Assessing the Effect of Stellar Companions from High-Resolution Imaging of Kepler Objects of Interest

1.9 MB·

by  Lea A. Hirsch

Accepted to Astronomical Journal, January 13, 2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
ASSESSING THE EFFECT OF STELLAR COMPANIONS FROM HIGH-RESOLUTION IMAGING OF Kepler
OBJECTS OF INTEREST
Lea A. Hirsch1,(cid:63), David R. Ciardi2, Andrew W. Howard3, Mark E. Everett4, Elise Furlan5, Mindy Saylors2,9,
Elliott P. Horch6, Steve B. Howell7, Johanna Teske8, Geoffrey W. Marcy1
1UniversityofCalifornia,Berkeley,510CampbellHall,AstronomyDepartment,Berkeley,CA94720
2NASAExoplanetScienceInstituteCaltech-IPAC,Pasadena,CA91125
3CaliforniaInstituteofTechnology,DepartmentofAstronomy;MC249-17,Caltech,Pasadena,California91125,USA
4NationalOpticalAstronomyObservatory,950N.CherryAve,Tucson,AZ85719
5Caltech-IPAC,MailCode100-22,Caltech,1200E.CaliforniaBlvd.,Pasadena,CA91125
6SouthernConnecticutStateUniversity,DeptofPhysics,501CrescentSt.,NewHaven,CT06515
7 7NASAAmesResearchCenter,MoffettField,CA94035
1 8CarnegieDTM,5241BroadBranchRoad,NW,Washington,DC20015and
9CollegeoftheCanyons,26455RockwellCanyonRd,SantaClarita,CA91355
0
Accepted to Astronomical Journal, January 13, 2017
2

n ABSTRACT
a We report on 176 close (<2”) stellar companions detected with high-resolution imaging near 170 hosts of
J
Kepler ObjectsofInterest. TheseKepler targetswereprioritizedforimagingfollow-upbasedonthepresence

3 ofsmallplanets,somostoftheKOIsinthesesystems(176outof204)havenominalradii<6R . EachKOI
⊕
2 inoursamplewasobservedinatleast2filterswithadaptiveoptics,speckleimaging,luckyimaging,orHST.
Multi-filter photometry provides color information on the companions, allowing us to constrain their stellar

] properties and assess the probability that the companions are physically bound. We find that 60 – 80% of
P companions within 1” are bound, and the bound fraction is > 90% for companions within 0.5”; the bound
E fractiondecreaseswithincreasingangularseparation. Thispictureisconsistentwithsimulationsofthebinary
. and background stellar populations in the Kepler field. We also reassess the planet radii in these systems,
h converting the observed differential magnitudes to a contamination in the Kepler bandpass and calculating
p theplanetradiuscorrectionfactor,X =R (true)/R (single). Undertheassumptionthatplanetsinbound
R p p
- binariesareequallylikelytoorbittheprimaryorsecondary,wefindameanradiuscorrectionfactorforplanets
o
instellarmultiplesofX =1.65. IfstellarmultiplicityintheKepler fieldissimilartothesolarneighborhood,
r R
t thennearlyhalfofallKepler planetsmayhaveradiiunderestimatedbyanaverageof65%,unlessvettedusing
s high resolution imaging or spectroscopy.
a
Subject headings: planetary systems: detection — planetary systems: fundamental parameters —
[
stars: binaries — techniques: photometric — techniques: high angular resolution

1
v
7 1. INTRODUCTION Inthesolarneighborhood,atleast46%ofsunlikestars
7 have bound stellar companions (Raghavan et al. 2010),
During the 4-year tenure of the Kepler Mission, over
5 with the orbital separation distribution peaking at 50
4000planetcandidateswereidentifiedandtheirradiies-
6 AU. Assuming the Kepler field has similar multiplicity
timated. The size of the Kepler sample allows for de-
0 statistics, nearly half of the Kepler target stars could
tailed population statistics to determine the occurrence
. have bound stellar companions falling within the same
1 rates of planets of various sizes and orbital distances.
0 Of primary interest is a determination of the occurrence Kepler pixel.
7 rate of small planets, especially those with radii smaller Unknownclosestellarcompanionswillcauseplanetary
1 than 1.6 R , which could potentially be rocky (Rogers radii to be underestimated, depending on the relative
v: 2015; Marc⊕y et al. 2014; Lopez & Fortney 2014). The brightness of the binary components, and which star the
planet is orbiting. For faint companions to planet hosts,
i transition from “non-rocky” to “rocky” planets appears
X to be extremely sharp, making the detection of accu- the contamination from the secondary component may
be limited to only a few percent; however, if the planet
r rateplanetradiicriticalforoccurrencerateanalyses(e.g.
a Rogers 2015; Ciardi et al. 2015) isdeterminedtobeorbitingthefaintersecondarycompo-
nent, the planet radius estimate could be off by an order
Planet radius estimates from Kepler light curves rely
of magnitude (Ciardi et al. 2015). Unfortunately, deter-
ontheinferredpropertiesoftheplanethoststar. Dueto
mining which star in a binary pair hosts the observed
the fairly low resolution and large pixel scale of the Ke-
transiting planet is not straightforward, and requires ex-
pler detector, stellar companions are difficult to detect
tensive individualized statistical modeling (e.g. Barclay
without ground-based follow-up observations. Higher-
et al. 2015).
resolutionimagingprovidesthemostefficientmethodfor
Neglecting to account for stellar multiplicity can have
detecting line-of-sight and bound companions within 1”.
ramifications for the accuracy of occurrence studies of
Thesecompanions,ifpresent,candilutetheKepler light
small planets. Since unknown stellar companions can
curves, preventing accurate assessment of the planet ra-
cause larger planets to masquerade as “small” plan-
dius.
ets, stellar companions can artificially boost estimates
of small planet occurrence by as much as 15 – 20 %
(cid:63)Towhomcorrespondenceshouldbeaddressed. E-mail: (Ciardi et al. 2015). High resolution imaging follow-up
[email protected] is therefore extremely important for obtaining accurate
2
measurements of planet radii. hereafter F17).
Binary companions may also affect the formation and We choose targets for this study by requiring that at
evolutionofplanetsinastellarsystem,andplanetsinbi- least one companion was detected within 2”, and that
nary systems are therefore an interesting sub-sample of the companion was detected in two or more filters, pro-
the wider Kepler sample. The full implications of stellar viding color information. We choose the 2” separation
multiplicity on planet formation and evolution are still limit to include all companions falling on the same Ke-
beingexplored. Previousstudies(e.g.Wangetal.2014b; pler pixel as the primary KOI host star. For a complete
Kraus et al. 2016) indicate that stellar multiplicity may list of detected companions, see F17. Because imaging
be suppressed in planet-hosting Kepler systems, com- campaigns typically targeted the hosts of small planets,
paredtofieldstarsinthesolarneighborhood(Raghavan oursamplecontainsahighfractionofsmallplanethosts.
et al. 2010). This may indicate that planet formation Figure 1 is a histogram of the apparent Kepler magni-
is more rare in close binary systems than in single star tudesofoursampleKOIhostsincomparisonwiththefull
systems. If this is the case, the problem of transit dilu- ensemble of KOI stars followed up with high-resolution
tionfromunknownstellarcompanionsmayimpactfewer imaging, described in F17. Although some efforts were
systems than expected based on field star multiplicity madetoimageveryfaintKepler targets,noneofoursam-
statistics. ple stars have Kepler magnitudes fainter than 16. The
On the other hand, stellar multiple systems contain majority of small Kepler planets orbit faint host stars;
morethanonestartohostpotentiallydiscoverableplan- however, this difficulty is currently remedied by the K2
ets,sotheirnumbermaybeenhancedintheKOIsample. and upcoming TESS missions.
Additionally,theaugmentedbrightnessofunresolvedbi- Foreachstellarprimary,theparametersT ,logg,and
eff
naries relative to single stars of the same spectral type [Fe/H] are taken from Huber et al. (2014). For many
allows the flux-limited Kepler survey to include stellar of the stars in our sample (71), these parameters come
multiples at larger distances than corresponding single from spectroscopic or asteroseismic analysis performed
star systems. This might also augment the expected by Huber et al. (2014); Chaplin et al. (2014); Huber
number of Kepler systems in which flux dilution plays et al. (2013); Ballard et al. (2013); Mann et al. (2013);
a role. The combined result of these various effects is Batalha et al. (2013); Buchhave et al. (2012); Muirhead
complex, and more detailed statistical work on Kepler et al. (2012). The spectroscopic and asteroseismic anal-
binary statistics is still needed. yses provide stellar parameters largely unaffected by in-
TRILEGAL galactic models with assumed multiplic- terstellarextinctiontowardtheKepler field. Thesetech-
ity statistics were applied to the Kepler field in order niques are also largely unaffected by undetected close
to determine the likelihood of chance alignments with stellarcompanions,unlessthecompanions’spectrallines
background stars. These models indicate that compan- contaminatetheprimarystellarspectrumtoasignificant
ions observed within 1” of a Kepler Object of Interest degree.
(KOI) are highly likely to be bound companions, and The remaining sample stars have stellar parameters
therefore potentially play a dynamical role in the for- calculated from photometry, reported in Huber et al.
mation and evolution of the stellar system (Horch et al. (2014). Of these, all but 13 have properties revised by
2014). More specifically, companions within 0.4” have Pinsonneault et al. (2012), Gaidos (2013), or Dressing &
a less than 10% likelihood of being chance background Charbonneau (2013), using new models and data to im-
alignments, and companions within 0.2” have a nearly proveontheoriginalKIC-derivedstellarparameters. For
zero percent chance, based on the TRILEGAL galaxy the purposes of our study, we do not re-analyze the stel-
models. larpropertiesofanystarsinoursample. Rather,wetake
We study KOI host stars with detected close (< 2”) theprimarystellarpropertiesfromHuberetal.(2014)as
companionsonacase-by-casebasis,incomparisontothe given, and assess the characteristics of the companions
statisticalstudyperformedbyHorchetal.(2014). In§2, detected around these stars.
wediscussthestellarsampleofKOIhostschosenforthis For the 13 stars with KIC stellar parameters, the stel-
study. In§3,wedescribetheDartmouthisochronemod- lar parameters are expected to be more uncertain than
els used to determine whether a companion is physically for stars with parameters derived from seismology, spec-
associated based on color information, and the TRILE- troscopy or improved photometric relationships. Addi-
GALmodelsusedtoassessthebackgroundstellarpopu- tionally, in the case of systems with nearby companions,
lation. In § 4, we isolate a population of KOI hosts with the photometry might be contaminated by the blended
bound companions and compare the bound fraction as a companion. The photometrically-derived stellar prop-
function of separation to the simulation results of Horch erties may therefore be biased. While we recognize this
et al. (2014). Finally, in § 5, we calculate radius correc- possibleeffect,itisbeyondthescopeofthispapertofully
tionfactorsforalloftheplanetcandidatesinoursample re-derivethestellarparametersfortheprimarystars,es-
for use in future occurrence studies. pecially in light of the fact that many of the stars have
parametersderivedfromspectroscopicandseismological
observations.
2. SAMPLE
Figure2showsthedistributionofstellarT ,logg,and
2.1. KOI Host Stars eff
[Fe/H] of our sample stars. The stars in this work are
Our sample consists of 170 stellar hosts of KOIs ob- primarily G and K dwarfs, but the sample also includes
served with various high-resolution imaging campaigns. 13 stars with T < 4000 K, and 6 hot stars with T
eff eff
This sample was drawn from the overall sample of KOI >8000K.Wealsoinclude4evolvedstarswithlogg<3.5
stars observed with high-resolution imaging, described (see Figure 3).
in the imaging compilation paper by (Furlan et al. 2017, Our sample contains 110 confirmed planets in 72 sys-
3
tems. Of these, 15 planets are confirmed including anal-
ysisofhighresolutionimagingobservations,allowingthe
authors to correct for the multiplicity of the host stars. 1000
These, we continue to treat as confirmed, and we do not
reanalyze the planetary parameters. However, the re-
maining 57 systems were confirmed without the input of
observationssensitivetostellarcompanions,sowedoin-
cludethesesystemsinourplanetradiusreanalysis. Eight
ofthesesystemswereconfirmedbynatureofmultiplicity 100
by Rowe et al. (2014), since transiting multi-planet sys-
tems have very low statistical probability of displaying
false positive signals in addition to true planets. Mor- N
ton et al. (2016) confirms 45 systems using statistical
argumentswherethepossibilityoftheplanetsorbitinga
secondarystarwithinastellarbinarysystemwasexplic-
10
itlyneglected. Finally, 2systemswereconfirmedbyVan
Eylen & Albrecht (2015) and 3 were confirmed by Xie
(2013) and Xie (2014) using TTV analysis to confirm
multi-planet systems. For these 57 systems, the high-
resolution imaging follow-up data available to the public
ontheExoFOP2wasnotemployedpriortoconfirmation,
1
or the possibility of planets orbiting a stellar companion
6 8 10 12 14 16 18 20
was not addressed. We therefore include these systems
Kepler magnitude
in our radius update analysis, while excluding confirmed
systems with extensive analysis of high-resolution imag-
Figure 1. Distribution of Kepler magnitudes for stars in this
ing data carried out by other groups.
study is plotted in purple. This is shown in comparison with the
Ofthetargetsystems,76haveoneormoreplanetcan- populationofKOIhostswithanyhigh-resolutionfollow-up(gray),
didate (PC), including many of the systems which also includingapparentlysinglestarsaswellasstarswithcompanions
detectedatseparations>2”orinonlyasinglefilter.
hostconfirmedplanets. Thereareatotalof94PCsinthe
sample. There are also 36 systems which host 38 false up observations, in order to be included in our sam-
positive (FP) signals, including a few which also have ple. These filters include J-band, H-band, and K-band
planet candidates or confirmed planets. These systems from adaptive optics imaging from the Keck/NIRC2,
were followed up with high-resolution imaging prior to Palomar/PHARO, Lick/IRCAL, and MMT/Aries in-
receiving a false positive disposition. We assess whether struments; 562 nm, 692 nm and 880 nm filters from
the stellar companions of these systems are bound, but theDifferentialSpeckleSurveyInstrument(DSSI)atthe
we do not include these transits in our analysis of planet GeminiNorthandWIYNtelescopes; iandz bandsfrom
radius updates in § 5. 39 KOI stars in our sample host the AstraLux lucky imaging campaign at the Calar Alto
multi-planet systems, with 105 total planets or planet 2.2m telescope (Lillo-Box et al. 2014); and LP600 and
candidates among these systems. i bands from Palomar/RoboAO (Law et al. 2014). We
It is important to note that the official Kepler project alsoincludeseeing-limitedobservationsintheU, B, and
used none of the ExoFOP1 data (e.g., images) to assess V bands from the UBV survey (Everett et al. 2012) and
candidatesorFPsinthepublishedplanetcandidatecat- “secure” detections (noise probability < 10%) in the J-
alogues(e.g.Batalhaetal.2013;Burkeetal.2014;Rowe band from the UKIRT Kepler field survey.
et al. 2015; Mullally et al. 2015). In several of our higher-order multiple systems, only
one component has detections in multiple filters, often
2.2. Stellar Companions
duetofield-of-viewcutoffsornon-detectionsofveryfaint
Table 1 documents the observations of companions to companions. Wedescribetheseadditionalcompanionsin
our KOI host star sample, compiled from the imaging thenotessectionofAppendixA,andincludetheminthe
compilation paper of F17. Columns (1) and (2) pro- planet radius correction, but cannot include them in our
vide the KOI number and component of the companion. physical association analysis.
Columns (3) and (4) describe the companion’s position Figure 4 displays the separation versus ∆m measured
relative to the KOI primary star, and column (5) de- foreachcompaniondetectedwithin2”ofoursampleKOI
scribes the differential magnitude between the primary stars in DSSI, Astralux, RoboAO, UBV, and AO filters
star and companion in the Kepler bandpass, ∆Kp, all (see F17).
taken from F17. Columns (6), (7), and (8) provide data It is important to note that the term “companion” is
leading to a determination of bound, uncertain, or un- usedheretodescribeanystardetectedangularlynearby
boundforeachcompanion(9), whichisexplainedin§3. a KOI host star. It is not used to imply physical asso-
F17 details the observations and measured differen- ciation. Instead, we will refer to physical binary or mul-
tial magnitudes (∆m= m − m ) for stars with high- tiple systems as “bound” companions, and unphysical,
2 1
resolution imaging, including our target systems. Each line-of-sight alignments as “unbound” or “background”
companion within 2” must have at least two measured companions.
∆m values from the full set of filters used for follow-
3. DETERMININGPHYSICALASSOCIATIONOFTHE
2 https://exofop.ipac.caltech.edu/cfop.php COMPANIONSTARS
4
45 45 45
40 40 40
35 35 35
30 30 30
25 25 25
N
20 20 20
15 15 15
10 10 10
5 5 5
0 0 0
2000300040005000600070008000900010000 2.0 2.5 3.0 l3o.5g(4g.0) 4.5 5.0 5.5 -1.5 -1.0 -[0.F5e/H0.]0 0.5 1.0
T
eff
Figure 2. HistogramsofstellarparametersT ,logg,and[Fe/H]fromHuberetal.(2014)forstarsinoursample. Themajorityofour
eff
sample stars have T < 7000 K and logg > 4.0. We include 5 stars that may be subgiants based on their reported logg values (logg
eff
<3.5),aswellas5hotterstars(T >8000K).
eff
1.5
10 U, B, V J-band (AO)
2.0 562, 692, 880 nm H-band (AO)
i, z, LP600 K-band (AO)
2.5
8
3.0
e
) d
g3.5 u 6
( t
g ni
o4.0 g
l a
m
4.5 4
5.0
2
5.5
6.0
00 00 00 00 00 00 00 00 00 0
0 0 0 0 0 0 0 0 0
0 9 8 7 6 5 4 3 2
1
0.0 0.5 1.0 1.5 2.0
T Separation (")
eff
Figure 3. HRDiagramoftargetKOIprimarystarsbasedontheir Figure 4. Separationvs. ∆mforeachcompaniondetectedwithin
stellarpropertiesfromHuberetal.(2014). Dartmouthisochrones 2”ofoursampleKOIstars. Colordenotesfilterinwhichobserva-
aredisplayedforcontext,spanningrangesinmetallicityfrom-2.4 tionsweremade: U, B, andV observationsderivefromtheUBV
to+0.5(instepsof0.1dex)andagefrom1.0to15.0Gyr(insteps seeing-limited survey. 562, 692, and 880 nm observations derive
of1Gyr). from the DSSI instrument. i, z, and LP600 observations derive
fromRoboAOandAstraLuxluckyimaging. J-band,H-band,and
Detection of a stellar companion near a KOI host star K-band measurements come from adaptive optics imaging. Note
that each companion has at least 2 measured ∆m values, so each
does not necessarily imply that the system is a phys-
companionhas2ormorepointsonthisplot,atthesameangular
ical binary. An assessment of the companion’s stellar separation.
properties must be made to determine if the detected
companion is physically bound, or simply a line-of-sight primary star, by comparing the measured color to the
alignmentofabackgroundorforegroundstar. Ifthesys- colorpredictedforamodelboundcompanion. Thistech-
tem is found to be a bound binary, then the companion nique has been employed in previous works by Everett
may have played a dynamical role in the evolution of et al. (2015), Teske et al. (2015), and Wittrock et al.
the planetary system; additionally, the planets may or- (2016). We provide sample figures to elucidate this pro-
bit either of the two stars in the system. If an unbound cess in Figures 5 and 6, choosing one unambiguously
companion, only the flux dilution from the background bound companion (KOI 1 B), and one unambiguously
source can be taken into account. unbound companion (KOI 3444 F) to make the tech-
WeusetheDartmouthStellarEvolutionmodels(Dot- nique clear. Note that KOI 3444 F, at a separation of
ter et al. 2008) to assess whether each detected com- 3.5”,isnotincludedinour2”sample,andwaspredicted
panion is consistent with the isochrone of its respective to be unbound prior to analysis due to its larger angular
5
separation from its primary KOI star. Not all compan- average companion model (which takes into ac-
ions have data available in as many colors as these two count each measured ∆m) to predict the model
stars;manyhaveonlyasingleplotpanel(onefilterpair). colors for every possible color pairing. We calcu-
A description of our technique and cutoffs follows: late the offset between model and observed color
for each color pair, in units of the uncertainties in
1. We use the Dartmouth models to produce a set the measurements and models.
of isochrones spanning ranges in metallicity from
For a set of observations for a given star, the mea-
-2.5 to +0.5 (in steps of 0.02 dex) and age from
suredcolorsarenotnecessarilyindependentofeach
1 to 15 Gyr (in steps of 0.5 Gyr). We further in-
other(e.g.,J−K =(J−H)+(H−K)). However,
terpolate these isochrones to achieve sampling in
tohelpmitigatetheeffectsofusinganyonespecific
stellar mass between 0.1 and 4 M , with intervals
(cid:12) filterovertheothers,wehavegeneratedallpossible
no larger than 0.02 M . We also incorporate filter
(cid:12) colors for the filters available to assess the agree-
transmission curves for the DSSI filters, allowing
ment between the observed and isochrone-model
absolute magnitudes to be predicted in these fil-
colors for each companion.
ters from the isochrone models.
6. Wetaketheaveragecoloroffsetbetweenthemodels
2. We use the primary stellar parameters T , logg,
eff andobservedcolors,weightingbythemeasurement
and [Fe/H] from Huber et al. (2014) to place the
andmodeluncertaintyinthetworelevantfiltersfor
primaryKOIhoststarontheisochronesandcalcu-
eachcolor. Thisaveragecoloroffset(aswellasthe
late a probability distribution for the primary star
weighted standard deviation of color offset) is pro-
absolute magnitude in each of the filters in which
videdincolumn(5)ofTable1. Iftheaveragecolor
that star was observed. Note that these distribu-
offset is less than 3σ, we designate the companion
tionsaresubjecttoinaccuracyforthe13starswith
asbound. Iftheaveragecoloroffsetisgreaterthan
original KIC photometrically-derived stellar prop-
3σ, we designate the companion as unbound.
erties,whichifbright,arelikelytobemoreevolved
than predicted by the original KIC.
7. We isolate and reclassify systems where the des-
ignation is uncertain. First, we look for compan-
3. To compute the observed colors of the detected
ions whose bound/unbound designation is reliant
companions, we add the measured ∆m values to
on a single very significant ∆m measurement. We
the modeled absolute magnitudes of the primary
re-calculate the average color offset, removing the
stars, and subtract in pairs. This is particularly
most significant observed color. If this procedure
importantforthestarsdetectedwithspeckleimag-
changes the conclusion, we reclassify the system as
ing,sincetheDSSIfiltersarenon-standard,andare
uncertain. Additional refinement of the ∆m mea-
notcalibratedagainstmorecommonly-usedfilters.
surementsisneededtodeterminewhetherthecom-
We therefore have no measured apparent magni-
panion is bound or not.
tudes for the primary stars in these filters, from
whichwecoulddeblendthecomponentstars. Thus
8. Next, we look for systems with large color offset
we use the isochrone magnitude of the primary to
standard deviations, indicating that the conclu-
derive a magnitude of the companion from the ob-
sions from each color pair are mutually inconsis-
served ∆m, then derive colors from the pairs of
tent for a single companion. If the conclusion can
filters. Foruniformity,weusethistechniqueforall
be changed by more than 0.5σ by adding or sub-
colors, even those including standard filters only
tracting the standard deviation from the average
(e.g. J−K), whereobservedapparentmagnitudes
color offset (i.e. a seemingly unbound companion
could be used.
with (cid:104)offset(cid:105)−σ <2.5σ or a seemingly bound
offset
4. We compute isochrone models for a bound stellar companionwith(cid:104)offset(cid:105)+σoffset >3.5σ),wereclas-
companion using each measured ∆m. We prop- sify the system as uncertain.
agate the primary star’s probability distribution
down the set of applicable isochrones by the mea- In Figures 5 and 6, we plot a representative set of
sured ∆m value. This provides an estimate of the isochrones,with[Fe/H]within±1σ oftheprimarystar’s
stellar parameters of a bound stellar companion input metallicity. In black, we plot the probability dis-
with the measured ∆m. Each companion has n tribution of the primary star in color-magnitude space,
“isochrone-shifted” models, where n is the num- based on the isochrone models for the primary star. Er-
ber of filters in which it is detected (at least 2 for ror bars indicate the ±1σ uncertainty contours.
each companion). We average these n models to The n “isochrone-shifted” companion probability dis-
obtain a weighted-average companion probability tributions are plotted in light blue, with the weighted
distribution. average companion model in dark blue. Finally, we plot
themeasuredcompanioncolorinred. Thehorizontaler-
5. For each pair of applicable filters, we calculate the rorbarsontheobservedcolorrepresentthemeasurement
probablecolorofahypotheticalboundcompanion. uncertaintyinthe∆mvaluesusedtocalculatethesecol-
We then compare this model color with the ob- ors. For n filters, we have n(n−1) panels in our plot,
servedcolorofthecompaniontoassesswhetherthe representing the number of colo2r combinations possible
companion is consistent with being bound. For a with the set of filters available. Our analysis determines
companion with ∆m measurements in n filters, we that KOI 1 B is consistent with being a bound compan-
can calculate n(n−1) colors. We use the weighted ion, while KOI 3444 F is clearly unbound.
2
6
KOI 1
4 4
4
5 5
6 5
Mi M8806 MJ
7 6
7
8
8 7
9
0.0 0.2 0.4 0.6 0.8 -0.20.0 0.2 0.4 0.6 0.8 1.0 1.2 1.0 1.5 2.0 2.5
692 i 692 880 692 J
3.0 3.0 4
3.5 3.5
5
4.0 4.0
MH45..50 MK45..50 M8806
7
5.5 5.5
6.0 6.0 8
6.5 6.5
1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 2.0 2.5 3.0 3.5 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
692 H 692 K i 880
3.0 3.0
4 3.5 3.5
4.0 4.0
5
4.5 4.5
MJ MH MK
5.0 5.0
6
5.5 5.5
7 6.0 6.0
6.5 6.5
1.0 1.5 2.0 1.0 1.5 2.0 2.5 3.0 1.0 1.5 2.0 2.5 3.0 3.5
i J i H i K
3.0 3.0
4 3.5 3.5
4.0 4.0
5
4.5 4.5
MJ MH MK
5.0 5.0
6
5.5 5.5
7 6.0 6.0
6.5 6.5
0.8 1.0 1.2 1.4 1.6 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
880 J 880 H 880 K
3.0 3.0 3.0
3.5 3.5 3.5
4.0 4.0 4.0
4.5 4.5 4.5
H K K
M M M
5.0 5.0 5.0
5.5 5.5 5.5
6.0 6.0 6.0
6.5 6.5 6.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -0.050.000.050.100.150.200.250.30
J H J K H K
Figure 5. Thisfiguredetailstheprocessweusetodeterminewhetheracompanion(inthiscase,KOI1B)isbound. Theisochronemodel
companioncolor(bluecircle)iscomparedwiththeobservedcompanioncolor(redsquare)todeterminethelikelihoodthatthecompanion
is bound. Light blue points show the positions of each “isochrone-shifted” model estimate of the companion’s position on the isochrone.
The dark blue point is the weighted average model position, and is compared with the red observed color point. We plot an extinction
vectorcorrespondingto1magnitudeofextinctioninV-band,asadarkgrayarrowintheupperrightcornerofeachpanel. Thisparticular
companionreceivesadesignationof“Bound”becauseitsmodeledandobservedcolorsagreetowithin3σ,forallcolorpairingsavailable.
7
Thereadershouldnotethatthisanalysismakestheim- dateboundcompanions), weadditionallychecktherela-
plicit assumption that the companion detected by each tive probabilities of the companions being bound versus
method is not itself an unresolved multiple. If a com- background alignment, before applying the designation
panion is itself an unresolved pair (i.e. a hierarchical of bound. Specifically, we use the known multiplicity
multiplesystem),theobserved∆mvalueswouldreferto statisticsoftheSolarneighborhoodfromRaghavanetal.
the composite light from the companions, and the anal- (2010) to determine the probability of a solar-type star
ysis may fail to accurately assess either companion star having a companion within ±3σ of the model mass ratio
individually. from the isochrone models, and at a separation greater
than the derived projected separation.
3.1. Interstellar Extinction
BasedontheRaghavanetal.(2010)multiplicitystatis-
Our approach makes the implicit assumption that the tics, we utilize a log-normal distribution for the proba-
companion is subject to the same interstellar extinction bility distribution in orbital period, which we calculate
as the primary star. We check for consistency between based on the observed angular separation, the predicted
the model and observed companion colors under this as- stellar distances from the ExoFOP website1, and the
sumption. modeled stellar masses of both the primary and stellar
Differential extinction between the primary and com- companion. The distance estimates to each KOI star
panion may cause the measured color to differ signifi- found on the ExoFOP website1 derive from models cal-
cantlyfromthecolorexpectedunderthemodelassump- culated by Huber et al. (2014). The uncertainties on
tions, causing our analysis to produce a designation of these distance estimates are typically of order 15%, and
unbound. Since the most likely scenario for producing are uncorrected based on the discovery of a stellar com-
this differential extinction is that the companion is more panion. For KOIs with a bright stellar companion in-
distantthantheprimaryKOIstar,andisthereforeonlya creasing the inferred brightness of the primary star, the
line-of-sight optical double, we would correctly conclude truedistancemaybelargerthanthedistancereportedby
that the companion is unbound. the Huber et al. (2014) models. Greater distances would
One potential source for a false negative – a bound imply larger projected separations, and would therefore
companion that fails to satisfy our bound criteria – is decrease the probability that the companion is bound.
a bound companion with a significant dusty envelope or To determine the probability of a companion within
disk,causingdistance-independentdifferentialextinction ±3σ of the modeled mass ratio, we assume a flat dis-
of the companion. However, this scenario is highly un- tribution in mass ratio q from values of zero to unity
likely, as the target stars are not expected to be young, (Raghavan et al. 2010). We integrate under the curve
so should not retain their natal dusty disks. from the lower to upper bound, and apply this fraction
Likewise, a plausible source for false positives would to the overall fraction of sunlike stars with one or more
be a background object that is attenuated and reddened stellar companions, 46%. We then apply the fraction
until consistent with the isochrone of the primary star. from integrating under the log-normal curve in orbital
To provide an indication of the direction and magnitude period,fromthecalculatedperiodtoinfinity. Wechoose
oftheeffectofextinctiononbackgroundcompanions,we this upper bound to account for projection effects allow-
haveplottedanextinctionvectoroneachpanelofFigures ing long orbital periods to appear as smaller separations
5and6. Thesevectorshavelengthscorrespondingtoone due to orbital orientation and phase.
magnitude of extinction in the V-band. Typical models We note that choosing the multiplicity statistics from
of interstellar extinction toward the Kepler field assume Raghavanetal.(2010)maynotbeaccurateforthissam-
1 magnitude of extinction in V for every kpc of distance ple,aspreviousworkontheKepler fieldplanethoststars
in the galactic plane, with extinction diminishing as a hasshownthatstellarmultiplicitymaybeaffectedbythe
functionofgalacticlatitudewithane-foldingscale-height presence of planets (Wang et al. 2014a,b; Kraus et al.
of 150 pc (Huber et al. 2014). 2016). However, the specifics of this multiplicity effect
While these possibilities exist, we do not have enough are not yet well-understood, so we default to using the
datatomaketheassessmentofwhetherthescenariosde- known multiplicity statistics of the Solar neighborhood.
scribed apply to any of our systems. Spectroscopic data We compare this derived bound probability to the
wouldprovidemoreinformationabouttheintrinsicprop- probability of a chance alignment within the measured
erties of the companion stars, and would allow a more angular separation, and at the measured apparent Ke-
conclusiveassessmentofwhetherthecompanionsarein- pler magnitudeofthecompanion. Weproduce9galactic
deedbound. However,spectroscopyisnotavailable(and stellar population models using the online TRILEGAL
is largely precluded by magnitude limits and the close- galaxy population simulator (Girardi et al. 2005) with
ness of the stellar primary) for the vast majority of the galacticlatitudesfrom6◦ to22◦,spanningoursampleof
companions included in this sample. Instead, we look KOIs, and areas of 1 square degree. For each KOI, we
at the predicted population of background stars to de- refertothetwogalacticmodelswithlatitudesmostsim-
termine the probability that each candidate bound com- ilar to that of the KOI, and we interpolate to determine
panion is a line-of-sight alignment. We compare this to the background probability. We filter the results of each
the probability of a solar-type primary hosting a bound TRILEGAL model to contain only those stars with Ke-
stellar companion at the predicted mass ratio and sepa- pler magnitudeswithin±3σoftheobservedKepler mag-
ration. nitudeofthestellarcompanion,sinceonlystarswithsim-
ilar brightnesses and colors to the observed stellar com-
3.2. Comparison with Stellar Population Models
panionswouldhavebeenconsistentwithourinitialcheck
For the companions in our sample with colors con- against the primary star’s isochrone. We then calculate
sistent with the same isochrone as the primary (candi- the stellar density of the field surrounding the KOI, and
8
KOI 3444 F
8 7 6
9 8 7
10
9 8
11
MV Mi10 Mz9
12
11 10
13
14 12 11
15 13 12
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
B V B i B z
4 7
6
5 8
7 6 9
MJ MK7 Mi10
8
8 11
9
9 12
10 10 13
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 3 4 5 6 7 0.5 1.0 1.5 2.0
B J B K V i
6 4
6
7 5
8 7 6
Mz9 MJ MK7
8
10 8
9
11 9
12 10 10
0.5 1.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
V z V J V K
6 4
6
7 5
8 7 6
Mz9 MJ MK7
8
10 8
9
11 9
12 10 10
0.0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.0 2.5 3.0
i z i J i K
4 4
6
5 5
7 6 6
MJ MK7 MK7
8
8 8
9
9 9
10 10 10
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.4 1.6 1.8 2.0 2.2 2.4 0.3 0.4 0.5 0.6 0.7 0.8 0.9
z J z K J K
Figure 6. ForKOI3444F,thefifthstellarcompaniontoKOI3444,theisochronemodelcompanioncolor(bluecircle)iscomparedwith
theobservedcompanioncolor(redsquare)todeterminethelikelihoodthatthecompanionisbound. Lightbluepointsshowthepositionsof
each“isochrone-shifted”modelestimateofthecompanion’spositionontheisochrone. Thedarkbluepointistheweightedaveragemodel
position, and is compared with the red observed color point. We plot an extinction vector corresponding to 1 magnitude of extinction in
V-band,asadarkgrayarrowintheupperleftcornerofeachpanel.Thisparticularcompanionreceivesadesignationof“Unbound”because
itsmodeledandobservedcolorsdonotagreetowithin3σ,forallcolorpairingsavailable.
9
multiply by the area within the observed angular sep- ties on these distance estimates are typically 15−20%.
aration of the companion to determine the probability Since the stellar companions to all of these KOI stars
of a background interloper with the required brightness may increase the apparent brightness, stars with com-
falling within the required area around the KOI. panions may be more distant than the models indicate,
WeuseonlytheKepler bandpasstofiltertheresultsof andthetrueprojectedseparationsmaythereforebecor-
the galactic models, and still find background probabili- respondingly larger. Mass ratios are calculated based on
ties of < 12% in all cases, and < 2% in all but 3 cases. the isochrone models for each component of the system.
These very low background probabilities are expected, For reference, we provide characteristic detection lim-
due to the very small angular region in which all of our its for each of several techniques used to find the stel-
observedcompanionsreside. Wefindsimilarbackground lar companions here. We include AO observations from
probabilities for stellar companions designated as uncer- Keck/NIRC2, Palomar/PHARO, and Lick/IRCAL, as
tain and unbound based on isochrone models, with no wellasDSSIspeckleobservationsfromtheGeminiNorth
distinctdifferenceamongthe3samples. Theseprobabil- andWIYNTelescopes,takenfromF17. Weconvertthese
ities would be further reduced if we filtered the galactic detectionlimitsfromangularseparationand∆mtopro-
models for consistency with all measured magnitudes or jected separation and mass ratio by assuming the pri-
colors, instead of only looking at the Kepler apparent mary star is a solar-mass star at a distance of 500 pc.
magnitude. Thesearetypicalvaluesfortheprimarystarsinoursam-
We calculate the ratio of bound probability to back- ple,whichhaveamediantemperatureof5780Kelvinand
groundprobabilityforthecandidateboundcompanions. a median distance of 420 pc. Note that the exact detec-
In all but two cases, these ratios exceed unity, typically tion limits will differ for each KOI system based on its
by one or more orders of magnitude. The median value primary star mass and distance.
of the probability ratio for stars in the bound category Inthefuture,thedistributionofstellarsystemsinthis
is 367.5. Only 11 stars have probability ratios less than diagramcouldbecomparedtoatheoreticaldistribution,
10, and only 2 (KOI 703 B and and KOI 6425 B) have basedonknownpropertiesofsolarneighborhoodbinaries
ratioslessthanunity. Wemovethesetwocompanionsto (e.g.Raghavanetal.2010),typicalstellarpropertiesand
the uncertain category, and do not include them in fur- distances to stars in the Kepler field, and the detection
ther analysis of bound systems. In Table 1, we provide limits of each of the techniques used here. This com-
the background probabilities, based on the TRILEGAL parison would allow us to test whether the multiplicity
models, for all companions. We also provide the bound of Kepler planet hosts is qualitatively similar to typical
probabilities based on multiplicity statistics of the solar fieldbinaries. However,thisanalysisisoutsidethescope
neighborhood(Raghavanetal.2010)forthecompanions of this paper, which is primarily focused on determining
consistent with being bound. whether the companions discovered by high-resolution
imaging are bound or not. For an ideal statistical study
4. BOUNDCOMPANIONSTOKEPLERPLANETHOSTS ofstellarmultiplicityasitrelatestoplanetoccurrence,a
Based on the isochrone analysis and comparison to more careful selection of a target stellar sample, as well
background stellar population models, we highlight a as a control sample, is required.
population of KOI hosts with likely bound companions, Horchetal.(2014)simulatethebinaryandbackground
listed in Table 1. This group of planet-hosting stellar stellar populations for the Kepler field, and conclude
multiplesystemsisavaluablecomparisonsampleforthe that within the detection limits of the DSSI instrument
wider Kepler planet host population. at either the WIYN 3.5-m or Gemini North Telescopes,
We plot the distributions of stellar properties for the the vast majority of sub-arcsecond companions detected
bound companions to our sample targets in Figure 7. with high-resolution imaging should be bound, rather
We also plot for reference the stellar parameters of the than line-of-sight companions. The bound fraction ver-
primary stars in these bound binary systems. The com- sus separation curve depends on the sensitivity of the
panion population has a lower average T and a higher instrument to high-contrast companions, and therefore
eff
average logg than their primary stars, as expected for a can differ for each instrument and telescope.
coeval pair. The bottom panels of Figure 7 show the ra- Weuseourboundandunbound/uncertainpopulations
dius and mass ratios of the bound stellar companions. toassessthefraction ofboundcompanions asafunction
This information feeds directly into the planet radius of angular separation. In Figure 9, we plot the sepa-
correction factors, described in § 5. Note that this dis- ration in arcseconds against the ∆Kp, the ∆m in the
tribution is subject to detection limits on much fainter Kepler bandpass, for each companion in our sample, in-
companions, so the lower number of stellar companions dicating with symbols which companions are bound, un-
atsmallradiusandmassratiolikelyreflectsthedifficulty certain, and unbound. ∆Kp values are taken from F17
in detecting high-contrast systems. Malmquist bias may forunboundanduncertainstars,andfromtheisochrone
alsoplayarole,sincesystemswithmassandradiusratios modelsforboundstars. Visually,itisclearthatcompan-
close to unity would be brighter, and therefore overrep- ions within 1” are most likely to be bound rather than
resented in both the Kepler sample and the subsample eitherunboundoruncertain,whilecompanionsat2”are
of stars with high-resolution imaging follow-up. approximately equally likely to be bound or unbound.
InFigure8, weplottheprojectedphysicalseparations Welistthefractionofcompanionsfoundtobebound,in
and mass ratios of each bound multiple system, in order bins of 0.2”, in Figure 9. For the reported fractions, we
todemonstratethesensitivityofhigh-resolutionimaging exclude uncertain companions.
campaignstocompanionsinphysicalspace. Wecalculate We choose bins of this size in direct comparison with
projectedseparationusingthedistanceestimatestoeach similar plots from Horch et al. (2014). The goal of this
KOIstarfoundontheExoFOPwebsite1. Theuncertain- comparison is to assess the theoretical results with ob-
10
45 45
Primary KOIs
40 40
Companions
35 35
30 30
25 25
N
20 20
15 15
10 10
5 5
0 0
3000 4000 5000 6000 7000 8000 9000 10000 1.5 2.0 2.5 3.0 log3.(5g) 4.0 4.5 5.0 5.5
T
eff
30 30
25 25
20 20
N15 15
10 10
5 5
0 0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
R \ R M / M
2 1 2 1
Figure 7. HistogramofthestellarpropertiesderivedfromisochronemodelsfortheboundcompanionstoKOIstarsinourtargetsample
are plotted in the diagonally hatched red histograms. The dark blue hatched histograms show the stellar properties of the primary KOI
starsineachoftheseboundsystemsforreference. Asexpected, companiontemperaturesareskewedcool, withmostcompanionshaving
T <6000K.Thesecompanionsallappeartobemainsequencestars,with4.0≤logg≤5.2,assumingtheirhoststars’stellarproperties
eff
areaccurate.
servational data. Our observational results confirm the KOI270, ontheotherhand, hasstellarparametersfrom
model results from that study, which indicate that com- asteroseismology (Huber et al. 2013). Additional data
panions within 1” are likely to be bound companions. are needed to resolve the anomaly of three such close,
We do find 3 anomalous unbound companions at very bright, but apparently unbound companions. For exam-
close separations: KOI 270 B, KOI 4986 B, and KOI ple, spectroscopic analysis might revise the stellar pa-
5971 B. Only the first two of these appear in our plot, rameters calculated for the primary KOI host star, and
sinceKOI5971hasinsufficientdatatocalculatethe∆Kp repeating our analysis might then produce different re-
value for the companion. We suspect that these might sults.
be anomalous false negatives, since a very bright, very Between0.2”and1.2”,ourboundfractionresultsagree
close companion may skew the initial predicted stellar with those predicted by Horch et al. (2014), falling in
parameters of the primary KOI stars, which are used as betweenthepredictionfortheGeminiNorthandWIYN
the basis for our analysis. If the assumed stellar param- 3.5-m telescopes. At 0.0 – 0.2”, our bound fraction is
eters of the primary star are incorrect, then the analysis lowerthanpredicted, mainlyduetothethreeveryclose,
may produce incorrect results. unbound companions described above. If these three
Indeed,twooftheseveryclosebutapparentlyunbound companions are removed, the bound fraction is 100%,
companions (KOI 4986 B and KOI 5971 B) have stellar in agreement with the expected bound fraction in this
parameters estimated using KIC photometry by Pinson- separation region. Outside of 1.2”, Horch et al. (2014)
neault et al. (2012). Without knowledge of a very close, can not provide a prediction for the fraction of detected
fairly bright stellar companion, the KIC photometry is companionsthatshouldbebound,sincethefieldofview
blended and may produce inaccurate stellar properties. of the DSSI camera excludes this region. We find that