass of Kepler-20d of 20 . M ⊕ (2 σ ). Subject headings: planetary systems — stars: individual (Kepler-20, KIC 6850504,2MASSJ19104752+4220194) — eclipses
1. Introduction
Systems with multiple exoplanets, and transiting exoplanets, each bolster confidencein the reality of the planetary interpretation of the signals and offer distinct constraints onmodels of planet formation.The first extrasolar planets were found around a pulsar (Wolszczan & Frail 1992), and itwas the multi-planetary nature — in particular the gravitational perturbations between theplanets (Rasio et al. 1992; Wolszczan 1994) — which solidified this outlandish claim. AroundSun-like stars as well, the origin of radial velocity signals continued to be questioned by some,at the time multiple planets were found around ups Andromeda (Butler et al. 1999). Theorbital configuration of planets relative to each other has shed light on a host of physicalprocesses, from smooth radial migration into resonant orbits (Lee & Peale 2002) to chaoticscattering into secular eccentricity cycles (Malhotra 2008; Ford et al. 2005). Now with ever-growing statistics of ever-smaller Doppler-detected planets in multiple systems (Mayor et al.2011), the formation and early history of planetary systems continues to come into sharperfocus. 4 –Concurrently, transiting exoplanets have paid burgeoning dividends, starting with thedefinitive proof that Doppler signals were truly due to gas-giant planets orbiting in close-inorbits (Charbonneau et al. 2000; Henry et al. 2000). Transit lightcurves offer precise geo-metrical constraints on the orbit of the planet (Winn 2010), such that radial velocity andphotometric measurements yield the density of the planet and hence point to its composition(Adams et al. 2008; Miller 2011). Transiting configurations also enable follow-up measure-ments (Charbonneau et al. 2002; Knutson et al. 2007; Triaud et al. 2010) which inform onthe mechanisms of planetary formation, evolution, and even weather.These two research streams, multiplanets and transiting planets, came together for thefirst time with the discovery of Kepler-9 (Holman et al. 2010; Torres et al. 2011). This dis-covery was enabled by data from the
Kepler
Mission (Borucki et al. 2010; Koch et al. 2010),which is uniquely suited for such detections as it offers near-continuous high-precision photo-metric monitoring of target stars. Based on the first 4 months of
Kepler data, Borucki et al.(2011) announced the detection of 170 stars each with 2 or more candidate transiting planets;Steffen et al. (2010) discussed in detail 5 systems each possessing multiple candidate tran-siting planets. A comparative analysis of the population of candidates with multiple planetsand single planets was published by Latham et al. (2011), and Lissauer et al. (2011a) dis-cussed the architecture and dynamics of the ensemble of candidate multi-planet systems.The path to confirming the planetary nature of such
Kepler candidates is arduous. Atpresent, three stars (in addition to Kepler-9) hosting multiple transiting candidates havebeen presented in detail and the planetary nature of each of the candidates has been estab-lished: These systems are Kepler-10 (Batalha et al. 2011; Fressin et al. 2011a), Kepler-11(Lissauer et al. 2011b), and Kepler-18 (Cochran et al. 2011). Transiting planets are mostprofitable when their masses can be determined directly from observation, either throughradial velocity (RV) monitoring of the host star or by transit timing variations (TTVs), aswas done for Kepler-9bc, Kepler-10b, Kepler-11bcdef, and Kepler-18bcd. When neither theRV or TTV signals is detected, statistical arguments can be employed to show that the plan-etary hypothesis is far more likely than alternate scenarios (namely blends of several starscontaining an eclipsing component), and this was the means by which Kepler-9d, Kepler-10c,and Kepler-11g were all validated. While such work proves the existence of a planet anddetermines its radius, the mass and hence composition remain unknown save for speculationfrom theoretical considerations.This paper presents the discovery of a new system, Kepler-20, with five candidate tran-siting planets. We validate three of these by statistical argument; we then proceed to useRV measurements to determine the masses of two of these, and we place an upper limit onthe mass of the third. We do not validate in this paper the remaining two signals (and hence 5 –remain only candidates, albeit very interesting ones, owing to their diminutive sizes), ratherthe validation of these two remaining signals is addressed in a separate effort (Fressin et al.2012). The paper is structured as follows: In §
2, we present our extraction of the
Kepler light curve ( § § § Kepler light curve ( § § § Spitzer photometry ( § § §
4, we present our statistical analysis that validates theplanetary nature of the three largest candidate planets in the system. In § § Throughout the course of the
Kepler
Mission, a given star is known by many differentnames (see Borucki et al. 2011, for an explanation of
Kepler naming conventions), and wepause here to explain the relationship of these names in the current context. The star thatis the subject of this paper is located at α =19 h m s . δ =+42 ◦ ′ ′′ . Kepler input catalog it wasdesignated KIC 6850504. After the identification of candidate transiting planets it becamea
Kepler
Object of Interest (KOI) and was further dubbed K00070, and it appeared as suchin the list of candidates published by Borucki et al. (2011). Some authors have elected todenote KOIs using a different nomenclature, in which case K00070 would be identified asKOI-70. After the confirmation of the planetary nature of three of these candidates it wasgiven its final moniker Kepler-20. This paper describes that process of confirmation, butfor simplicity we refer to the star as Kepler-20 throughout. The three confirmed exoplanetswere initially assigned KOI designations representing the chronological order in which thetransiting signals were identified, but to avoid confusion we will refer to them henceforthby their Kepler-20 designations in which they are ordered by increasing orbital period P ;Kepler-20b (K00070.02, P = 3 .
70 d), Kepler-20c (K00070.01, P = 10 .
85 d), and Kepler-20d(K00070.03, P = 77 .
61 d). We will refer to the two remaining candidates as K00070.04and K00070.05, but note (as described below) that the period of K00070.04 ( P = 6 .
10 d)is intermediate between those of Kepler-20b and Kepler-20c, and the period of K00070.05( P = 19 .
58 d) is intermediate between those of Kepler-20c and Kepler-20d. 6 –
2. Kepler Photometry and Analysis2.1. Light Curve Extraction
Kepler observations of Kepler-20 commenced UT 2009 May 13 with Quarter 1 (Q1),and the
Kepler data that we describe here extend through UT 2011 March 14 correspond-ing to the end of Quarter 8 (Q8), resulting in near-continuous monitoring over a span of22.4 months. The
Kepler bandpass spans 423 to 897 nm for which the response is greaterthan 5% (Van Cleve & Caldwell 2009). This wavelength domain is roughly equivalent to the V + R -band (Koch et al. 2010). These observations have been reduced and calibrated by the Kepler pipeline (Jenkins et al. 2010a). The
Kepler pipeline produces calibrated light curvesreferred to as Simple Aperture Photometry (SAP) data in the
Kepler archive, and this is thedata product we used as the initial input for our analysis to determine the system parameters(see below). The pipeline provides time series with times in Barycentric Julian Days (BJD),and flux in photo-electrons per observation. The data were initially gathered at long cadence(Caldwell et al. 2010; Jenkins et al. 2010b) consisting of an integration time per data pointof 29.426 minutes. After the identification of candidate transiting planets in the data fromQ1, the target was also observed at short cadence (Gilliland et al. 2010) corresponding toan integration time of 1 minute for Q2 − Q6. We elected to use the long cadence version ofthe entire Q1 − Q8 time series for computational efficiency. There are 29,595 measurementsin the Q1 − Q8 time series. The upper panel of Figure 1 shows the raw
Kepler Q1 − Q8 lightcurve of Kepler-20. The data are available electronically from the Multi Mission Archive atthe Space Telescope Science Institute (MAST) Web site . The five candidate transiting planets that are the subject of the paper were identifiedby the procedure described in Borucki et al. (2011). Four of them (Kepler-20b, Kepler-20c,Kepler-20d, K00070.04) are listed in that paper, and K00070.05 was detected subsequently.We first cleaned the Q1 − Q8 long-cadence
Kepler
SAP photometry of Kepler-20 ofinstrumental and long-term astrophysical variability not related to the planetary transits byfitting and removing a second-order polynomial to each contiguous photometric segment. Wedefined a segment to be a series of long-cadence observations that does not have a gap largerthan five measurements (spanning at least 2.5 hours). In this process, we gave no statistical http://archive.stsci.edu/kepler Kepler light curve of Kepler-20 at a cadence of 30 minutes.
Upper panel:
Thenormalized raw SAP light curves for Q1 − Q8. The star is positioned on one of four differentdetectors, depending upon the particular quarter, which results in the most obvious offsetsthat occur roughly 4 times per year. The other discontinuities are due to effects such asspacecraft safe-mode events and loss of fine pointing.
Lower panel:
The SAP light curveafter removing instrumental and long-term astrophysical variability via polynomial fitting(see § § ρ ⋆ and the radial velocity instrumental zero point γ , and7 parameters for each of the 5 planet candidates i = { Kepler-20b, Kepler-20c, Kepler-20d,K00070.04, K00070.05 } , namely the epoch of center of transit T ,i , the orbital period P i ,the impact parameter b i , the ratio of the planetary and stellar radii ( R p /R ⋆ ) i , the radialvelocity semi-amplitude K i , and the two quantities, ( e cos ω ) i and ( e sin ω ) i , relating theeccentricity e i and the argument of pericenter ω i . The ratios of the semi-major axes to thestellar radius, ( a/R ⋆ ) i , were calculated from ρ ⋆ and the orbital periods P i assuming e = 0 andthat M ⋆ ≫ sum of the planet masses. (We note that our observations do not constrain theeccentricity, but we include it so that our error estimates of the other parameters are inflatedto account for this possibility. Similarly, we are not able to detect the radial-velocity signals K i for Kepler-20d, K00070.04, or K00070.05, but by including these parameters, we includeany inflation these may imply for the uncertainties on the mass estimates of Kepler-20b andKepler-20c, and the upper limit on the mass of Kepler-20d.)We computed each transit shape using the analytic formulae of Mandel & Agol (2002).We adopted a fourth-order non-linear limb-darkening law with coefficients fixed to thosepresented by Claret & Bloemen (2011) for the Kepler bandpass using the parameters T eff ,log g , and [Fe/H] determined from spectroscopy ( § §
4. Using the validationapproach presented in §
4, we are not able to validate the remaining two candidates K00070.04and K00070.05. Instead this difficult problem is deferred to a subsequent study (Fressin et al.2012). We further assumed that the planets followed non-interacting Keplerian orbits, andthat the eccentricity of each planetary orbit was constrained to be less than the value atwhich it would cross the orbit of another planet, e ≤ .
396 (Kepler-20b), 0 .
319 (Kepler-20c), 0 .
601 (Kepler-20d), 0 .
283 (K00070.04), and 0 .
325 (K00070.05). Finally, we includedan additional error term on the radial velocities (beyond those appearing in Table 5) with atypical amplitude of 2 m s − , to assure that we were not underestimating the uncertaintieson the radial velocities (and hence the planetary masses).We included a prior on ρ ⋆ as follows. We matched the spectroscopically-estimated T eff , log g , and [Fe/H] and the corresponding error estimates (see § M ⋆ and stellar radius R ⋆ which in turn we used to generate the prior on ρ ⋆ used for the determination of the best-fitmodel. The posterior distributions of ( a/R ⋆ ) i were obtained by calculating ( a/R ⋆ ) i for eachelement of the Markov chain.We identified the best-fit model by minimizing the χ statistic using a Levenberg-Marquardt algorithm. We estimated the uncertainties via the construction of a co-variancematrix (these results were also used below in the estimate of the width of the Gibbs samplefor our MCMC analysis). We then adopted the best-fit model (and its estimated uncertain-ties) as the seed for an MCMC analysis to determine the posterior distributions of all themodel parameters. We used a Gibbs sampler to identify new jump values of test parameterchains by drawing from a normal distribution. The width of the normal distribution for eachfitted parameter was initially determined by the error estimates from the best-fit model. Wegenerated 500 elements in the chain and then stopped to examine the success rate, and thenwere scaled the normal distributions using Equation 8 from Gregory (2011). We repeatedthis process until the success rate for each parameter fell between 22 − − a/R ⋆ for K00070.04 and K00070.05 were misstated in Table 1of Fressin et al. (2012). The correct values are 14 . +1 . − . and 31 . +3 . − . , respectively. The valuesof the stellar parameters were also stated incorrectly in the same table, and should read T eff = 5455 ±
100 K, logg = 4 . ± .
1, [Fe / H] = +0 . ± . v sin i < − , and L/L ⊙ = 0 . +0 . − . . These changes have no effect on the conclusions of Fressin et al. (2012). 11 –Table 1. Parameters for the Star Kepler-20. Parameter Value NotesRight Ascension (J2000) 19 h m s . ◦ ′ ′′ . Kepler
Magnitude 12.498r Magnitude 12.423
Spectroscopically Determined Parameters
Effective temperature T eff (K) 5455 ±
100 ASpectroscopic gravity log g (cgs) 4 . ± . . ± .
04 AMt. Wilson S-value 0 . ± .
005 Alog R ′ HK − . ± .
05 AProjected rotation v sin i (km s − ) < − ) − . ± .
96 ARadial Velocity Instrumental Zero Point γ (m s − ) − . +0 . − . B Derived stellar properties
Mass M ⋆ ( M ⊙ ) 0 . ± .
034 CRadius R ⋆ ( R ⊙ ) 0 . +0 . − . CDensity ρ ⋆ (cgs) 1 . ± .
38 CLuminosity L ⋆ ( L ⊙ ) 0 . +0 . − . CAge (Gyr) 8 . +4 . − . CDistance (pc) 290 ±
30 CNote. — A: Based on the spectroscopic analysis ( § § §
12 –Fig. 2.—
Kepler light curves with an observational cadence of 30 minutes (black points) ofKepler-20, phased to each of the periods of the 5 candidate transiting planets (only data in thevicinity of each phased transit are shown). Kepler-20b, 20c, 20d, K00070.04 and K00070.05are shown from top to bottom. Blue points with error bars show these measurements binnedin phase in increments of 30 minutes. The red curve shows the global best-fit model (see § Upper Panel:
Radial velocities of Kepler-20 after correcting for the best-fit am-plitudes of Kepler-20b, Kepler-20d, K00070.04, and K00070.05, leaving the effect of onlyKepler-20c and plotted as a function of its orbital phase of Kepler-20c. Individual measure-ments as shown as gray points and these values binned in increments of 0.1 phase units areshown in blue. The phase coverage is extended by 0.25 phase units on either side to showdata continuity, but it should be noted the values in these gray regions are plotted twice.The red curve is the best-fit model for the radial velocity variation of the star after the sub-traction of the effect of Kepler-20b, Kepler-20d, K00070.04, and K00070.05.
Lower Panel:
Same as above, but showing the radial velocities (in gray, with binned points in blue) andmodel (in red) of Kepler-20 after correcting for effect of Kepler-20c, Kepler-20d, K00070.04,and K00070.05, leaving the effect of only Kepler-20b and plotted as a function of its orbitalphase. 14 –Table 2. Physical and orbital parameters for Kepler-20b, Kepler-20c, and Kepler-20d
Parameter Kepler-20b Kepler-20c Kepler-20d NotesOrbital period P (days) 3 . +0 . − . . ± . . +0 . − . AMidtransit time T (BJD) 2454967 . +0 . − . . ± . . +0 . − . AScaled semi-major axis a/R ⋆ . +0 . − . . +2 . − . . +7 . − . AScaled planet radius R p /R ⋆ . +0 . − . . ± . . +0 . − . AImpact parameter b . +0 . − . . +0 . − . . +0 . − . A e cos ( ω ) − . +0 . − . − . +0 . − . − . +0 . − . A e sin ( ω ) − . +0 . − . − . +0 . − . − . +0 . − . AOrbital inclination i (deg) 86 . +0 . − . . +0 . − . . +0 . − . AOrbital eccentricity e < . < . < .
60 AOrbital semi-amplitude K (m s − ) 3 . +0 . − . . +1 . − . . +1 . − . AMass M p ( M ⊕ ) 8 . +2 . − . . +3 . − . < . σ ) BRadius R p ( R ⊕ ) 1 . +0 . − . . +0 . − . . +0 . − . BDensity ρ p (g cm − ) 6 . +2 . − . . +0 . − . < .
07 BOrbital semi-major axis a (AU) 0 . +0 . − . . ± . . +0 . − . BEquilibrium temperature T eq (K) 1014 713 369 CNote. — A: Based on the joint modeling ( § M ⋆ and/or R ⋆ from Table 1.C: Calculated assuming a Bond albedo of 0.5 and isotropic re-radiation of absorbed flux from the entire planetary surface.
15 –
While the analysis above provides the parameter estimates of the five planet candidatesunder the assumption that each are planets orbiting Kepler-20, it does not address theconcern that some or all of these five candidates result instead from an astrophysical falsepositive (i.e. a blend of several stars within the
Kepler photometric aperture, containing aneclipsing component). In § BLENDER method to demonstrate that this possibilityis extremely unlikely for Kepler-20b, Kepler-20c, and Kepler-20d, and it is this
BLENDER workthat is the basis for our claim that each of these three objects are planets. Another means toidentify astrophysical false positives is to examine the
Kepler pixel data to detect the shiftin the photocentroid of the image (e.g. Batalha et al. 2010; Torres et al. 2011; Ballard et al.2011) of Kepler-20 during times of transit, which we discuss below. Although we do not usethe results presented below as part of the
BLENDER work, we include a description of it hereas it provides an independent argument against the hypothesis that the photometric signalsresult from an astrophysical false positive and not from planetary companions to Kepler-20.We use two methods to examine the
Kepler pixel data to evaluate the location of thephotocenter and thus to search for astrophysical false positives: (1) the direct measurementof the source location via difference images, the PRF centroid method, and (2) the inferenceof the source location from photocenter motion associated with the transits, the flux weightedcentroid method. In principle both techniques are similarly accurate, but in practice the fluxweighted centroid technique is more sensitive to noise for low signal-to-noise ratio (SNR)transits. We use both techniques because they are both subject to biases due to varioussystematics, but respond to those systematics in different ways.In our difference image analysis (Torres et al. 2011), we evaluate the difference betweenaverage in-transit pixel images and average out-of-transit images. In the absence of pixel-level systematics, the pixels with the highest flux in the difference image will form a starimage at the location of the transiting object, with amplitude equal to the depth of thetransit. A fit of the
Kepler pixel response function (PRF, Bryson et al. 2010) to both thedifference and out-of-transit images provides the offset of the transit source from Kepler-20.We measure difference images separately in each quarter, and estimate the transit sourcelocation as the robust uncertainty-weighted average of the quarterly results.We measure photocenter motion by computing the flux-weighted centroid of all pixelsdownlinked for Kepler-20, generating a centroid time series for row and column. We fit themodeled transit to the whitened centroid time series transformed into sky coordinates. Weperform a fit for each quarter, and infer the source location by scaling the difference of thesetwo centroids by the inverse of the flux as described in Jenkins et al. (2010c). 16 –Both the difference image and photocenter motion methods are vulnerable to varioussystematics, which may bias the result. The PRF fit to the difference and out-of-transit pixelimages is biased by PRF errors described in Bryson et al. (2010). The photocenter techniqueis biased by stars not being completely captured by the available pixels. These types of biaseswill vary from quarter to quarter. Both methods are vulnerable to crowding, dependingon which pixels are downlinked, which varies from quarter to quarter. We ameliorate thesebiases by taking the uncertainty-weighted robust average of the source locations over availablequarters. Because the biases of these difference image and photocenter motion techniquesdiffer, we take agreement of the multi-quarter averages as evidence of that we have faithfullymeasured the source location of the transit signal.Table 3 provides the offsets of the transit signal source from Kepler-20 averaged overQ1 − Q7 for all five planet candidates. The quarterly measurements and averages for thePRF centroid method are shown in Figure 4. All the average offsets are within 2 sigma ofKepler-20.Table 3. Offsets between Photocenter of Transit Signal and Kepler-20
Candidate PRF Centroid [ arcsec ] Significance a Flux-weighted Centroid [ arcsec ] Significance a Kepler-20b 0 . ± .
25 0.29 0 . ± .
24 1.72Kepler-20c 0 . ± .
17 0.12 0 . ± .
22 0.32Kepler-20d 0 . ± .
74 0.92 3 . ± .
96 1.59K00070.04 0 . ± .
51 0.47 2 . ± .
79 1.20K00070.05 0 . ± .
45 1.62 1 . ± .
91 0.93 a offset/uncertainty
17 – −1.5 −1 −0.5 0 0.5 1 1.5−1.5−1−0.500.511.5 6850504, 12.498 ← E (arcsec) N ( a r cs e c ) → Kepler−20b −1.5 −1 −0.5 0 0.5 1 1.5−1.5−1−0.500.511.5 6850504, 12.498 ← E (arcsec) N ( a r cs e c ) → Kepler−20c −3 −2 −1 0 1 2 3−3−2−10123 6850504, 12.498 ← E (arcsec) N ( a r cs e c ) → Kepler−20d−3 −2 −1 0 1 2 3−3−2−10123 6850504, 12.498 ← E (arcsec) N ( a r cs e c ) → KOI−70.04 −3 −2 −1 0 1 2 3−3−2−10123 6850504, 12.498 ← E (arcsec) N ( a r cs e c ) → KOI−70.05
Fig. 4.— Quarterly and average source locations using the difference image (PRF centroid)method for Kepler-20b (top row left), Kepler-20c (top row center), Kepler-20d (top rowright), K00070.04 (bottom row left), and K00070.05 (bottom row right). The light crossesshow the individual quarter measurements and the heavy crosses show the uncertainty-weighted robust average. The length of the crosses show the 1 σ uncertainty of each mea-surement in RA and Dec. The circles have radius 3 σ and are centered at the averagemeasured source location. The location of Kepler-20 is shown by the red asterisk and la-beled with its KIC number. In all the panels, the offset between the measured source locationand the target is less than 2 σ . 18 – Kepler
Light Curve
While the polynomial-fitting approach in § § Kepler photometry from Q1 − Q8 using the new pipeline
PDC-MAP (Jenkins et al. 2011), which moreeffectively removes non-astrophysical systematics in the photometry while leaving the stellarvariability intact. We used this
PDC-MAP corrected light curve to evaluate the rotationalperiod and stellar activity of the star. We computed a Lomb-Scargle periodogram, andfound the highest power peak at a period of 25 days, with a lobe on that peak at around26 days. This peak is also accompanied by significant power at periods between 24 and32 days. The distribution of periodicities and in particular the lobed, broad appearance ofthe peak with the highest power is strongly reminiscent of the activity behavior of the Sun,where differential rotation is responsible for a range of periods from approximately 25 daysat the equator to 34 days at the poles. Indeed, the amplitude of spot-related variabilityon Kepler-20 is very similar to that of the active Sun, as measured during the 2001 seasonby the SOHO Virgo instrument. Using the SOHO light curves treated to resemble Keplerphotometry (as described in Basri et al. 2011), we compared the amplitude of variability ofKepler-20 and the active Sun; the two light curves (and the Lomb-Scargle periodogram ofeach) are shown in Figure 5. We found that Kepler-20 has spot modulation roughly 30%higher in amplitude than that of our Sun. Our estimate of the rotation period (above) forKepler-20 is consistent with both its spectroscopically estimated v sin i < − and anestimate of the rotation period, 31 d, based on its Ca H and K emission log R ′ HK (see § Upper panel:
PDC-MAP corrected lightcurve for Kepler-20 from Q1 to Q8 (blackpoints), showing Kepler-20’s intrinsic stellar variability after removal of instrumental effects.Orange points show the lightcurve for the 2001 active sun from the SOHO Virgo instrument g + r observations for comparison (lightcurve prepared as described in Basri et al. 2010). Lower panel:
Lomb-Scargle periodogram for each of the two curves appearing in the upperpanel. 20 –
3. Follow-Up Observations3.1. High-Resolution Imaging
In order to place limits upon the presence of stars near the target that could be thesource of one or more of the transit signals, we gathered high-resolution imaging of Kepler-20with three separate facilities: We obtained near-infrared adaptive optics images with both thePalomar Hale 5m telescope and the Lick Shane 3m telescope, and we gathered optical speckleobservations with the Wisconsin Indiana Yale NOAO (WIYN) 3.5m telescope. Ultimatelywe used only the Palomar observations in our
BLENDER analysis ( §
4) as these were the mostconstraining, but we describe all three sets of observations here for completeness.
We obtained near-infrared adaptive optics imaging of Kepler-20 on the night of UT 2009September 09 with the Palomar Hale 5m telescope and the PHARO near-infrared camera(Hayward et al. 2001) behind the Palomar adaptive optics system (Troy et al. 2000). Weused PHARO, a 1024 × ′′ . We gathered our observations in the J ( λ = 1 . µ m) filter. We collected thedata in a standard 5-point quincunx dither pattern of 5 ′′ steps interlaced with an off-source(60 ′′ East and West) sky dither pattern. The integration time per source was 4.2 seconds at J . We acquired a total of 15 frames for a total on-source integration time of 63 seconds. Theadaptive optics system guided on the primary target itself; the full width at half maximum(FWHM) of the central core of the resulting point spread function was 0 . ′′ ×
256 pixel PICNICarray with a plate scale of 75.6 mas/pixel, yielding a total field of view of 19 . ′′
6. We gatheredour observations using the K s ( λ = 2 . µ m) filter, and, as with the Palomar observations,we used a standard 5-point dither pattern. The integration time per frame was 120 seconds;we acquired 10 frames for a total on-source integration time of 1200 seconds. The adaptiveoptics system guided on the primary target itself; the FWHM of the central core of theresulting point spread function were 0 . ′′ . The final coadded images at J and K s are shownin Figure 6.In addition to Kepler-20, we detected two additional sources. The first source is 3 . ′′ J ≈ . Ks ≈ . J − K s = 0 . ± .
02 mag which yields anexpected
Kepler magnitude of Kp = 16 . ± . ′′ to the southeast, was detected only in the Palomar J data and is ∆ J = 8 . Kp − J colors (Howell et al. 2011a), has an expected Kepler magnitude of Kp = 21 . ± . σ limits of the J -band and K -bandimaging were approximately 20 mag and 16 mag, respectively (see Figure 7). The respective J -band and K -band imaging limits are approximately 8 . . Kepler bandpass of approximately 9 mag and 6 . We obtained speckle observations of Kepler-20 at the WIYN 3.5m telescope on twodifferent nights, UT 2010 June 18 and UT 2010 September 17. We gathered both sets ofobservations with the new dual channel speckle camera described in Horch et al. (2011). Onboth nights the data consisted of 3 sets of 1000 exposures each with an individual exposuretime of 40ms, with images gathered simultaneously in two filters. The data collection,reduction, and image reconstruction process are described in the aforementioned paper aswell as in Howell et al. (2011b), and the latter presents details of the 2010 observing seasonof observations with the dual channel speckle camera for the
Kepler follow up program.On both occasions our speckle imaging did not detect a companion to Kepler-20 withinan annulus of 0 . − . V ) and 3.54 (in R ) magnitudes fainter than Kepler-20. The June observationyielded limits of 3.14 and 4.92 fainter in V and R respectively. Therefore we rule out thepresence of a second star down to 3.82 magnitudes fainter in V and 4.92 magnitudes fainterin R over an angular distance of 0.05 − J (left) and Lick K s (right) adaptive optics images of Kepler-20. Thetop row displays a 10 ′′ × ′′ field of view for the Palomar J image and a 20 ′′ × ′′ for theLick K s image. The bottom row displays zoomed images highlighting the area immediatelyaround the target . 23 –Fig. 7.— Left panel:
The sensitivity limits of the Palomar J -band adaptive optics imagingare plotted as a function of radial distance from the primary target. The filled circles andsolid line represent the measured J -band limits; each filled circle represents one step inFWHM. The dashed line represents the derived corresponding limits in the Kepler bandpassbased upon the expected Kp − J colors (Howell et al. 2011a). Right panel:
Same as above,but showing the sensitivity limits of the Lick K s -band adaptive optics imaging. The dashedline is based upon the expected Kp − K s colors. 24 – Spitzer
Space Telescope
An essential difference between true planetary transits and astrophysical false positivesresulting from blends of stars is that the depth of a planetary transit is achromatic (ne-glecting the small effect of stellar limb-darkening), whereas false positives are not (exceptin the unlikely case that the effective temperatures of the contributing stars are extremelysimilar). By providing infrared time series spanning times of transit, the Warm
Spitzer
Mis-sion has assisted in the validation of many transiting planet systems, including Kepler-10(Fressin et al. 2011a), Kepler-14 (Buchhave et al. 2011), Kepler-18 (Cochran et al. 2011),Kepler-19 (Ballard et al. 2011), and CoRoT-7 (Fressin et al. 2011b). We describe belowour observations and analysis of Warm
Spitzer data spanning transits of Kepler-20c andKepler-20d, which provide independent support of their planetary nature.
Spitzer
Time Series
We used the IRAC camera (Fazio et al. 2004) on board the
Spitzer
Space Telescope(Werner et al. 2004) to observe Kepler-20 spanning one transit of Kepler-20c and two transitsof Kepler-20d. We gathered our observations at 4.5 µ m as part of program ID 60028. Thevisits lasted 8.5 hours for Kepler-20c and 16.5 hours for both visits of Kepler-20d. We usedthe full-frame mode (256 ×
256 pixels) with an exposure time of 12 s per image, which yielded2451 and 4643 images per visit for Kepler-20c and Kepler-20d, respectively.The method we used to produce photometric time series from the images is describedin D´esert et al. (2009). It consists of finding the centroid position of the stellar point spreadfunction (PSF) and performing aperture photometry using a circular aperture on individ-ual Basic Calibrated Data (BCD) images delivered by the
Spitzer archive. These files arecorrected for dark current, flat-fielding, detector non-linearity and converted into flux units.We converted the pixel intensities to electrons using the information given in the detectorgain and exposure time provided in the image headers; this facilitates the evaluation of thephotometric errors. We adjusted the size of the photometric aperture to yield the smallesterrors; for these data the optimal aperture was found to have a radius of 3 . σ . We also discarded the first half-hour of observations,which are affected by a significant jitter before the telescope stabilizes. We estimated thebackground by fitting a Gaussian to the central region of the histogram of counts from thefull array. Telescope pointing drift resulted in fluctuations of the stellar centroid position,which, in combination with intra-pixel sensitivity variations, produces systematic noise in 25 –the raw light curves. A description of this effect, known as the pixel-phase effect, is givenin the Spitzer /IRAC data handbook (Reach et al. 2006) and is well known in exoplanetarystudies (e.g. Charbonneau et al. 2005; Knutson et al. 2008). After correction for this effect(see below) we found that the point-to-point scatter in the light curve indicated an achievedSNR of 220 per image, corresponding to 85% of the theoretical limit.
Spitzer
Light Curves
We modeled the time series using a model that was a product of two functions, onedescribing the transit shape and the other describing the variation of the detector sensitivitywith time and sub-pixel position, as described in D´esert et al. (2011a). For the transitlight curve model, we used the transit routine
OCCULTNL from Mandel & Agol (2002). Thisfunction depends on the parameters ( R p /R ⋆ ) i , ( a/R ⋆ ) i , b i , and T ,i , where i = { Kepler-20c,Kepler-20d } , the two candidate planets for which we gathered observations. The contributionof stellar limb-darkening at 4.5 µ m is negligible given the low precision of our Warm Spitzer data and so we neglect this effect. We allow only ( R p /R ⋆ ) i to vary in our analysis; the otherparameters are set to the values derived from the analysis of the Kepler light curve (seeTable 2). Because of the possibility of transit-timing variations (see § T ,i to the values measured from Kepler for the particular event. Our model for the variationof the instrument response consists of a sum of a linear function of time and a quadraticfunction (with four parameters) of the x and y sub-pixel image position. We simultaneouslyfit the instrumental function and the transit shape for each individual visit. The errors oneach photometric point were assumed to be identical, and were set to the root-mean-squaredresiduals to the initial best fit obtained.To obtain an estimate of the correlated and systematic errors in our measurements,we use the residual permutation bootstrap method as described in D´esert et al. (2009). Inthis method, the residuals of the initial fit are shifted systematically and sequentially byone frame and added to the transit light curve model, which is then fit once again andthe process is repeated. We assign the error bars to be the region containing 34% of theresults above and 34% of the results below the median of the distributions, as described inD´esert et al. (2011b). As we observed two transits of Kepler-20d we further evaluated theweighted mean of the transit depth for this candidate. In Table 4, we provide a summaryof the Spitzer observations and report our estimates of the transit depths and uncertainties.In Figure 8, we plot both the raw and corrected time series for each candidate, and overplotthe theoretical curve expected using the parameters estimated from the
Kepler photometry(see below). 26 –The adaptive optics images described in § J -band that Kepler-20, and locatedat an angular separation of 3 . ′′ , which corresponds to 3.1 IRAC pixels. We tested whetherthe measured transit depths have to be corrected to take into account the contribution fromthis stellar companion. We computed the theoretical dilution factor by extrapolating the J -band measurements to the Spitzer bandpass at 4.5 µ m. We estimate that 1.6% of thephotons recorded during the observation come from the companion star. For a blend of twosources, the polluted transit depth would be d/ (1 + ǫ ), where d is the unblended transitdepth, and ǫ = 1 . d is well below our detection threshold, we concludethat the presence of the contaminant star near Kepler-20 does not affect our estimates ofthe transit depths.We calculate the transit shapes that would be expected from the parameters estimatedfrom the Kepler photometry (Table 2) and overplot these on the
Spitzer time series in Fig-ure 8. The depths we measure with
Spitzer are in agreement with the depths expected fromthe
Kepler -derived parameters at the 1 σ level. Our Spitzer observations demonstrate thatthe transit signals of Kepler-20c and Kepler-20d are achromatic, as expected for planetarycompanions and in conflict with the expectation for most (but not all) astrophysical falsepositives resulting from blends of stars within the photometric aperture of
Kepler .Table 4. Transit Depths at 4.5 µ m from Warm Spitzer
Candidate AOR Name Date of Observation [UT] Data Number Time of Transit Center [BJD] Transit Depth(%)Kepler-20c r41165824 2010-12-05 2291 2455536.0209 0 . ± . . +0 . − . Kepler-20d r41164544 2010-12-10 4383 2455540.9925 0 . ± . − − − . ± .
27 –Fig. 8.— Warm
Spitzer transit light curves of Kepler-20 observed in the IRAC band-pass at4.5 µ m spanning times of transit of Kepler-20c ( upper half of figure ) and Kepler-20d ( lowerhalf of figure ). For each candidate, the raw and unbinned time series are shown in the upperpanels, and the red solid lines correspond to the best-fit models, which include both theeffects of the instrumental variation with time and image position and the planetary transit(see § Kepler observations(Table 2) are over-plotted as dashed green lines. The transit depths measured in the
Spitzer and
Kepler bandpasses agree to better than 1 σ . 28 – We obtained 30 high resolution spectra of Kepler-20 between UT 2009 August 30 and2011 June 16 using the HIRES spectrometer on the Keck I 10-m telescope (Vogt et al.1994). We took spectra with the same spectrometer set up of HIRES, and with the samespectroscopic analysis, that we normally use for precise Doppler work of nearby FGK stars(Johnson et al. 2011), which typically yields a Doppler precision of 1.5 m s − for slowlyrotating FGKM stars. Typical exposure times ranged from 30 −
45 minutes, yielding anSNR of 120 per pixel (1.3 km s − ). The first 9 observations were made with the B5 decker(0 . ′′
87 x 3 . ′′
0) that does not permit moonlight subtraction. The remaining 21 observationswere made with the C2 decker (0 . ′′
87 x 14 . ′′
0) that permits sky subtraction. The internalerrors were estimated to be between 1.5 − − . We augmented these uncertainties byadding a jitter term of 2.0 m s − in quadrature. The earlier 9 observations are vulnerable tomodest contamination from moonlight, and we have further augmented the uncertainties forthese 9 values by adding in quadrature a term of 2.7 m s − , which is based on the ensembleperformance of stars similarly affected for this magnitude. The final uncertainties range from2.5 − − . The estimated RVs and uncertainties are given in Table 5. We also undertooka study of these spectra to determine the spectral line bisectors with the goal of placinglimits on these sufficient to preclude astrophysical false positives. However, we found thatthe scatter in the bisector centers was somewhat larger than the RV variations, renderingthe RV detection, while sufficient for mass constraint, inconclusive for confirmation. Wetherefore undertook the statistical study described in § R = 60 , R = 60 , Spectroscopy Made Easy (SME; Valenti & Piskunov 1996; Valenti & Fischer 2005)to estimate the values of T eff , log g [Fe/H] and v sin i . We found that the estimates from eachspectrum were consistent to within 1 σ , and hence we averaged our two estimates to obtain T eff = 5455 ±
44 K, log g = 4 . ± .
1, [Fe/H]= 0 . ± .
04, and v sin i < − ; the errorslisted are those resulting from the analysis of each individual spectrum, and we have refrainedfrom assuming a decrease by a factor of √
2. We also proceeded to measure the flux in thecores of the Ca II H and K lines to evaluate the chromospheric activity. We measured that theratio of emission in these lines to the bolometric emission was log R ′ HK = − . ± .
05. This 29 –estimate was derived from a Mt. Wilson-style S-value of 0 . ± .
005 (Isaacson & Fischer2010), using the measured color B − V = 0 . R ′ HK value suggests a low activitylevel for a star of this spectral type, which is consistent with the measured v sin i < − .Using the relations of Noyes et al. (1984) and Mamajek & Hillenbrand (2008), we infer arotation period of 31 days.We also gathered three moderate signal-to-noise ratio, high-resolution spectra of Kepler-20 for reconnaissance purposes, two with the FIbre–fed ´Echelle Spectrograph (FIES) at the2.5 m Nordic Optical Telescope (NOT) at La Palma, Spain (Djupvik & Andersen 2010) andone with the Tull Coud´e Spectrograph on the McDonald observatory 2.7m Harlan SmithTelescope. The FIES spectra were taken on 2009 August 5 and 6 using the medium and highresolution fibers resulting in a resolution of 46,000 and 67,000, respectively. Each spectrumhas a wavelength coverage of approximately 360 −
740 nm. The McDonald spectrum wastaken on 2010 October 25, with a spectral resolution of 60,000. This spectrum was exposedto a SNR of 55 per resolution element for the specific purpose of deriving reliable atmosphericparameters for the star.As an independent check on the parameters derived from the SME analysis of theKeck/HIRES data described above, we derived stellar parameters following Torres et al.(2002) and Buchhave et al. (2010). As part of this analysis, we employed a new fittingscheme that is currently under development by L. Buchhave, allowing us to extract precisestellar parameters from the spectra. We analyzed the two FIES spectra, the McDonaldspectrum and the three HIRES template spectra. These results were found to be consistentwithin the errors. Taking the average of the stellar parameters from the different instrumentsyielded the following parameter estimates: T eff = 5563 ±
50 K, log g = 4 . ± .
10, [m/H]=+0 . ± .
08, and v sin i = 1 . ± .
50 km s − , in agreement with the parameters from SMEwithin the uncertainties. The average systemic radial velocity of the six observations was − . ± .
96 km s − on the IAU standard scale, which includes the correction for thegravitational redshift of the Sun.We note that the two analyses yielded consistent results for log g , metallicity, and v sin i ,but that the estimates of T eff differed by twice the formal error. Hence we elected to adoptthe results of the SME analysis for our final values, but we increased the uncertainty on T eff to 100 K to reflect the difference between the two estimates. We list our estimates for thespectroscopically determined parameters in Table 1. 30 –Table 5. Keck HIRES Radial Velocity Measurements for Kepler-20 Date of Obs. [BJD] Radial Velocity [m s − ] Uncertainty [m s − ] a − − − − − − − − − − − − − − − − − − − − a Includes jitter of 2 m s −
31 –
4. Validation of the Planets Kepler-20b, Kepler-20c, and Kepler-20d
While the analysis of the radial-velocity ( § apriori estimate of the likelihood that the signal is due to a true planet. We consider thesignal to be validated when the likelihood of a planet exceeds that of a false positive by asufficiently large ratio, typically at least 300 (i.e. 3 σ ).Our tabulation of the viable scenarios resulting from blends was accomplished with the BLENDER algorithm (Torres et al. 2004, 2011; Fressin et al. 2011a,b) combined with some ofthe follow-up observations described earlier (high-resolution imaging, centroid motion analy-sis, spectroscopy, and
Spitzer observations).
BLENDER attempts to fit the
Kepler photometrywith a vast array of synthetic light curves generated from blend configurations consisting ofchance alignments with background or foreground eclipsing binaries (EBs), as well as eclips-ing binaries physically associated with Kepler-20 (hierarchical triples). We also consideredcases in which the second star is eclipsed by a larger planet, rather than by another star. Awide range of parameters is explored for the eclipsing pair, as well as for the relative distanceseparating it from the target. Scenarios giving poor fits to the data (specifically, a χ valuethat indicates a discrepancy of at least 3 σ worse than that corresponding to the transitingplanet model) are considered to be ruled out. For full details of this technique we refer thereader to the above sources.The combination of the shorter periods and deeper transits for Kepler-20b and Kepler-20c results in higher SNR for those signals compared to the others. Consequently the shapeof the transit is better defined, and this information makes it easier to reject false positiveswith BLENDER , as we show below. The transit depths of K00070.04 and K00070.05 are only82 and 101 parts per million; this renders these signals far more challenging to validate, andwe find below that we are currently not able to demonstrate unambiguously that these twosignals are planetary in origin. Kepler-20d is similar in depth to Kepler-20b, but due to itslonger orbital period, far fewer transits have been observed. This results in a lower SNR inthe phase light curve. We begin by describing this case.Figure 9 illustrates the
BLENDER results for Kepler-20d. The three panels represent 32 –cuts through the space of parameters for blends consisting of background EBs, backgroundor foreground stars transited by larger planets, and physically associated triples. In thelatter case we find that the only scenarios able to mimic the signal are those in whichthe companion star is orbited by a larger planet, rather than another star. The orange-red-brown-black shaded regions correspond to different levels of the χ difference betweenblend models and the best transiting planet fit to the Kepler data, expressed in terms ofthe statistical significance of the difference ( σ ). The 3 σ level is represented by the whitecontour, and only blends inside it ( < σ ) are considered to give acceptable fits to the Kepler photometry. Other constraints further restrict the area allowed for blends. Thegreen hatched areas are excluded because the EB is within one magnitude of the target inthe Kp band, and would generally have been noticed in our spectroscopic observations. Theblue hatched areas are also excluded because the overall color of the blend is either too red(left in the top two panels) or too blue (right) compared to the measured Sloan-2MASS r − K s color of Kepler-20, as listed in the Kepler
Input Catalog (KIC; Brown et al. 2011).Additionally,
Spitzer observations rule out blends involving EBs (or star+planet pairs) withstars less massive than about 0.78 M ⊙ (gray shaded area to the left of the vertical dotted line),because the predicted depth of the transits in the 4.5 µ m bandpass of Warm Spitzer wouldbe more than 3 σ larger than our Spitzer observations indicate. Note that the combinationof these constraints rules out all physically associated triple configurations for Kepler-20d,so that only certain blend scenarios involving background EBs or background/foregroundstars transited by larger planets present suitable alternatives to a true planet model.We estimate the frequency of these remaining blends following Torres et al. (2011) andFressin et al. (2011a), as the product of three factors: the expected number density of stars inthe vicinity of Kepler-20, the area around the target within which we would miss such stars,and an estimate of how often we expect those stars to be in EBs or be transited by a largerplanet of the right characteristics (specified by the stellar masses, planetary sizes, orbitaleccentricities, and other characteristics as tabulated by
BLENDER ). For the number densitieswe appeal to the Besan¸con Galactic structure model of Robin et al. (2003). Constraintsfrom our high-resolution imaging (see § ρ max ) at which blended stars would be undetected, as a function of brightness.We derive our estimates of the frequencies of EBs and larger transiting planets involved inblends from recent studies by the Kepler
Team (Slawson et al. 2011; Borucki et al. 2011), inthe same way as done for our earlier studies of Kepler-9 d, Kepler-10 c, and Kepler-11 g (seeTorres et al. 2011; Fressin et al. 2011a; Lissauer et al. 2011b).The results of our calculations for Kepler-20d, performed in half-magnitude bins, areshown in Table 6 separately for background EBs and for background or foreground starstransited by a larger planet. The first two columns give the Kp magnitude range of each bin, 33 –and the magnitude difference ∆ Kp relative to the target, calculated at the faint end of eachbin. Column 3 reports the stellar density near the target, subject to the mass constraints from BLENDER as shown in Figure 9. Column 4 gives the maximum angular separation at whichbackground stars would escape detection in our imaging observations. In this particular casethose observations are more constraining than the 3 σ exclusion limit set by our analysisof the flux centroids (0 . ′′
65; see § ρ max and thedensities in the previous column are listed in column 5, in units of 10 − . Column 6 is theresult of multiplying this number of stars by the frequency of suitable EBs ( f EB = 0 . f planet = 0 . BLENDER for these types of scenarios,which is 0.4–2.0 R Jup (see Borucki et al. 2011). The sum of the contributions in each binis given at the bottom of columns 6 and 10. The total number of blends (i.e., the blendfrequency) we expect a priori is reported in the last line of the table by adding these twonumbers together, and is approximately BF = 6 . × − .We now compare this estimate with the likelihood that Kepler-20d is a true transitingplanet (planet prior). To calculate the planet prior we again make use of the census of 1,235candidates reported by Borucki et al. (2011) among the 156,453 Kepler targets observedduring the first four months of operation of the Mission . We count 100 candidates that arewithin 3 σ of the measured radius ratio of Kepler-20d, implying an a priori transiting planetfrequency of PF = 100 / ,
453 = 6 . × − . The likelihood of a planet is therefore severalorders of magnitude larger than the likelihood of a false positive (PF / BF = 6 . × − / . × − ≈ BLENDER is able to rule out all scenarios involving background EBs consisting of two stars,as well as all physically associated triples. This reduces the blend frequencies by one to twoorders of magnitude compared to Kepler-20d. For Kepler-20c,
Spitzer observations are avail-able as well, although the constraints they provide are redundant with color information alsoavailable for the star, which already rules out contaminants of late spectral type. The areasof parameter space in which
BLENDER finds false positives providing acceptable fits to thephotometry are shown in Figure 10. The detailed calculations of the blend frequencies for While these 1,235 candidates have not yet been confirmed as true planets, the rate of false positives isexpected to be quite low (10% or less; see Morton & Johnson 2011), so our results will not be significantlyaffected by the assumption that all of the candidates are planets. We further assume here that the censusof Borucki et al. (2011) is complete at these planetary radii.
34 –Kepler-20b and Kepler-20c are presented in Table 7 and Table 8, respectively, using appro-priate ranges for the larger planets orbiting the blended stars as allowed by
BLENDER , alongwith the corresponding transiting planet frequencies specified in the headings of column 6.Planet priors for these two candidates were computed as before using the catalog ofBorucki et al. (2011). We count 52 cases in that list within 3 σ of the measured radius ratioof Kepler-20b, leading to an a priori planet frequency of 52 / ,
453 = 3 . × − . This isnearly 20,000 times larger than the blend frequency given in Table 7 (BF = 1 . × − ). ForKepler-20c the planet prior based on the measured radius ratio is 28 / ,
453 = 1 . × − ,which is approximately 10 times larger than the likelihood of a blend. Therefore, bothKepler-20b and Kepler-20c are validated as planets with a very high degree of confidence.We carried out similar calculations for the candidates K00070.04 and K00070.05. Thetransit signals of these two candidates are much more shallow than those of Kepler-20b,Kepler-20c, and Kepler-20d. As a result, the constraint on the shape of the transit is con-siderably weaker than in the cases described above, and many more false positives thanbefore are found with BLENDER that provide acceptable fits within 3 σ of the quality of aplanet model. Additionally, neither of these candidates were observed with Spitzer , so theconstraint on the near-infrared depth of the transit that allowed us to rule out some of theblends for Kepler-20d is not available here. In particular, physically associated stars tran-sited by a larger planet cannot all be ruled out, and this ends up contributing significantlyto the overall blend frequency. We conclude that the
BLENDER methodology as implementedabove is insufficient to validate either K00070.04 or K00070.05, and we defer this issue to asubsequent study (Fressin et al. 2012).
Table 6. Blend frequency estimate for Kepler-20d (K00070.03).
Blends Involving Stellar Tertiaries Blends Involving Planetary Tertiaries Kp Range ∆ Kp Stellar Density a ρ max Stars EBs Stellar Density a ρ max Stars Blends ( × − )(mag) (mag) (per sq. deg) ( ′′ ) ( × − ) f EB = 0 .
78% (per sq. deg) ( ′′ ) ( × − ) R p ∈ (cid:2) . − . R Jup (cid:3) , f Plan = 0 . · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Totals 5203 · · · · · ·
Blend frequency (BF) = (0 . . × − ≈ . × − The number densities in Columns 3 and 7 differ because of the different secondary mass ranges permitted by
BLENDER for the two kinds of blend scenarios, as shownin the top two panels of Figures 9.Note. — Magnitude bins with no entries correspond to brightness ranges in which all blends are ruled out by a combination of
BLENDER and other constraints.
36 –Table 7. Blend frequency estimate for Kepler-20b (K00070.02).
Blends Involving Planetary Tertiaries Kp Range ∆ Kp Stellar Density ρ max Stars Blends ( × − )(mag) (mag) (per sq. deg) ( ′′ ) ( × − ) R p ∈ (cid:2) . − . R Jup (cid:3) , f Plan = 0 . · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Totals 2669 · · ·
Blend frequency (BF) = 1 . × − Note. — Magnitude bins with no entries correspond to brightness ranges in which all blends are ruled outby a combination of
BLENDER and other constraints.
37 –Table 8. Blend frequency estimate for Kepler-20c (K00070.01).
Blends Involving Planetary Tertiaries Kp Range ∆ Kp Stellar Density ρ max Stars Blends ( × − )(mag) (mag) (per sq. deg) ( ′′ ) ( × − ) R p ∈ (cid:2) . − . R Jup (cid:3) , f Plan = 0 . · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Totals 495 · · ·
Blend frequency (BF) = 1 . × − Note. — Magnitude bins with no entries correspond to brightness ranges in which all blends are ruled outby a combination of
BLENDER and other constraints.
38 –
Allowed Region
Allowed Region
Fig. 9.—
BLENDER goodness-of-fit contours corresponding to three different blend scenariosfor Kepler-20d: background EBs ( top left ), background or foreground stars transited by alarger planet ( top right ), and stars physically associated with the target that are transitedby a larger planet ( bottom ). The mass of the intruding star (referred to in the
BLENDER nomenclature as the secondary) is shown along the horizontal axis, and the distance betweenthis star and the target is shown on the vertical axis of the top two panels, expressed forconvenience in terms of the distance modulus difference. The vertical axis in the bottompanel shows the sizes of the planets (tertiaries) orbiting physically associated stars. Viableblend models are those giving fits with χ values within 3 σ of the best planet fit, and lieinside the white contours. Other colored areas outside the white contours indicate regionsof parameter space with increasingly worse fits to the data. Blends excluded by our Spitzer constraints are shown with the shaded gray area (secondary masses < . M ⊙ ). Blue cross-hatched areas indicate regions in which blends are excluded because they are either too red(left) or too blue (right) compared to the measured r − K s color of Kepler-20. Blend scenariosin the green cross-hatched areas are also ruled out because they are within ∆ Kp = 1 . Kp ≈ Kp ≈ Spitzer observations, colorindex, and brightness, all physically associated triples are excluded. 39 –
Allowed RegionAllowed Region
Fig. 10.—
BLENDER constraints for Kepler-20b (top panels) and Kepler-20c (bottom) , show-ing chance alignments with a star+planet pair on the left and physically associated stellarcompanions transited by a larger planet on the right. See Figure 9 for the meaning of thevarious lines. The space of parameters for background EBs is not shown as all of thosescenarios provide very poor fits to the transit light curve, and are ruled out. All blendsinvolving physically associated stars transited by a larger planet (right panels) are excludedby a combination of spectroscopic constraints (specifically, on the absence of a secondaryspectrum) and color constraints. 40 –
5. Constraints on Transit Times and Long-term Stability
In this section we discuss the transit times and long-term stability of the system ofplanets orbiting Kepler-20. Both are consistent with the planet interpretation for all 5candidates: transit timing variations (TTVs; Holman & Murray 2005; Agol et al. 2005) arenot seen or expected, and the system is expected to be stable over long timescales.The individual transit times are measured by allowing a template transit light curve toslide in time to fit the data for each transit (Ford et al. 2011). The resulting transit timesare given in Table 9. Aside from slightly more scatter than expected from the formal errorbars there is no indication of perturbations such as coherent patterns. Such excess scatter isnot atypical of transit times measured by the standard pipeline (Ford et al. 2011). Thus, wefind no evidence for dynamical interactions among either the transiting planets or additional,non-transiting planets.To calculate predicted transit times, we numerically integrate our baseline model, whichconsists of a central star of mass 0.912 M ⊙ surrounded by planets with periods and epochsgiven in Table 2 (given at dynamical epoch BJD 2454170), and with masses of 8.7, 0.65,16.1, 1.1 and 8.0 M ⊕ (from least to greatest orbital period), corresponding to the best-fitmasses for Kepler-20b and Kepler-20c, a guess of M p = M ⊕ ( R p /R ⊕ ) . (Lissauer et al.2011b) for Kepler-20d, and masses giving Earth’s density for K00070.04 and K00070.05.(We remind the reader that we have not, in this paper, validated these two candidates asplanets. However, considering them as such for the purposes of evaluating dynamical stabilityis the conservative choice, since the presence of 5 planets, as opposed to 3, is more likelyto induce dynamical instabilities. Fressin et al. (2012) presents the validation of K00070.04and K00070.05, gives their sizes, from which the masses above are derived, and discussesconstraints on their masses.) The orbits are chosen to be initially circular, coplanar, andedge-on to the line of sight. The root mean square deviations of the model transit times fromthe best-fit linear ephemeris projected over 8 years are approximately 3s, 76s, 9s, 95s and10s (from least to greatest orbital period), all significantly smaller than the measurementprecision shown in Figure 11.Next, we investigated long-term stability for this system by integrating the baselinemodel with the hybrid algorithm in Mercury (Chambers 1999). As no close encounters wererecorded, this algorithm reduced to the symplectic algorithm (Wisdom & Holman 1991),with time steps of 0.1 days, roughly 2.7% of the period of the innermost planet. Over the10 Myr integration duration, there were no indications of instability. The orbital eccentrici-ties fluctuated on the scale between approximately 3 × − (for Kepler-20d) and 0 .
001 (forK00070.04). We conclude that plausible, low-eccentricity models for the system are stableover long timescales. 41 –Finally, we performed an ensemble of N-body integrations using the time-symmetric 4thorder Hermite integrator (Kokubo et al. 1998) implemented in
Swarm-NG to estimate themaximum plausible eccentricity for each planet consistent with long-term stability. For eachN-body integration, we set four planets on circular orbits and assigned one planet a non-zero eccentricity. The eccentricity and pericenter directions for the planet on a non-circularorbit were drawn from uniform distributions. The maximum for the uniform distributionof eccentricities was chosen to be slightly larger than necessary for its orbit to cross one ofits neighbors. We report e max , the maximum initial eccentricity that resulted in a systemwith no close encounters (within one mutual Hill radius) and semi-major axes (in a Jacobiframe) which varied by less than 1% for the duration of the integrations. Based on 100integrations per planet and relatively short integrations (10 years), we estimate e max to be0.19, 0.16, 0.16, 0.38 and 0.55 (from smallest to largest orbital period). Technically, we cannot completely exclude larger eccentricities, due to various assumptions (such as the planetmasses, coplanarity, prograde orbits, absence of false positives, and the potential for smallislands of stability at higher eccentricity). Nevertheless, the N-body integrations supportthe assumption of non-crossing orbits, as the vast majority of systems with an eccentricitylarger than e max are dynamical unstable. ∼ eford/code/swarm/
42 –Table 9. Transit Times for Kepler-20
We request that this table be published in electronicformat.
ID n t n TTV n σ n BJD-2454900 (d) (d)Kepler-20b 67 . n × .
43 –Table 9—Continued
ID n t n TTV n σ n BJD-2454900 (d) (d)Kepler-20b 48 244.9212 0.0071 0.0035Kepler-20b 49 248.6075 -0.0028 0.0033Kepler-20b 50 252.3057 -0.0007 0.0045Kepler-20b 52 259.6893 -0.0093 0.0043Kepler-20b 53 263.4017 0.0070 0.0046Kepler-20b 54 267.0944 0.0036 0.0039Kepler-20b 55 270.7832 -0.0038 0.0051Kepler-20b 56 274.4814 -0.0017 0.0042Kepler-20b 57 278.1816 0.0024 0.0049Kepler-20b 58 281.8728 -0.0026 0.0041Kepler-20b 59 285.5734 0.0020 0.0044Kepler-20b 60 289.2635 -0.0041 0.0041Kepler-20b 61 292.9654 0.0017 0.0053Kepler-20b 62 296.6559 -0.0040 0.0028Kepler-20b 63 300.3544 -0.0015 0.0039Kepler-20b 64 304.0540 0.0019 0.0035Kepler-20b 65 307.7479 -0.0002 0.0040Kepler-20b 66 311.4449 0.0005 0.0045Kepler-20b 67 315.1474 0.0070 0.0042Kepler-20b 68 318.8345 -0.0020 0.0045Kepler-20b 69 322.5374 0.0048 0.0040Kepler-20b 70 326.2274 -0.0014 0.0039Kepler-20b 74 341.0195 0.0062 0.0040Kepler-20b 75 344.7166 0.0072 0.0041Kepler-20b 76 348.4024 -0.0031 0.0048Kepler-20b 77 352.1038 0.0022 0.0038Kepler-20b 78 355.8025 0.0047 0.0029Kepler-20b 79 359.4904 -0.0035 0.0043Kepler-20b 80 363.1916 0.0016 0.0045Kepler-20b 81 366.8831 -0.0031 0.0041Kepler-20b 82 370.5829 0.0006 0.0037Kepler-20b 83 374.2740 -0.0044 0.0027Kepler-20b 84 377.9727 -0.0018 0.0040Kepler-20b 85 381.6793 0.0086 0.0039Kepler-20b 86 385.3678 0.0011 0.0033Kepler-20b 87 389.0654 0.0025 0.0041Kepler-20b 88 392.7595 0.0005 0.0045Kepler-20b 89 396.4618 0.0067 0.0042Kepler-20b 90 400.1460 -0.0053 0.0042Kepler-20b 91 403.8471 -0.0003 0.0043Kepler-20b 92 407.5457 0.0022 0.0027Kepler-20b 93 411.2340 -0.0056 0.0049Kepler-20b 94 414.9291 -0.0066 0.0036Kepler-20b 95 418.6325 0.0007 0.0034Kepler-20b 96 422.3282 0.0003 0.0029
44 –Table 9—Continued
ID n t n TTV n σ n BJD-2454900 (d) (d)Kepler-20b 97 426.0243 0.0002 0.0017Kepler-20b 98 429.7166 -0.0036 0.0043Kepler-20b 99 433.4211 0.0047 0.0030Kepler-20b 101 440.8062 -0.0024 0.0049Kepler-20b 102 444.4994 -0.0053 0.0044Kepler-20b 103 448.2026 0.0018 0.0035Kepler-20b 104 451.9098 0.0129 0.0053Kepler-20b 105 455.5917 -0.0013 0.0045Kepler-20b 106 459.2855 -0.0037 0.0039Kepler-20b 107 462.9828 -0.0025 0.0027Kepler-20b 108 466.6899 0.0084 0.0038Kepler-20b 109 470.3763 -0.0012 0.0040Kepler-20b 110 474.0741 0.0004 0.0041Kepler-20b 111 477.7694 -0.0004 0.0033Kepler-20b 112 481.4629 -0.0030 0.0034Kepler-20b 113 485.1567 -0.0053 0.0034Kepler-20b 114 488.8559 -0.0023 0.0025Kepler-20b 115 492.5534 -0.0009 0.0035Kepler-20b 116 496.2526 0.0022 0.0033Kepler-20b 118 503.6411 -0.0015 0.0039Kepler-20b 119 507.3215 -0.0173 0.0045Kepler-20b 120 511.0371 0.0022 0.0055Kepler-20b 121 514.7318 0.0008 0.0049Kepler-20b 122 518.4255 -0.0016 0.0027Kepler-20b 123 522.1195 -0.0037 0.0043Kepler-20b 124 525.8160 -0.0034 0.0030Kepler-20b 125 529.5154 -0.0001 0.0044Kepler-20b 126 533.2147 0.0031 0.0046Kepler-20b 127 536.9038 -0.0039 0.0029Kepler-20b 128 540.6034 -0.0004 0.0037Kepler-20b 129 544.3084 0.0084 0.0042Kepler-20b 130 548.0018 0.0057 0.0041Kepler-20b 131 551.6946 0.0024 0.0035Kepler-20b 132 555.3912 0.0028 0.0030Kepler-20b 133 559.0861 0.0016 0.0037Kepler-20b 135 566.4817 0.0050 0.0043Kepler-20b 136 570.1738 0.0009 0.0054Kepler-20b 137 573.8736 0.0046 0.0032Kepler-20b 138 577.5612 -0.0039 0.0040Kepler-20b 139 581.2539 -0.0074 0.0051Kepler-20b 140 584.9482 -0.0092 0.0040Kepler-20b 141 588.6502 -0.0032 0.0035Kepler-20b 142 592.3510 0.0014 0.0050Kepler-20b 143 596.0490 0.0033 0.0034Kepler-20b 144 599.7493 0.0075 0.0044
45 –Table 9—Continued
ID n t n TTV n σ n BJD-2454900 (d) (d)Kepler-20b 145 603.4392 0.0013 0.0056Kepler-20b 146 607.1344 0.0004 0.0038Kepler-20b 147 610.8329 0.0027 0.0043Kepler-20b 148 614.5286 0.0023 0.0032Kepler-20b 149 618.2205 -0.0019 0.0027Kepler-20b 150 621.9156 -0.0029 0.0031Kepler-20b 151 625.6180 0.0033 0.0039Kepler-20b 152 629.3115 0.0007 0.0039Kepler-20b 153 633.0118 0.0049 0.0050Kepler-20b 154 636.6958 -0.0072 0.0043Kepler-20b 155 640.3937 -0.0054 0.0045Kepler-20b 157 647.7922 0.0008 0.0046Kepler-20b 158 651.4935 0.0060 0.0042Kepler-20b 163 669.9606 -0.0075 0.0041Kepler-20b 164 673.6626 -0.0017 0.0094Kepler-20b 165 677.3552 -0.0052 0.0037Kepler-20b 166 681.0550 -0.0015 0.0062Kepler-20b 167 684.7541 0.0014 0.0030Kepler-20b 168 688.4526 0.0038 0.0046Kepler-20b 169 692.1463 0.0014 0.0017Kepler-20b 171 699.5324 -0.0047 0.0039Kepler-20b 172 703.2330 -0.0002 0.0067Kepler-20b 173 706.9307 0.0014 0.0038Kepler-20b 174 710.6210 -0.0045 0.0032Kepler-20b 175 714.3175 -0.0041 0.0037Kepler-20b 176 718.0073 -0.0105 0.0063Kepler-20b 177 721.7094 -0.0044 0.0042Kepler-20b 178 725.4097 -0.0003 0.0039Kepler-20b 179 729.1068 0.0007 0.0039Kepler-20b 180 732.8057 0.0035 0.003270.04 68 . n × .
46 –Table 9—Continued
ID n t n TTV n σ n BJD-2454900 (d) (d)70.04 15 160.4350 0.0240 0.012270.04 16 166.5186 0.0091 0.015270.04 17 172.6143 0.0063 0.012370.04 18 178.7111 0.0047 0.014170.04 19 184.8108 0.0059 0.050370.04 20 190.9342 0.0307 0.017170.04 21 196.9966 -0.0054 0.013770.04 22 203.1011 0.0007 0.014870.04 23 209.2095 0.0106 0.017770.04 24 215.3090 0.0115 0.018170.04 25 221.3969 0.0010 0.016370.04 26 227.5457 0.0513 0.011270.04 27 233.6113 0.0183 0.013270.04 28 239.7084 0.0170 0.022670.04 29 245.7739 -0.0160 0.019270.04 30 251.8802 -0.0082 0.014770.04 31 257.9671 -0.0198 0.014770.04 32 264.0366 -0.0488 0.017570.04 33 270.1797 -0.0042 0.031470.04 34 276.2872 0.0048 0.016170.04 35 282.3650 -0.0159 0.019770.04 36 288.4550 -0.0244 0.021170.04 37 294.5290 -0.0489 0.018670.04 38 300.6801 0.0037 0.016370.04 39 306.7537 -0.0211 0.016970.04 40 312.9025 0.0292 0.019070.04 41 318.9743 0.0024 0.013170.04 42 325.0517 -0.0186 0.012970.04 45 343.4285 0.0627 0.018370.04 46 349.4757 0.0114 0.018970.04 47 355.5391 -0.0236 0.012070.04 48 361.6421 -0.0192 0.011370.04 49 367.7477 -0.0120 0.010470.04 50 373.8366 -0.0217 0.010670.04 51 379.9503 -0.0065 0.010970.04 52 386.0611 0.0059 0.012870.04 53 392.1451 -0.0086 0.013970.04 54 398.2748 0.0226 0.020470.04 55 404.3426 -0.0082 0.013970.04 57 416.5261 -0.0216 0.016470.04 58 422.6521 0.0059 0.014270.04 59 428.7752 0.0305 0.015570.04 60 434.8565 0.0133 0.016470.04 61 440.9316 -0.0101 0.015170.04 62 447.0528 0.0127 0.0172
47 –Table 9—Continued
ID n t n TTV n σ n BJD-2454900 (d) (d)70.04 63 453.1351 -0.0035 0.013570.04 64 459.2399 0.0028 0.011970.04 65 465.3240 -0.0116 0.014770.04 67 477.5344 0.0017 0.012070.04 68 483.6637 0.0326 0.009770.04 69 489.7101 -0.0195 0.015270.04 70 495.8219 -0.0062 0.015870.04 71 501.9295 0.0029 0.013570.04 72 507.9607 -0.0644 0.015570.04 73 514.1161 -0.0075 0.014870.04 74 520.1992 -0.0229 0.012770.04 75 526.3201 -0.0005 0.012170.04 76 532.4389 0.0198 0.013370.04 77 538.5127 -0.0049 0.014370.04 78 544.6282 0.0121 0.011370.04 79 550.7134 -0.0011 0.018270.04 80 556.8084 -0.0046 0.009270.04 82 568.9873 -0.0227 0.018970.04 83 575.1346 0.0261 0.015470.04 84 581.2328 0.0258 0.015770.04 85 587.2972 -0.0083 0.014770.04 87 599.4992 -0.0033 0.013970.04 88 605.6078 0.0068 0.015870.04 89 611.6560 -0.0435 0.011170.04 90 617.8120 0.0141 0.016970.04 92 630.0025 0.0075 0.015170.04 93 636.1181 0.0247 0.014770.04 94 642.1929 0.0010 0.010670.04 95 648.3022 0.0118 0.017170.04 99 672.6873 0.0029 0.019270.04 100 678.7764 -0.0065 0.015370.04 101 684.8819 0.0006 0.014470.04 102 690.9771 -0.0027 0.016570.04 103 697.0837 0.0053 0.016670.04 104 703.1848 0.0079 0.022870.04 105 709.3466 0.0713 0.017170.04 106 715.3852 0.0113 0.010870.04 107 721.4592 -0.0132 0.015570.04 108 727.5689 -0.0019 0.016970.04 109 733.6590 -0.0104 0.0103Kepler-20c 71 . n × .
48 –Table 9—Continued
ID n t n TTV n σ n BJD-2454900 (d) (d)Kepler-20c 5 125.8775 -0.0005 0.0020Kepler-20c 6 136.7324 0.0003 0.0018Kepler-20c 7 147.5848 -0.0014 0.0018Kepler-20c 8 158.4418 0.0015 0.0013Kepler-20c 9 169.2901 -0.0043 0.0014Kepler-20c 10 180.1483 -0.0002 0.0018Kepler-20c 11 191.0000 -0.0025 0.0018Kepler-20c 12 201.8560 -0.0006 0.0015Kepler-20c 13 212.7127 0.0020 0.0016Kepler-20c 14 223.5737 0.0089 0.0034Kepler-20c 15 234.4203 0.0014 0.0023Kepler-20c 16 245.2744 0.0013 0.0013Kepler-20c 18 266.9898 0.0086 0.0027Kepler-20c 19 277.8388 0.0034 0.0018Kepler-20c 20 288.6911 0.0017 0.0019Kepler-20c 21 299.5445 0.0009 0.0018Kepler-20c 22 310.3963 -0.0013 0.0016Kepler-20c 23 321.2501 -0.0016 0.0018Kepler-20c 25 342.9608 0.0009 0.0018Kepler-20c 26 353.8129 -0.0011 0.0014Kepler-20c 27 364.6678 -0.0003 0.0014Kepler-20c 29 386.3751 -0.0011 0.0020Kepler-20c 30 397.2301 -0.0002 0.0013Kepler-20c 32 418.9392 0.0007 0.0021Kepler-20c 33 429.7823 -0.0103 0.0032Kepler-20c 34 440.6474 0.0007 0.0032Kepler-20c 35 451.5008 0.0000 0.0012Kepler-20c 36 462.3549 0.0000 0.0022Kepler-20c 37 473.2071 -0.0019 0.0015Kepler-20c 38 484.0631 0.0000 0.0017Kepler-20c 39 494.9177 0.0006 0.0029Kepler-20c 40 505.7737 0.0024 0.0011Kepler-20c 41 516.6244 -0.0010 0.0016Kepler-20c 42 527.4780 -0.0015 0.0013Kepler-20c 43 538.3328 -0.0008 0.0014Kepler-20c 44 549.1875 -0.0001 0.0021Kepler-20c 45 560.0406 -0.0011 0.0015Kepler-20c 46 570.8982 0.0024 0.0014Kepler-20c 47 581.7495 -0.0004 0.0021Kepler-20c 48 592.6034 -0.0006 0.0034Kepler-20c 49 603.4558 -0.0023 0.0033Kepler-20c 50 614.3101 -0.0021 0.0023Kepler-20c 51 625.1658 -0.0005 0.0014Kepler-20c 52 636.0218 0.0014 0.0014Kepler-20c 53 646.8745 0.0000 0.0016
49 –Table 9—Continued
ID n t n TTV n σ n BJD-2454900 (d) (d)Kepler-20c 55 668.5835 0.0009 0.0016Kepler-20c 56 679.4363 -0.0005 0.0025Kepler-20c 57 690.2898 -0.0010 0.0023Kepler-20c 58 701.1466 0.0017 0.0023Kepler-20c 59 711.9975 -0.0015 0.0018Kepler-20c 60 722.8602 0.0071 0.0024Kepler-20c 61 733.7038 -0.0034 0.001470.05 68 .
219 + n × . . n × .
50 –Table 9—Continued
ID n t n TTV n σ n BJD-2454900 (d) (d)Kepler-20d 6 563.4005 0.0024 0.0029Kepler-20d 7 641.0100 0.0001 0.0022Kepler-20d 8 718.6231 0.0013 0.0026
Fig. 11.— Measured and predicted transit timing for the planets of Kepler-20.
Left panels :Observed times minus calculated times according to a constant-period model ( O − C ) areplotted as points with error bars, versus transit time. The timing simulations using circular,coplanar planets with nominal masses are plotted as lines. Right panels: The simulationsare shown in more detail (30 × zoom of each panel) to show the timescale and structure ofvariations. 51 –
6. Constraints on the Planetary Compositions and Formation History
The Kepler-20 system, harboring multiple sub-Neptune planets with constrained radiiand masses, informs our understanding of both models of planet formation and the interiorstructure of planets that straddle the boundary between sub-Neptunes and super-Earths.The transit radii measured by
Kepler and the planetary masses measured (or bounded)by radial velocity observations together constrain the interior compositions of Kepler-20b,Kepler-20c, and Kepler-20d, as illustrated by the mass-radius diagram (Figure 12). We em-ploy planet interior structure models (Rogers & Seager 2010; Rogers et al. 2011) to explorethe range of plausible planet compositions. The interpretation is challenging because we donot yet know if these sub-Neptune planets had a stunted formation, or if they formed asgas giants and then lost significant mass to evaporation (Baraffe et al. 2004). This is partlyowing to the uncertainties involved in atmospheric escape modeling.Notably, both Kepler-20c and Kepler-20d require significant volatile contents to accountfor their low mean densities, and cannot be composed of rocky and iron material alone. Thevolatile material in these planets could take the form of ices (H O, CH , NH ) and/or H/Hegas accreted during planet formation. Outgassing of rocky planets releases an insufficientquantity of volatiles (no more than 23% H O and 3.6% H relative to the planet mass) toaccount for Kepler-20c and could account for Kepler-20d only in fine-tuned near-optimaloutgassing scenarios (Elkins-Tanton & Seager 2008; Schaefer & Fegley 2008; Rogers et al.2011). For Kepler-20c, ices (likely dominated by H O) would need to constitute the major-ity of its mass, in the absence of a voluminous, though low-mass, envelope of light gases.Alternatively, a composition with approximately 1% by mass H/He surrounding an Earth-composition refractory interior also matches the observed properties of the planet within1 σ . Intermediate scenarios, wherein both H/He and higher mean molecular weight volatilespecies from ices contribute to the planet mass, are also possible. For Kepler-20d, the 2 σ upper limit on the planet density demands at least a few percent H O by mass, or a fewtenths of a percent H/He by mass.The nature of Kepler-20b’s composition is ambiguous: Kepler-20b could be terrestrial(with the transit radius defined by a rocky surface), or it could support a significant gasenvelope (like Kepler-20c and Kepler-20d). In the mass-radius diagram (Figure 12), themeasured properties of Kepler-20b straddle the pure-silicate composition curve that definesa strict upper bound to rocky planet radii. If Kepler-20b is in fact a terrestrial planetconsisting of an iron core surrounded by a silicate mantle, the 1 σ limits on the planet massand radius constrain the iron core to be less than 62% of the planet mass. In particular,an Earth-like composition (30% iron core, 70% silicate mantle) is possible and matches theobservational constraints to within 1 σ , but a Mercury-like composition (70% iron core, 52 –30% silicate mantle) is not acceptable. Alternatively, Kepler-20b may harbor a substantialgas layer like its sibling planets Kepler-20c and Kepler-20d at larger orbital semi-majoraxes, and/or contain a significant component of astrophysical ices such as H O. The 1 σ lower limits on the planet density constrain the fraction of Kepler-20b’s mass that can becontributed by H O ( . . × kg s − , which corre-sponds to 0.02 M ⊕ Gyr − . Following the same approach, the estimated hydrogen mass lossrates for Kepler-20c and Kepler-20d are 2 × kg s − (0 . M ⊕ Gyr − ) and 8 × kg s − (0 . M ⊕ Gyr − ), respectively. Our theoretical understanding of atmospheric escape fromhighly irradiated super-Earth and sub-Neptune exoplanets is very uncertain, and higher massloss rates are plausible (especially at earlier times when the host star was more active). It isintriguing that Kepler-20b, with its shorter orbital period and greater vulnerability to massloss, also has a higher mean density than Kepler-20c and Kepler-20d. More detailed mod-eling may constrain Kepler-20b’s compositional history and the extent to which its relativepaucity of volatiles can be attributed to evaporation.The Kepler-20 planetary system shares several remarkable attributes with Kepler-11(Lissauer et al. 2011b), namely the presence of multiple transiting low-density low-massplanets in a closely spaced orbital architecture. The Kepler-20 system is less extreme thanKepler-11 in the realms of both low planet densities (Figure 12) and dynamical compactness(the Kepler-11 planets exhibit TTVs while the Kepler-20 planets do not).A striking feature of the Kepler-20 planetary system is the presence of Earth-size rockyplanet candidates interspersed between volatile-rich sub-Neptunes at smaller and larger or-bital semi-major axes, as also seen in Kepler candidate multi-planet systems (Lissauer et al.2011a). Assuming that both K00070.04 and K00070.05 are planets, the distribution of theKepler-20 planets in orbital order is as follows: Kepler-20b (3.7 days, 1.9 R ⊕ ), K00070.04(6.1 days, 0.9 R ⊕ ), Kepler-20c (10.9 days, 3.1 R ⊕ ), K00070.05 (19.6 days, 1.0 R ⊕ ), andKepler-20d (77.6 days, 2.8 R ⊕ ). Given the radii and irradiation fluxes of the two Earth-sizeplanet candidates, they would not retain gas envelopes. The first, second, and fourth planetshave high densities indicative of solid planets, while the other two planets have low densitiesrequiring significant volatile content. The volatile-rich third planet, Kepler-20c dominatesthe inner part of the Kepler-20 system, by holding much more mass than the other three inner 53 –planets put together. In the Solar System, the terrestrial planets, gas-giants, and ice giantsare neatly segregated in regions with increasing distance from the sun. Planet formationtheories were developed to retrodict these Solar System composition trends (e.g., Safronov1969; Chambers 2010; D’Angelo et al. 2010). In the Kepler-20 system, the locations of thelow-density sub-Neptunes that are rich in water and/or gas, and the Earth-size planet can-didates does not exhibit a clean ordering with orbital period, challenging the conventionalplanet formation paradigm. In situ assembly may form multi-planet systems with close-inhot-Neptunes and super-Earths, provided the initial protoplanetary disk contained massiveamounts of solids ( ∼ M ⊕ ) within 1AU of the star (Hansen & Murray 2011). Kepler was competitively selected as the tenth Discovery mission. Funding for thismission is provided by NASA’s Science Mission Directorate. The authors thank many peoplewho gave so generously of their time to make this mission a success. This work is also basedin part on observations made with the
Spitzer Space Telescope , which is operated by theJet Propulsion Laboratory, California Institute of Technology under a contract with NASA.Support for this work was provided by NASA through an award issued by JPL/Caltech.We would like to thank the
Spitzer staff at IPAC and in particular Nancy Silbermann forscheduling the Spitzer observations of this program. Some of the data presented hereinwere obtained at the W. M. Keck Observatory, which is operated as a scientific partnershipamong the California Institute of Technology, the University of California and the NationalAeronautics and Space Administration. The Observatory was made possible by the generousfinancial support of the W. M. Keck Foundation. (c) 2011 all rights reserved. 54 –
VEM U N
Fig. 12.— Mass-radius relationships of small transiting planets. The three confirmed planetsin the Kepler-20 system are highlighted in green. Kepler-20b and Kepler-20c are plotted witherror bars delimiting the 1 σ uncertainties on the planet mass and radius, while Kepler-20dis plotted with bands illustrating the 2 σ mass upper limit. Other small transiting exo-planets with measured masses (Kepler-10b, CoRoT-7b, Kepler-11bcdef, Kepler-18b, 55Cnce, GJ 1214b, HD 97658b, GJ 436b, Kepler-4b, HAT-P-11b) are plotted in black. TheSolar System planets are indicated with the first letters of their names. The curves areillustrative constant-temperature (300 K) mass-radius relations for bodies devoid of H/Hefrom Seager et al. (2007). The solid lines are homogeneous-composition planets: water ice(blue solid), MgSiO perovskite (red solid), and iron (magenta solid). The non-solid linesare mass-radius relations for differentiated planets: 75% water ice, 22% silicate shell, and3% iron core (blue dashed); Ganymede-like with 45% water ice, 48.5% silicate shell, and6.5% iron core (blue dot-dashed); 25% water ice, 52.5% silicate shell, and 22.5% iron core(blue dotted); Earth-like with 67.5% silicate mantle and 32.5% iron core (red dashed); andMercury-like with 30% silicate mantle and 70% iron core (red dotted). The minimal radiuscurve based on simulations of collisional mantle stripping from differentiated silicate-ironplanets (Marcus et al. 2010) is denoted by the dashed magenta line. 55 – REFERENCES
Adams, E. R., Seager, S. & Elkins-Tanton, L. 2008, ApJ, 673, 1160Agol, E., Steffen, J., Sari, R., & Clarkson, W. 2005, MNRAS, 359, 567Ballard, S., Fabrycky, D., Fressin, F., et al. 2011, ApJ, in press, arXiv:1109.1561Baraffe, I., Selsis, F., Chabrier, G., et al. 2004, A&A, 419, L13Basri, G., Walkowicz, L. M., Batalha, N., et al. 2010, ApJ, 713, L155Basri, G., Walkowicz, L. M., Batlaha, N., et al. 2011, AJ, 141, 20Batalha, N. M., Rowe, J. F., Gilliland, R. L., et al. 2010, ApJ, 713, L103Batalha, N. M., Borucki, W. J., Bryson, S. T., et al. 2011, ApJ, 729, 27Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977Borucki, W. J., Koch, D. G., Basri, G., et al. 2011, ApJ, 736, 19Brown, T. M., Latham, D. W., Everett, M. E., & Esquerdo, G. A. 2011, AJ, 142, 112Bryson, S. T., Tenenbaum, P., Jenkins, J. M., et al. 2010, ApJ, 713, L97Buchhave, L. A., Bakos, G. ´A., Hartman, J. D., et al. 2010, ApJ, 720, 1118Buchhave, L. A., Latham, D. W., Carter, J. A., et al. 2011, ApJS, 197, 3Butler, R. P., Marcy, G. W., Fischer, D. A., et al. 1999, ApJ, 526, 916Caldwell, D. A., Kolodziejczak, J. J., Van Cleve, J. E., et al. 2010, ApJ, 713, L92Chambers, J. E. 1999, MNRAS, 304, 793Chambers, J. 2010, Exoplanets, 297Charbonneau, D., Brown, T. M., Latham, D. W., & Mayor, M. 2000, ApJ, 529, L45Charbonneau, D., Brown, T. M., Noyes, R. W. & Gilliland, R. L. 2002. ApJ, 568, 377Charbonneau, D., Allen, L. E., Megeath, S. T., et al. 2005, ApJ, 626, 523Claret, A., & Bloemen, S. 2011, A&A, 529, A75Cochran, W. D., Fabrycky, D. C., Torres, G., et al. 2011, ApJS, 197, 7 56 –D’Angelo, G., Durisen, R. H., & Lissauer, J. J. 2010, Exoplanets, 319Demarque, P., Woo, J.-H., Kim, Y.-C., & Yi, S. K. 2004, ApJS, 155, 667D´esert, J.-M., Lecavelier des Etangs, A., H´ebrard, G., Sing, D. K., Ehrenreich, D., Ferlet,R., & Vidal-Madjar, A. 2009, ApJ, 699, 478D´esert, J.-M., Sing, D., Vidal-Madjar, A., et al. 2011a, A&A, 526, A12D´esert, J.-M., Charbonneau, D., Fortney, J. J., et al. 2011b, ApJS, 197, 11Djupvik, A. A., & Andersen, J. 2010, Highlights of Spanish Astrophysics V, 211Elkins-Tanton, L. T., & Seager, S. 2008, ApJ, 685, 1237Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10Ford, E. B., Lystad, V. & Rasio, F. A. 2005, Nature, 434, 873Ford, E. B., Rowe, J. F., Fabrycky, D. C., et al. 2011, ApJS, 197, 2Fressin, F., Torres, G., D´esert, J.-M., et al. 2011a, ApJS, 197, 5Fressin, F., Torres, G., Pont, F., et al. 2011b, ApJ, accepted, arXiv:1110.5336Fressin, F., Torres, G., Rowe, J. F., et al. 2012, Nature, acceptedGilliland, R. L., Jenkins, J. M., Borucki, W. J., et al. 2010, ApJ, 713, L160Gregory, P. C. 2011, MNRAS, 410, 94Hansen, B. M. S. & Murray N. 2011, arXiv:1105.2050Hayward, T. L., Brandl, B., Pirger, B., Blacken, C., Gull, G. E., Schoenwald, J., & Houck,J. R. 2001, PASP, 113, 105Henry, G. W., Marcy, G. W., Butler, R. P., & Vogt, S. S. 2000, ApJ, 529, L41Holman, M. J., & Murray, N. W. 2005, Science, 307, 1288Holman, M. J., Fabrycky, D. C., Ragozzine, D., et al. 2010, Science, 330, 51Horch, E. P., Gomez, S. C., Sherry, W. H., Howell, S. B., Ciardi, D. R., Anderson, L. M. &van Altena, W. F. 2011, AJ, 141, 45Howell, S. B. et al. 2011a, ApJ, submitted 57 –Howell, S. B., Everett, M. E., Sherry, W., Horch, E., & Ciardi, D. R. 2011b, AJ, 142, 19Isaacson, H., & Fischer, D. 2010, ApJ, 725, 875Jenkins, J. M., Caldwell, D. A., Chandrasekaran, H., et al. 2010a, ApJ, 713, L87Jenkins, J. M., Caldwell, D. A., Chandrasekaran, H., et al. 2010b, ApJ, 713, L120Jenkins, J. M., Borucki, W. J., Koch, D. G., et al. 2010c, ApJ, 724, 1108Jenkins, J. M., J. C. Smith, P. Tenenbaum, J. D. Twicken, and Van Cleve, J. 2011, in Ad-vances in Machine Learning and Data Mining for Astronomy (eds. M. Way, J. Scargle,K. Ali, A. Srivastava), Chapman and Hall/CRC PressJohnson, J. A., Clanton, C., Howard, A. W. et al. 2011, ApJS, 197, 26Knutson, H. A. et al. 2007, Nature, 447, 183Knutson, H. A., Charbonneau, D., Allen, L. E., Burrows, A., & Megeath, S. T. 2008, ApJ,673, 526Koch, D. G., Borucki, W. J., Basri, G., et al. 2010, ApJ, 713, L79Kokubo, E., Yoshinaga, K., & Makino, J. 1998, MNRAS, 297, 1067Latham, D. W., Rowe, J. F., Quinn, S. N., et al. 2011, ApJ, 732, L24Lecavelier Des Etangs, A. 2007, A&A, 461, 1185Lee, M. H. & Peale, S. J. 2002, ApJ, 567, 596Lissauer, J. J., Ragozzine, D., Fabrycky, D. C., et al. 2011a, ApJS, 197, 8Lissauer, J. J., Fabrycky, D. C., Ford, E. B., et al. 2011b, Nature, 470, 53Lloyd, J. P., Liu, M. C., Macintosh, B. A., Severson, S. A., Deich, W. T. S. & Graham, J.R. 2000, Proc. SPIE, 4008, 814Malhotra, R. 2008, ApJ, 575, L33Mamajek, E. E., & Hillenbrand, L. A. 2008, ApJ, 687, 1264Mandel, K., & Agol, E. 2002, ApJ, 580, L171Marcus, R. A., Sasselov, D., Hernquist, L., & Stewart, S. T. 2010, ApJ, 712, L73 58 –Mayor, M., Marmier, M., Lovis, C., et al. 2011, arXiv1109.2497Miller, N. & Fortney, J. J. 2011, ApJ, 736, L29Morton, T. D. & Johnson, J. A. 2011, ApJ, 738, 170Noyes, R. W., Hartmann, L. W., Baliunas, S. L., Duncan, D. K., & Vaughan, A. H. 1984,ApJ, 279, 763Rasio, F. A., Nicholson, P. D., Shapiro, S. L. & Teukolsky, S. A. 1992, Nature, 355, 325Reach, W. T., et al. 2006, IRAC Data Handbook v3.0Robin, A. C., Reyl´e, C., Derri`ere, S., & Picaud, S. 2003, A&A, 409, 523Rogers, L. A., & Seager, S. 2010b, ApJ, 716, 1208Rogers, L. A., Bodenheimer, P., Lissauer, J. J., & Seager, S. 2011, ApJ, 738, 59Safronov, V. S. 1969, Evoliutsiia doplanetnogo oblaka, Nauka, MoscowSchaefer, L., & Fegley, B. 2008, Meteoritics and Planetary Science Supplement, 43, 5037Seager, S., Kuchner, M., Hier-Majumder, C. A., & Militzer, B. 2007, ApJ, 669, 1279Slawson, R. W., Prˇsa, A., Welsh, W. F., et al. 2011, AJ, 142, 160Steffen, J. H., Batalha, N. M., Borucki, W. J., et al. 2010, ApJ, 725, 1226Ter Brakk, C. J. F. 2006, Statistical Computing, 16, 239Torres, G., Neuh¨auser, R., & Guenther, E. W. 2002, AJ, 123, 1701Torres, G., Konacki, M., Sasselov, D. D., & Jha, S. 2004, ApJ, 614, 979Torres, G., Fressin, F., Batalha, N. M., et al. 2011, ApJ, 727, 24Triaud, A. H. M. J. et al. 2010 ˚a, 524, 25Troy, M., et al. 2000, Proc. SPIE, 4007, 31Valenti, J. A. & Piskunov, N. 1996, A&A, 118, 595Valenti, J. A. & Fischer, D. A. 2005, ApJS, 159, 141Van Cleve, J., & Caldwell, D. A. 2009, Kepler Instrument Handbook, KSCI 19033-001.Moffett Field, CA: NASA Ames Research Center 59 –Vogt, S. S., Allen, S. L., Bigelow, B. C., et al. 1994, Proc. SPIE, 2198, 362Werner, M. W., Roellig, T. L., Low, F. J., et al. 2004, ApJS, 154, 1Winn, J. N. 2010, in
Exoplanets (ed. S. Seager), pp. 55Wisdom, J., & Holman, M. 1991, AJ, 102, 1528Wolszczan, A. & Frail, D. A. 1992, Nature, 355, 145Wolszczan, A. 1992, Science, 264, 538Yi, S., Demarque, P., Kim, Y.-C., et al. 2001, ApJS, 136, 417