arXiv:1012.4791v1 [astro-ph.EP] 21 Dec 2010 fteesmlssosta h bevdlc fhot of lack observed at the censored are that sub- hot shows and follow Neptunes Comparison samples which these distributions. clusters of two period–radius different into very fall space –density as such on or parameters, periods, biased radii. versus orbital of as Be- combination such the 2009). parameters, concentrate currently either unbiased the should al. on in tests et effects Guillot sample, Chabrier selection exoplanet known obvious (e.g. 2007, are structure there al. interior cause et the Fortney of being 2005, tracer radius, and prime mass most the are The parameters tests. transiting planet statistical of important perform number to sufficient This periods is planets orbital 2010). and (Schneider, radii known masses, are precise which for lished evolution. planet further of the and processes phase physical al. nebular the the of et in spec- tracer formation (Howard mass direct the a range of is period trum confirmation observational The 3–100 observations hot 2010). the by that confirmed in Jupiters is been recently has hot range popu- which outnumber period 2006) the with (Broeg, orbital significantly of masses day always feature 1–16 larger key Neptunes the multi- to A in move or Neptune lation periods. peaks bimodal of orbital Both mass a increasing the exhibit . near masses, and peaking the cover of distribution, functions of range mass modal effects Initial tidal wide or- 2008). and the a al. thermal on et (Wuchterl the depend star will via planets distances The of bital disk. spectrum the mass of matter initial gaseous the accrete protoplanets est fSde,NW20,Australia 2006, NSW Sydney, of versity Austin Hungary Budapest, H-1525 67, Box PO. nti ae edmntaeta xpaesi the in exoplanets that demonstrate we paper this In pub- been have exoplanets transiting 106 writing, of As formation, planet on-going with disks circumstellar In rpittpstuigL using 2018 typeset 8, Preprint November version Draft 3 2 1 ynyIsiuefrAtooy colo hsc 2,Uni- A28, at Physics of Texas School Astronomy, for of Institute Sydney University the at E¨otv¨os Fellow Hungarian Sciences, of Academy Hungarian the of Observatory Konkoly as hscutrn sntpeitdb urn hoiso planet of theories current headings: by Subject predicted not briefly. is review clustering also This days. rnho u-uie aseolnt scnoe yteorbital the by censored 0.02–0.8 is perio between mass the exoplanets with in mass planets distributions sub-Jupiter different of strikingly branch follow clusters two These o etnsadhtJptr,ehbtn upiigynro per narrow surprisingly a exhibiting Jupiters, hot and Neptunes hot ntems-est pc,oewt o uieswt ierneof range (1.2 wide radii cu a planet the with of of observatio Jupiters range analysis hot this narrow with cluster for a one a explanation and space, discuss possible mass-density we a the Here in investigate days. to 2.5 exoplanets than less period HR-EIDCNO FSBJPTRMS XPAESWT L WITH EXOPLANETS MASS SUB-JUPITER OF CENSOR SHORT-PERIOD A ept h xsec fmn hr-eidhtJptr,teeis there Jupiters, hot short-period many of existence the Despite 1. A INTRODUCTION T E tl mltajv 8/13/10 v. emulateapj style X p y .Szab M. Gy. M rf eso oebr8 2018 8, November version Draft J < rwt aisbten0.25–1.0 between radius with or ± 2 0 . day 5 . 2 ABSTRACT R J o ´ ;adaohroewt itr fsuper-Earths, of mixture a with one another and ); 1,2 .L Kiss L. L. , Dsae eaaigtosblse feolnt,here- exoplanets, the on of in after subclasses Based diagram two discrimination separating space, a space. MD propose period-radius we finding, the this in dif- two sequences distinguishes ferent color- space mass-density that the found from have we coding plots strategy, pa- color-coded trial-and-error few stellar a a Drawing with and analysis. inclination, our density, in and average rameters axis refer- size, semi-major mass, and included period, Interactive 2010 We the (Schneider, therein). from ences Catalog For data Planet collected tools. we Extrasolar statistical analysis clus- by investigated an suspected as- be such the System further of Solar can structure for ters and 2002 Existence al. a Ivezi´c e.g. et teroids). in is (see example heuristically colors nice clusters specified a find the to technique with powerful diagram another plotting similar distributions. a may period–mass suffer that observed scenarios not the candidate do explain several Jupiters address We hot while censor. range, period h odriebtentetocutr a h equa- the has clusters two log( of the tions 2000). between Maesschalk, (De borderline cluster- correlations The Ma- in severe used with Appendix). successfully data in ing been in distributions has details two distance (see halanobis the space of dis- period-radius Mahalanobis the 1936) the (Mahalanobis, maximizing by tance determined was 1) abscissa. labels, the the in by water indicated indicated 50% mass masses and total initial and silicate various al. 50% et with contain (Fortney core models indicated is The analog of solar 0.045 2007). a at purpose to exoplanets With of distance isochrone AU Myr space. 500 the mass–density illustration, the in transiters borderline). the to right mass, larger ) while 1), ter oo-oigtepit noedsrbto n then and distribution one in points the Color-coding aeaysses—paesadstlie:general satellites: and planets — systems lanetary h odrbtentetocutr pnlBo Fig. of B (panel clusters two the between border The involved the all plot we 1, Fig. of A panel the In hscasfiaincni atb sindt objects to assigned be part in can classification This D D 1 1 st h et(pnsmosi ae fFig. pf B panel in symbols (open left the to is ojcswt oe as and mass) lower with (objects D 1,3 2. 2 ρ o n o etn iha orbital an with Neptune hot one not LSE NLSSO H DATA THE OF ANALYSIS CLUSTER st h right. the to is 0 = ) eida h ag-aised no end: large-radius the at period .W n w itntclusters distinct two find We n. omto n vlto htwe that evolution and formation o itiuin(3.7 distribution iod -aisprmtrpae The plane. parameter d-radius ria eid 0814days) (0.8–114 periods orbital R . rnl nw 0 transiting 106 known rrently 21 log( 12513 J r nw with known are M − WDENSITY OW 0 . 30779) ± P 0 orb . D days). 8 2 < − ojcswith (objects 0 2 . 83645 . 5 clus- , 2 Szab´oand Kiss

20.0 20.0

100 ME core 10.0 10.0

50 ME core 5.0 5.0 25 ME core

10 ME core

) no core )

J 2.0 J 2.0 ρ ρ ( (

ρ 1.0 ρ 1.0

0.5 0.5

0.2 0.2

0.1 A 0.1 B

0.02 0.10 0.50 2.00 10.00 0.02 0.10 0.50 2.00 10.00

M (MJ) M (MJ)

2.0 CoRoT−3 b WASP−12 b 10.00 XO−3 b WASP−18 b SWEEPS−11 HAT−P−2 b HAT−P−23 b WASP−19 b 5.00 OGLE−TR−56 b WASP−18 b HD 80606 b HD 17156 b 1.0 HD 17156 b CoRoT−9 b CoRoT−10 b CoRoT−10 b HD 80606 b Kepler−9 b WASP−29 b Kepler−9 c WASP−12 b

) 1.00 WASP−19 b ) J J CoRoT−8 b CoRoT−9 b HD 149026 b 0.50 0.5 HAT−P−26 b HD 149026 b CoRoT−8 b R (R M (M GJ 436 b HAT−P−11 b WASP−29 b Kepler−9 b HAT−P−12 b HAT−P−18 b Kepler−9 c Kepler−4 b 0.10 GJ 436 b HAT−P−11 b Kepler−4 b 0.05 HAT−P−26 b GJ 1214 b 0.2 CoRoT−7 b CoRoT−7 b GJ 1214 b C 0.01 D

1 2 5 10 20 50 100 1 2 5 10 20 50 100

period (d) period (d) Fig. 1.— A: The mass–density diagram of the currently known transiting exoplanets. Four planetary models with various core masses and one other without a core are plotted with illustrative purposes. B: The proposed clustering in the mass–density space. Open and filled dots (magenta and blue on-line) distinguish the two clusters. Two planets, Kepler-9 b and c are plotted with diamonds. C: Clusters form two apparent sequences in the period–radius space. Note the lack of D1 exoplanets with period < 2.2 days. D: The distribution of the cluster members in the period–mass space. discriminated by mass. D1 exoplanets contain super- branch of massive D1 members overlap with D2 cluster Earths (Valencia et al. 2007, Adams et al. 2008), hot members at the large-radius end in the period–radius Neptunes, and low-mass, low-density hot Jupiters. Hot space. All D1 cluster members have periods > 2.88 Jupiters exceeding the mass or the density of Jupiter days in the R > 0.5 RJ size range, while there are 33 are assorted in D2. In sake of a suggestive distinction, hot Jupiters in the 0.79–2.88 day range. D1 may be referred as sub-Jupiters though cluster mem- Because these planets have similar radius and only their bership slightly depend on density, too. For example, a density differs, we conclude that the density is a major planet with 0.6 Jupiter mass will be D2 if its density is parameter in relation to the period censor. around that of Jupiter and will be D1 if the density is Kepler 9b and c (Holman et al. 2010) are two impor- significantly lower. tant outliers with orbital periods of 19.2 and 38.9 days. 3. RESULTS However, these planets exhibit prominent variation of the period together with timing variations as sig- The defined clusters (panel B of Fig. 1) are well sep- natures of gravitational interaction of two planets near arated in the period–radius and period–mass parameter the 2:1 orbital resonance (Holman et al. 2010). Because planes (panels C and D). D2 cluster members cover a of this known instability, designated them with diamond period range of more than 2 orders of magnitude, begin- symbols (green on-line). ning from 0.7 days. The radius of D2 members are in- In the lower two panels of Fig. 1, a period desert of dicatively 1–2 times that of Jupiter, slightly decreasing D1 exoplanets is apparent, outlined by planets CoRoT- with orbital period (panel C of Fig. 2, solid dots). The 7b, GJ 1214 b, GJ 436 b, and HD149026 b. This means dependence of radius on period is due to the sensitivity that no sub-Jupiters have orbital period less than 2.5 of planet atmospheres to stellar irradiation (Fortney et days, except the super Earths. In the followings we es- al. 2007). timate the probability of a low-period desert in the D1 Transiters in D cluster exhibit a narrow period distri- 1 sample to occur by chance. There are 2 of 31 (6.5%) D1 bution: 85% of them lie in the 2.5–5 days range. The Ashort-periodcensorofsub-Jupitermassexoplanets 3

20.00 dius of D1 exoplanets, and a very slight anticorrelation 10.00 exists for hot Jupiters.

5.00 4. DISCUSSION

) 2.00 In contradiction with the current models of planet for- J 1.00 mation nearby a star (e.g. Broeg et al. 2009), we found that sub-Jupiter exoplanets (more exactly: the D clus- 0.50 1 ter members in the mass-density parameter space) ex- hibit a desert for Porb < 2.5 day periods. The observed M sin(i) (M 0.20 sub−Jupiter distribution is inconsistent with models assuming that 0.10 desert most planets are born near or beyond the snow-line and 0.05 then migrate inwards (Ida & Lin, 2008, Mordasini et al. 0.02 2009). These models lead to a super-Earth desert pre- dicting a paucity of planets in the mass range of 1–30 MEarth and orbiting inside 1 AU. Instead, our analy- 1 2 5 10 20 50 100 sis showed that there are many sub-Jupiters between 3– 5 day orbital period, which confirms the conclusion of period (d) Howard et al. (2010), telling that the current population Fig. 2.— The period–minimum mass diagram of the currently synthesis models are inadequate to explain the distribu- known exoplanets. Large (red) dots: transiters; small (grey) dots: tion of low-mass planets. non-transiting planets. The axis ranges fit the panel D of Fig. 1. Discussing possible modifications of planet formation models lies out the scope of this work, here we suggest exoplanets with a period less than 2.5 days. The upper some possible hypotheses to account for. boundary of the period range of D1 exoplanets is 7 days. We compare the period distribution of D1 exoplanets to 1) Hot Neptunes may evaporate rapidly in the close hot Jupiters which have period less than 2.5 days. There vicinity of the star. Highly exposed planets with less are 64 transiting hot Jupiters within this period range, potential energy evaporate more rapidly (Lecavelier des and 24 of them (38%) have a period less than 2.5 days. Etangs, 2007) which can be a candidate explanation for The two-sided Fisher’s exact test (Fisher 1925, Dou- the period censor. An argument for this procedure is the glas 1976) is a statistical test used to determine if there dependence of D1–D2 clustering on the density: planets are nonrandom associations between two categorical vari- with loose atmospheres are classified as D1 in the mass ables. Testing the above contingencies, the asymmet- range of 0.5–1 MJ . Indeed, these are the planets which ric distribution is confirmed at the 99% confidence level, exhibit the period censor. which is an evidence for the presence of a low-period However, the presence of short-period super-Earths desert in the data. The period censor does not affect raises questions in regards of the evaporation framework. large density hot Jupiters which is evidently seen at the The internal energy of their atmosphere, if there is any, large-radius end of the D1 distribution, where it overlaps is evidently low and they should evaporate more rapidly with D2s. The censor may be density selective, and this than Neptunes. In the contrary, the hot super-Earth GJ would be the primary cause of the “hole” in the period– 1214 is considered to have a thick atmosphere (Rogers radius distribution. and Seager, 2010). A possible explanation could be that The period–mass diagram can be completed with non- the incident UV flux is low around the host M dwarf star transiting exoplanets. In this case the minimum mass, and the atmosphere can survive. M sin i is known, and mass information is ambiguous to 2) As sufficient explanation for the low period desert, some extent. This is not a serious problem because the one could assume that hot Neptunes spiral in or migrate sub-Jupiter desert has an extension of 1.5 orders of mag- outwards in a short time-scale, while hot Jupiters do nitude in mass, and the hole in the period–mass distribu- not. An argument against the selective in-spiraling of tion will remain recognizable. In Fig. 2 we plot minimum hot Neptunes is found by Armitage (2007), concluding mass versus period, using different symbols for transiters that the mass function is not affected significantly by and non-transiting planets. Because of the strategy of migration. Since many hot Jupiters with orbital periods radial velocity surveys, the period distribution of non- of 0.7–2.5 days survived type II/III migration, it may transiting planets is Nyquist-limited at around P ≈ 2 be difficult to explain why hot Neptunes did not. Tidal day frequency, and there they exhibit not much over- disruption cannot explain the censor either, because hot lap with the sub-Jupiter desert. However, there are 9 super-Earths with 1 day orbital periods are still stable non-transiting planets with orbital periods shorter than against tidal disruption (Schlaufman et al. 2010). Hot 3 days, falling around the long-period edge of the desert, Neptunes can migrate outwards (Martin et al. 2007), but none coinciding with the desert itself. The lack of which process could also have evacuated the sub-Jupiter sub-Jupiters with semi-major axes less than 0.03 AU, or desert. However, outward migration requires a massive at least an anticorrelation between mass and semi-major inner planet (Martin et al. 2007) which lacks in the case axis was suggested by previous authors (e.g. Winn et al. of the known hot Neptunes. 2010). It has to be noted that the “hole” is more appar- 3) Based on their completely different distributions in ent in the period-radius distribution that we plot in this the period–mass diagrams, one could assume that D1 paper. Moreover, we concluded that there are important and D2 planets differ in the amount and strength of sub-structures in the distribution: nearly zero or slightly planet-planet perturbation. However, this idea is gen- positive correlation exists between the period and the ra- erally challenged by the distribution of eccentricities and 4 Szab´oand Kiss stellar obliquity. Both D1 and D2 cluster exoplanets it is about 0.03 AU for a disk having the same surface share similar eccentricity properties, probably reflecting density profile as the minimum mass solar nebula. This similar perturbation history. To check this, we applied scenario correctly predicts the 2–2.5 day period censor a Kolmogorov-Smirnov test to the eccentricities of D1 of sub-Jupiters migrating in a tenuous disk environment. and D2 members, resulting in a p =0.55 value, suggest- However, this scenario cannot explain the bottom edge ing that the eccentricities are very similarly distributed. of the sub-Jupiter desert, i.e. the presence of short- Stellar obliquities follow a similar distribution in D1 and period hot super-Earths – which should also have been D2, too. There are nine systems with large stellar obliq- trapped at the disk cavity. To resolve the contradiction uity known among D2 exoplanets and two are known with observations, an appropriate modification is necces- in the D1 cluster. Confirmed by a Fischer’s Exact Test, sary to explain low-mass (M <0.02 MJup) exoplanets on there is no significant difference in the occurrence of large P < 2.5 day orbits. obliquity. 4) The observed long-period edge of the sub-Jupiter desert fits the type I migration model predictions of Mas- set et al. (2006) with disk torques accounted. Near the ACKNOWLEDGMENTS disk cavity, a density radial jump forms in the proto- This project has been supported by the Hungarian planetary nebula. In the theory of Masset et al. (2006), OTKA Grants K76816, K83790 and MB08C 81013, the low-mass objects reaching the disk cavity will be trapped “Lend¨ulet” Program of the Hungarian Academy of Sci- and halt migrating. The radius of the jump highly de- ences. GyMSz was supported by the “E¨otv¨os” Fellowship pends on the structure and the density of the disk, and of the Hungarian Republic.

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APPENDIX CLUSTERING WITH MAXIMAL MAHALANOBIS DISTANCE

The Mahalanobis distance of a generic vector x and the µ1 barycenter of a given distribution, D1, is calculated with accounting for the coordinate correlations of D1:

T −1 dM (x, D1)= q(x − µ1) SD1 (x − µ1), (A1) where SD1 is the covariance matrix of D1, and acts as the metric tensor in this definition. We define the Mahalanobis distance of D1 and D2 clusters as the sum of Mahalanobis distances of all points in D1 from D2, plus that of all points is D2 from D1: d (D ,D )= d (x ,D )+ d (x ,D ). (A2) M 1 2 X M 1 2 X M 2 1 ∀x1∈D1 ∀x2∈D2 The discrimination curve was defined in the MD space, allowing for a curvature as

c3 log(ρ)= c1 log(M − c2) , (A3) where c1,2,3 are free parameters to be fitted, ρ is the average density and M is the mass of exoplanets. In fact, maximizing dM (D1,D2) does not lead to the desired result because it converges to one large cluster and another single outlier. The quantity to be optimized for is the increment of the Mahalanobis distance due to the clustering, i.e.

dM (D ,D ) − dM (F , F ) , (A4) 1 2 1 2 where F1 and F2 are disjunct clusters randomly selected from the whole sample by elements, and they have the same amount of elements as D1 and D2. Since there are numerical fluctuations in dM (F1, F2) due to the stochastical selection, Mahalanobis distances of many random clusterings must be calculated and averaged (which is represented Ashort-periodcensorofsub-Jupitermassexoplanets 5 by the hi symbols, here standing for the expectation value). Via altering c1,2,3, the D1–D2 clustering varies and in such way the discrimination in the MD space can be optimized for the maximal Mahanalobis distance in the PR space. In our calculus, initial parameters were c1,2,3 =0.13, 0.3, 0.85, clustering 33 objects to D1. Mahalanobis distance was minimized with a random walk algorithm, altering the initial parameters by a factor randomly distributed normally with 1 expectation value and 1.5% FWHM. When the clustering converged, in total 27 exoplanets remained in the D1 cluster.