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The Abundance Of Circumbinary Planets
D. Armstrong, D. Pollacco University Of Warwick d.j.armstrong@warwick.ac.uk Introduc)on
The Kepler s a t e l l i t e h a s d i s c o v e r e d s e v e n circumbinary planet systems to date. These, and the sample of ~2000 eclipsing binaries surveyed, allow us to investigate the general properties of circumbinary planets. We use the ~1700 binaries in the catalogue which are not classified as overcontact

Rates of Occurrence
This gives us posterior probabilities for the rate of occurrence of CB planets
Figure: Example probability distributions (planet radius decreasing from left to right, with same radius groups as table) Table: Derived rates of occurrence, given as maximal likelihood values with super and su ong et. al. Armstrbscripted rates of occurrence at 50 and 95% confidence 5 intervals. 5. Rates of occurrence for planets within 10.2P . Valu
Rplanet (lower limit) (R ) > 10 8 6 4 8 10 10 10 10 (inc Kepler-34b)

Transit Search and Debiasing
6 We searched the whole eclipsing binary sample On the Abundance of Circumbinary Planets for planetary transits, allowing for large timing and Table weurso tiolledvarstritions[1] by d al a tria n a diia bution where Table 3. Candidate Planets
Kepler ID Pbin (d) 11.26 28.16 27.32 e
bin

such, nets located within the inner stability limit ' and placed randomly between 1.1 and 1.4 6 . O k res wn sys to be ge at limit/7 urnoults proved tems nerally his, and so final results are presented without



bin

es are maximum likelihoods, with 50 and 95% confidence intervals.

P

Planetary Inclination Distribution Coplanar Gauss =5 Gauss 0
0.67 2.8 4. 2 7. 6 1.8 0.57 6.8 11.7 3. 4 1. 4 12.2 21 6. 1 2. 6 5 2 8 4 . . . . 4 7 3 5 9. 3 1. 1 13.5 2. 1

=10

Gauss 0
3.7 15.9

=20

Gauss 0
9. 0 39 60 28 80 46

=40

Uniform 0 100 100 100 100
26 84 70 27 79 40 81 44 78 38

candidate

(d) 0.15 0.094 0.093 550 or 1110 170 240

0

1.1 4.8 7.6 13.9 3. 3 1. 1 12.7 22 6. 3 2. 7 5 24.7 400 11 5. 9.9 17.0 4. 9 2. 1 . 0 1535 250 8. 4.

0

1.9 8.0 12.9 24 5.7 2.0 22 37 10.7 4.5 40 68 20 8.6 16. 8. 4 27 14. 8 29 3. 5 43 3 6. 9

recovered, plus 3 other strong candidates

5473556 6504534 9632895

2.0 4.2 7.1 3.1

3 .7 7 .5 13. 5 .8

7.1 13 25

15.0 25 48 20

26 48 11.7 4.1 44 73 22 9.4 72 95 39 17.2 34 58 17.1 7.3 54 82 29 14.2

33 68

92 10.1 97 21

100 51

75 35 95 17.0 98 29

6 10 r Kepler-34b) 5 87 The(inc ates of.5occu10.rence 17.0arOn dr35 bundanccalCircumbinarythlanets r v y the amati e of ly with100 83 49 cessary hnary earch rs are oready mownas teste4. Other ng simulated A Pe Table d usi Signals T bie s paramete alg alrith kn w as described in Section 2.1. Binary inclinaunderlying planet inclination distribution. For a iinrmlcterosstrhensigts,itcirewhted using: Comment je y ac d t a ran e w h n a ich wn un fo Kepler ID Table distrioccurrence for planets withianaralues are maximum likhods, t th 50na95% , the intervals. 6. Rates of bution copln 300 d. V with the elihoo s wi bi and ryconfidence ll at least partially eclipse. It is critical to in6144827 Additional eclipsing binary (EB) signal at 1.94d ry inclination variation, as for preferentially rates ware consistentDistribution those for single star Transit Times and Durations ­ NRplanet (lo er limit) Planetary Inclination with 7871200 Highly eccentric (e ' 0.7) additional EB ts on much larger semima jor axes a change of (R ) C pla signal at 38.02d be dynintegt atorsequences for observo sig i ficanr con planets [4]. oFnarr maosre isotropi0c distribuGauss ns0, they o G u s =5 Gauss =1 Gauss =20 tio =4 Uniform can hav

Distributions

10.2

73 39 86 56

7

Transit Depths ­ including dilution from companion. Stellar radii were derived from SED fit ion, a temperioturesbusiries the maigned a proport a n of ina ng are ass in ly based qn en cnpcalobcurrencs oft[2]. t this seo u an i e ut i c ration e ra e. A

8113154 10223618

ant binary and planet parameters are drawn, p en checked for observability. We limit ourp p ts tranFiiting coTeecetiveiln, i.e.sample, forbtiransit i s gure: ns stud b yary on every or t, , h ne % d t bu lr it t sents a real signal. The candidate period shown by iing otra(nhrowgth irecov2Pbin . 5Tradiifis>r10tatbol,n8p1ae et,sow-n ofRrhefraonm the appropriate radius bins in their paper. Both of these are ts lef= t5situ i t) n 10. ering 0he o unis R i es-a0n sh 6n10 o ( d t to righ planets with R , 3n 0drperiode complecrofor csnsecutiwhere transit recovery was successful, and 0 ou sampl s ­ red te sse o show ve ve show i e rreni ly as e c R density tion 5.2 le ds t occu down p reg . signals also corresponds to 6Pbin , similar to thepcluu4-10Rton Thed>s10ribed in Secfunction)hasabeenoscaledrrence by a consistent with our coplanar results, although our modal ect of repasisent miessample ius isd to cult ve results. Dashed line shows the minimum occ re onal th s ed trans t se di deri to known planets and outside the inner stability limratefowhtchisthree 1or cllowy,randplanetsa withinethisdgrcopltheaothers values are higher. It is worth noting that were we to assume it sfactorhofare erof0% arite for take s300 erenrio ,moup.an r r ito the z detections of th e di d p t for to due constraint requires athreh delgreesed.lignment group, and unchanged for the 10.2 Pbin group. These further the single star rate of occurrence holds in the circumbinary significance hig sho d u of a system. Given these considerations, we include KIC6504534 reduce in significance for more uniform inclination distribucase, for the 6 10R , within 300d bin the 10 Gaussian y plane, to a degree commensurate with the in the planet count when calculating rates of occurrenand are well within the 50% confidence limits. c e. t io n s, inclination distribution would be excluded with probability e then obtain a total number of observable KIC 5473556 was mentioned in Welsh et al. (2012) as >99.9%, along with all more misaligned distributions. As given occurrence rate and set of parameter The occurrence rates are however critically dependent For close to coplanar showing a single transit. There are now two, implying a pesuch, should a large very misaligned population of circumbi10,000 times, we gain a distribution of obon the input planetary inclination distribution. As such reriod of 550 or 1100 d (due to a gap in the light curve where nary pcnetnxistit wnlddistribumbionpla, ets in la li s eat, ioou imply that circu ti nary s n sults are shown as a function of this, and are summarised s for each of a range of occurrence rates. This a t C B o l d h e e b en Simkulgaour knoon numbopupan- on ofransit cpulanavts eis missed). This candidateindFoigeusrenot6. The full list of values and confidence limits exist in significantly greater numbers than planets with sintion w f a p er of lla ti s 3­ verted - ta in th llar hostsc gle stee oc. urrence rate of have enough transits to show TTVs, leaving the an osssieeil-in Tables 5 and 6. Our planet radius bins are c p b e bn 1) wercaquirhod many timn our umeer cted planet count into an e n see ew to tur es this n d b te ity of a background blend open. Our remaining ckaptdliadaeteue to the low number of planetary detections. e n rg d , gTantveCpBbaplltadenettsnc(>1a0o allow us i he deri d ro bi i y n si y fu tions ls each rate, thereby producing a distribution to investigate dierences between planetary radius groups. It KIC9632895, shows three transits, implying an For the ppeo-ds below 10.2 Pbin we present results both with 240 d eri rates implied plate count. ccurirence. The prior distributions for a given r anet of o Assum ng a Ree earsed th is t ( ign l ke c anets shou a h wi t ev t K has b_n propoth)at giansJupiter iifi) plantlyld be riod with TTVs of magnitude over 1d. There arend owhouer epler-34b. Strictly Kepler-34b lies at 10.4Pbin , ributed prior on the occurrence rate (as is apless common in coplanar circumbinary orbits than Saturnlight curve regions where consecutive transits shoujudt laboviemhe period threshold. In the case of CBs it seems l s i e, t usedlawereb:servational evidence), l or smallr ethaen Fugeurteo 3i fooas< Rc < 10R the current ck of o pleusiblrbiowever that a more suitable boundary would be a d o e h t. likeoweerFiquive l5. ts, thatncr 6f ed p hances of ejecre gur a nAs d i plying that this candidate is on a slightly misalign caled to form probability density functions. defined by multiples of the binary inner stability limit. In tion maller splanets etsns & Nelson 2008). We r s tforathtigheKemaers spalmpns(uPipeort s this, with the rate of ale p re As such it is not within our consecutive transit threshold, find h he pl Planetary inclination - As the underlyinaninislinatioeddio trimuuten ofnCB ccurrences. the Kepler-34 case, this limit is particularly large, at 190 g d c not us n t sco b ptio pla et o det occurrence for planets >10R within 300 d being signifiplanets is unknown, we trialled several, rangengso detectod laveralwith sesetoo deep to bd, puano ttsh.e high eccentricity of the binary. Under this i al from c e psenar eclip th W e e definlition, Kepler-34b would clearly lie within a similarly cantly lower than the other radius groups. In the coplanar Fi, iged Rates ofand r95% confidenceian planetarys for CB planets >10 Earth Radii, for a gur u3. : 50 occur ence for a range of Gauss interval binary to isotropic Many of these are already known multiple star sysdefinesFperioreboundary. As such we present both results t em d a n d case the significance of this dierence is 99.8% (4 10R ), S inclination distributions, for planets within 10.2Pbin with Rp > ra fare we will not list them here. However a few other andrearele.vgnt. lorf einoxeisnatwo0%dostdebultiimits,s.i th the thin 98.4% (6 10R ), and 96.4% (8 10R ). This finding besa whe 10R n The a g b cl sho i 5n c infi rince on w `whisk se d Tertiary tSignals - drawn using the distribution are Kepler nknewtssof ins weret, lso found, and theers' extending to 95% limits. comes less significant for distributions more misaligned than as we of aware uobjo cn ignal teres a Plane period Although a large range of planetary inclination distributhe 10 Gaussian case. merit noting. They are summarised in Table 4. tWe imasked, previous work suggests that some are more io n s s t e t e ree stcutg candidaw thanietnryr sstaemsty wo it for each binary derived in [3] ron off belo te pl e na e yst bili , t lim no comment on the possible nature of these ob jecltkel­satmaee.others, lat dhthsamplsetrono shortrendelonr coepla- bihl i s y th pnreW sp i n t e at a intg prefe a c fo g p riod Finally, it has also been proposed that there is a prefithin our period limit of 300 d. These are in n b y rie ed a n e ( p ri art u 2 0 d . . U i o p a n c p la p l r is a significant chance that some of them representaritlnaindsrousiblg aFoeucod c&tLoafi 10 13)Forscng lthear oCB naanets erence for CBs to have longer period binary hosts (Welsh e s p, b e currentlyry nown mlaters - nd stebina4ies were given their known parameters from k para p e nets aHo K pler- r13b Bina e s e with acu ndn aess e han 10w Pbin , we t nhothespp 9babilio y that a pl riods l v t c s .2 fi aro ha fis d rt ro 5% t n background source for example, but others mayrebultste sopneirreiccetirateaise,loweer nd tund thereeir a eriod cbin-aries et al. 2013). All of the known planets so far orbit binari c th 2014), ell of which taeregste, ngithdecected, icities derived from binary eclipse th a Kepler ca w lo u ro w ly e t centr fidento upp96.3%(4-10Rhe o97.7%(6-10opoante%(8R10) at ries with eriis gaatdean rd, desof tCe longer pece It er lait on t een pe rate )of nds5.(6 d -th ). ther pe ods re er th a 7 th pite hes B be hims b ), ccurrenc r R a gi 9 >10 R star systems or simply stellar activity. ler-47. We do not andlyoe atiottsmpt to conn s ana l s c or a n e planets iwitecomes.2 Pre siofni2.can.t Mr king cmispairinonsinclina- riod binaries being significantly undersampled in the Kepler Th s b hin 10 mo bin g fi 8% fo a more om al g s ed to duratio date systems, as this is beyond the scope of the stnonedsitantteoofs, ccsag noe9(F9%sforeth520Gaulsoiser datasn.aries le to test we ther this eect is due to a i i gplsaribuen o ri un rtc und thal. e 1c i d f- case bi et We are ab of th he Kepler l tr ra i ts irre o 9. res in t e 3) ssian can however give approximate periods of the ficultanas highdr. notnuse thnasame riod odtonat ss.eveowdayr, (be- sampling bias or represents a real trend using our debiased , d we eo Usi g a bi e ry pe peri cu ra ge H n eves s l publi p d C . W ts) s uc l th signific debiased sample into short 6.2 Occurrence Rates low alamsheleB planee redpesit e ourance of the systems would represent if they prove real. result, to a 92.6% probability for the 6-10R sample. This Fi re fo 4 Rp 000 again b ec 0 es m re s gn fica i for ore misa gned d st e Prodcuuci RAS, MNRAtes our input and derived parameters for these Using these detections and our debiased sample, we can(<1omd) obiiniarntesmand lithoisri- longer. gure 6. As Fig20023nrg


4 67 100 100 100 100 As10such, if20the CB planet inclination distribution is no calibrated stellar radii, the transit depth of 0.2% would rept generally coplanar, planet formation in CB resent a planet radius of 4.3 R .While thisplanetitsnhet presenks a pilusit plaet srigs niar theantlyooking siter lthst no inges, 0.8­245 d and 0.8­418 c i nl ea at heir arge atw ran o t o dos ce of me up n bne pei od ne fic infirmed, the presence of clear transits with strong timisnabiaindimit. Without full confirmation of its existence ner t ggurte 2. Probability density functions for the rate of occurrence d, these rates are 5% for planets with R > 6R and 8% l yl Fi Fi R 4. As , ur 3 te oop tplanets nt al te Gaussian inclination but nc ud e v < ys duratoon variations siuppplas ets atypothesis thatwe t hreserecresefollosuesawilaut tes piuivalielnts. for planets withgure> 4R Fitghe elatforr 8d 78 38 81 44 82 44 85 50

Broad 5d long faint regions on 40d p eriod For several consecutive quarters binary secondary eclipses gain an additional 1% dip just after eclipse

a8re signific.antly h.igher. 10 64 17 5
> 10 0 0 6 10 10
11.6 5. 7 . .0 162 8. 34 17.2 19.7 2. 5 3 28 3. 5 58 7.4

1.4 5.9

3.4 14.8

0

7. 1 31 62 32 78 44 91 13.7 96 19.7

0

16.8 67 71 32 77 37

0

33 89 80 42 81 43

0 100 100

45 93 83 44 83 47

30

31 53 15.4 6.6 47 77 23 10.0 82 98 49 22

38 58

100 100

100 100

A Lack of Jupiters

Popula)on Synthesis

Short Period Binaries Missing Planets

References



NRAS 000, ??­??