Kepler-445, Kepler-446 and the Occurrence of Compact Multiples Orbiting Mid-M Dwarf Stars

2.5 MB·English

by  Philip S. Muirhead

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.