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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

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