Draftversion January8,2015 PreprinttypesetusingLATEXstyleemulateapjv.05/12/14 KEPLER-445,KEPLER-446AND THE OCCURRENCE OF COMPACT MULTIPLES ORBITING MID-M DWARF STARS Philip S. Muirhead,1 Andrew W. Mann,2,10,11 Andrew Vanderburg,3 Timothy D. Morton,4 Adam Kraus,2 Michael Ireland,5 Jonathan J. Swift,6 Gregory A. Feiden,7 Eric Gaidos,8 J. Zachary Gazak9 1DepartmentofAstronomy,BostonUniversity,725CommonwealthAve.,Boston,MA,02215USA 2DepartmentofAstronomy,TheUniversityofTexas atAustin,Austin,TX78712,USA 3Harvard-SmithsonianCenter forAstrophysics,60GardenSt.,Cambridge,MA02138, USA 5 4DepartmentofAstrophysicalSciences, 4IvyLane,PeytonHall,PrincetonUniversity,Princeton,NJ08544,USA 1 5AustralianNationalUniversity,CanberraACT2611,Australia 6DepartmentofAstrophysics,CaliforniaInstituteofTechnology, MC249-17,Pasadena, CA91125, USA 0 7DepartmentofPhysicsandAstronomy,UppsalaUniversity,Box516,Uppsala75120,Sweden 2 8DepartmentofGeologyandGeophysics,UniversityofHawai’iatManoa,Honolulu,HI96822,USA 9Institute forAstronomy,UniversityofHawai’iatManoa,2680WoodlawnDrive,Honolulu,HI96822,USA n Draft version January 8, 2015 a J ABSTRACT 6 We confirm and characterize the exoplanetary systems Kepler-445 and Kepler-446: two mid-M ] dwarf stars, each with multiple, small, short-period transiting planets. Kepler-445 is a metal-rich R ([Fe/H]=+0.25 0.10) M4 dwarf with three transiting planets, and Kepler-446 is a metal-poor ± S ([Fe/H]=-0.30 0.10) M4 dwarf also with three transiting planets. Kepler-445c is similar to GJ ± . 1214b: both in planetaryradius andthe propertiesof the host star. The Kepler-446systemis similar h to the Kepler-42 system: both are metal-poor with large galactic space velocities and three short- p period, likely-rocky transiting planets that were initially assigned erroneously large planet-to-star - o radius ratios. We independently determined stellar parameters from spectroscopy and searched for r and fitted the transit light curves for the planets, imposing a strict prior on stellar density in order t to remove correlations between the fitted impact parameter and planet-to-star radius ratio for short- s a duration transits. Combining Kepler-445, Kepler-446 and Kepler-42, and isolating all mid-M dwarf [ stars observed by Kepler with the precision necessary to detect similar systems, we calculate that 21 +7 % of mid-M dwarf stars host compact multiples (multiple planets with periods of less than 10 1 −5 v days) for a wide range of metallicities. We suggest that the inferred planet masses for these systems 5 support highly efficient accretion of protoplanetary disk metals by mid-M dwarf protoplanets. 0 Subjectheadings: stars: fundamentalparameters—stars: individual(Kepler-445,Kepler-446,Kepler- 3 42,Barnard’sStar)—stars: late-type—stars: low-mass–stars: planetarysystems 1 0 . 1. INTRODUCTION The same calculation for the Sun results in only 5% of 1 diskmetals contributing torockyplanets (Earth,Venus, 0 The Kepler-42 exoplanetary system is rather remark- MarsandMercury),withsignificantlymorecontributing 5 able: it consists of three sub-Earth-sized planets all or- 1 biting and transiting a mid-M dwarf host star with pe- to the cores of the solar system’s gas giant planets. : riods of less than two days (Muirhead et al. 2012), a The preference for metals to contribute to rocky plan- v ets rather than gas-giant cores would be strong evi- so-called “compact multiple.” Consider that Kepler-42 i X is a metal-poor star, with a measured [M/H] of -0.27 dence for the planet-formation scenario suggested by Laughlin et al. (2004), in which gas-giant-core embryos r in Muirhead et al. (2012). Following the calculation of a Schlaufman & Laughlin(2010),ifweassumetheplanets form in the protoplanetary disks around M dwarf stars; however, the gas in the disk dissipates before those em- formedfrommaterialinaprotoplanetarydiskwithato- bryos grow large enough to accrete and are cut-off as tal disk mass equal to 1% of the current host star mass, terrestrial planets. The scenario is already supported and that the disk had identical metal abundance to the by the relative scarcity of gas-giant exoplanets found to startoday,thatleadstoadiskmetalcontenttotaling4.1 orbit M dwarf stars. Using radial velocity observations, Earthmasses. Assumingthethreeplanetshaveprimarily Johnson et al.(2010)foundastatisticaldecreaseingiant rocky compositions, and combining the predicted plan- planetplanetoccurrencewithdecreasinghoststarmass, etary mass-radius relationships of Fortney et al. (2007) including M dwarfs in the radial velocity sample. How- with the measured planetary radii in Muirhead et al. ever, Gaidos & Mann (2014) do not find strong support (2012), the total mass of the three planets is calculated for a statistical deficiency of gas giant planets orbiting to be 0.71 Earth masses. Under these admittedly sim- Mdwarfs,thoughtheycannotstatisticallyruleoutade- plistic assumptions, nearly 20% of Kepler-42’s disk met- ficiency. Regardless, the presence of failed embryos in als went into the formation of these three rocky planets. some consistent proportion to the amount of available metalsinthe protoplanetarydiskwouldprovidesupport 10HarlanJ.SmithFellow,TheUniversityofTexas atAustin for the cut-off accretion scenario. 11Visiting Researcher, Institute for Astrophysical Research, It is important to determine whether the planetary BostonUniversity 2 system orbiting Kepler-42 is an outlier or a common two or more planets oribiting with periods of less than type of system around mid-M dwarf stars, and whether 10 days. Finally, in Section 5, we discuss the implica- metallicityaffectsthesizesoffailedembryos. Theoccur- tionsofthesesystemsforplanetformationscenariosand renceofcompactmultiplesystemsorbitingmid-Mdwarf accretion of disk metals by protoplanets orbiting mid-M stars has not been thoroughly analyzed. Recent investi- dwarf stars. gations aimed at understanding the planet occurrence statistics from Kepler, such as Howard et al. (2012), 2. DATAANDANALYSIS Petigura et al. (2013) and Silburt et al. (2014) do not 2.1. High-contrast Imaging consider mid-M dwarf stars. Dressing & Charbonneau (2013), Gaidos et al. (2014) and Morton & Swift (2014) High-contrast imaging of Kepler planet-candidates investigatedtheoccurrenceofplanetsaroundspecifically servestwopurposes: withhigh-contrastimages,thelevel M dwarf stars and found a propensity for Earth-sized ofcontaminationbyunresolvedobjectswithintheKepler planets, the latter finding roughly two planets per M aperture can be determined, and in the event that there dwarf star with periods of less than 150 days. How- are no contaminating objects within the aperture, high- ever,those investigationsdid not addressthe occurrence contrast imaging provides constraints on false-positive of compact multiples, and many Kepler mid-M dwarf scenarios that could mimic the detected transit signal stars were not included in that study, including Kepler- (e.g.Adams et al.2012; Lillo-Box et al. 2012; Law et al. 42. Swift et al. (2013) investigated the occurrence of 2013; Lillo-Box et al. 2014; Dressing et al. 2014). compact multiples orbiting Kepler M dwarf stars us- We observed Kepler-445 and Kepler-446 with the ing Kepler-32 as a representative of the Kepler M dwarf Keck II telescope at Mauna Kea Observatories using stars. They found that Kepler planet detections around the facility near-infraredadaptive-optics imager NIRC2, Mdwarfstarscouldbe recreatedreasonablywellassum- operated in K′ band. We observed the stars using ingallplanetarysystemsareclonesoftheKepler-32sys- both conventional imaging and using non-redundant tem, indicating a high occurrence of compact multiples. aperture masks, which can be placed near an im- In this paper we confirm and characterize two new age of the telescope pupil within the NIRC2 cryostat. compact multiple systems with mid-M-dwarf host stars: Non-redundant aperture masks enable high-contrast Kepler-4453 and Kepler-4464, initially discovered by the imaging by measuring individual spatial frequencies Kepler exoplanet search pipeline to host two and three corresponding to each baseline produced by a pair short-period planets, respectively. Kepler-445c, Kepler- of apertures (Haniff et al. 1987; Nakajima et al. 1989; 445b, Kepler-446b and Kepler-446d were first reported Tuthill et al. 1999; Monnier et al. 2004; Lloyd et al. as planet-candidates by Burke et al. (2014) as KOI- 2006; Martinache et al. 2009; Kraus & Ireland 2012; 2704.01,KOI-2704.02,KOI-2842.01andKOI-2842.02re- Ireland 2013). By making the apertures non-redundant, spectively, and Kepler-446c was reportedas a threshold- high fringe-contrastand phase information is not lost to crossing event by Tenenbaum et al. (2013), and later incoherent addition of fringes from redundant baselines, added to the NASA Exoplanet Archive as KOI-2842.03. enabling contrast performance better than the full-dish With regard to the host stars, Kepler-445 was identi- diffraction limit of the telescope. Phases from combi- fied as a mid-M dwarf star in an optical spectroscopic nations of three individual baselines are combined into survey of late-type KOIs by Mann et al. (2013a), and closure-phases, which probe azimuthal asymmetries in bothKepler-445andKepler-446wereidentifiedasmid-M the image while remaining robust against phase-errors dwarfstarsinaseparateinfraredspectroscopicsurveyof from instrument distortions or uncorrected atmospheric late-type KOIs by Muirhead et al. (2014). We searched fluctuations. thelightcurvesforadditionalplanets,andfoundanaddi- We observed Kepler-445 on UT 17 July 2013 and tionalplanetorbitingKepler-445notdetectedbytheKe- Kepler-446 on UT 29 July 2014. For each target, we ac- pler pipeline, whichwe refer to as Kepler-445b. Refining quiredthree,conventionalK′bandAOimages,eachwith theparametersforthehoststarsandrefittingtheplanet 20-secondintegrations,eachditheredacrossthedetector, transitlightcurves,wefindthatKepler-445cissimilarto using multiple-correlated sampling with a Fowler depth GJ1214b: botharelikelymini-Neptunes orbitingmetal- of 16 (Fowler & Gatley 1990). The non-redundantaper- rich mid-M dwarf stars, and that Kepler-446 is similar ture masking images were acquired in the same manner to Kepler-42 in multiple ways: the low-metallicity of the as Kraus & Ireland (2012): we used a nine-hole mask, host star, the multiplicity, sizes, and orbital periods of with 1.5-meter-equivalent apertures creating baselines the orbiting planets, and the planets’ initial mischarac- with separations of 1.5 to 9.2 meters. We acquired six terization. aperture-maskedimages in K band, eachwith 20-second Wepresenttheobservations,dataandanalysisofthese integrations and using mutliple-correlated sampling. systems inSection2. InSection3 we calculatethe false- We reduced the data using the methods described positive probabilities for the planets orbiting Kepler-445 in Kraus et al. (2008), as well as a kernel-phase tech- and Kepler-446, confirming the planetary nature of the nique with the POISE calibration algorithm (Ireland transits. InSection4wecombineKepler-445,Kepler-446 2013), that included subsampling of the Keck pupil andKepler-42with the full sampleofmid-Mdwarfstars sub-apertures. The kernel-phase technique yielded observed by Kepler with similar precision from quarters marginally superior contrast limits, and those limits are 1 to 16 to estimate the occurrence of compact multiple reported here. systems around mid-M dwarf stars, which we define as ForKepler-445,wedetectedafaintobjectatasepara- tion of 3.908 0.004 arcseconds, with a position angle 3 KOI-2704,KIC9730163, α=298.736115◦,δ=46.498634◦ of 279.62 0.±05 degrees east of north, and a magnitude 4 KOI-2842,KIC8733898, α=282.250214◦,δ=44.921108◦ difference±of ∆K‘ = 7.60 0.07 magnitudes. With such ± 3 Survey(2MASS,Cutri et al.2003;Skrutskie et al.2006). 0 They are alsoincluded inthe KIC,whichaimed to mea- sureSDSS-likeu,g,r,i,andz magnitudesforallobserv- able stars in the Kepler field. However, owing to their mit 2 faintness, the KIC lacks u and z magnitudes for Kepler- Li 445 and u for Kepler-446. Other photometric surveys n o of the Kepler field include the UBV Photometric Sur- cti 4 vey (Everett et al. 2012), which contains both Kepler- e et 445andKepler-446andtheirBandV magnitudes. How- D ever, comparing the independent V band measurements K’ 6 ofKepler-42inMuirhead et al.(2012)withthemeasure- ∆ σ ments in the UBV Survey shows a significant offset of 6 0.23magnitudes,a4σdiscrepancy,whichcouldbedueto 8 Kepler −445 inaccuratecalibrationeffectsforveryredlow-massstars. Yet another survey of the Kepler field is the Kepler- INT Survey (KIS, Greiss et al. 2012), which contains u, 0.01 0.10 1.00 g and r magnitudes for Kepler-446, but no photometry Separation (arcseconds) forKepler-445. Interestingly,Greiss et al.(2012)founda systematicoffsetof 0.05magnitudesbetweentheKISi 0 ∼ magnitudesandthemagnitudesreportedintheKIC,and Pinsonneault et al.(2012)foundasimilaroffsetbetween SDSSandthe KIC.Wealsonotethatthe r’-bandCarls- mit 2 berg Meridian Catalogue overlaps significantly with the Li Kepler field, andcontains a measurementfor Kepler-446 n o (r’ = 16.731, Copenhagen University et al. 2006). How- cti 4 ever, it does not contain a measurement for Kepler-445. e et Owing to the discrepancies and incompleteness of the D varioussurveys,wechosetomeasureu,g,r,iandzmag- K’ 6 nitudes of Kepler-445 and Kepler-446 independently us- ∆ σ ingthe LargeMonolithicImager(LMI)onthe 4.3-meter 6 DiscoveryChannelTelescope(DCT)inHappyJack,Ari- 8 Kepler −446 zona (Massey et al. 2013). LMI contains the full com- pliment of SDSS filters and a 6k x 6k full-wafer deep depletion e2V CCD, with a field of view of 0.25 x 0.25 0.01 0.10 1.00 degrees. We observedKepler-445 and Kepler-446 on UT Separation (arcseconds) 2014 August 6, along with two nearby SDSS fields cen- Fig.1.— Contrast curves for Kepler-445 (top) and Kepler-446 teredonα=290.60299,δ=38.75381andonα=270.00583, (bottom) showing the 6σ ∆K′ detection limits for objects at the δ=270.00583,forcalibration. Conditionswerephotomet- plotted separations. The breaks at 0.150 arcseconds arise from ric. We observed each SDSS field at four different air- a switch from contrast measured using aperture-masking to that masses, spanning 1.00 to 1.30. We observed Kepler-445 measured using conventional adaptive-optics imaging and PSF- subtraction. Wedetectedafaintobjectroughly4arcsecondsfrom and Kepler-446 twice, at two separate airmasses each, Kepler-445, with ∆K = 7.60 ± 0.07 magnitudes. Such a faint with all observations between 1.00 and 1.30 airmasses. objectcouldnotaccount forthetransitsseenaroundKepler-445. We also observed Kepler-42 following the same strategy as Kepler-446 and Kepler-445. a large contrast, the object’s contribution to the Kepler For each pointing, we cycled through the SDSS filters lightcurveisnegligibleanditisunlikelytheobjectshow- in LMI, acquiring u, g, r, i and z band images using ingthetransitsignals. Nevertheless,weconsiderthepos- 2x2 pixel binning. Each exposure was 20 seconds long sibility in our false positive analysis in Section 3. Aside in order to match or exceed the signal-to-noise of the fromthisdetectedobject,wedetectnootherobjectsnear archival SDSS photometry without saturating the LMI Kepler-445, with 6σ contrast limits shown in Figure 1. detector. We performed standard flat-fielding and bias Interestingly, this is inconsistent with the Kepler Input subtraction, using twilight flats for u and g bands, and Catalog (KIC, Batalha et al. 2010; Brown et al. 2011) dome flats for r, i and z bands. To calibrate the LMI and the NOMAD Catalog (Zacharias et al. 2005), both measured fluxes to SDSS magnitudes, we cross-matched of which record a similar visible-brightness star 2.”2 all non-saturated point-sources in our SDSS calibration ∼ away: KIC 9730159and NOMAD 1364-0341824,respec- imageswiththeSDSSDR9catalogofsources(Ahn et al. tively. Consideringthe infraredadaptiveopticsimaging, 2012). We extracted the flux for each detectable point andthe seeing-limitedvisible-wavelengthimaging we re- source in the calibration images using a modified ver- portinthe followingsectionwhichalsolacksthisnearby sion of DAOPHOT (Stetson 1987), and converted the object,webelievethattheNOMADcatalogandtheKIC object counts into “detector” magnitudes with a arbi- may have inadvertently recorded Kepler-445 twice. trary zero point. For those point sources with a reliable match in the SDSS DR9 catalog, we calculated the dif- 2.2. Host-star Magnitudes ference between our detector magnitudes and the SDSS BothKepler-445 andKepler-446 have reliable infrared archival “PSF” magnitudes, for each band, at each air- J, H and Ks magnitudes in the Two-Micron All Sky mass. We only used SDSS PSF magnitudes for objects 4 metricparallaxes,relativelyaccuratemass-luminosityre- TABLE 1 lations canbe used to determine stellar massesbasedon Host-star Magnitudes their absolute infrared magnitudes (Henry & McCarthy 1993; Delfosse et al. 2000). The stellar masses can be Band Kepler-42 Kepler-445 Kepler-446 combinedwith empiricalor theoreticalmass-radiusrela- ua 19.922±0.121 21.944±0.493 20.929±0.142 tionships to determine stellar radius (e.g. Torres et al. g 17.142±0.043 19.024±0.032 18.258±0.031 r 15.503±0.022 17.626±0.016 16.828±0.016 2010). Or, in some cases, stellar parameters can be i 14.276±0.015 16.024±0.011 15.614±0.011 determined from the transit light curve itself, either z 13.537±0.023 15.087±0.016 14.887±0.016 by measuring photometric signatures from asteroseis- Jb 12.177±0.021 13.542±0.029 13.591±0.021 mic pulsations (e.g. Bedding et al. 2011; Huber et al. H 11.685±0.018 12.929±0.035 13.075±0.026 2013), or by using an exoplanet transit light curve to K 11.465±0.018 12.610±0.028 12.827±0.024 infer the host star’s density assuming a low-eccentricity W1c 11.240±0.023 12.478±0.024 12.707±0.023 or circular orbit (e.g. Seager & Mall´en-Ornelas 2003; W2 11.054±0.021 12.353±0.025 12.476±0.023 W3 10.831±0.059 11.252±0.087 12.931±0.415 Carter et al. 2011), or a combination of both techniques (e.g. Ballard et al. 2014). a ugrizmeasuredwithDCT-LMIandreportedasequivalent In the case of Kepler-445 and Kepler-446, asteroseis- SDSSPSFABmagnitudes(Oke&Gunn1983). b J,H,andK from2MASS(Cutrietal.2003). mic signatures are very difficult to measure because, be- c W1,W2 andW3 fromWISE (Cutri&etal.2012). ing M dwarf stars, they are dense, with mean densities over 10 gm/c, where the asteroseismic signals are low that were listed as having a star-like point spread func- and the stellar oscillation frequencies are high. Also, tion, not saturated, with a magnitude of less than 22. the signal-to-noise of the Kepler light curves is simply We also limited the calibrating SDSS sources to those not high enough to provide strong constraints on the listed as a star and having 0.9 < r i < 2.25, similar stellar density from transit light curve fitting. With- − to M3 to M6 dwarf stars (Bochanski et al. 2007). Lim- out astrometric parallaxes, asteroseismic or transit light iting calibration sources to stars of similar spectral type curve constraints, we must rely on colors and spec- eliminates errors arising from different spectral shapes troscopy to determine the stellar parameters. In the across the SDSS bands. This resulted in 6 calibration case of M dwarf stars burning hydrogen on the main- stars for u band, 83 in g band, 249 in r band, 465 in sequence, spectroscopy probes primarily effective tem- i band and 361 in z band for the SDSS calibration field perature, T , and metallicity, [Fe/H] or [M/H]. Typi- eff withmoreoverallsources. Forthisfieldwefittedalineto cally,surfacegravity,log(g),is anotherphysicalparame- the detector minus SDSS magnitude versus airmass for terprobedby spectroscopy. Inthe caseofMdwarfstars eachband. Finally, weapplied the fitted relationsto the on the main sequence, log(g) is predicted to be a strict measured detector magnitudes for Kepler-445, Kepler- functionofT andmetallicity. WithT andmetallicity 446 and Kepler-42, again for each band. We estimated eff eff alone,thestellarmass,radiusandbolometricluminosity the uncertainty in our measured magnitudes by combin- can be determined using either predictions from stellar ingtheuncertaintyduetophotonnoisewithasystematic evolutionary models (e.g. Dotter et al. 2008), or empir- uncertainty based on the linear fit to airmass. The esti- ical relations (e.g. S´egransanet al. 2003; Boyajianet al. mated uncertainties are roughly consistent with the dif- 2012). ference between magnitude determinations for the two Moderate-resolution infrared spectra (R 2700, 1.5 to pointings on Kepler-445 and Kepler-446. We averaged 2.5µm) forKepler-445andKepler-446wer∼eobtainedby the two pointings for Kepler-445 and Kepler-446 to ob- Muirhead et al. (2014), who determined stellar parame- tainourbestvalues,andtheresultsarelistedinTable1. ters based on the K-band indices of Rojas-Ayala et al. We do notdetect anystellarcompanionsthatwouldsig- (2012), then interpolated those values on a new set nificantlycontaminatetheKeplerlightcurvesneareither of models based on the Dartmouth Stellar Evolution Kepler-445 or Kepler-446 in any of the images, despite Database (Dotter et al. 2008), calculated by G. Fei- the listed of a similar brightness star near to Kepler-445 den. A visible low-resolution spectrum for Kepler-445 in NOMAD and the KIC. (R 900, 3200 to 9200˚A) was obtain by Mann et al. With r i values of 1.68 and 1.28, and i z val- ∼ ues of 0.8−6 and 0.64, Kepler-445 and Kepler-−446 fall (2013a), who used a new calibration to measure ef- fective temperature. They then used the mass-radius- squarelyinthecolor-colorlimitsforM4dwarfstarsfrom temperature relations of Boyajian et al. (2012) for their Bochanski et al.(2007,Table1),whocomparedcolorsto sample, but were unable to determine the stellar mass spectral types of M dwarf stars in the SDSS survey. We and radius of Kepler-445 as it was too cool for these re- note this only for consistency. In the next section, we lations. Kepler-446 was not discovered by the Kepler use our photometry to flux calibrate and stitch together pipeline at the time of their study. optical and infrared spectra, which provide a far greater In this paper, we combine the techniques from handle on the properties of the host stars. We also note Mann et al. (2013a) and Muirhead et al. (2014) to pro- thatneitherKepler-42,Kepler-445norKepler-446shows duce the best possible physical parameters of the stars. a u-band excess, indicating low chromospheric activity. We choose to use the Mann et al. (2013a) visible-light This is further supported by the lack of Hα in emission, spectroscopiceffectivetemperaturecalibration,sinceitis described in the next section. calibratedusing truly empiricalmeasurements ofnearby M dwarf stars from optical-long baseline interferometry 2.3. Moderate-resolution Spectra and Stellar Parameters (Boyajianet al.2012). WeusetheK-bandspectroscopic NeitherKepler-445norKepler-446currentlyhasapub- metallicity measurements from Muirhead et al. (2014), lished astrometric parallax measurement. With astro- 5 asthoseusedempiricalcalibrationsbyRojas-Ayala et al. setusedinMuirhead et al.(2014)andthisstudy. Wees- (2012), who verified the metallicities by comparison to timated the distance to the stars by inverting the mass- space-motionsofnearbyMdwarfstars. Finally,weinter- luminosityrelationsofDelfosse et al.(2000)todetermine polatethosevaluesontothenewsuiteofDartmouthevo- the stars absolute K-band magnitudes, and compared lutionary models as was done in Muirhead et al. (2014), that to the measured K-band magnitude from 2MASS. but with a small correctionbased on the empirical mea- All three stars are relatively nearby with distances less surements of Barnard’s Star (similar to Muirhead et al. than 150 parsecs. 2012). The stellar parameter determinations for Kepler-445 Todothis,weusedprimarilythearchivalspectroscopy and Kepler-446 presented here revise values published described above, but acquired a new visible spectrum of in the literature. Compared to Muirhead et al. (2014), Kepler-446. Our additional spectrum of Kepler-446 was the masses and radii presented here are slightly larger acquired with the SNIFS instrument on the University owing to the use of the Mann et al. (2013a) effective of Hawaii88-inchTelescope at Mauna Kea Observatory. temperature calibration rather than the K-band tech- Wefollowedidenticalobservingandreductionprocedures nique. The most recent evaluation of stellar param- described in Mann et al. (2013a). eters for Kepler targets was compiled by Huber et al. Tostitchthevisibleandnear-infraredspectratogether (2014), who assign both Kepler-445 and Kepler-446 for each star, we combine the r magnitudes measured smaller and larger radii (respectively) than presented in the previous section with the H and Ks magnitudes here. We ascribe this to erroneous metallicity deter- from 2MASS. We acquiredthe filter transmissioncurves minations in that catalog, which lists Kepler-445 as a for each band (r, H and K) and computed a synethic metal-poor star ([Fe/H] = -0.380) and Kepler-446 as spectralmagnitudeusingthe transmissioncurveandthe a metal-rich star ([Fe/H]=+0.30), the inverse of our measured spectrum, keeping in mind that 2MASS used measurements. The source for the Kepler-446 parame- amodifiedVegasystem,andourmeasuredSDSSmagni- ters in Huber et al. (2014) is Dressing & Charbonneau tudesusetheABsystem(Oke & Gunn1983). Wecalcu- (2013), who used photometry to estimate stellar param- lated the difference between the synthetic spectral mag- eters. As Dressing & Charbonneau (2013) admit, pho- nitudeandthemeasuredmagnitudefromeachrespective tometryaloneplacespoorconstraintsonMdwarfmetal- survey,andusedthatdifferencetorenormalizeandcom- licity, and Kepler-446’s erroneously large radius in both bine the visible and near-infraredspectra. Dressing & Charbonneau(2013)andHuber et al.(2013) Figure 2 plots the visible and infrared spectra of is a direct consequence of the imprecise metallicity mea- Kepler-445 and Kepler-446, with spectra of Barnard’s surement. Star from Mann et al. (2013a) and Kepler-42 from 2.4. High-resolution Spectra and Space Motions Muirhead et al. (2014) for comparison,subject to an ar- bitrarilytotalnormalizationsuchthattheyoverlapinH- We also acquired higher-resolution spectra in order to band. Clearly,thespectraareverysimilar: areallidenti- measure the absolute radial velocities of the stars and fiablyM4dwarfstars. Wedidnotcorrectforinterstellar their galactic space motions. We observed Kepler-445 reddening because all stars are likely well within 150 pc andKepler-446withtheEchelletteSpectrographandIm- of the sun (see Section 2). None of the stars show Hα in ager (ESI) on the Keck-II telescope (Sheinis et al. 2002) emission, indicating low quiescent-activity and that all on UT 25 July 2014. We operated ESI in echellette of the stars are likely old (t > 5 Gyr, West et al. 2008). mode using a slit width of 0.5 arcseconds, achieving a However, we note that Barnard’s Star does show occa- resolvingpower of 8000 from 4000to 10000˚A, spread sionalHαflaring(e.g.Paulson et al.2006),andthatage- across ten cross-dis∼persedorders. For Kepler-446 we ac- activity relationships are a statistical toolfor estimating quiredasingle1000secondexposure,andforKepler-445 the age of an ensemble of stars, and are subject to large we co-added three 900 second exposures. We also ob- uncertainties when applied to any specific star. served GJ 687 and GJ 905 as M-dwarf radial velocity To determine any offsets to apply to the new Dart- standard stars with published radial velocities and un- mouth models, we interpolated the empirical effective certainties in Nidever et al. (2002) and Deshpande et al. temperature and metallicity measurements of Barnard’s (2012), respectively. We reduced the data using the Star onto the new Dartmouth models to determine the publicly available ESIRedux pipeline5, using dome flats predicted stellar mass and radius. The predicted mass for flat-fielding and arclamps for wavelengthcalibration and radius are marginally different from the empirical (Prochaska et al. 2003; Bochanski et al. 2009). mass(determinedusing mass-luminosityrelationshipsof We then cross-correlated the radial velocity standard Delfosse et al. 2000) andthe empiricalradius (measured spectrawithKepler-445andKepler-446tomeasuretheir using optical long-baseline interferometry, Lane et al. absoluteradialvelocities. Weusedthefull-width-at-half- 2001; Boyajianet al. 2012), with offsets of -0.004 Msun maximumofthepeakinthecross-correlationfunctionas and 0.002 Rsun, both of which are well below the typi- our measurement uncertainty, combined in quadrature cal uncertainty in those quantities. Nevertheless we still with the archival measurement errors for the radial ve- applied those corrections to the interpolated values. locity standard stars. We found agreement within our Our results for the stellar parameters appear in Table uncertainties when using GJ 687 or GJ 905 separately 2. In addition to calculating the parameters for Kepler- as standards, and we report the mean of those measure- 445andKepler-446,we also recalculatedthe parameters ments here. For Kepler-445 we measured an absolute for Kepler-42 using identical methods, and find agree- radialvelocity of -61 1 km s−1, and for Kepler-446 we ment with Muirhead et al. (2012), who used a similar measured -118 1 km±s−1. technique, but applied a correction to the original Dart- ± mouth models (Dotter et al. 2008), rather than the new 5 http://www2.keck.hawaii.edu/inst/esi/ESIRedux/index.html 6 5 4 Kepler −446 s) Kepler−42 nit 3 Barnard’s Star u y Kepler −445 ar 2 bitr ar F (λ 1 0 −1 0.5 1.0 1.5 2.0 2.5 λ (µm) Fig.2.—Visibleandnear-infraredspectraofKepler-445andKepler-446,withspectraofBarnard’sStar andKepler-42forcomparison, all normalized to match in H-band (λ ∼ 1.65 µm). The visible spectrum of Kepler-446 is part of this work, with the remaining visible andinfraredspectracomingfromMannetal.(2013a)andMuirheadetal.(2014). Thespectrawerefirstrenormalizedpiece-wisetomatch infraredphotometry fromtheTwo-MicronAllSkySurvey(2MASS,Cutrietal.2003;Skrutskieetal.2006)andour independent SDSSr bandphotometry. ThesimilarshapestothespectrastronglysupportourinterpretationthatKepler-445andKepler-446aremid-Mdwarf starswithsimilarmassesandradiitoBarnard’sStarandKepler-42. Wehavemadenocorrectionforinterstellarreddening,asthesestars areallexpected tobewithin150pcofthesun(seeTable2). TABLE 2 StellarParameters†† Mid-MDwarfStar Teff [Fe/H] [M/H] M⋆ R⋆ Distance Kepler-445 3157±60Ka +0.27±0.13c +0.19±0.12c 0.18±0.04M⊙ 0.21±0.03R⊙ ∼90pc Kepler-446 3359±60K -0.30±0.12c -0.21±0.12c 0.22±0.05M⊙ 0.24±0.04R⊙ ∼120pc Kepler-42 3241±57Ka -0.48±0.12d -0.33±0.12d 0.15±0.03M⊙d 0.18±0.02R⊙d ∼40pcd Barnard’sStar 3238±11Ka -0.39±0.17c -0.27±0.12c 0.159±0.013M⊙a 0.1867±0.0012R⊙e 1.824±0.005pcf †† Values without a markare fromthis work, values with amarkare fromthe following: (a) Mannetal.(2013a), (b) Rojas-Ayalaetal. (2012), (c) Muirheadetal. (2014), (d) Muirheadetal. (2012), (e) Boyajianetal. (2012), (f) Hipparcos astrometric parallax from vanLeeuwen (2007). Whencombinedwitharchivalpropermotionmeasure- space motions to be 10 km s−1. ∼ ments and our distance estimates from the previous sec- tion, we can estimate the stars’ space motions. The 2.5. Kepler Photometry most recent proper motion measurements available for Kepler-445wasobservedbyKeplerinquarters6,8and Kepler-445 and Kepler-446 are from the PPMXL cata- 9 in long-cadence mode as part of guest observer pro- log (Roeser et al. 2010). They report a proper motion gram GO20031, a search for microlensing by observing ofµα=42.2µδ=132.7masyr−1 forKepler-445andµα=- high-propermotionstars (Di Stefano 2010). It was later 13.2µδ=-30.6masyr−1forKepler-446. Bothpropermo- observed in quarters 12, 13, 14 and 16 in long-cadence tionmeasurementsarerelativelylargeandareconsistent mode and in quarter 17 in short-cadence mode as an with M dwarf stars within 150 pc. exoplanet search target as part of the primary Kepler Combiningpropermotion,radialvelocityanddistance Mission. However, quarter 17 was cut short due to a estimates, we measure the galactic space velocity mo- malfunction in the spacecraft ending the primary mis- tions of Kepler-445 to be U = 59, V = -39, W = 9 km sion, so we did not include it in our analysis. s−1, and for Kepler-446 we measure U = 8, V = -98, Kepler-446 was observed by Kepler in quarter 7 in W = -31 km s−1. We corrected for the galactic solar long-cadence mode as part of guest observer program motionusingthe values ofCo¸skunogˇlu et al.(2011):U = GO20001,asearchforeclipsingbinarysystemsinasam- -8.5, V = 13.38,and W = 6.49 km/s. Figure 3 plots the ple of M dwarf stars (Harrison 2010). It was again ob- spacemotionsforKepler-445,Kepler-446,Kepler-42and served in quarters 12, 13, 14 15 and 16 in long-cadence Barnard’sStarwith nearbydwarfstarsinaToomredia- mode and in quarter 17 in short-cadence mode as an gramwiththindisk,thickdiskandhaloboundariesfrom exoplanet search target as part of the primary Kepler Fuhrmann(2004). Kepler-42andKepler-446arelocated Mission, though we do not include the quarter 17 data inthe thickdiskregime,consistentwiththeirlowmetal- for the reason stated above. licities, whereas Kepler-445 is located in the thin disk regime,consistentwithitshighmetallicity. Wenotethat 2.5.1. Known Transiting Planets the distances to Kepler-42, Kepler-445 and Kepler-446 Atthetimethismanuscriptwassubmitted,theNASA and their corresponding tangential motions are highly ExoplanetArchive (NEA, Akeson et al. 2013) listed two uncertain,asisthetruesolarmotionthroughthegalaxy. planetsorbitingKepler-445(KOI-2704),withorbitalpe- Therefore, we estimate the uncertainty in their galactic riods (P) of 4.871229 1.1e-05 and 2.984151 1.1e- ± ± 7 still significantly larger than the values we calculate in 200 Section 2.5.3. 2.5.2. Independent Planet Search The Kepler-445 and Kepler-446 transiting planet- 150 Barnard’s Star candidates found by the Kepler pipeline did not uti- -1m s] Halo lize all quarters of data available currently. Therefore, 21/2W) [k 100 Kepler-42 wpleanceotnsdounctethdeocuormopwlentes,eaarvcahilafobrleaKddeiptlieornaldatrtaansestitifnogr + Kepler-445, Kepler-446 and Kepler-42. We downloaded 2U Kepler-445 the Kepler light curves for Kepler-445 and Kepler-446 ( Thick Disk 50 from the NASA’s Mikulski Archive for Space Telescopes Kepler-446 (MAST). The light curve data files contain flux values measured using simple aperture photometry on the Ke- 0 Thin Disk pler pixels using pre-defined apertures (SAP FLUX), and -200 -100 0 100 flux values that have been detrended using custom tools V [km s-1] toremoveslowly-varyinginstrumentalfluctuationsinthe Fig.3.— Toomre Diagram of G K and M type stars with mea- Kepler photometric response as well as fluctuations due sured trigonometric parallaxes greater than 100 mas, the same to stellar rotation and intrinsic variability: the “pre- stars used in a similar figure in Muirheadetal. (2012, , Fig. 9). search data conditioning simple aperture photometry We include the thin disk, thick disk and halo boundaries from Fuhrmann(2004)forreference. Barnard’sStar,Kepler-42,Kepler- flux” (PDCSAP FLUX. Smith et al. 2012). We choose to 445 and Kepler-446 are all shown. Kepler-42 and Kepler-446 are use the PDCSAP FLUX for the independent planet search located in the thick disk regime, consistent with their low metal- and for fitting the transit events. licities,whereasKepler-445islocatedinthethindiskregime,con- For each star, we fitted the PDCSAP FLUX light curve sistentwithitshighmetallicity. Wecorrectedforthesolarmotion usingthe values of Co¸skunoˇglu etal.(2011):U =-8.5, V = 13.38, with a cubic basis spline (cubic B-spline) with break- and W = 6.49 km/s. We note that the distances to Kepler-42, pointslocated1.5daysapart,anddividedthelightcurve Kepler-445andKepler-446andtheircorrespondingtangentialmo- by the B-spline fit to remove stellar and instrumental tionsarehighlyuncertain,asisthetruesolarmotionthroughthe variability. We excluded outlier data points (both astro- galaxy. physical and otherwise) from the B-spline fit by itera- tively fitting the B-spline, locating points falling more 05 days, for Kepler-445c and Kepler-445b respectively than 3σ away from the fit, and re-calculating the B- (KOI-2704.01 and KOI-2704.02), with planetary radii spline while excluding the outliers. We repeated this (RP) of 2.9 and 1.96 R⊕, respectively. The NEA listed process until convergence, typically 5 iterations. We three planets orbiting Kepler-446 (KOI-2842) with or- then searched for transits by calculating a Box Least bitalperiodsof1.5654088 3.3e-06,5.148921 2.2e-05, Squaredperiodogram(BLS,Kov´acs et al.2002)foreach ± ± 3.03617925 5.49e-06daysforKepler-446b,Kepler-446d star. We evaluated the BLS periodogram over periods andKepler-±446crespectively(KOI-2842.01,KOI-2842.02 ranging from 0.15 days (or 3.6 hours) to the total du- and KOI-2842.03), with planetary radii (R ) of 25 ration of the Kepler observations. We evaluated the P 15, 26 15 and 2.393 0.582 R⊕. For Kepler-446, th±e BLS power spectrum at roughly 105 to 106 discrete pe- ± ± NEAlistednotablylargeimpactparameters(b)ofof1.17 riods, depending on the total time baseline of Kepler 0.92, 1.19 0.99 and 0.90 0.177, for Kepler-446b, observations, and we spaced the trial periods to ensure ± ± ± Kepler-446d and Kepler-446c respectively. that the BLS signal of a short duration transit around The planetary radii listed in the NEA as initially a mid M-dwarf would not be smeared out by coarse pe- downloaded were determined using either an MCMC riod spacing. After we calculated the BLS power spec- fitting routine, as in the case of Kepler-445c, Kepler- trum, we subtracted away a noise floor from the power 445b, Kepler-446b and Kepler-446d (Burke et al. 2014), spectrumandestimateditstypicalscatterbycalculating or by the Kepler pipeline when initially searching for the Median Absolute Deviation (MAD) and dividing by threshold-crossing events, as in the case of Kepler-446c 0.67 to convert to an equivalent standard deviation. We (Tenenbaum et al. 2014), with the stellar parameters considered any peak with a BLS signal-to-noise ratio of from Huber et al. (2014). For Kepler-446b and Kepler- greater than 9 to be significant. Upon detecting a sig- 446dWeattributethelargeradiianduncertaintiesinthe nificantsignal,wemaskedoutthe signalinquestionand NEA to correlations between the transit impact param- re-calculated the periodogram. eter and planet-to-star radius ratio. The parameters are In all three systems, we recovered the planets discov- typically not strongly correlated; however in the case of ered by the Kepler pipeline at high significance. For Kepler-446thetransitdurations(T)arerelativelyshort, Kepler-42 and Kepler-446, after removing the three sig- lasting only about an hour each, and the long-cadence nals detected by the Kepler pipeline, there remained no integrations times are 30 minutes. This results in the significantpeaksintheBLS,butforKepler-445,afterre- ∼ light-curve being significantly smoothed and appearing movingthetwoknownplanetcandidates,thereremained tobeV-shaped,whereatrulyflat-bottomed,low-impact a series of significant peaks spaced like harmonics of a parametertransitcurveis indistinguishable froma graz- transiting planet signal, shown in Figure 4. The highest ing eclipse. peak in the BLS spectrum indicated a candidate period We note that when this manuscript was accepted, the of 8.15275 days. Hereafter, we refer to this new planet parameters listed in the NEA had changed, listing more candidate as Kepler-445d, orbiting near a 5:3 resonance reasonablevaluesfortheplanetradiiforKepler-446,but withKepler-445c,andweconfirmalloftheplanetinSec- 8 KKOOII 22770044:: BBLLSS PPeerriiooddooggrraamm 1155 densityprior. WeassumedaGaussianpriorwithamean of 26.51 gm cm−3 and a standard deviation of 6.54 gm cm−3 for Kepler-445,and a mean of 22.73 gm cm−3 and 1100 a standard deviation of 6.06 gm cm−3 for Kepler-446. WealsoassumedthatalloftheplanetsorbitingKepler- NN S/S/ 445 and Kepler-446 have low eccentricity (e), and fix S S 55 the value to zero in our fit. Following Wu & Goldreich LL BB (2002,,Eq. 1),andassumingreasonableplanetdensities with tidal Q′ values of 100 to 10000, all of the planets 00 orbiting KepPler-445 and Kepler-446 have circularization timescalesoflessthan1Gyr. Giventhelackofquiescent Hα or u-band emission in either Kepler-445 or Kepler- --55 446,andKepler-446’shighgalacticspacemotion,weare 11 1100 110000 confident that the stars are older than 1 Gyr and likely PPeerriioodd [[ddaayyss]] older than 5 Gyr. We note, however, that planets can Fig. 4.— BLS periodogram of Kepler-445 with the two planets sustain eccentricities over long timescales via spin-orbit detected by the Kepler pipeline removed. There are a series of coupling, and that in multiple-planet systems non-zero peakswithpowergreaterthanourthreshold(horizontalblueline) eccentricitycanbesustainedviaorbitalresonances. The correspondingtothetrueperiod(denotedbytheverticalredhash mark)andharmonicsofthenewplanetKepler-445d. assumption of zero eccentricity also negates the impor- tance of the longitude of periastron parameter for the transit fit or for the imposed prior on stellar density. tion 3. We also detected no significant photocenter shift For limb-darkening, we fit a linear (u1) and quadratic in the centroid of the Kepler image of Kepler-445 dur- (u2)coefficient to the transits. For eachsystem, Kepler- ingtheKepler-445dtransitevents. Takingthedifference 445 and Kepler-446, we tied the limb-darkening param- between the centroid of the image in and out of transit, eters across each of the transiting planet fits. We used we calculate a photocenter shift of 0.00054 0.00033 Gaussianpriorsforthelimb-darkeningcoefficients,based ± arcseconds. on the expected coefficients from Claret & Bloemen (2011) using our measured stellar parameters and their 2.5.3. Transit Fits uncertainties. For Kepler-445 we used a Gaussian prior Given the large uncertainties on the physical radii of with a mean linear limb-darkening parameter of 0.50 theplanetsorbitingKepler-446,andthenewdetectionof with standard deviation of 0.17, and a quadratic limb- Kepler-445d, we chose to fit the the transit light curves darkening parameter of 0.35 with a standard deviation for Kepler-445 and Kepler-446 independently. We fitted of0.13. ForKepler-446,weusedaGaussianpriorwitha transit light curves to the data using a modified version meanlinearlimb-darkeningparameterof0.42withstan- of the Transit Analysis Package, or TAP, an IDL soft- dard deviation of 0.12, and a quadratic limb-darkening ware package developed by Gazak et al. (2012). TAP parameter of 0.35 with a standard deviation of 0.11. employs a Markov-Chain Monte Carlo algorithm within Finally, we chose to fix the orbital periods and transit a Bayesian framework for determining transit parame- epochs(t )oftheplanetstothevalueslistedintheNEA 0 ters. In order to reduce the degeneracy between impact for all but Kepler-445d, for which we fit a separate tran- parameter and planet-to-star radius ratio, we modified sit model to the Kepler light curve using a Levenberg- TAP to impose a strict prior on the stellar densities for Marquardt minimization routine. We used the best fit Kepler-445andKepler-446. AsSeager & Mall´en-Ornelas period and transit epoch for the TAP fit. Allowing the (2003) showed, ingress/egress duration and full transit periods of the planets to vary within TAP had no sig- duration can be combined in such a way so as to de- nificant effect on the resulting transit parameters. Our termine the density of the host star, assuming knowl- final transit parameters for the six planets are listed in edge of the planet’s orbital period, orbital eccentricity Tables 3 and 4, and we show the phase-folded Kepler and longitude of periastron. Likewise, knowledge of the light curves and fitted transit curves in Figure 5. We host star density, orbital eccentricity and longitude of combine the stellar parameters with the transit parame- periastron can be combined to constrain the relation- terstodeterminethephysicalparametersfortheplanets, ship between ingress/egress duration and transit dura- which are also listed in Table 3, and Figure 6 illustrates tion. In the case of the planets orbiting Kepler-445 and the planets with Kepler-42 and the Galilean moons of Kepler-446, ingress/egress duration is difficult to mea- Jupiter for comparison. We also calculate the incident sure due to the V-shaped nature of the light curves as flux on the planets as a fraction of the solar flux inci- discussed above, and imposing such a constraint is a dent on the Earth’s upper atmosphere (S = 1360 W 0 powerful way to fit accurate transit parameters. Indeed, m−2). The values indicate that all of the planets are Muirhead et al.(2012)usedthistechniquetofitthetran- likely too hot to be located within their host stars’ hab- sit light curves for the Kepler-42 system, although they itable zones, using habitable-zone limits calculated by fixed the stellar density rather than applying a prior. Kopparapu (2013). However, with an S/S of 2.24, one 0 We assumed a stellar density prior based on the mea- couldarguethat Kepler-445dis near the habitable zone. sured masses and radii for Kepler-445 and Kepler-446 We alsoinclude coarseestimates for the planetmasses fromspectroscopydescribedintheprevioussection. Due and expected semi-amplitude radial velocity signatures to the use of evolutionary models, the mass and radius in Table 3, using the recentempirically-measuredplanet uncertainties are nearly 100% covariant for the stars, so mass-radius relations of Marcy et al. (2014). All of the weonlyusetheuncertaintyinmasswhencalculatingthe 9 TABLE 3 Transit ParametersforKepler-445 Parameter Kepler-445b Kepler-445c Kepler-445d P (days)a 2.984151±0.000011 4.871229±0.000011 8.15275±0.00040 t0 -2454833 (BJD)a 133.1194±0.0033 133.6408 ±0.0019 3.7512226±0.05 RP/R⋆ 0.0676±0.0018 0.1075±0.0014 0.0533±0.0029 b 0.001+−00..200031 0.000+−00..100010 0.011+−00..407100 T (hours) 1.0304±0.0180 1.2287±0.0154 1.3860±0.0888 µ1 b 0.141±0.080 0.141±0.080 0.141±0.080 µ2 b 0.263±0.071 0.263±0.071 0.263±0.071 ea 0 0 0 Inc(degrees)c 89.74+−00..1288 89.91+−00..0170 89.61+−00..2275 a/R⋆c 21.94±0.30 30.21±0.38 42.95±0.58 RP (R⊕)c 1.58±0.23 2.51±0.36 1.25±0.19 S/S0d 8.57±0.60 4.52±0.31 2.24±0.17 MP (M⊕)e 4to6 8to9 3to4 K (ms−1)e 6to8 9to10 2to4 aHeldfixedinfittingprocedure. PeriodsandephemeridesforKepler-445candKepler-445b arefromtheNASAExoplanet Archive(Akesonetal.2013). b Limb-darkening coefficients were tied between planets, and subject a prior based on Claret&Bloemen(2011). c Calculatedfromparametrization. d S0 =1360Wm−2,thesolarfluxincidentonEarth’supperatmosphere. e Coarsely estimated using the empirically-measured planet mass-radius relationships of Marcyetal.(2014). TABLE 4 Transit ParametersforKepler-446 Parameter Kepler-446b Kepler-446c Kepler-446d P (days)a 1.565409±0.0000033 3.036179±0.0000055 5.148921±0.000022 t0 -2454833 (BJD)a 132.9135±0.0019 134.069573 ±0.000945 133.3196±0.0042 RP/R⋆ 0.0574±0.0026 0.0424±0.0018 0.0519±0.0022 b 0.601+−00..009868 0.025+−00..502295 0.705+−00..005676 T (hours) 0.6456±0.0456 0.9432±0.0504 0.8832±0.0480 µ1 b 0.447±0.059 0.446±0.059 0.446±0.059 µ2 b 0.353±0.065 0.353±0.065 0.353±0.065 ea 0 0 0 Inc(degrees)c 87.42+−00..6327 88.97+−00..5476 88.72+−00..1179 a/R⋆c 14.20±0.94 22.40±1.36 31.60±2.08 RP (R⊕)c 1.50±0.25 1.11±0.18 1.35±0.22 S/S0d 26.22±4.70 10.54±2.03 5.30±0.83 MP (M⊕)e 4to5 2to4 3to5 K (ms−1)e 6to8 2to5 3to5 aHeldfixedinfittingprocedure. PeriodsandephemeridesarefromtheNASAExoplanetArchive (Akesonetal.2013). b Limb-darkening coefficients were tied between planets, and subject a prior based on Claret&Bloemen(2011). c Calculatedfromparametrization. d S0 =1360Wm−2,thesolarfluxincidentonEarth’supperatmosphere. e Coarsely estimated using the empirically-measured planet mass-radius relationships of Marcyetal.(2014). 10 planets have anticipated radial velocity semi-amplitudes of over 1 m s−1. However, being mid-M dwarf stars, Kepler −445b 1.01 the stars are relatively faint for current-generation ux vBiositbtolem-ligethtalp.re2c0i1si3o)n.-radInial-tvheelocfuittyursep,ectthroemsettaerrss (me.agy. ative Fl1.00 el be compelling targets for next-generation, infrared R0.99 precision-radial-velocity instruments (Mahadevan et al. 2012; Halversonet al. 2014; Quirrenbach et al. 2012; −3 −2 −1 0 1 2 3 Barrick et al. 2012; Artigau et al. 2012; Thibault et al. Time from mid−transit (hours) 2012;Micheau et al.2012;Par`eset al.2012;Crepp et al. 2014; Ge et al. 2014). Such measurements would 1.02 Kepler −445c prove useful for precisely measuring the planet masses ux1.01 aMnidllefro-rRipclcaicKinegmcpotnosntreatinatl.s o2n01t2h)eiarnadtminotseprhioerresst(reu.gc-. ative Fl1.00 tures (e.g. Rogers & Seager 2010; Valencia et al. 2013), Rel0.99 as well as measuring any non-zero eccentricity (e.g. 0.98 Anglada-Escud´e et al. 2013). −3 −2 −1 0 1 2 3 Time from mid−transit (hours) 3. FALSEPOSITIVE ANALYSIS AswiththevastmajorityofKepler planetcandidates, Kepler −445d the transitsignalsdetected inthe lightcurvesof Kepler- 1.01 445 and Kepler-446 are not amenable to dynamical con- Flux firmationasbonafide planets,eitherbyradialvelocityor ative 1.00 transittimingvariationmeasurements. Confirmingtheir Rel 0.99 planetary nature thus requires probabilistic validation; that is, demonstrating that the probability for them to be caused by a blended stellar eclipsing binary, or any −3 −2 −1 0 1 2 3 Time from mid−transit (hours) other astrophysicalfalse positive scenario, is very low. 1.006 While broad arguments have demonstrated that only 1.004 Kepler −446b a small number of Kepler planet candidates are ex- pected to turn out to be astrophysical false positives Flux1.002 (Morton & Johnson 2011; Fressin et al. 2013), any spe- ative 1.000 cificplanetcandidatesofparticularinterestshouldbein- Rel0.998 dividually investigated more thoroughly to ensure their 0.996 planetary nature. To this end, we have employed the 0.994 methoddescribedindetailbyMorton(2012)tocalculate −3 −2 −1 0 1 2 3 Time from mid−transit (hours) false positive probabilities (FPPs) for all six of the can- 1.006 didates discussed in this paper. This method compares the shapes of the observed light curves to the shapes of 1.004 Kepler −446c simulated planet and astrophysicalfalse positive scenar- ux1.002 Fl isoigsnianlsotrodebretcoaduesetedrmbyintehethdeiffreerleantitvescleinkaelriihoos.ods of the Relative 01..909080 The basic assumption of this analysis is that the ob- 0.996 served transit signal is roughly spatially coincident with 0.994 the target star—that is, that the flux decrement in the −3 −2 −1 0 1 2 3 aperture of the target star is not due, for example, to Time from mid−transit (hours) a different star several arcseconds separated from the 1.006 target star. An important part of the Kepler vetting 1.004 Kepler −446d pipeline islookingforsuchoffsets(Bryson et al.2013)— ux1.002 Fl opnrolymcoatenddidtoate“sptlahnaettdcoannodtidsahtoew” ssitgantuifisc.antTohffesertessugletts Relative 01..909080 of these tests are summarized in the NASA Exoplanet 0.996 Archivetablesinthecolumntitled“PRF∆θ ”andas- MQ sociateduncertainty,whichindicatesthedifferenceinpo- −3 −2 −1 0 1 2 3 sitionbetweentheKepler pixelresponsefunction(PRF) Time from mid−transit (hours) fitted to the in- and out-of-transit data. For Kepler- Fig. 5.—Phase-foldedlightcurvesfortheKepler-445andKepler- 446b, c and d and Kepler-445b and d, all these offsets 446 transiting planets with our best fit transit light curves. Raw are significantly smaller than 1 arcsecond. For Kepler- data are shown as grey dots, binned data as blue circles, and the 445d, which is not in the Kepler catalogs, we perform model as red lines. Note the V-shaped transits for Kepler-446, which is due to the ∼30 minute integration times of the Kepler our own in- and out-of-transit centroid analysis, finding data. Wespeculate that thiscontributed totheerroneous planet- no noticeable shift. While we note that this analysis is to-star radius ratios returned by the Kepler pipeline. Also note notasdetailedastheBryson et al.(2013)PRFanalysis, thatthescaleofthey-axischangesfortheKepler-445andKepler- it certainly indicates that there is no large offset of the 446plots. candidate signal.