HAT-P-65b and HAT-P-66b: Two Transiting Inflated Hot Jupiters and Observational Evidence for the Re-Inflation of Close-In Giant Planets
Joel D. Hartman, Gáspár Á. Bakos, Waqas Bhatti, Kaloyan Penev, Allyson Bieryla, David W. Latham, Géza Kovács, Guillermo Torres, Zoltan Csubry, Miguel de Val-Borro, Lars Buchhave, Tamás Kovács, Samuel Quinn, Andrew W. Howard, Howard Isaacson, Benjamin J. Fulton, Mark E. Everett, Gilbert A. Esquerdo, Bence Béky, Tamás Szklenar, Emilio Falco, Alexandre Santerne, Isabelle Boisse, Guillaume Hébrard, Adam Burrows, Jozsef Lázár, István Papp, Pál Sári
aa r X i v : . [ a s t r o - ph . E P ] S e p Draft version August 3, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
HAT-P-65b AND HAT-P-66b: TWO TRANSITING INFLATED HOT JUPITERS AND OBSERVATIONALEVIDENCE FOR THE RE-INFLATION OF CLOSE-IN GIANT PLANETS † J. D. Hartman , G. ´A. Bakos , W. Bhatti , K. Penev , A. Bieryla , D. W. Latham , G. Kov´acs , G. Torres ,Z. Csubry , M. de Val-Borro , L. Buchhave , T. Kov´acs , S. Quinn , A. W. Howard , H. Isaacson ,B. J. Fulton , M. E. Everett , G. Esquerdo , B. B´eky , T. Szklenar , E. Falco , A. Santerne , I. Boisse ,G. H´ebrard , A. Burrows , J. L´az´ar , I. Papp , P. S´ari Draft version August 3, 2018
ABSTRACTWe present the discovery of the transiting exoplanets HAT-P-65b and HAT-P-66b, with orbitalperiods of 2 . . . ± . M J and 0 . ± . M J , and inflated radiiof 1 . ± . R J and 1 . +0 . − . R J , respectively. They orbit moderately bright ( V = 13 . ± . V = 12 . ± . . ± . M ⊙ and 1 . +0 . − . M ⊙ . The stars are at themain sequence turnoff. While it is well known that the radii of close-in giant planets are correlatedwith their equilibrium temperatures, whether or not the radii of planets increase in time as theirhosts evolve and become more luminous is an open question. Looking at the broader sample of well-characterized close-in transiting giant planets, we find that there is a statistically significant correlationbetween planetary radii and the fractional ages of their host stars, with a false alarm probability ofonly 0.0041%. We find that the correlation between the radii of planets and the fractional ages oftheir hosts is fully explained by the known correlation between planetary radii and their present dayequilibrium temperatures, however if the zero-age main sequence equilibrium temperature is used inplace of the present day equilibrium temperature then a correlation with age must also be includedto explain the planetary radii. This suggests that, after contracting during the pre-main-sequence,close-in giant planets are re-inflated over time due to the increasing level of irradiation received fromtheir host stars. Prior theoretical work indicates that such a dynamic response to irradiation requiresa significant fraction of the incident energy to be deposited deep within the planetary interiors. Subject headings: planetary systems — stars: individual ( HAT-P-65, GSC 1111-00383, HAT-P-66,GSC 3814-00307 ) techniques: spectroscopic, photometric Department of Astrophysical Sciences, PrincetonUniversity, Princeton, NJ 08544, USA; email: [email protected] ∗ Alfred P. Sloan Research Fellow ∗∗ Packard Fellow Harvard-Smithsonian Center for Astrophysics, Cambridge,MA 02138, USA Konkoly Observatory of the Hungarian Academy of Sci-ences, Budapest, Hungary Centre for Star and Planet Formation, Natural HistoryMuseum of Denmark, University of Copenhagen, DK-1350Copenhagen, Denmark Department of Physics and Astronomy, Georgia StateUniversity, Atlanta, GA 30303, USA Institute for Astronomy, University of Hawaii, Honolulu, HI96822, USA Department of Astronomy, University of California, Berke-ley, CA, USA National Optical Astronomy Observatory, Tucson, AZ, USA Google Hungarian Astronomical Association, Budapest, Hungary Aix Marseille Universit´e, CNRS, LAM (Laboratoired’Astrophysique de Marseille) UMR 7326, F-13388, Marseille,France Instituto de Astrofisica e Ciˆencias do Espa¸co, Universidadedo Porto, CAUP, Rua das Estrelas, PT4150-762 Porto, Portugal Institut d’Astrophysique de Paris, UMR7095 CNRS,Universit´e Pierre & Marie Curie, 98bis boulevard Arago, 75014Paris, France † Based on observations obtained with the Hungarian-madeAutomated Telescope Network. Based on observations obtainedat the W. M. Keck Observatory, which is operated by the Uni-versity of California and the California Institute of Technology.Keck time has been granted by NOAO (A289Hr, A245Hr) andNASA (N029Hr, N154Hr, N130Hr, N133Hr, N169Hr, N186Hr). Based on observations obtained with the Tillinghast Reflector1.5 m telescope and the 1.2 m telescope, both operated by theSmithsonian Astrophysical Observatory at the Fred LawrenceWhipple Observatory in AZ. Based on observations madewith the Nordic Optical Telescope, operated on the island ofLa Palma jointly by Denmark, Finland, Norway, Sweden, inthe Spanish Observatorio del Roque de los Muchachos of theIntituto de Astrof´ısica de Canarias. Based on observationsmade with the SOPHIE spectrograph on the 1.93 m telescopeat Observatoire de Haute-Provence (OHP, CNRS/AMU),France (programs 15A.PNP.HEBR and 15B.PNP.HEBR). Datapresented herein were obtained at the WIYN Observatoryfrom telescope time allocated to NN-EXPLORE through thescientific partnership of the National Aeronautics and SpaceAdministration, the National Science Foundation, and theNational Optical Astronomy Observatory. This work wassupported by a NASA WIYN PI Data Award, administered bythe NASA Exoplanet Science Institute.
Hartman et al. INTRODUCTION
The first transiting exoplanet (TEP) discovered,HD 209458b (Henry et al. 2000; Charbonneau et al.2000), surprised the community in having a ra-dius much larger than expected based on theoreticalplanetary structure models (e.g., Burrows et al. 2000;Bodenheimer et al. 2001). Since then many more in-flated transiting planets have been discovered, thelargest being WASP-79b with R P = 2 . ± . R J (Smalley et al. 2012). It has also become apparentthat the degree of planet inflation is closely tied to aplanet’s proximity to its host star (e.g., Fortney et al.2007; Enoch et al. 2011b; Kov´acs et al. 2010; B´eky et al.2011; Enoch et al. 2012). This is expected on theoreti-cal grounds, as some additional energy, beyond the ini-tial heat from formation, must be responsible for mak-ing the planet so large, and in principle there is morethan enough energy available from stellar irradiation ortidal forces to inflate close-in planets at a < . K2 ) is a possible example of a re-inflated planetaround a giant star, with the planet having a largerthan usual radius of 1 . ± . R J given its orbital pe-riod of 8 . R p = 0 . ± . R J ) despite beingfound on a very short period orbit around a sub-giant star. This planet, however, is in the Super-Neptune massrange ( M p = 0 . ± . M J ) and may not have a gas-dominated composition.Here we present the discovery of two transiting in-flated planets by the Hungarian-made Automated Tele-scope Network (HATNet; Bakos et al. 2004). As wewill show, the planets have radii of 1 . ± . R J and1 . +0 . − . R J , and are around a pair of stars that are leav-ing the main sequence. HATNet, together with its south-ern counterpart HATSouth (Bakos et al. 2013), has nowdiscovered 17 highly inflated planets with R ≥ . R J17 .Adding those found by WASP (Pollacco et al. 2006),
Ke-pler (Borucki et al. 2010), TrES (e.g., Mandushev et al.2007) and KELT (e.g., Siverd et al. 2012), a total of 45well-characterized highly inflated planets are now known,allowing us to explore some of their statistical prop-erties. In this paper we find that inflated planets aremore commonly found around moderately evolved starsthat are more than 50% of the way through their mainsequence lifetimes. Smaller radius close-in giant plan-ets, by contrast, are generally found around less evolvedstars. Taken at face value, this suggests that planets arere-inflated as they age, and indicates that energy mustbe transferred deep into the planetary interiors (e.g.,Liu et al. 2008).Of course, observational selection effects or systematicerrors in the determination of stellar and planetary prop-erties could potentially be responsible for the correlationas well. We therefore consider a variety of potentiallyimportant effects, such as the effect of stellar evolutionon the detectability of transits and our ability to confirmplanets through follow-up observations, and systematicerrors in the orbital eccentricity, transit parameters, stel-lar atmospheric parameters, or in the comparison to stel-lar evolution models. We conclude that the net selectioneffect would, if anything, tend to favor the discovery oflarge planets around less evolved stars, while potentialsystematic errors are too small to explain the correla-tion. We also show that the correlation remains signif-icant even after accounting for non-trivial truncationsplaced on the data as a result of the observational selec-tion biases. We are therefore confident in the robustnessof this result.The organization of the paper is as follows. In Section 2we describe the photometric and spectroscopic observa-tions made to discover and characterize HAT-P-65b andHAT-P-66b. In Section 3 we present the analysis carriedout to determine the stellar and planetary parametersand to rule out blended stellar eclipsing binary false pos-itive scenarios. In Section 4 we place these planets intocontext, and find that large radius planets are more com-monly found around moderately evolved, brighter stars.We provide a brief summary of the results in Section 5. OBSERVATIONS
Photometric detection
Both HAT-P-65 (R . A . =21 h m . . =+11 ◦ ′ . ′′ (J2000), V = 13 . ± .
029 mag,spectral type G2) and HAT-P-66 (R . A . =10 h m . . =+53 ◦ ′ . ′′ (J2000), V = 12 . ± .
052 mag, This radius is chosen simply for illustrative purposes, and isnot meant to imply that planets with radii above this value arephysically distinct from those with radii below this value.
AT-P-65b and HAT-P-66b 3spectral type G0) were selected as candidate transitingplanet systems based on Sloan r -band photometrictime series observations carried out with the HATNettelescope network (Bakos et al. 2004).HATNet consists of six 11 cm aperture telephoto lenses,each coupled to an APOGEE front-side-illuminated CCDcamera, and each placed on a fully-automated telescopemount. Four of the instruments are located at FredLawrence Whipple Observatory (FLWO) in Arizona,USA, while two are located on the roof of the Submillime-ter Array hangar building at Mauna Kea Observatory(MKO) on the island of Hawaii, USA. Each instrumentobserves a 10 . ◦ × . ◦ field of view, and continuouslymonitors one or two fields each night, where a field cor-responds to one of 838 fixed pointings used to cover thefull 4 π celestial sphere. A typical field is observed for ap-proximately three months using one or two instruments(e.g., field G342 containing HAT-P-65), while a handfulof fields have been observed extensively using all six in-struments in the network and with observations repeatedin multiple seasons (e.g., field G101 containing HAT-P-66). The former observing strategy maximizes the skycoverage of the survey, while maintaining nearly com-plete sensitivity to transiting giant planets with orbitalperiods of a few days. The latter strategy substantiallyincreases the sensitivity to Neptune and Super-Earth-size planets, as well as planets with periods greater than10 days, but with the trade-off of covering a smaller areaof the sky.Table 1 summarizes the properties of the HATNetobservations collected for each system, including whichHAT instruments were used, the date ranges over whicheach target was observed, the median cadence of the ob-servations, and the per-point photometric precision aftertrend filtering.We reduce the HATNet observations to light curves, forall stars in a field with r < .
5, following Bakos et al.(2004). We used aperture photometry routines basedon the FITSH software package (P´al 2012), and fil-tered systematic trends from the light curves follow-ing Kov´acs et al. (2005) (i.e., TFA) and Bakos et al.(2010) (i.e., EPD). Transits were identified in the fil-tered light curves using the Box-Least Squares method(BLS; Kov´acs et al. 2002). After identifying the transitswe then re-applied TFA while preserving the shape of thetransit signal as described in Kov´acs et al. (2005). Thisprocedure is referred to as signal-reconstruction TFA.The final trend-filtered, and signal-reconstructed lightcurves are shown phase-folded in Figure 1, while the mea-surements are available in Table 3.We searched the residual HATNet light curves of bothobjects for additional periodic signals using BLS. Nei-ther target shows evidence for additional transits withBLS, however this conclusion depends on the set of tem-plate light curves used in applying signal-reconstructionTFA to remove systematics. For HAT-P-65 we find thatwith an alternative set of templates the residuals displaya marginally significant transit signal with a period of2 .
573 days, which is only slightly different from the maintransit period of 2 . ± . .
25 when phased at the primary transitperiod. Since the detection of this additional signal de-pends on the template set used, and since any planet orbiting with a period so close to (but not equal to) thatof the hot Jupiter HAT-P-65b would almost certainly beunstable, we suspect that the P = 2 .
573 day transit sig-nal is not of physical origin.We also searched the residual light curves for peri-odic signals using the Generalized Lomb-Scargle method(GLS; Zechmeister & K¨urster 2009). For HAT-P-65 nostatistically significant signal is detected in the GLS pe-riodogram either. The highest peak in the periodogramis at a period of 0 .
035 d and has a semi-amplitude of1.2 mmag (using a Markov-Chain Monte Carlo procedureto fit a sinusoid with a variable period yields a 95% con-fidence upper limit of 1.7 mmag on the semi-amplitude).For HAT-P-66, for our default light curve (i.e., the oneincluded in Table 3), we do see significant peaks in theperiodogram at periods of P = 83 . . − , and semi-amplitudes of ∼ .
02 mag. Giventhe effective sampling rate of the observations, the twosignals are aliases of each other. Based on an inspec-tion of the light curve, we conclude that this detectedvariability is likely due to additional systematic errors inthe photometry which were not effectively removed byour filtering procedures, and that the signal is not astro-physical in nature. Indeed if we use an alternative TFAtemplate set in filtering the HAT-P-66 light curve, we de-tect no significant signal in the GLS spectrum, and placean upper limit on the amplitude of any periodic signal of1 mmag.
Spectroscopic Observations
Spectroscopic observations of both HAT-P-65 andHAT-P-66 were carried out using the Tillinghast Re-flector Echelle Spectrograph (TRES; F˝uresz 2008) onthe 1.5 m Tillinghast Reflector at FLWO, and HIRES(Vogt et al. 1994) on the Keck-I 10 m at MKO. For HAT-P-65 we also obtained observations using the FIbre-fed´Echelle Spectrograph (FIES) on the 2.5 m Nordic OpticalTelescope (NOT; Djupvik & Andersen 2010) at the Ob-servatorio del Roque de los Muchachos on the Spanishisland of La Palma. For HAT-P-66 spectroscopic obser-vations were also collected using the SOPHIE spectro-graph on the 1.93 m telescope at the Observatoire deHaute-Provence (OHP; Bouchy et al. 2009) in France.The spectroscopic observations collected for each systemare summarized in Table 2. Phase-folded high-precisionRV and spectral line bisector span (BS) measurementsare plotted in Figure 2 together with our best-fit modelsfor the RV orbital wobble of the host stars (Section 3.3).The individual RV and BS measurements are made avail-able in Table 7 at the end of the paper.The TRES observations were reduced to spectra andcross-correlated against synthetic stellar templates tomeasure the RVs and to estimate T eff ⋆ , log g ⋆ , and v sin i . Here we followed the procedure of Buchhave et al.(2010), initially making use of a single order containingthe gravity and temperature-sensitive Mg b lines. Basedon these “reconnaissance” observations we quickly ruledout common false positive scenarios, such as transitingM dwarf stars, or blends between giant stars and pairsof eclipsing dwarf stars (e.g., Latham et al. 2009). ForHAT-P-65 we only obtained a single TRES observationwhich, in combination with the FIES observations dis- Hartman et al. -0.04-0.02 0 0.02 0.04 -0.4 -0.2 0 0.2 0.4 ∆ m ag Orbital phase
HAT-P-65 -0.04-0.02 0 0.02 0.04-0.15 -0.1 -0.05 0 0.05 0.1 0.15 ∆ m ag Orbital phase -0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 -0.4 -0.2 0 0.2 0.4 ∆ m ag Orbital phase
HAT-P-66 -0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04-0.1 -0.05 0 0.05 0.1 ∆ m ag Orbital phase
Figure 1.
Phase-folded unbinned HATNet light curves for HAT-P-65 (left) and HAT-P-66 (right). In each case we show two panels.The top panel shows the full light curve, while the bottom panel shows the light curve zoomed-in on the transit. The solid lines show themodel fits to the light curves. The dark filled circles in the bottom panels show the light curves binned in phase with a bin size of 0.002.
Table 1
Summary of photometric observationsInstrument/Field a Date(s) b Filter Precision c (sec) (mmag) HAT-P-65
HAT-6/G342 2009 Sep–2009 Dec 2738 231 r r i i i i z i i HAT-P-66
HAT-10/G101 2011 Feb–2012 Mar 2029 212 r r r r r r i z i a For HATNet data we list the HATNet unit and field name from which the observations are taken. HAT-5, -6, -7 and -10 are located at Fred Lawrence Whipple Observatory in Arizona. HAT-8 and -9 are locatedon the roof of the Smithsonian Astrophysical Observatory Submillimeter Array hangar building at MaunaKea Observatory in Hawaii. Each field corresponds to one of 838 fixed pointings used to cover the full4 π celestial sphere. All data from a given HATNet field are reduced together, while detrending throughExternal Parameter Decorrelation (EPD) is done independently for each unique unit+field combination. b The median time between consecutive images rounded to the nearest second. Due to factors such asweather, the day–night cycle, guiding and focus corrections the cadence is only approximately uniformover short timescales. c The RMS of the residuals from the best-fit model. cussed below, rules out these false positive scenarios. ForHAT-P-66 the initial TRES RVs showed evidence of anorbital variation consistent with a planetary-mass com-panion producing the transits detected by HATNet, sowe continued collecting higher S/N observations of thissystem with TRES. High precision RVs and BSs weremeasured from these spectra via a multi-order analysis(e.g., Bieryla et al. 2014).The FIES spectra of HAT-P-65 were reduced in a sim-ilar manner to the TRES data (Buchhave et al. 2010),and were used for reconnaissance. Two exposures wereobtained using the medium-resolution fiber, while the third was obtained with the high-resolution fiber. One ofthe two medium resolution observations had sufficientlyhigh S/N to be used for characterizing the stellar atmo-spheric parameters (Section 3.1).The HIRES observations of HAT-P-65 and HAT-P-66 were reduced to relative RVs in the Solar Systembarycenter frame following the method of Butler et al.(1996), and to BSs following Torres et al. (2007). Wealso measured Ca II HK chromospheric emission in-dices (the so-called S and log R ′ HK indices) followingIsaacson & Fischer (2010) and Noyes et al. (1984). TheI -free template observations of each system were alsoAT-P-65b and HAT-P-66b 5used to determine the adopted stellar atmospheric pa-rameters (Section 3.1).The SOPHIE spectra of HAT-P-66 were collected asdescribed in Boisse et al. (2013) and reduced followingSanterne et al. (2014). One of the observations was ob-tained during a planetary transit and is excluded fromthe analysis. Photometric follow-up observations
In order to better determine the physical parametersof each TEP system, and to aid in excluding blendedstellar eclipsing binary false positive scenarios, we con-ducted follow-up photometric time-series observations ofeach object using KeplerCam on the 1.2 m telescope atFLWO. These observations are summarized in Table 1,where we list the dates of the observed transit events, thenumber of images collected for each event, the cadenceof the observations, the filters used, and the per-pointphotometric precision achieved after trend-filtering. Theimages were reduced to light curves via aperture photom-etry based on the FITSH package (following Bakos et al.(2010)), and filtered for trends, which were fit to thelight curves simultaneously with the transit model (Sec-tion 3.3). The resulting trend filtered light curves areplotted together with the best-fit transit model in Fig-ure 3 for HAT-P-65 and in Figure 4 for HAT-P-66. Thedata are made available in Table 3.
Imaging Constraints on Resolved Neighbors
In order to detect possible neighboring stars whichmay be diluting the transit signals we obtained J and K S -band snapshot images of both targets using theWIYN High-Resolution Infrared Camera (WHIRC) onthe WIYN 3.5 m telescope at Kitt Peak National Ob-servatory (KPNO) in AZ. Observations were obtainedon the nights of 2016 April 24, 27 and 28, with seeingvarying between ∼ . ′′ ∼ ′′ . Images were col-lected at different nod positions. These were calibrated,background-subtracted, registered and median-combinedusing the same tools that we used for reducing the Ke-plerCam images.We find that HAT-P-65 has a neighbor located 3 . ′′ J = 4 . ± .
01 mag and ∆ K = 4 . ± .
03 mag relative to HAT-P-65 (Figure 5). The neighbor is too faint and distantto be responsible for the transits detected in either theHATNet or KeplerCam observations. The neighbor hasa J − K color that is the same as HAT-P-65 to withinthe uncertainties, and is thus a background star with aneffective temperature that is similar to that of HAT-P-65,and not a physical companion. No neighbor is detectedwithin 10 ′′ of HAT-P-66.Figure 6 shows the J and K -band magnitude contrastcurves for HAT-P-65 and HAT-P-66 based on these ob-servations. These curves are calculated using the methodand software described by Espinoza et al. (2016). Thebands shown in these images represent the variation inthe contrast limits depending on the position angle of theputative neighbor. ANALYSIS
Properties of the parent star
High-precision atmospheric parameters, including theeffective surface temperature T eff ⋆ , the surface gravitylog g ⋆ , the metallicity [Fe / H], and the projected rota-tional velocity v sin i , were determined by applying theStellar Parameter Classification (SPC; Buchhave et al.2012) procedure to our high resolution spectra. ForHAT-P-65 this analysis was performed on the highestS/N FIES spectrum and on our Keck-I/HIRES I -freetemplate spectrum (we adopt the weighted average ofeach parameter determined from the two spectra). ForHAT-P-66 this analysis was performed on our Keck-I/HIRES I -free template spectrum. We assume a min-imum uncertainty of 50 K on T eff ⋆ , 0.10 dex on log g ⋆ ,0.08 dex on [Fe / H], and 0.5 km s − on v sin i , which re-flects the systematic uncertainty in the method, and isbased on applying the SPC analysis to observations ofspectroscopic standard stars.Following Sozzetti et al. (2007) we combine the T eff ⋆ and [Fe / H] values measured from the spectra with thestellar densities ( ρ ⋆ ) determined from the light curves(based on the analysis in Section 3.3) to determine thephysical parameters of the host stars (i.e., their masses,radii, surface gravities, ages, luminosities, and broad-band absolute magnitudes) via interpolation within theYonsei-Yale theoretical stellar isochrones (YY; Yi et al.2001). Figure 7 compares the model isochrones to themeasured T eff ⋆ and ρ ⋆ values for each system.For HAT-P-65 the log g ⋆ value determined from thisanalysis differed by 0.19 dex ( ∼ . σ ) from the initialvalue determined through SPC. A difference of this mag-nitude is typical and reflects the difficulty of accuratelymeasuring all four atmospheric parameters simultane-ously via cross-correlation with synthetic templates (e.g.,Torres et al. 2012). We therefore carried out a secondSPC analysis of HAT-P-65 with log g ⋆ fixed based on thisanalysis, and then repeated the light curve analysis andstellar parameter determination, finding no appreciablechange in log g ⋆ . For HAT-P-66 the log g ⋆ value deter-mined from the YY isochrones differed by only 0 .
007 dexfrom the initial spectroscopically determined value, so wedid not carry out a second SPC iteration in this case.The adopted stellar parameters for HAT-P-65 andHAT-P-66 are listed in Table 4. We also collect in thistable a variety of photometric and kinematic propertiesfor each system from catalogs. Distances are determinedusing the listed photometry and assuming a R V = 3 . . ± . M ⊙ and 1 . +0 . − . M ⊙ for HAT-P-65 and HAT-P-66, respectively, and with respective radii of 1 . ± . R ⊙ and 1 . +0 . − . R ⊙ . The stars are moderatelyevolved, with ages of 5 . ± .
61 Gyr and 4 . +0 . − . Gyr(these are 84 ±
10% and 83 +9 − % of each star’s full lifetime,respectively). As we point out in Section 4, there appearsto be a general trend among the host stars of highly in-flated planets in which the largest planets are preferen-tially found around moderately evolved stars. HAT-P-65and HAT-P-66 are in line with this trend. Excluding blend scenarios
In order to exclude blend scenarios we carried outan analysis following Hartman et al. (2012). Here weattempt to model the available photometric data (in- Hartman et al.
Table 2
Summary of spectroscopy observationsInstrument UT Date(s) a γ RVb
RV Precision c ( λ /∆ λ )/1000 (km s − ) (m s − ) HAT-P-65
NOT 2.5 m/FIES 2010 Aug 21–22 2 46 24–28 − .
131 100FLWO 1.5 m/TRES 2010 Oct 27 1 44 16.5 − .
768 100NOT 2.5 m/FIES 2011 Oct 8 1 67 15 − .
799 1000Keck-I/HIRES 2010 Dec 14 1 55 80 · · · · · ·
Keck-I/HIRES+I · · · HAT-P-66
FLWO 1.5 m/TRES 2014 Nov–2015 Jun 10 44 17–22 7 .
973 43OHP 1.93 m/SOPHIE 2015 Mar–2016 Jan 14 39 12–33 7 .
226 20Keck-I/HIRES+I · · · · · · · · · a S/N per resolution element near 5180 ˚A. b For high-precision RV observations included in the orbit determination this is the zero-point RV from the best-fit orbit.For other instruments it is the mean value. We do not provide this information for Keck-I/HIRES for which only relativevelocities are measured. c For high-precision RV observations included in the orbit determination this is the scatter in the RV residuals from thebest-fit orbit (which may include astrophysical jitter), for other instruments this is either an estimate of the precision (notincluding jitter), or the measured standard deviation. We do not provide this quantity for the I -free templates obtainedwith Keck-I/HIRES. Table 3
Light curve data for HAT-P-65 and HAT-P-66.Object a BJD b Mag c σ Mag
Mag(orig) d Filter Instrument(2,400,000+)HAT-P-65 55128 . − . . · · · r HATNetHAT-P-65 55115 . − . . · · · r HATNetHAT-P-65 55120 . − . . · · · r HATNetHAT-P-65 55115 . − . . · · · r HATNetHAT-P-65 55094 . − . . · · · r HATNetHAT-P-65 55128 . − . . · · · r HATNetHAT-P-65 55154 . − . . · · · r HATNetHAT-P-65 55102 . − . . · · · r HATNetHAT-P-65 55128 . − . . · · · r HATNetHAT-P-65 55115 . . . · · · r HATNet
Note . — This table is available in a machine-readable form in the online journal. A portionis shown here for guidance regarding its form and content. a Either HAT-P-65 or HAT-P-66. b Barycentric Julian Date is computed directly from the UTC time without correction for leapseconds. c The out-of-transit level has been subtracted. For observations made with the HATNet in-struments (identified by “HATNet” in the “Instrument” column) these magnitudes have beencorrected for trends using the EPD and TFA procedures applied in signal-reconstruction mode.For observations made with follow-up instruments (anything other than “HATNet” in the “Instru-ment” column), the magnitudes have been corrected for a quadratic trend in time, for variationscorrelated with three PSF shape parameters, and with a linear basis of template light curvesrepresenting other systematic trends, which are fit simultaneously with the transit. d Raw magnitude values without correction for the quadratic trend in time, or for trends correlatedwith the shape of the PSF. These are only reported for the follow-up observations. cluding light curves and catalog broad-band photomet-ric measurements) for each object as a blend between aneclipsing binary star system and a third star along theline of sight (either a physical association, or a chancealignment). The physical properties of the stars areconstrained using the Padova isochrones (Girardi et al.2002), while we also require that the brightest of thethree stars in the blend have atmospheric parametersconsistent with those measured with SPC. We also sim-ulate composite cross-correlation functions (CCFs) anduse them to predict RVs and BSs for each blend scenario considered.Based on this analysis we rule out blended stellareclipsing binary scenarios for both HAT-P-65 and HAT-P-66. For HAT-P-65 we are able to exclude blend sce-narios, based solely on the photometry, with greater than3 . σ confidence, while for HAT-P-66 we are able to ex-clude them with greater than 3 . σ confidence. For bothobjects, the blend models which come closest to fittingthe photometric data (those which could not be rejectedwith 5 σ confidence) can additionally be rejected dueto the predicted large amplitude BS and RV variationsAT-P-65b and HAT-P-66b 7 Table 4
Stellar parameters for HAT-P-65 and HAT-P-66 a HAT-P-65 HAT-P-66
Parameter Value Value SourceAstrometric properties and cross-identifications2MASS-ID . . . . . . . 21033731+1159218 10021743+5357031GSC-ID . . . . . . . . . . GSC 1111-00383 GSC 3814-00307R.A. (J2000) . . . . . 21 h m .
44s 10 h m .
52s 2MASSDec. (J2000) . . . . . +11 ◦ ′ . ′′ +53 ◦ ′ . ′′ µ R . A . (mas yr − ) 5 . ± . − . ± . µ Dec . (mas yr − ) − . ± . − . ± . T eff ⋆ (K) . . . . . . . . . 5835 ±
51 6002 ±
50 SPC b log g ⋆ (cgs) . . . . . . . 4 . ± .
10 3 . ± .
10 SPC c [Fe / H] . . . . . . . . . . . . 0 . ± .
080 0 . ± .
080 SPC v sin i (km s − ) . . . 7 . ± .
50 7 . ± .
50 SPC v mac (km s − ) . . . . 1 . . v mic (km s − ) . . . . 2 . . γ RV (m s − ) . . . . . . − . ± .
10 7 . ± .
10 TRES d S HK . . . . . . . . . . . . . . · · · · · · HIRESlog R ′ HK . . . . . . . . . . · · · · · · HIRESPhotometric properties B (mag). . . . . . . . . . 13 . ± .
021 13 . ± .
027 APASS e V (mag). . . . . . . . . . 13 . ± .
029 12 . ± .
052 APASS e I (mag) . . . . . . . . . . 12 . ± .
10 12 . ± .
084 TASS Mark IV f g (mag) . . . . . . . . . . 13 . ± .
016 13 . ± .
021 APASS e r (mag) . . . . . . . . . . 12 . ± .
033 12 . ± .
064 APASS e i (mag) . . . . . . . . . . . 12 . ± .
097 12 . ± .
064 APASS e J (mag) . . . . . . . . . . 11 . ± .
026 12 . ± .
022 2MASS H (mag) . . . . . . . . . 11 . ± .
022 11 . ± .
022 2MASS K s (mag) . . . . . . . . 11 . ± .
025 11 . ± .
022 2MASSDerived properties M ⋆ ( M ⊙ ) . . . . . . . . 1 . ± .
050 1 . +0 . − . YY+ ρ ⋆ +SPC g R ⋆ ( R ⊙ ) . . . . . . . . . 1 . ± .
096 1 . +0 . − . YY+ ρ ⋆ +SPClog g ⋆ (cgs) . . . . . . . 3 . ± .
035 3 . ± .
045 YY+ ρ ⋆ +SPC ρ ⋆ (g cm − ) . . . . . . 0 . ± .
035 0 . ± .
040 Light curves L ⋆ ( L ⊙ ) . . . . . . . . . . 3 . ± .
40 4 . +0 . − . YY+ ρ ⋆ +SPC M V (mag). . . . . . . . 3 . ± .
13 3 . ± .
15 YY+ ρ ⋆ +SPC M K (mag,ESO) . . 1 . ± .
12 1 . ± .
14 YY+ ρ ⋆ +SPCAge (Gyr) . . . . . . . . 5 . ± .
61 4 . +0 . − . YY+ ρ ⋆ +SPC A V (mag) . . . . . . . . 0 . ± .
052 0 . ± . ρ ⋆ +SPCDistance (pc) . . . . . 841 ±
45 927 +75 − YY+ ρ ⋆ +SPC Note . — For both systems the fixed-circular-orbit model has a higher Bayesianevidence than the eccentric-orbit model. We therefore assume a fixed circular orbit ingenerating the parameters listed here. a We adopt the IAU 2015 Resolution B3 nominal values for the Solar and Jovian pa-rameters (Prˇsa et al. 2016) for all of our calculations, taking R J to be the nominal equa-torial radius of Jupiter. Where necessary we assume G = 6 . × − m kg − s − .Because Yi et al. (2001) do not specify the assumed value for G or M ⊙ , we take thestellar masses from these isochrones at face value without conversion. Any discrepancyresults in an error that is less than one percent, which is well below the observationaluncertainty. We note that the standard values assumed in prior HAT planet discoverypapers are very close to the nominal values adopted here. In all cases the conversionresults in changes to measured parameters that are indetectable at the level of precisionto which they are listed. b SPC = Stellar Parameter Classification procedure for the analysis of high-resolutionspectra (Buchhave et al. 2012), applied to the TRES spectra of HAT-P-65 and theKeck/HIRES spectra of HAT-P-66. These parameters rely primarily on SPC, but havea small dependence also on the iterative analysis incorporating the isochrone searchand global modeling of the data. c The spectroscopically determined value of log g ⋆ is from our initial SPC analysiswhere T eff ⋆ , log g ⋆ , [Fe / H] and v sin i were all varied. Systematic errors are commonwhen all four parameters are varied. The adopted values for T eff ⋆ , [Fe / H] and v sin i stem from a second iteration of SPC, where log g ⋆ is fixed to the value determinedthrough the light curve modeling and isochrone comparison. This value is listed underthe “Derived Properties” section of the table. d In addition to the uncertainty listed here, there is a ∼ . − systematic uncer-tainty in transforming the velocities to the IAU standard system. e From APASS DR6 for as listed in the UCAC 4 catalog (Zacharias et al. 2013). f Droege et al. (2006). g YY+ ρ ⋆ +SPC = Based on the YY isochrones (Yi et al. 2001), ρ ⋆ as a luminosityindicator, and the SPC results. Hartman et al. -150-100-50 0 50 100 150 R V ( m s - ) HAT-P-65
HIRES-60-40-20 0 20 40 60 80 O - C ( m s - ) -40-20 0 20 40 60 80 100 0.0 0.2 0.4 0.6 0.8 1.0 BS ( m s - ) Phase with respect to T c -150-100-50 0 50 100 150 R V ( m s - ) HAT-P-66
HIRESTRESSophie-100-50 0 50 100 150 200 O - C ( m s - ) -300-250-200-150-100-50 0 50 100 0.0 0.2 0.4 0.6 0.8 1.0 BS ( m s - ) Phase with respect to T c Figure 2.
Phase-folded high-precision RV measurements for HAT-P-65 and HAT-P-66. The instruments used are labelled in the plots.In each case we show three panels. The top panel shows the phased measurements together with our best-fit circular-orbit model (seeTable 5) for each system. Zero-phase corresponds to the time of mid-transit. The center-of-mass velocity has been subtracted. The secondpanel shows the velocity O − C residuals from the best fit. The error bars include the jitter terms listed in Table 5 added in quadrature tothe formal errors for each instrument. The third panel shows the bisector spans (BS). Note the different vertical scales of the panels. ForHAT-P-66 the crossed-out SOPHIE measurement was obtained during transit and is excluded from the analysis. ∆ ( m ag ) - A r b i t r a r y o ff s e t s Time from transit center (days)
HAT-P-65 i-bandiiizii -0.1 -0.05 0 0.05 0.1 0.15Time from transit center (days)
HAT-P-65 i-bandiiizii
Figure 3.
Left: Unbinned transit light curves for HAT-P-65. The light curves have been filtered of systematic trends, which were fitsimultaneously with the transit model. The dates of the events, filters and instruments used are indicated. Light curves following thefirst are displaced vertically for clarity. Our best fit from the global modeling described in Section 3.3 is shown by the solid lines. Right:The residuals from the best-fit model are shown in the same order as the original light curves. The error bars represent the photon andbackground shot noise, plus the readout noise.
AT-P-65b and HAT-P-66b 9 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 ∆ ( m ag ) - A r b i t r a r y o ff s e t s Time from transit center (days)
HAT-P-66 i-bandzi
Figure 4.
Similar to Figure 3, here we show unbinned transitlight curves for HAT-P-66. The residuals in this case are shownbelow in the same order as the original light curves. NE Figure 5. J -band image of HAT-P-65 from WHIRC on theWIYN 3.5 m showing the ∆ J = 4 . ± .
01 mag neighbor located3 . ′′ ′′ . which we do not observe. Global modeling of the data
In order to determine the physical parameters of theTEP systems, we carried out a global modeling of theHATNet and KeplerCam photometry, and the high-precision RV measurements following P´al et al. (2008);Bakos et al. (2010); Hartman et al. (2012). We use the Mandel & Agol (2002) transit model to fit the lightcurves, with limb darkening coefficients fixed to the val-ues tabulated by Claret (2004) for the atmospheric pa-rameters of the stars and the broad-band filters usedin the observations. For the KeplerCam follow-up lightcurves we account for instrumental variations by using aset of linear basis vectors in the fit. The vectors that weuse include the time of observations, the time squared,three parameters describing the shape of the PSF, andlight curves for the twenty brightest non-variable stars inthe field (TFA templates). For the TFA templates we usethe same linear coefficient (which is varied in the fit) forall light curves collected for a given transiting planet sys-tem through a given filter, while for the other basis vec-tors we use a different coefficient for each light curve. Forthe HATNet light curves we use a Mandel & Agol (2002)model, and apply the fit to the signal-reconstruction TFAdata (see Section 2.1). The RV curves are modeled us-ing a Keplerian orbit, where we allow the zero-point foreach instrument to vary independently in the fit, and weinclude an RV jitter term added in quadrature to theformal uncertainties. The jitter is treated as a free pa-rameter which we fit for, and is taken to be independentfor each instrument.All observations of an individual system are modeledsimultaneously using a Differential Evolution MarkovChain Monte Carlo procedure (ter Braak 2006). Wevisually inspect the Markov Chains and also apply aGeweke (1992) test to verify convergence and determinethe burn-in period. For both systems we consider twomodels: a fixed-circular-orbit model, and an eccentric-orbit model. To determine which model to use we es-timate the Bayesian evidence ratio from the MarkovChains following Weinberg et al. (2013), and find thatfor both systems the fixed-circular model has a greaterevidence, and therefore adopt the parameters that comefrom this model. The resulting parameters for both plan-etary systems are listed in Table 5. We also list the 95%confidence upper-limit on the eccentricity for each sys-tem.We find that HAT-P-65b has a mass of 0 . ± . M J , a radius of 1 . ± . R J , an equilibrium tem-perature (assuming zero albedo, and full redistributionof heat) of 1930 ±
45 K, and is consistent with a cir-cular orbit, with a 95% confidence upper limit on theeccentricity of e < . . ± . M J , a radius of1 . +0 . − . R J , an equilibrium temperature (same assump-tions) of 1896 +66 − K, and an eccentricity of e < .
090 with95% confidence. DISCUSSION
Large Radius Planets More Commonly FoundAround More Evolved Stars
With radii of 1 . ± . R J and 1 . +0 . − . R J , HAT-P-65b and HAT-P-66b are among the largest hot Jupitersknown. Both planets are found around moderatelyevolved stars approaching the end of their main sequencelifetimes. With an estimated age of 5 . ± .
61 Gyr, HAT-P-65 is 84 ±
10% of the way through its total lifespan,while HAT-P-66, with an age of 4 . +0 . − . Gyr, is 83 +9 − %of the way through its lifespan. Looking at the broadersample of TEPs that have been discovered to date, we0 Hartman et al. Table 5
Orbital and planetary parameters for HAT-P-65b and HAT-P-66b a HAT-P-65b HAT-P-66b
Parameter Value ValueLight curve parameters P (days) . . . . . . . . . . . . . . . . . . . . 2 . ± . . ± . T c (BJD) b . . . . . . . . . . . . . . . . . 2456409 . ± . . ± . T (days) b . . . . . . . . . . . . . . . . 0 . ± . . ± . T = T (days) b . . . . . . . . . . 0 . ± . . ± . a/R ⋆ . . . . . . . . . . . . . . . . . . . . . . . . 4 . ± .
20 5 . +0 . − . ζ/R ⋆ c . . . . . . . . . . . . . . . . . . . . . . 12 . ± .
080 11 . ± . R p /R ⋆ . . . . . . . . . . . . . . . . . . . . . . 0 . ± . . ± . b . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 . +0 . − . . +0 . − . b ≡ a cos i/R ⋆ . . . . . . . . . . . . . . . 0 . +0 . − . . +0 . − . i (deg) . . . . . . . . . . . . . . . . . . . . . . 84 . ± . . ± . d c , r . . . . . . . . . . . . . . . . . . . . . . . . . 0 . . c , r . . . . . . . . . . . . . . . . . . . . . . . . . 0 . . c , i . . . . . . . . . . . . . . . . . . . . . . . . . 0 . . c , i . . . . . . . . . . . . . . . . . . . . . . . . . 0 . . c , z . . . . . . . . . . . . . . . . . . . . . . . . . 0 . . c , z . . . . . . . . . . . . . . . . . . . . . . . . . 0 . . K (m s − ) . . . . . . . . . . . . . . . . . . 68 ±
11 93 . ± . e e . . . . . . . . . . . . . . . . . . . . . . . . . . < . < . − ) f . . 26 . ± . < . − ) . . . . . · · · < . − ) . . · · · < . M p ( M J ) . . . . . . . . . . . . . . . . . . . . 0 . ± .
083 0 . ± . R p ( R J ) . . . . . . . . . . . . . . . . . . . . . 1 . ± .
13 1 . +0 . − . C ( M p , R p ) g . . . . . . . . . . . . . . . . 0 .
10 0 . ρ p (g cm − ) . . . . . . . . . . . . . . . . . 0 . ± .
025 0 . +0 . − . log g p (cgs) . . . . . . . . . . . . . . . . . . 2 . ± .
090 2 . +0 . − . a (AU) . . . . . . . . . . . . . . . . . . . . . . 0 . ± . . +0 . − . T eq (K) . . . . . . . . . . . . . . . . . . . . . 1930 ±
45 1896 +66 − Θ h . . . . . . . . . . . . . . . . . . . . . . . . . 0 . ± . . ± . h F i (cgs) i . . . . . . . . . . . . . 9 . ± .
041 9 . +0 . − . Note . — For both systems the fixed-circular-orbit model has a higher Bayesian evidencethan the eccentric-orbit model. We therefore assume a fixed circular orbit in generating theparameters listed here. a We adopt the IAU 2015 Resolution B3 nominal values for the Solar and Jovian parameters(Prˇsa et al. 2016) for all of our calculations, taking R J to be the nominal equatorial radius ofJupiter. Where necessary we assume G = 6 . × − m kg − s − . Because Yi et al. (2001)do not specify the assumed value for G or M ⊙ , we take the stellar masses from these isochrones atface value without conversion. Any discrepancy results in an error that is less than one percent,which is well below the observational uncertainty. We note that the standard values assumedin prior HAT planet discovery papers are very close to the nominal values adopted here. In allcases the conversion results in changes to measured parameters that are indetectable at the levelof precision to which they are listed. b Times are in Barycentric Julian Date calculated directly from UTC without correction forleap seconds. T c : Reference epoch of mid transit that minimizes the correlation with the orbitalperiod. T : total transit duration, time between first to last contact; T = T : ingress/egresstime, time between first and second, or third and fourth contact. c Reciprocal of the half duration of the transit used as a jump parameter in our MCMCanalysis in place of a/R ⋆ . It is related to a/R ⋆ by the expression ζ/R ⋆ = a/R ⋆ (2 π (1 + e sin ω )) / ( P √ − b √ − e ) (Bakos et al. 2010). d Values for a quadratic law, adopted from the tabulations by Claret (2004) according to thespectroscopic (SPC) parameters listed in Table 4. e The 95% confidence upper limit on the eccentricity determined when √ e cos ω and √ e sin ω are allowed to vary in the fit. f Term added in quadrature to the formal RV uncertainties for each instrument. This is treatedas a free parameter in the fitting routine. In cases where the jitter is consistent with zero we listthe 95% confidence upper limit. g Correlation coefficient between the planetary mass M p and radius R p estimated from theposterior parameter distribution. h The Safronov number is given by Θ = ( V esc /V orb ) = ( a/R p )( M p /M ⋆ ) (seeHansen & Barman 2007). i Incoming flux per unit surface area, averaged over the orbit.
AT-P-65b and HAT-P-66b 11 ∆ J ( m a g ) Magnitude contrast HAT-P-65 ∆ K ( m a g ) Magnitude contrast HAT-P-65 ∆ J ( m a g ) Magnitude contrast HAT-P-66 ∆ K ( m a g ) Magnitude contrast HAT-P-66
Figure 6.
Contrast curves for HAT-P-65 (top) and HAT-P-66 (bottom) in the J -band (left) and K -band (right) based on observationsmade with WHIRC on the WIYN 3.5 m as described in Section 2.4. The bands show the variation in the contrast limits depending on theposition angle of the putative neighbor. ρ * [ g / c m ] Effective temperature [K]
HAT-P-65 ρ * [ g / c m ] Effective temperature [K]
HAT-P-66
Figure 7.
Model isochrones from Yi et al. (2001) for the measured metallicities of HAT-P-65 and HAT-P-66. We show models for agesof 0.2 Gyr and 1.0 to 14.0 Gyr in 1.0 Gyr increments (ages increasing from left to right). The adopted values of T eff ⋆ and ρ ⋆ are showntogether with their 1 σ and 2 σ confidence ellipsoids. The initial values of T eff ⋆ and ρ ⋆ for HAT-P-65 from the first SPC and light curveanalyses are represented with a triangle. T eff ⋆ – ρ ⋆ diagram.These two parameters are directly measured for TEP sys-tems, and together with the [Fe / H] of the star, are theprimary parameters used to characterize the stellar hosts.Here we limit the sample to systems with planets hav-ing R p > . R J and P <
10 days. Because observationalselection effects vary from survey to survey, we show sep-arately the systems discovered by HAT (both HATNetand HATSouth), WASP,
Kepler , TrES and KELT, whichare the surveys that have discovered well-characterizedplanets with R p > . R J . The data for the HAT, WASP,TrES and KELT systems are drawn from a database ofTEPs which we privately maintain, and are listed, to-gether with references, in Table 8 at the end of this pa-per. These are planets which have been announced onthe arXiv pre-print server as of 2016 June 2, and sup-plemented by some additional fully confirmed planetsfrom HAT which had not been announced by that date.For Kepler we take the data from the NASA Exoplanetarchive . In Figure 8 we distinguish between hosts withplanets having R p > . R J , and hosts with planets hav-ing R p < . R J . The lower bound in each panel showsthe solar metallicity, 200 Myr ZAMS isochrone from theYY models, while the upper bound shows the locus ofpoints for stars having an age that is the lesser of 13.7 Gyror 90% of their total lifetime, again assuming solar metal-licity and using the YY models. For all of the surveysconsidered, planets with R > . R J tend to be foundaround host stars that are more evolved (closer to the90% lifetime locus) than planets with R < . R J . More-over, very few highly inflated planets have been discov-ered around stars close to the ZAMS. The largest planetsalso tend to be found around hot/massive stars, and havethe highest level of irradiation.For another view of the data, in Figure 9 we plot themass–radius relation of close-in TEPs with the color-scale of each point showing the fractional isochrone-based age of the system (taken to be equal to τ = http://exoplanetarchive.ipac.caltech.edu , accessed 2016Mar 4 ( t −
200 Myr) / ( t tot −
200 Myr)). Here t tot for a system isthe maximum age of a star with a given mass and metal-licity according to the YY models (Figure 10). We showthe fractional age, rather than the age in Gyr, as the stel-lar lifetime is a strong function of stellar mass, and thelargest planets also tend to be found around more mas-sive stars with shorter total lifetimes. Because the starformation rate in the Galaxy has been approximatelyconstant over the past ∼ τ to be uniformlydistributed between 0 and 1. In order to perform a con-sistent analysis, we re-compute ages for all of the WASP, Kepler , TrES and KELT systems using the YY modelstogether with the spectroscopically measured T eff ⋆ and[Fe / H], and transit-inferred stellar densities listed in Ta-ble 8. In Figure 9 we focus on systems with
P <
10 daysand t tot <
10 Gyr. Again it is apparent that the largestradius planets tend to be around stars that are relativelyold. Note that due to the finite age of the Galaxy, therehas been insufficient time for stars with t tot >
10 Gyr toreach their main sequence lifetimes. The restriction on t tot , which is effectively a cut on host star mass, limits thesample to stars which could be discovered at any stagein their evolution. If we do not apply this cut then theapparent correlation between fractional age and planetradius becomes even more significant, but this is likelydue to observational bias.The planets shown in Figure 9 have a variety of orbitalseparations and host star masses. Because the evolutionof a planet depends on its stellar environment, we expectthere to be a variance in the planet radius at fixed planetmass. In order to better compare planets likely to havesimilar histories (but which have different ages, and thusare at different stages in their history), in Figure 11 were-plot the mass–radius relation, but this time binning byhost star mass and orbital semi-major axis. Note that incomparing planets with the same semi-major axis we areassuming that orbital evolution can be neglected. Againwe use the color-scale of points to denote the fractionalage of the system. We choose a 3 × ρ [ g c m - ] Teff [K]
HAT
R < 1.5 R J R > 1.5 R J ρ [ g c m - ] Teff [K]
WASP
R < 1.5 R J R > 1.5 R J ρ [ g c m - ] Teff [K]
Kepler
R < 1.5 R J R > 1.5 R J ρ [ g c m - ] Teff [K]
TrES + KELT
R < 1.5 R J R > 1.5 R J Figure 8.
Host stars for TEPs with
R > . R J and P <
10 days from the HAT, WASP,
Kepler , TrES and KELT surveys. The lower linein each panel is the 200 Myr solar-metallicity isochrone from the YY stellar evolution models, while the upper line is the locus of points forstars having an age that is the lesser of 13.7 Gyr or 90% of their total lifetime, again assuming solar metallicity and using the YY models.Note that the maximum stellar age is a smooth function of stellar mass according to the models (Figure 10), but the 90% lifetime locus inthe T eff ⋆ – ρ plane is jagged due to the sensitive dependence on mass of the late stages of stellar evolution. We distinguish here between starswith planets having R P > . R J and stars with planets having R P < . R J . Large planets have been preferentially discovered aroundmore evolved stars than smaller planets. This appears to be true for all of the surveys considered. Moreover, few, if any, ZAMS stars areknown to host planets with R P > . R J . irradiation.To establish the statistical significance of the trendsseen in Figures 8–11, in Figure 12 we plot the frac-tional isochrone-based age τ against planetary radius,restricted to systems with t tot <
10 Gyr. Both the HATand WASP data have positive correlations between R P and the fractional age. A Spearman non-parametricrank-order correlation test gives a correlation coefficientof 0 .
344 between R P and the fractional age for HAT,with a 1.4% false alarm probability. For the WASP sam-ple we find a correlation coefficient of 0 .
277 and a falsealarm probability of 3.5%. The
Kepler , TrES and KELTdatasets are too small to perform a robust test for corre-lation, but they each show a similar trend. When all ofthe data are combined, we find a correlation coefficientof 0 .
347 and a false alarm probability of only 0.0041%.While the correlation is relatively weak, explaining onlya modest amount of the overall scatter in the data, it hasa high statistical significance, and is extremely unlikelyto be due to random chance.Figure 13 is similar to Figure 12, except that here werestrict the analysis to planets with 0 . M J < M p < . M J , which is roughly the range over which the mosthighly inflated planets have been discovered (e.g., Fig-ure 9). In this case we still find a statistically significantdifference between the fractional ages of stars hostinglarge radius planets and those hosting small radius plan- ets, though, due to the smaller sample size, the overallsignificance is somewhat reduced compared to the samplewhen no restriction is placed on planet mass (the correla-tion coefficient itself is somewhat higher). Quantitativelywe find that the HAT sample has a Spearman correlationcoefficient of 0 .
428 and a false alarm probability of 0.84%,the WASP sample has a correlation coefficient of 0 . .
398 and a falsealarm probability of 0.0068%.In order to compare planets with similar evolution-ary histories, and in analogy to Figure 11, in Figure 14we plot the fractional age against planet radius griddedby host star mass and orbital semimajor axis. Here wecombine all of the data, but restrict the sample to onlyplanets with 0 . M J < M P < . M J around stars with t tot <
10 Gyr. We see the correlation again in severalgrid cells, so long as there is a sufficiently large sample.Of course these correlations are likely biased due toobservational selection effects. We estimate the effectof observational selections on the measured correlationbelow in Section 4.1.2, where we conclude that the cor-relation is reduced, but still significant, after accountingfor selections.We conclude that there is a statistically significant pos-itive correlation between R p and the fractional age of thesystem. This correlation is seen in samples of transiting4 Hartman et al. R P [ R J up ] M P [M Jup ] HAT R P [ R J up ] M P [M Jup ] WASP R P [ R J up ] M P [M Jup ] Kepler R P [ R J up ] M P [M Jup ] TrES + KELT
Figure 9.
Mass–radius relation for TEPs from HAT (top left), WASP (top right),
Kepler (bottom left) and TrES and KELT (bottomright) with
R > . R J and P <
10 days around stars with total lifetimes t tot <
10 Gyr. The color-scale for each point indicates thefractional age of the system (taken to be τ = ( t −
200 Myr) / ( t tot −
200 Myr), where t is the age determined from the YY isochrones using T eff ⋆ , ρ ⋆ and [Fe / H] and t tot is the maximum age in the YY models for a star with the same mass and [Fe / H]). A handful of stars withbulk densities indicating very young ages show up as black points in the figure. The largest planets are found almost exclusively aroundmoderately evolved ( τ & .
5) stars. M a x i m u m A ge [ G y r ] Stellar Mass [M
Sun ] [Fe/H] = -0.5[Fe/H] = +0.0[Fe/H] = +0.5STAREVOL
Figure 10.
The maximum age of a star as a function of itsmass based on interpolating within the YY isochrones. These areshown for three representative metallicities. The maximum age isartificially capped at 19.95 Gyr which is the largest age at whichthe models are tabulated. For stars with M & . M ⊙ , whichhave maximum ages below this artificial cap, there is a smoothpower-law dependence between the maximum age and mass. Weuse this relation to estimate the fractional age τ of a planetarysystem. For comparison we also show the terminal main sequenceage as a function of stellar mass from the STAREVOL evolutiontracks (Charbonnel & Palacios 2004; Lagarde et al. 2012), takenfrom Table B.6 of Santerne et al. (2016). planets found by multiple surveys, with strikingly simi-lar results found for the largest two samples (from WASPand HAT). The largest radius planets have generally beenfound around more evolved stars. Relation to the Correlation Between Radius andEquilibrium Temperature
It is important to note that the correlation betweenradius and equilibrium temperature (or flux) is muchstronger than the apparent correlation between planetradius and the fractional age of the host star. In fact thedata are consistent with the latter correlation being en-tirely a by-product of the former correlation. However,the data also indicate that the radii of planets dynam-ically increase in time as their host stars become moreluminous and the planetary equilibrium temperatures in-crease.To demonstrate this we perform a Bayesian linear re-gression model comparison using the
BayesFactor pack-age in R which follows the approach of Liang et al.(2008) and Rouder & Morey (2012). We test models ofthe form:ln R p = c + c ln T eq , now + c ln T eq , ZAMS + c ln a + c τ (1)where c – c are varied linear parameters, and we com-pare all combinations of models where parameters otherthan c are fixed to 0. This particular parameterizationis motivated by Enoch et al. (2012) who found that theradii of close-in Jupiter-mass planets are best modelledby a function of the form given above with c ≡ c ≡ T eq , ZAMS and τ parameters to http://bayesfactorpcl.r-forge.r-project.org/ AT-P-65b and HAT-P-66b 15 . < a < . R p [ R J up ] star < 1.230.811.21.41.61.822.2 . < a < . R p [ R J up ] . < a < . R p [ R J up ] Mass [M
Jup ] 1.23 < M star < 1.460.1 1 10Mass [M
Jup ] 1.46 < M star < 1.7 0.20.40.60.810.20.40.60.810.1 1 10Mass [M
Jup ] 00.20.40.60.81
Figure 11.
Similar to Figure 9, here we combine all of the data from the different surveys, and show the mass–radius relation for differenthost star mass ranges (the selections are shown at the top of each column in solar mass units) and orbital semi-major axes (the selectionsare shown to the left of each row in AU). The overall range of semi-major axis and stellar mass shown here is chosen to encompass thesample of well-characterized highly inflated planets with
R > . R J around stars with total lifetimes t tot <
10 Gyr. Within a given panelthe largest planets tend to be found around more evolved stars. This is the opposite of what one would expect if high irradiation slows aplanet’s contraction, but does not supply energy deep enough into the interior of the planet to re-inflate as the luminosity of its host starincreases. test whether age is an important additional variable,and/or whether the data could be equally well describedif we used the initial equilibrium temperature of theplanet (which does not change in time) rather than thepresent-day equilibrium temperature (which increases intime due to the evolution of the host). Here we con-sider the full sample of well-characterized planets with
P <
10 days, R p > . R J , 0 . M J < M p < . M J , and t tot <
10 Gyr. Table 6 lists the linear coefficient esti-mates and the Bayesian evidences, sorting from highestto lowest, for each of the 15 models under comparison.We find that the model with the highest Bayesian ev-idence has the form:ln R p = c + c ln T eq , now + c ln a (2)with an evidence that is 2 . × times higher than theevidence for a model where c ≡ c ≡ c ≡ c ≡
0. Thisfinding is consistent with that of Enoch et al. (2012).The next highest evidence model has the form:ln R p = c + c ln T eq , now + c ln a + c τ (3)with an evidence that 0 .
37 times that of the highest ev-idence model. So indeed including τ provides no addi-tional explanatory power beyond what is already pro-vided by T eq , now and a .At the same time, we also find that models withln T eq , now have substantially higher evidence than modelsusing ln T eq , ZAMS in place of ln T eq , now , while the model using both ln T eq , ZAMS and τ has higher evidence thanthe model using ln T eq , ZAMS alone. Moreover, we findthat the maximum posterior value for c is greater thanzero in all cases where it is allowed to vary. In otherwords, planet radii are more strongly correlated with thepresent day equilibrium temperature than they are withthe ZAMS equilibrium temperature, and if the latter isused in place of the former then a significant positivecorrelation between radius and host star fractional ageremains.Based on this we conclude that the radii of close-in Jupiter-mass giant planets are determined by theirpresent-day equilibrium temperature and semi-majoraxis, and that the radii of planets increase over time astheir equilibrium temperatures increase. Selection EffectsThe Effect of Stellar Evolution on the Detectability of Plan-ets: — The sample of known TEPs suffers from a broadrange of observational selection effects which in princi-ple might explain a preference for finding large planetsaround evolved stars. As stars evolve their radii increase,which, for fixed R p , a and M ⋆ , reduces the transit depthby a factor of R − ⋆ (reducing their detectability), but in-creases the duration of the transits by a factor of R ⋆ (increasing their detectability). It also increases the geo-metrical probability of a planet being seen to transit bya factor of R ⋆ (increasing planet detectability). As stars6 Hartman et al. -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] HAT -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] WASP -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] Kepler -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] TrES+KELT -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] Combined
HATWASPKeplerTrESKELT
Figure 12.
Top:
The fractional isochrone-based age of the system (see Figure 9) vs. the planetary radius, shown separately for TEPsystems discovered by HAT (left) and WASP (right). We only show systems with
P <
10 days and t tot <
10 Gyr. Both the HAT andWASP samples have positive correlations between R P and τ . For HAT a Spearman non-parametric rank-order correlation test gives acorrelation coefficient of 0 .
344 with a 1.4% false alarm probability. For the WASP sample we find a correlation coefficient of 0 .
277 and afalse alarm probability of 3.5%.
Middle:
Same as the top, here we show planets from
Kepler , TrES and KELT, with the same selectionsapplied.
Bottom:
Same as top, here we combine data from all of the surveys. The combined data set has a correlation coefficient of 0 . evolve they also become more luminous, meaning that at fixed distance they may be monitored with greater photo-AT-P-65b and HAT-P-66b 17 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] HAT -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] WASP -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] Kepler -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] TrES+KELT -0.2 0 0.2 0.4 0.6 0.8 1 1.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 F r a c t i ona l A ge R P [R Jup ] Combined
HATWASPKeplerTrESKELT
Figure 13.
Same as Figure 12, here we only consider systems with planets having masses in the range 0 . M J < M p < . M J , whichis roughly the radius range over which highly inflated planets have been discovered. In this case the Spearman non-parametric rank-ordercorrelation test gives a correlation coefficient of 0 .
428 with a 0.84% false alarm probability. For the WASP sample we find a correlationcoefficient of 0 .
273 and a false alarm probability of 7.7%. The combined sample has a correlation coefficient of 0 .
398 and a false alarmprobability of 0 . metric precision (further increasing planet detectability).To determine the relative balance of these competingfactors for the HAT surveys, for each TEP system discov- ered by HAT we estimate the relative number of ZAMSstars with the same stellar mass and metallicity aroundwhich one could expect to find a planet with the same ra-8 Hartman et al. -0.200.20.40.60.811.2 . < a < . F r a c t i ona l A ge star < 1.23-0.200.20.40.60.811.2 . < a < . F r a c t i ona l A ge -0.200.20.40.60.811.2 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 . < a < . F r a c t i ona l A ge R P [R Jup ] 1.23 < M star < 1.460.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4R P [R Jup ] 1.46 < M star < 1.70.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4R P [R Jup ] Figure 14.
Similar to Figures 13 and 11, here we combine all of the data from the different surveys, and show the fractional isochrone-based age vs. planet radius for different host star mass ranges (the selections are shown at the top of each column in solar mass units)and orbital semi-major axes (the selections are shown to the left of each row in AU). The overall range of semi-major axis and stellarmass shown here is chosen to encompass the sample of well-characterized highly inflated planets with
R > . R J around stars with totallifetimes t tot <
10 Gyr. We also restrict the sample to planets with 0 . M J < M P < . M J . dius and orbital period and with the same signal-to-noiseratio. To do this we use the following expression: N ZAMS /N t = V ZAMS V t Prob
ZAMS
Prob t (4)where N ZAMS /N t is the relative number of ZAMS planethosts expected compared to those with age t , V ZAMS /V t is the relative volume surveyed for ZAMS-equivalent ver-sions of the TEP system (for simplicity we assume auniform space density of stars), and Prob ZAMS / Prob t = R ⋆,ZAMS /R ⋆,t is the relative transit probability, whichis equal to the ratio of the stellar radii. To estimate V ZAMS /V t we note that for fixed photometric precision,and assuming white noise-dominated observations, thetransit S/N of a given TEP scales as the transit depthtimes the square root of the number of points in tran-sit, or as ( R ⋆,ZAMS /R ⋆,t ) − / . If the data are red-noisedominated, then the S/N scales simply as the transitdepth, which would increase V ZAMS /V t . We then deter-mine the r magnitude of stars in the HAT field contain-ing the TEP in question for which the per-point RMS islarger than the RMS of the observed TEP light curve by( R ⋆,ZAMS /R ⋆,t ) − / . Accounting for the change in ab-solute r magnitude between the ZAMS and the presentday for the system, this gives us the relative distance of aZAMS-equivalent system for which the transits would bedetected with the same S/N. The cube of this distanceis equal to V ZAMS /V t .In Figure 15 we show N ZAMS /N t vs R p for HAT plan- R e l a t i v e N u m be r o f Z A M S S t a r s S ea r c hed R P [R Jup ] Figure 15.
The relative number of ZAMS-equivalent starssearched for a given TEP discovered by HAT to the same tran-sit S/N as the observed TEP system (equation 4) computed asdescribed in Section 4.1.2. This is shown as a function of planetradius. For the largest planets with R P > . R J the HAT surveyis more sensitive to finding the same planet around a ZAMS starthan it is to finding the planet around the moderately evolved starwhere it was discovered. ets. For most TEP systems discovered by HAT, includ-ing most of the systems with R p > . R J , we have N ZAMS /N t >
1. In other words, the greater transitdepths expected for ZAMS systems more than compen-sates for the lower luminosities, shorter duration tran-sits, and lower transit probabilities. Thus, from a puretransit-detection point-of-view, we should expect to be more sensitive to TEPs around ZAMS stars than toTEPs around stars with the measured host star ages.AT-P-65b and HAT-P-66b 19
Table 6
Parameter Estimates and Bayesian Evidence For Models of the Form Eq. 1ln T eq , now ln T eq , ZAMS ln a τ Bayesian c c c c Evidence0 . ± .
12 0 0 . ± .
075 0 2 . × . ± .
14 0 0 . ± .
086 0 . ± .
088 9 . × . ± . − . ± .
21 0 . ± .
079 0 5 . × . ± .
099 0 0 0 . ± .
077 2 . × . ± .
25 0 . ± .
23 0 . ± .
086 0 . ± .
096 2 . × . ± . − . ± .
24 0 0 . ± .
088 4 . × . ± .
099 0 0 0 2 . × . ± .
098 0 0 . ± .
077 1 . × . ± . − . ± .
21 0 0 1 . × . ± .
14 0 . ± .
084 0 . ± .
080 9 . × . ± .
14 0 . ± .
086 0 7 . × . ± .
11 0 0 1 . × − . ± .
067 0 . ± .
086 2 . × . ± .
087 9 . × − . ± .
074 0 4 . × − Note . — The models tested are sorted from highest to lowest evidence. TheBayesian evidence is reported relative to that for a model with only a freely varyingmean for the ln R p values. For each parameter we report the mean and standarddeviation of its posterior probability distribution. Put another way, while selection effects may lead tofewer small planets being found around older stars (miss-ing planets in the upper left corner of Figure 12), basedon the estimate in Figure 15, selection effects due to tran-sit detectability do not explain why we find fewer largeplanets around unevolved stars (missing planets in thelower right corner of Figure 12). If the occurrence rateof large radius planets is independent of host star age, orif it is larger for unevolved stars than for evolved stars,we would expect to have found more large planets aroundunevolved stars than evolved stars.
The Effect of Stellar Evolution on the Ability to ConfirmPlanets: — Other observational selection effects may stillbe at play. If the orbits of these planets shrink over timedue to tidal evolution, then the transit probability andthe fraction of points in transit both increase in time bymore that what we estimated. Beyond simply detect-ing the transits, further selections are imposed in thefollow-up program carried out to confirm the planets.Figure 16 compares the present day effective tempera-ture and v sin i for HAT TEPs to the expected values onthe ZAMS (estimated as discussed below). For all of the R p > . R J planets found by HAT the host star had ahigher T eff ⋆ on the ZAMS than at the present day. Themost extreme case is HAT-P-7 which had an estimatedZAMS effective temperature of 6860 K compared to itspresent-day temperature of 6350 ±
100 K. While preci-sion RVs are more challenging for early F dwarfs thanfor later F dwarfs, the ZAMS temperatures of the hostsof the largest TEPs found by HAT are still within therange where we carry out follow-up observations (we donot follow-up hosts of spectral type A or earlier if theyare faint stars with V & v sin i ∝ R − ⋆ (as-suming I ∝ R ⋆ ). The most rapidly rotating ZAMS hostis HAT-P-41 for which we estimate a ZAMS rotation ve-locity of 24 km s − , which is still well within the rangewhere we continue follow-up (we do not follow-up hostswith v sin i &
50 km s − if they are around faint starswith V & Correcting the Correlation Coefficient for Observational Se-lections: — In order to determine quantitatively how se-lection effects impact the correlation measured between R p and τ , we follow Efron & Petrosian (1999) in calcu-lating a modified Kendall correlation coefficient that isapplicable to data suffering a non-trivial truncation. Theprocedure is as follows. We will call the observed datapoints ( R P,i , τ i ) and ( R P,j , τ j ), with i = j , comparable ifeach point falls within the other point’s selection range.Here point j is within the selection range for point i if,holding everything else constant, we could still have dis-covered the planet around star i if the system had valuesof ( R P,i , τ j ), ( R P,j , τ i ) or ( R P,j , τ j ) instead of ( R P,i , τ i ).Letting J be the set of all comparable pairs, and N p be the total number of such pairs, the modified Kendallcorrelation coefficient is then given by r K = 1 N p X ( i,j ) ∈J sign (( R P,i − R P,j )( τ i − τ j )) . (5)For uncorrelated data r K has an expected value of 0,whereas perfectly correlated data has r K = 1 and per-fectly anti-correlated data has r K = −
1. To determinethe probability of finding | r K | > | r K, observed | it is neces-sary to carry out bootstrap simulations. To do this we0 Hartman et al. Z A M S T e ff [ K ] Present Day T eff [K]
All HAT Planets
R < 1.5 R J R > 1.5 R J
10 100 10 100 Z A M S vs i n i [ k m / s ] Present Day vsin i [km/s]
HAT Planets with T eff,ZAMS > 6250K
R < 1.5 R J R > 1.5 R J Figure 16.
Left: The estimated TEP host-star effective temperature on the ZAMS vs. its present day measured effective temperaturefor all TEP systems discovered to date by HAT. While stars hosting planets with R P > . R J had higher effective temperatures on theZAMS, none of them would have been too hot for us to proceed with confirmation follow-up observations. Right: The estimated projectedrotation velocity on the ZAMS vs. present day measured rotation velocity for HAT TEP hosts with T eff , ZAMS > v sin i is calculated by scaling the measured v sin i by R ⋆ /R ⋆,ZAMS assuming the spin-down for these radiative-envelope stars isdue entirely to changes in the moment of inertia, and assuming the latter scales as R ⋆ . While stars hosting planets with R P > . R J would have been rotating more rapidly on the ZAMS than at the present day, none of them would have been rotating too rapidly for us toproceed with confirmation follow-up observations. calculate r K for N sim simulated data sets, and for eachsimulated data set we randomly select N values of i , withreplacement, from the observed samples, adopt R P,i foreach simulated point, and associate with it a value of τ drawn at random from the set of points that are compa-rable to i (including i itself in this case).The primary challenge in calculating equation 5 for theobserved sample of close-in giant planets is to determinethe set of comparable pairs. We do this for the HATplanets by subtracting the observed transit signal fromthe survey light curve, rescaling the scatter to match theexpected change in r.m.s. due to the change in the stellarluminosity with age, adding the expected transit signalgiven the new trial planetary and stellar radii, but assum-ing the original ephemeris and orbital inclination, andusing BLS to determine whether or not the transit couldbe recovered. Using the set of comparable pairs deter-mined in this fashion, we find r K = 0 . . r K = 0 .
284 with a 2 .
92% false alarm probabilitywhen restricted to planets with 0 . M J < M p < . M J ).For comparison, if we ignore the selection effects and as-sume all points are comparable, we find r K = 0 .
235 witha false alarm probability of 1 .
52% (or r K = 0 .
297 with a0 .
87% false alarm probability when restricted to planetswith 0 . M J < M p < . M J ). The false alarm probabil-ities in the latter case are essentially the same as whatwas reported above using the Spearman rank-order cor-relation test instead of the Kendall test, demonstratingthe consistency of the two methods.We conclude that while observational selections doslightly bias the measured correlation between R p and τ for HAT, the effect is small. While we cannot deter-mine the set of comparable pairs for WASP, the selec-tions are likely very similar to HAT, and we expect theeffect on the measured correlation of accounting for ob-servational selections to be similarly small. We thereforeexpect that the full combined set of planets would stillexhibit a highly significant correlation between R p and τ , even after accounting for observational selections. Systematic Errors in Stellar Parameters
The radii of TEPs are not measured directly, but ratherare measured relative to the stellar radii, which in turnare determined by matching the effective temperatures,stellar densities, and stellar metallicities to models (ei-ther theoretical stellar evolution models, as done for ex-ample for most HAT systems, or by utilizing empiricalmodels calibrated with stellar eclipsing binary systems,as has been done for many WASP systems). Any sys-tematic error in the stellar radius would lead to a pro-portional error in the planet radius, and the fact thatthe largest planets are more commonly found around themost evolved (and largest) stars is what one would ex-pect to see if there were significant unaccounted-for sys-tematic errors. Here we consider a variety of potentialsystematic errors, and argue that none of these are re-sponsible for the observed correlation.
Eccentricity: — One potentially important source of sys-tematic errors in this respect is the planetary eccentric-ity, which is constrained primarily by the RV data, andwhich is needed to determine the stellar density from themeasured transit duration, impact parameter, and radiusratio. The host stars of the largest radius planets areamong the hottest, fastest rotating, and highest jitterstars around which transiting planets have been found(e.g., Figure 16, and Hartman et al. 2011c). For thesesystems the eccentricity is typically poorly constrained,and circular orbits have often been adopted. If the sys-tems were actually highly eccentric, with transits nearapastron, then the stellar densities would be higher thanwhat was inferred assuming circular orbits, and the stel-lar and planetary radii would be smaller than what hasbeen estimated. There are, however, several large planetstransiting moderately evolved stars for which secondaryeclipses have been observed, providing tight constraintson the eccentricity (e.g., TrES-4b Knutson et al. 2009,WASP-12b Campo et al. 2011, HAT-P-32b Zhao et al.2014, and WASP-48b O’Rourke et al. 2014). Moreover, If circular orbits are not adopted, then there is a bias to-ward overestimating the eccentricity as shown by Lucy & Sweeney(1971). This bias may affect some of the earliest discovered planetsespecially.
AT-P-65b and HAT-P-66b 21the most inflated planets are on short period orbits,where we expect circularization. This expectation hasbeen observationally verified in cases where sufficientlyhigh precision RVs have been possible, or when secondaryeclipse follow-up observations have been made. We alsonote that at least for the majority of the very large radiusHAT planets, when the eccentricity is allowed to vary, theplanet and stellar radii determined from the median ofthe posterior distributions are found to be larger thanwhen the eccentricity is fixed to zero. N o r m a li z ed I m pa c t P a r a m e t e r R P [R J ]HATWASP Figure 17.
Normalized impact parameter vs. planetary radiusfor TEPs found by HAT and WASP. The impact parameters ofWASP TEPs appear to be uniformly distributed between 0 and 1,as expected for random orientations in space. The largest HATplanets have, if anything, a bias toward low impact parameters. Ifthese suffer from a systematic error, the stellar and planetary radiiwould be underestimated.
Impact Parameter: — Another potential source of system-atic error is if the impact parameter is in error, perhapsdue to an incorrect treatment of limb darkening (e.g.,Espinoza & Jord´an 2015). Errors in the impact param-eter will translate into concomitant errors in the stellardensity, and in the stellar radius and age. In order toover-estimate the size of the planets, the impact param-eter would need to have been overestimated. Looking atthe distribution of measured planetary impact parame-ters, however, shows no evidence for this being the case(Figure 17). The impact parameter for the WASP plan-ets appears to be uniformly distributed between 0 and 1,as expected for random orbital orientations, whereas theHAT planets are, if anything, biased toward low impactparameters (if these are in error, the stars and planetswould be even larger than currently estimated).
Stellar Atmospheric Parameters: — Other potentialsources of systematic errors include errors in the stellareffective temperatures (if the stars are hotter thanmeasured, they would be closer to the ZAMS) ormetallicities, or an error in the assumed stellar abun-dance pattern (generally stars are modelled assumingsolar-scaled abundances). A check on the spectroscopictemperature estimates can be performed by comparingthe broad-band photometric colors to the spectro-scopically determined temperatures. We show thiscomparison in Figure 18 where we use the color of thepoints to show the planet radius. While there is perhapsa slight systematic difference in the V − K vs. T eff ⋆ rela-tion between large and small radius planets, with largeradius planets being found, on average, around slightly V - K [ m ag ] Teff [K] R < 1.5 R J R > 1.5 R J Figure 18.
Photometric V − K color (not corrected for redden-ing) vs. effective temperature for TEP host stars from HAT andWASP with R P > . R J and P <
10 days. The blue and redcolors are used to distinguish between stars hosting planets with R P > . R J and R P < . R J , respectively. No systematic dif-ference in the color-temperature relation is seen between these twoclasses of planets. Such a difference might have indicated a sys-tematic error in the stellar effective temperature measurements ofthe stars hosting large planets. R e l a t i v e N u m be r [Fe/H]R < 1.5 R J R > 1.5 R J Figure 19.
Normalized histograms of [Fe / H] for transiting planethost stars from HAT and WASP, separated by planetary radius. Nosignificant difference is seen between metallicities of large planetradius host stars, and small planet radius host stars. redder stars at fixed T eff ⋆ than small radius planets, thedifference is too small to be responsible for the detectedtrend between planet radius and fractional host age.Moreover, the difference is also consistent with moreevolved/luminous stars generally being more distantfrom the Solar System than less evolved stars, and thusexhibiting greater reddening. No systematic differenceis seen in the host star metallicity distributions of smalland large radius planets (Figure 19). Priors Used In Stellar Modelling: — Stars evolve faster asthey age such that a large area on the Hertzsprung-Russell diagram is covered by stellar models spanninga small range of ages near the end of a star’s life. Asa result, when observed stellar properties are comparedto models there can be a bias toward matching to late-ages. This well-known effect, dubbed the stellar termi-nal age bias by Pont & Eyer (2004), can be correctedby adopting appropriate priors on the model parameters(e.g., adopting a uniform prior on the age). Similarly,failing to account for the greater prevalence of low-massstars in the Galaxy relative to high-mass stars can leadto overpredicting stellar masses (e.g., Lloyd 2011). Formost transiting planets in the literature, these possible2 Hartman et al.biases have not been accounted for in performing thiscomparison (i.e., generally the analyses have adopteduniform priors on the relevant observables, namely theeffective temperature, density and metallicity). Whilethese effects could lead to over-estimated stellar radii, po-tentially explaining the preference for large radius plan-ets around evolved stars, in practice we only expectsuch biases to be significant if the observed parame-ters are not well constrained relative to the scale overwhich the astrophysically-motivated priors change sub-stantially. To estimate the importance of this effect, wecalculate new stellar parameters for each of the HATTEP systems with
R > . R J . Here we place a uni-form prior on the stellar age between the minimum ageof the isochrones and 14 Gyr (this amounts to assuming aconstant star formation rate over this period), we use theChabrier (2003) initial mass function to place a prior onthe stellar mass, and we assume a Gaussian prior on themetallicity with a mean of [Fe / H]= 0 dex, and a standarddeviation of 0.5 dex. The details of how we implementthis are described in Appendix A.We find that for all 17 systems the changes to the pa-rameters are much smaller than the uncertainties (thechanges are all well below 0.1%, and in most cases below0.01%). We also find that the prior on the stellar mass,which increases toward smaller mass stars, generally hasa larger impact than the priors on the age or metallic-ity. The result is that in most cases the stellar massesand radii are very slightly lower when priors are placedon the stellar properties, while the ages are very slightlyhigher. The latter is due to the prior on stellar masspulling the solution toward lower effective temperatures,which at the measured stellar densities requires higherages. We conclude that since the changes in the stellarparameters are insignificant, the correlation between theplanetary radii and host star fractional age is not dueto biases in the stellar parameters stemming from usingincorrect priors.
Theoretical Significance
As we have shown, there is a significant correlation be-tween the radii of close-in giant planets and the fractionalages of their host stars. This correlation is apparently aby-product of the more fundamental correlation betweenplanet radius and equilibrium temperature, but the dataalso indicate that planetary radii increase over time astheir host stars evolve and become more luminous.Such an effect is contrary to models of planet evolutionwhere excess energy associated with a planet’s proximityto its host star does not penetrate deep into the planetinterior, but only acts to slow the planet’s contraction.Burrows et al. (2000) and Baraffe et al. (2008) are ex-amples of such “default” models. Other examples ofsuch models include Burrows et al. (2007), who showed,among other things, how additional opacity which fur-ther slows the contraction could explain the radii of in-flated planets known at that time, and Ibgui et al. (2010)who showed how extended tidal heating of the planet at-mosphere can increase the final “equilibrium” radius ofa planet. More generally, Spiegel & Burrows (2013) ex-plored a variety of effects related to planet inflation, in-cluding the effect on planetary evolution of varying thedepth at which additional energy is deposited in the in-terior (see also Lopez & Fortney 2016 for a recent dis- cussion). If the inflation mechanism only slows, but doesnot reverse, the contraction, one would expect that atfixed semimajor axis, older planets should be smallerthan younger planets, despite the increase in equilibriumtemperature as the host stars evolve. This is not whatwe see (Figure 11, also Section 4.1.1).On the other hand theories in which the energy isdeposited deep in the core of the planet may allowplanets to become more inflated as the energy sourceincreases over time (Spiegel & Burrows 2013). Exam-ples of such models include tidal heating of an eccentricplanet’s core as considered by Bodenheimer et al. (2001),Liu et al. (2008) and Ibgui et al. (2011), or the Ohmicheating model proposed by Batygin & Stevenson (2010);Batygin et al. (2011) (though see Huang & Cumming2012 and Wu & Lithwick 2013 who argue that this mech-anism cannot heat the deep interior). Our finding thatplanets apparently re-inflate over time is evidence thatsome mechanism of this type is in operation. SUMMARY
The existence of highly inflated close-in giant planetsis one of the long-standing mysteries that has emergedin the field of exoplanets. By continuing to build upthe sample of inflated planets we are beginning to seepatterns in their properties, allowing us to narrow downon the physical processes responsible for the inflation.Here we presented the discovery of two transiting highlyinflated planets HAT-P-65b and HAT-P-66b. The plan-ets are both around moderately evolved stars, which wefind to be a general trend—highly inflated planets with R & . R J have been preferentially found around mod-erately evolved stars compared to smaller radius planets.This effect is independently seen in the samples of planetsfound by HAT, WASP, Kepler , TrES and KELT. We ar-gue that this is not due to observational selection effects,which tend to favor the discovery of large planets aroundyounger stars, nor is it likely to be the result of system-atic errors in the planetary or stellar parameters. We findthat the correlation can be explained as a by-product ofthe more fundamental, and well known, correlation be-tween planet radius and equilibrium temperature, andthat the present day equilibrium temperature of close-in giant planets, which increases with time as host starsevolve, provides a significantly better predictor of planetradii than does the initial equilibrium temperature at thezero age main sequence.We conclude that, after contracting during the pre-main-sequence, close-in giant planets are re-inflated overtime as their host stars evolve. This provides evidencethat the mechanism responsible for this inflation depositsenergy deep within the planetary interiors.The result presented in this paper motivates furtherobservational work to discover and characterize highlyinflated planets. In particular more work is needed todetermine the time-scale for planet re-inflation. The ex-pected release of accurate parallaxes for these systemsfrom Gaia should enable more precise ages for all of thesesystems. Many more systems are needed to trace theevolution of planet radius with age as a function of plan-etary mass, host star mass, orbital separation, and otherpotentially important parameters. Furthermore, the ev-idence for planetary re-inflation presented here providesadditional motivation to search for highly inflated long-AT-P-65b and HAT-P-66b 23period planets transiting giant stars.HATNet operations have been funded by NASAgrants NNG04GN74G and NNX13AJ15G. Follow-upof HATNet targets has been partially supportedthrough NSF grant AST-1108686. G. ´A.B., Z.C., andK.P. acknowledge partial support from NASA grantNNX09AB29G. J.H. acknowledges support from NASAgrant NNX14AE87G. K.P. acknowledges support fromNASA grant NNX13AQ62G. We acknowledge partialsupport also from the
Kepler
Mission under NASA Co-operative Agreement NCC2-1390 (D.W.L., PI). A.S. issupported by the European Union under a Marie CurieIntra-European Fellowship for Career Development withreference FP7-PEOPLE-2013-IEF, number 627202. Partof this work was supported by Funda¸c˜ao para a Ciˆencia ea Tecnologia (FCT, Portugal, ref. UID/FIS/04434/2013)through national funds and by FEDER through COM-PETE2020 (ref. POCI-01-0145-FEDER-007672). Datapresented in this paper are based on observations ob-tained at the HAT station at the Submillimeter Array ofSAO, and the HAT station at the Fred Lawrence Whip-ple Observatory of SAO. This research has made use ofthe NASA Exoplanet Archive, which is operated by theCalifornia Institute of Technology, under contract withthe National Aeronautics and Space Administration un-der the Exoplanet Exploration Program. Data presentedherein were obtained at the WIYN Observatory fromtelescope time allocated to NN-EXPLORE through thescientific partnership of the National Aeronautics andSpace Administration, the National Science Foundation,and the National Optical Astronomy Observatory. Thiswork was supported by a NASA WIYN PI Data Award,administered by the NASA Exoplanet Science Institute.We gratefully acknowledge R. W. Noyes for his manycontributions to the HATNet transit survey, and we alsogratefully acknowledge contributions from J. Johnson,and from G. Marcy to the collection and reduction of theKeck/HIRES observations presented here. The authorswish to recognize and acknowledge the very significantcultural role and reverence that the summit of MaunaKea has always had within the indigenous Hawaiian com-munity. We are most fortunate to have the opportunityto conduct observations from this mountain.4 Hartman et al.
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ESTIMATING TRANSITING PLANET HOST STAR PARAMETERS WITH PRIORS ON THE STELLAR MASS, AGE, ANDMETALLICITY
The physical parameters of transiting planet host stars are determined by comparing the observed parameters T eff ⋆ , ρ ⋆ and [Fe / H] to theoretical stellar evolution models. In practice the light curve analysis produces a Markov Chainof ρ ⋆ values, which we combine with simulated chains of T eff ⋆ and [Fe / H] values (we assume the three parameters areuncorrelated, and that T eff ⋆ and [Fe / H] have Gaussian uncertainties). For a given ( ρ ⋆ , T eff ⋆ , [Fe / H]) link in the chain,we perform a trilinear interpolation within a grid of isochrones from the YY models to get the corresponding stellarmass, age, radius, luminosity, and absolute magnitudes in various pass-bands. Our interpolation routine can use anycombination of three parameters as the independent variables, below we make use of this feature using the mass, ageand metallicity as the independent variables. The resulting chain of stellar physical parameters is then used to providebest estimates and uncertainties for each of these parameters.As discussed in Section 4.1.3 this process may lead to systematic errors in the stellar parameters if priors are notadopted to account for the intrinsic distribution of stars in the Galaxy. The prior is applied as a multiplicative weightthat is associated with each link in the Markov Chain. The weights are calculated as follows.Let P m ( m ), P t ( t ), and P [Fe / H] ([Fe / H]) be prior probability densities to be placed on the stellar mass, age andmetallicity, respectively. Here we use the Chabrier (2003) initial mass function for the prior on the stellar mass,a uniform distribution for the prior on the stellar age, and a Gaussian distribution with mean 0 dex and standarddeviation 0 . C m ( m ), C t ( t ), and C [Fe / H] ([Fe / H]) be the correspondingcumulative distributions of these prior probability densities.For a given ( m, t, [Fe / H]) link generated from an input set of ( ρ ⋆ , T eff ⋆ , [Fe / H]), we find m + = C − m ( C m ( m ) + ∆ u m ), t + = C − t ( C t ( t ) + ∆ u t ) and [Fe / H] + = C − / H] (C [Fe / H] ([Fe / H]) + ∆u [Fe / H] ) for some small probability steps ∆ u m ≪ u t ≪ u [Fe / H] ≪
1. Likewise we calculate m − , t − and [Fe / H] − for a negative ∆ u . We then perform trilinearinterpolation within the isochrones to find ( ρ m + , T eff ,m + , [Fe / H] m+ ) associated with the point ( m + , t, [Fe / H]), andsimilarly for m − , t + , etc.Letting v m = ( ρ m + − ρ m − , T eff ,m + − T eff ,m − , [Fe / H] m+ − [Fe / H] m − ) (A1)AT-P-65b and HAT-P-66b 27be the vector running from the m − point to the m + point, and similarly for v t and v [Fe / H] , the weight w is thencalculated as w = ∆ u m ∆ u t ∆ u [Fe / H] v m · ( v t × v [Fe / H] ) (A2)where the denominator is the volume of the parallelepiped spanned by the three vectors. We use these weights incalculating the weighted median and 1 σ confidence regions of each parameter chain.8 Hartman et al. Table 7
Relative radial velocities and bisector spans for HAT-P-65 and HAT-P-66.Star BJD RV a σ RVb BS σ BS Phase Instrument(2,450,000+) (m s − ) (m s − ) (m s − ) (m s − ) HAT-P-65
HAT-P-65 5544 . · · · · · · . . .
161 HIRESHAT-P-65 5544 . − .
18 7 .
33 59 . . .
167 HIRESHAT-P-65 5545 . .
09 6 .
31 20 . . .
542 HIRESHAT-P-65 5814 . .
96 5 . − . . .
880 HIRESHAT-P-65 5850 . .
48 5 .
64 43 . . .
675 HIRESHAT-P-65 5853 . .
84 5 . − . . .
821 HIRESHAT-P-65 5878 . − .
79 5 . − . . .
361 HIRESHAT-P-65 5879 . .
69 5 . − . . .
756 HIRESHAT-P-65 5880 . − .
82 5 .
50 0 . . .
152 HIRESHAT-P-65 5881 . − .
35 6 . − . . .
541 HIRESHAT-P-65 5904 . − .
04 4 .
62 2 . . .
324 HIRESHAT-P-65 6193 . − .
59 5 .
57 5 . . .
319 HIRESHAT-P-65 6534 . − .
37 5 .
92 5 . . .
231 HIRES
HAT-P-66
HAT-P-66 6991 . − .
96 45 . · · · · · · .
227 TRESHAT-P-66 7061 . .
42 58 . · · · · · · .
713 TRESHAT-P-66 7064 . .
13 59 . · · · · · · .
731 TRESHAT-P-66 7079 . .
56 57 . · · · · · · .
730 TRESHAT-P-66 7110 . − .
24 49 . · · · · · · .
233 TRESHAT-P-66 7112 . .
38 17 .
40 4 . . .
740 SophieHAT-P-66 7136 . .
58 12 .
70 0 . . .
838 SophieHAT-P-66 7146 . − .
08 42 . · · · · · · .
272 TRESHAT-P-66 7166 . d .
19 73 . · · · · · · .
004 TRESHAT-P-66 7167 . − .
39 54 . · · · · · · .
343 TRESHAT-P-66 7168 . .
29 42 . · · · · · · .
686 TRESHAT-P-66 7180 . .
92 75 . · · · · · · .
710 TRESHAT-P-66 7191 . − .
24 20 . − . . .
324 SophieHAT-P-66 7193 . d .
63 47 . − . . .
989 SophieHAT-P-66 7195 . .
00 16 .
30 61 . . .
671 SophieHAT-P-66 7331 . − .
35 16 .
10 30 . . .
515 SophieHAT-P-66 7333 . − .
69 13 .
40 33 . . .
196 SophieHAT-P-66 7334 . .
77 10 .
60 17 . . .
529 SophieHAT-P-66 7335 . .
91 11 .
70 57 . . .
868 SophieHAT-P-66 7379 . − .
16 4 .
52 5 . . .
492 HIRESHAT-P-66 7400 . .
74 13 .
00 48 . . .
721 SophieHAT-P-66 7402 . − .
77 17 . − . . .
424 SophieHAT-P-66 7403 . .
28 18 . − . . .
695 SophieHAT-P-66 7404 . − .
72 17 . − . . .
061 SophieHAT-P-66 7405 . − .
84 14 .
00 25 . . .
382 SophieHAT-P-66 7412 . .
53 3 .
81 4 . . .
604 HIRESHAT-P-66 7413 . .
91 3 . − . . .
913 HIRESHAT-P-66 7413 . − .
66 2 .
93 5 . . .
202 HIRESHAT-P-66 7415 . .
83 3 . − . . .
572 HIRESHAT-P-66 7422 . · · · · · · . . .
230 HIRESa The zero-point of these velocities is arbitrary. An overall offset γ rel fitted independently to the velocities from each instrument has beensubtracted. RVs are not measured for the I -free HIRES template spectra, but spectral line BSs are measured for these spectra.b Internal errors excluding the component of astrophysical jitter considered in Section 3.3.c Ca II HK line core emission index measured from the Keck-I/HIRES spectra following Isaacson & Fischer (2010).d These observations were excluded from the analysis because they were obtained during transit and the RVs may be affected by the Rossiter-McLaughlin effect. Table 8
Adopted Parameters for Transiting Planet Systems Discovered by HAT, KELT, TrES andWASP.Planet Period
Mp Rp T eq T eff ⋆ ρ⋆ [Fe / H] M⋆ Age t tot Refs.(d) ( M J) ( R J) (K) (K) (g cm −
3) ( M ⊙ ) (Gyr) (Gyr)HAT-P-10/ 3 .
722 0 . ± .
018 1 . . − .
027 1020 ±
17 4980 ±
60 2 . . − .
189 0 . ± .
08 0 . ± .
030 7 . ± .
80 19 .
95 28WASP-11bHAT-P-11b 4 .
888 0 . ± .
009 0 . ± .
014 878 ±
15 4780 ±
50 2 . . − .
222 0 . ± .
05 0 . . − .
030 6 . . − .
10 19 .
95 45HAT-P-12b 3 .
213 0 . ± .
012 0 . . − .
021 963 ±
16 4650 ±
60 2 . . − . − . ± .
05 0 . ± .
018 2 . ± .
00 19 .
95 32HAT-P-13b 2 .
916 0 . ± .
038 1 . ± .
079 1656+46 −
43 5653 ±
90 0 . . − .
071 0 . ± .
08 1 . . − .
100 5 . . − .
70 6 .
80 34,51HAT-P-14b 4 .
628 2 . ± .
059 1 . ± .
052 1570 ±
34 6600 ±
90 0 . . − .
066 0 . ± .
08 1 . ± .
045 1 . ± .
40 4 .
20 50HAT-P-15b 10 .
864 1 . ± .
066 1 . ± .
043 904 ±
20 5568 ±
90 1 . . − .
122 0 . ± .
08 1 . ± .
043 6 . . − .
60 13 .
10 55HAT-P-16b 2 .
776 4 . ± .
094 1 . ± .
066 1626 ±
40 6158 ±
80 0 . . − .
113 0 . ± .
08 1 . ± .
039 2 . ± .
80 6 .
60 52HAT-P-17b 10 .
339 0 . ± .
019 1 . ± .
030 787 ±
15 5246 ±
80 2 . . − .
188 0 . ± .
08 0 . ± .
039 6 . ± .
30 19 .
95 97HAT-P-18b 5 .
508 0 . ± .
013 0 . ± .
052 852 ±
28 4803 ±
80 2 . . − .
359 0 . ± .
08 0 . ± .
031 12 . . − .
40 19 .
95 75HAT-P-19b 4 .
009 0 . ± .
018 1 . ± .
072 1010 ±
42 4989 ±
126 2 . . − .
353 0 . ± .
08 0 . ± .
042 8 . ± .
20 19 .
95 75HAT-P-1b 4 .
465 0 . ± .
031 1 . ± .
059 1306 ±
30 6076 ±
27 1 . . − .
161 0 . ± .
03 1 . . − .
079 2 . . − .
00 8 .
70 11,13,18
AT-P-65b and HAT-P-66b 29
Table 8 — Continued
Planet Period
Mp Rp T eq T eff ⋆ ρ⋆ [Fe / H] M⋆ Age t tot Refs.(d) ( M J) ( R J) (K) (K) (g cm −
3) ( M ⊙ ) (Gyr) (Gyr)HAT-P-20b 2 .
875 7 . ± .
187 0 . ± .
033 970 ±
23 4595 ±
80 3 . . − .
297 0 . ± .
08 0 . ± .
028 6 . . − .
80 19 .
95 84HAT-P-21b 4 .
124 4 . ± .
161 1 . ± .
092 1283 ±
50 5588 ±
80 0 . . − .
200 0 . ± .
08 0 . ± .
042 10 . ± .
50 15 .
00 84HAT-P-22b 3 .
212 2 . ± .
061 1 . ± .
058 1283 ±
32 5302 ±
80 1 . . − .
140 0 . ± .
08 0 . ± .
035 12 . ± .
60 18 .
85 84HAT-P-23b 1 .
213 2 . ± .
111 1 . ± .
090 2056 ±
66 5905 ±
80 0 . . − .
152 0 . ± .
04 1 . ± .
035 4 . ± .
00 8 .
55 84HAT-P-24b 3 .
355 0 . ± .
033 1 . ± .
067 1637 ±
42 6373 ±
80 0 . . − . − . ± .
08 1 . ± .
042 2 . ± .
60 5 .
95 56HAT-P-25b 3 .
653 0 . ± .
022 1 . . − .
056 1202 ±
36 5500 ±
80 1 . . − .
247 0 . ± .
08 1 . ± .
032 3 . ± .
30 13 .
50 96HAT-P-26b 4 .
235 0 . ± .
007 0 . . − .
032 1001+66 −
37 5079 ±
88 2 . . − . − . ± .
08 0 . ± .
033 9 . . − .
90 19 .
95 77HAT-P-27b 3 .
040 0 . ± .
033 1 . . − .
058 1207 ±
41 5302 ±
88 1 . . − .
306 0 . ± .
10 0 . ± .
035 4 . . − .
60 17 .
10 80HAT-P-28b 3 .
257 0 . ± .
037 1 . . − .
075 1371 ±
50 5681 ±
88 1 . . − .
239 0 . ± .
08 1 . ± .
046 5 . ± .
30 12 .
05 79HAT-P-29b 5 .
723 0 . . − .
040 1 . . − .
082 1260+64 −
45 6087 ±
88 0 . . − .
251 0 . ± .
08 1 . ± .
046 2 . ± .
00 6 .
90 79HAT-P-2b 5 .
633 9 . ± .
240 1 . . − .
062 1540 ±
30 6290 ±
60 0 . . − .
065 0 . ± .
08 1 . ± .
040 2 . ± .
50 4 .
55 60HAT-P-30b 2 .
811 0 . ± .
028 1 . ± .
065 1630 ±
42 6304 ±
88 0 . . − .
113 0 . ± .
08 1 . ± .
041 1 . . − .
50 6 .
05 81HAT-P-31b 5 .
005 2 . . − .
077 1 . . − .
320 1450+230 −
110 6065 ±
100 0 . . − .
260 0 . ± .
08 1 . . − .
063 3 . . − .
11 6 .
55 74HAT-P-32b 2 .
150 0 . ± .
164 1 . ± .
025 1786 ±
26 6207 ±
88 0 . . − . − . ± .
08 1 . ± .
041 2 . ± .
80 7 .
00 85HAT-P-33b 3 .
474 0 . ± .
101 1 . ± .
045 1782 ±
28 6446 ±
88 0 . . − .
030 0 . ± .
08 1 . ± .
040 2 . ± .
30 4 .
25 85HAT-P-34b 5 .
453 3 . ± .
211 1 . . − .
092 1520 ±
60 6442 ±
88 0 . . − .
122 0 . ± .
04 1 . ± .
047 1 . . − .
50 4 .
35 95HAT-P-35b 3 .
647 1 . ± .
033 1 . ± .
098 1581 ±
45 6096 ±
88 0 . . − .
098 0 . ± .
08 1 . ± .
048 3 . . − .
50 6 .
10 95HAT-P-36b 1 .
327 1 . ± .
099 1 . ± .
071 1823 ±
55 5560 ±
100 1 . . − .
159 0 . ± .
10 1 . ± .
049 6 . . − .
80 12 .
80 95HAT-P-37b 2 .
797 1 . ± .
103 1 . ± .
077 1271 ±
47 5500 ±
100 1 . . − .
351 0 . ± .
10 0 . ± .
043 3 . . − .
20 16 .
25 95HAT-P-38b 4 .
640 0 . ± .
020 0 . . − .
063 1082 ±
55 5330 ±
100 1 . . − .
415 0 . ± .
10 0 . ± .
044 10 . ± .
80 19 .
50 104HAT-P-39b 3 .
544 0 . ± .
099 1 . . − .
081 1752 ±
43 6430 ±
100 0 . . − .
063 0 . ± .
10 1 . ± .
051 2 . ± .
40 4 .
20 94HAT-P-3b 2 .
900 0 . . − .
026 0 . . − .
049 1127+49 −
39 5185 ±
46 2 . . − .
281 0 . ± .
04 0 . . − .
054 1 . . − .
40 18 .
15 3,11,59HAT-P-40b 4 .
457 0 . ± .
038 1 . ± .
062 1770 ±
33 6080 ±
100 0 . . − .
020 0 . ± .
10 1 . . − .
109 2 . . − .
30 3 .
35 94HAT-P-41b 2 .
694 0 . ± .
102 1 . . − .
051 1941 ±
38 6390 ±
100 0 . . − .
042 0 . ± .
10 1 . ± .
047 2 . ± .
40 4 .
05 94HAT-P-42b 4 .
642 0 . ± .
126 1 . ± .
149 1427 ±
58 5743 ±
50 0 . . − .
111 0 . ± .
08 1 . ± .
067 5 . . − .
70 7 .
65 112HAT-P-43b 3 .
333 0 . ± .
083 1 . . − .
034 1361 ±
24 5645 ±
74 1 . . − .
106 0 . ± .
08 1 . . − .
042 5 . . − .
10 11 .
65 112HAT-P-44b 4 .
301 0 . ± .
031 1 . . − .
074 1126+67 −
42 5295 ±
100 1 . . − .
388 0 . ± .
10 0 . ± .
041 8 . ± .
90 17 .
50 123HAT-P-45b 3 .
129 0 . . − .
099 1 . . − .
087 1652+90 −
52 6330 ±
100 0 . . − .
220 0 . ± .
10 1 . ± .
058 2 . ± .
80 5 .
65 123HAT-P-46b 4 .
463 0 . . − .
052 1 . . − .
133 1458+140 −
75 6120 ±
100 0 . . − .
291 0 . ± .
10 1 . . − .
060 2 . . − .
00 5 .
75 123HAT-P-47b 4 .
732 0 . ± .
039 1 . ± .
045 1605 ±
22 6703 ±
50 0 . . − .
045 0 . ± .
08 1 . ± .
038 1 . ± .
30 3 .
95 161HAT-P-48b 4 .
409 0 . ± .
024 1 . ± .
054 1361 ±
25 5946 ±
50 0 . . − .
093 0 . ± .
08 1 . ± .
041 4 . . − .
80 8 .
80 161HAT-P-49b 2 .
692 1 . ± .
205 1 . . − .
077 2131+69 −
42 6820 ±
52 0 . . − .
069 0 . ± .
08 1 . ± .
051 1 . ± .
20 2 .
95 126HAT-P-4b 3 .
057 0 . ± .
068 1 . . − .
044 1686+30 −
26 5860 ±
80 0 . . − .
058 0 . ± .
08 1 . . − .
120 4 . . − .
00 6 .
20 5,11,71HAT-P-50b 3 .
122 1 . ± .
073 1 . ± .
064 1862 ±
34 6280 ±
49 0 . ± . − . ± .
08 1 . . − .
115 3 . . − .
27 4 .
75 135HAT-P-51b 4 .
218 0 . ± .
018 1 . ± .
054 1192 ±
21 5449 ±
50 1 . . − .
135 0 . ± .
08 0 . ± .
028 8 . ± .
70 15 .
15 135HAT-P-52b 2 .
754 0 . ± .
029 1 . ± .
072 1218 ±
37 5131 ±
50 1 . ± .
290 0 . ± .
08 0 . ± .
027 9 . ± .
10 19 .
95 135HAT-P-53b 1 .
962 1 . ± .
056 1 . ± .
091 1778 ±
48 5956 ±
50 0 . ± .
130 0 . ± .
08 1 . ± .
043 4 . . − .
83 8 .
90 135HAT-P-54b 3 .
800 0 . ± .
032 0 . ± .
028 818 ±
12 4390 ±
50 3 . . − . − . ± .
08 0 . ± .
020 3 . . − .
10 19 .
95 132HAT-P-55b 3 .
585 0 . ± .
056 1 . ± .
055 1313 ±
26 5808 ±
50 1 . . − . − . ± .
08 1 . ± .
037 4 . ± .
70 11 .
50 151HAT-P-56b 2 .
791 2 . ± .
250 1 . ± .
040 1840 ±
21 6566 ±
50 0 . ± . − . ± .
08 1 . ± .
036 2 . ± .
35 4 .
75 140HAT-P-57b 2 .
465 0 . . − .
000 1 . ± .
054 2200 ±
76 7500 ±
250 0 . . − . − . ± .
25 1 . ± .
120 1 . . − .
51 2 .
85 137HAT-P-58b 4 .
014 0 . ± .
034 1 . . − .
063 1500+49 −
29 5931 ±
50 0 . ± .
066 0 . ± .
08 1 . . − .
042 6 . . − .
66 8 .
45 162HAT-P-59b 4 .
142 1 . ± .
061 1 . ± .
066 1273 ±
27 5665 ±
50 1 . ± .
130 0 . ± .
08 1 . ± .
022 4 . ± .
00 10 .
20 162HAT-P-5b 2 .
788 1 . ± .
110 1 . . − .
056 1539+33 −
32 5960 ±
100 1 . . − .
129 0 . ± .
15 1 . . − .
081 2 . . − .
40 8 .
10 6,11HAT-P-60b 4 .
795 0 . ± .
049 1 . . − .
064 1662+73 −
42 6462 ±
50 0 . . − . − . ± .
08 1 . ± .
070 2 . ± .
56 4 .
10 162HAT-P-61b 1 .
902 1 . . − .
071 0 . . − .
047 1526 ±
36 5551 ±
50 1 . ± .
180 0 . ± .
08 1 . ± .
022 2 . . − .
50 11 .
95 162HAT-P-62b 2 .
645 0 . ± .
088 1 . . − .
053 1523 ±
31 5601 ±
50 0 . ± .
087 0 . ± .
08 1 . ± .
028 5 . ± .
89 9 .
60 162HAT-P-63b 3 .
378 0 . ± .
023 1 . ± .
094 1246 ±
32 5365 ±
50 1 . ± .
180 0 . ± .
08 0 . ± .
022 7 . ± .
00 14 .
95 162HAT-P-64b 4 .
007 0 . ± .
160 1 . ± .
140 1741+48 −
35 6302 ±
50 0 . . − . − . ± .
08 1 . ± .
046 2 . ± .
30 4 .
10 162HAT-P-65b 2 .
605 0 . ± .
083 1 . ± .
130 1930 ±
45 5835 ±
51 0 . ± .
036 0 . ± .
08 1 . ± .
050 5 . ± .
61 6 .
50 166HAT-P-66b 2 .
972 0 . ± .
057 1 . . − .
100 1897+66 −
42 6002 ±
50 0 . ± .
040 0 . ± .
08 1 . . − .
054 4 . . − .
12 5 .
60 166HAT-P-6b 3 .
853 1 . . − .
052 1 . . − .
058 1675+32 −
31 6570 ±
80 0 . . − . − . ± .
08 1 . . − .
066 2 . . − .
60 4 .
65 10,11,58HAT-P-7b 2 .
205 1 . ± .
030 1 . ± .
020 2140+110 −
60 6350 ±
80 0 . ± .
003 0 . ± .
08 1 . ± .
040 2 . ± .
26 3 .
25 12,46,47,48HAT-P-8b 3 .
076 1 . . − .
160 1 . . − .
060 1700 ±
35 6200 ±
80 0 . . − .
063 0 . ± .
08 1 . ± .
040 3 . ± .
00 5 .
20 31HAT-P-9b 3 .
923 0 . ± .
090 1 . ± .
060 1530 ±
40 6350 ±
150 0 . . − .
135 0 . ± .
20 1 . ± .
130 1 . . − .
40 5 .
50 23,103HATS-10b 3 .
313 0 . ± .
081 0 . . − .
045 1407 ±
39 5880 ±
120 1 . . − .
160 0 . ± .
10 1 . ± .
054 3 . ± .
70 9 .
40 138HATS-11b 3 .
619 0 . ± .
120 1 . ± .
078 1637 ±
48 6060 ±
150 0 . . − . − . ± .
06 1 . ± .
060 7 . . − .
60 9 .
40 156HATS-12b 3 .
143 2 . ± .
110 1 . ± .
170 2097 ±
89 6408 ±
75 0 . . − . − . ± .
04 1 . ± .
071 2 . ± .
31 3 .
00 156HATS-13b 3 .
044 0 . ± .
072 1 . ± .
035 1244 ±
20 5523 ±
69 1 . ± .
110 0 . ± .
06 0 . ± .
029 2 . ± .
70 14 .
55 131HATS-14b 2 .
767 1 . ± .
070 1 . . − .
022 1276 ±
20 5408 ±
65 1 . . − .
126 0 . ± .
03 0 . ± .
024 4 . ± .
70 15 .
70 131,145HATS-15b 1 .
747 2 . ± .
150 1 . ± .
040 1505 ±
30 5311 ±
77 1 . ± .
120 0 . ± .
05 0 . ± .
023 11 . . − .
00 19 .
95 150HATS-16b 2 .
687 3 . ± .
190 1 . ± .
150 1592+61 −
82 5738 ±
79 0 . . − .
130 0 . ± .
05 0 . ± .
035 9 . ± .
80 14 .
50 150HATS-17b 16 .
255 1 . ± .
065 0 . ± .
056 814 ±
25 5846 ±
78 1 . ± .
270 0 . ± .
03 1 . ± .
030 2 . ± .
30 8 .
95 154HATS-18b 0 .
838 1 . ± .
077 1 . . − .
049 2060 ±
59 5600 ±
120 1 . . − .
210 0 . ± .
08 1 . ± .
047 4 . ± .
20 12 .
25 167HATS-19b 4 .
570 0 . ± .
071 1 . . − .
210 1570 ±
110 5896 ±
77 0 . . − .
110 0 . ± .
05 1 . ± .
083 3 . . − .
50 5 .
40 164HATS-1b 3 .
446 1 . . − .
196 1 . . − .
098 1359+89 −
59 5870 ±
100 1 . . − . − . ± .
12 0 . ± .
054 6 . ± .
80 12 .
50 114HATS-20b 3 .
799 0 . ± .
035 0 . ± .
055 1147 ±
36 5406 ±
49 1 . ± .
480 0 . ± .
05 0 . ± .
026 6 . ± .
40 17 .
50 164HATS-21b 3 .
554 0 . . − .
030 1 . . − .
054 1284+55 −
31 5695 ±
67 1 . ± .
380 0 . ± .
04 1 . ± .
026 2 . ± .
70 10 .
60 164HATS-22b 4 .
723 2 . ± .
110 0 . . − .
029 858+24 −
17 4803 ±
55 3 . ± .
680 0 . ± .
04 0 . ± .
019 4 . . − .
00 19 .
95 163HATS-23b 2 .
161 1 . ± .
072 1 . . − .
400 1654 ±
54 5780 ±
120 0 . . − .
110 0 . ± .
07 1 . ± .
046 4 . ± .
50 9 .
20 163HATS-24b 1 .
348 2 . ± .
180 1 . . − .
054 2067 ±
39 6346 ±
81 1 . . − .
085 0 . ± .
05 1 . ± .
033 0 . . − .
45 6 .
15 163HATS-25b 4 .
299 0 . ± .
042 1 . ± .
100 1277 ±
42 5715 ±
73 1 . ± .
200 0 . ± .
05 0 . ± .
035 7 . ± .
90 12 .
70 159
Table 8 — Continued
Planet Period
Mp Rp T eq T eff ⋆ ρ⋆ [Fe / H] M⋆ Age t tot Refs.(d) ( M J) ( R J) (K) (K) (g cm −
3) ( M ⊙ ) (Gyr) (Gyr)HATS-26b 3 .
302 0 . ± .
076 1 . ± .
210 1918 ±
61 6071 ±
81 0 . ± . − . ± .
05 1 . . − .
056 4 . . − .
94 4 .
85 159HATS-27b 4 .
637 0 . ± .
130 1 . ± .
140 1661 ±
50 6438 ±
64 0 . ± .
059 0 . ± .
04 1 . ± .
045 2 . ± .
21 3 .
90 159HATS-28b 3 .
181 0 . ± .
087 1 . ± .
070 1253 ±
35 5498 ±
84 1 . ± .
270 0 . ± .
06 0 . ± .
036 6 . ± .
80 16 .
10 159HATS-29b 4 .
606 0 . ± .
063 1 . ± .
061 1212 ±
30 5670 ±
110 1 . ± .
110 0 . ± .
08 1 . ± .
049 5 . . − .
70 11 .
95 159HATS-2b 1 .
354 1 . ± .
150 1 . ± .
030 1577 ±
31 5227 ±
95 1 . . − .
127 0 . ± .
05 0 . ± .
037 9 . ± .
90 19 .
95 111HATS-30b 3 .
174 0 . ± .
039 1 . ± .
052 1414 ±
32 5943 ±
70 1 . ± .
190 0 . ± .
05 1 . ± .
031 2 . ± .
20 9 .
20 159HATS-31b 3 .
378 0 . ± .
120 1 . ± .
220 1823 ±
81 6050 ±
120 0 . . − .
061 0 . ± .
07 1 . ± .
096 4 . ± .
10 5 .
25 165HATS-32b 2 .
813 0 . ± .
100 1 . . − .
096 1437 ±
58 5700 ±
110 1 . ± .
230 0 . ± .
05 1 . ± .
044 3 . ± .
80 9 .
90 165HATS-33b 2 .
550 1 . ± .
053 1 . . − .
081 1429 ±
38 5659 ±
85 1 . ± .
170 0 . ± .
05 1 . ± .
032 3 . ± .
70 11 .
25 165HATS-34b 2 .
106 0 . ± .
072 1 . ± .
190 1445 ±
42 5380 ±
73 1 . ± .
250 0 . ± .
07 0 . ± .
031 7 . ± .
70 16 .
30 165HATS-35b 1 .
821 1 . ± .
077 1 . . − .
130 2100 ±
100 6300 ±
100 0 . ± .
180 0 . ± .
06 1 . ± .
060 2 . ± .
55 4 .
85 165HATS-3b 3 .
548 1 . ± .
136 1 . ± .
035 1648 ±
24 6351 ±
76 0 . . − . − . ± .
07 1 . ± .
036 3 . . − .
40 5 .
70 115HATS-4b 2 .
517 1 . ± .
028 1 . ± .
037 1315 ±
21 5403 ±
50 1 . . − .
122 0 . ± .
08 1 . ± .
020 2 . ± .
60 13 .
65 127HATS-5b 4 .
763 0 . ± .
012 0 . ± .
025 1025 ±
17 5304 ±
50 2 . . − .
165 0 . ± .
08 0 . ± .
028 3 . . − .
90 17 .
25 124HATS-6b 3 .
325 0 . ± .
070 0 . ± .
019 712 ± ±
100 4 . ± .
150 0 . ± .
09 0 . . − .
027 0 . ± .
00 19 .
95 133HATS-7b 3 .
185 0 . ± .
012 0 . . − .
034 1084 ±
32 4985 ±
50 2 . . − .
356 0 . ± .
08 0 . ± .
027 7 . ± .
00 19 .
95 143HATS-8b 3 .
584 0 . ± .
019 0 . . − .
075 1324+79 −
38 5679 ±
50 1 . . − .
373 0 . ± .
08 1 . ± .
037 5 . ± .
70 11 .
25 139HATS-9b 1 .
915 0 . ± .
029 1 . ± .
098 1823+52 −
35 5366 ±
70 0 . . − .
070 0 . ± .
05 1 . ± .
039 10 . ± .
50 12 .
55 138KELT-10b 4 .
166 0 . . − .
038 1 . . − .
049 1377+28 −
23 5948 ±
74 0 . . − .
088 0 . . − .
10 1 . . − .
061 3 . . − .
51 7 .
50 148KELT-15b 3 .
329 0 . . − .
220 1 . . − .
057 1642+45 −
25 6003+56 −
52 0 . . − .
076 0 . ± .
03 1 . . − .
050 3 . . − .
19 5 .
95 149KELT-1b 1 .
218 27 . . − .
480 1 . . − .
022 2422+32 −
26 6518 ±
50 0 . . − .
039 0 . ± .
07 1 . ± .
026 1 . . − .
17 4 .
30 99KELT-2Ab 4 .
114 1 . ± .
088 1 . . − .
067 1716+39 −
33 6148+48 −
49 0 . . − . − . ± .
07 1 . . − .
029 3 . . − .
12 3 .
95 98KELT-3b 2 .
703 1 . . − .
066 1 . . − .
069 1821+35 −
37 6304 ±
49 0 . . − .
054 0 . . − .
08 1 . . − .
060 2 . . − .
26 4 .
90 116KELT-4Ab 2 .
990 0 . . − .
059 1 . . − .
045 1823 ±
27 6206 ±
75 0 . . − . − . . − .
07 1 . . − .
061 3 . . − .
17 4 .
65 153KELT-6b 7 .
846 0 . . − .
046 1 . . − .
077 1313+59 −
38 6102 ±
43 0 . . − . − . . − .
04 1 . . − .
040 5 . . − .
27 7 .
00 125KELT-7b 2 .
735 1 . ± .
180 1 . . − .
047 2048 ±
27 6789+50 −
49 0 . . − .
035 0 . . − .
08 1 . . − .
054 1 . . − .
10 2 .
95 134KELT-8b 3 .
244 0 . . − .
061 1 . . − .
160 1675+61 −
55 5754+54 −
55 0 . . − .
067 0 . ± .
04 1 . . − .
066 4 . . − .
25 5 .
55 141TrES-1b 3 .
030 0 . . − .
046 1 . . − .
021 1140+13 −
12 5230 ±
50 2 . . − .
120 0 . ± .
05 0 . . − .
040 1 . . − .
74 17 .
70 11,22TrES-2b 2 .
471 1 . . − .
053 1 . ± .
041 1498 ±
17 5850+38 −
38 1 . . − . − . . − .
06 0 . . − .
063 2 . . − .
50 9 .
85 1,2,11,18,19TrES-4b 3 .
554 0 . . − .
082 1 . . − .
086 1785 ±
29 6200 ±
75 0 . . − .
032 0 . ± .
09 1 . . − .
134 2 . . − .
18 3 .
80 4,25TrES-5b 1 .
482 1 . ± .
063 1 . ± .
021 1484 ±
41 5171 ±
36 1 . . − .
098 0 . ± .
08 0 . ± .
024 5 . . − .
78 18 .
45 83WASP-100b 2 .
849 2 . ± .
120 1 . ± .
290 2190 ±
140 6900 ±
120 0 . . − . − . ± .
10 1 . ± .
100 1 . . − .
13 2 .
35 128WASP-101b 3 .
586 0 . ± .
040 1 . ± .
050 1560 ±
35 6380 ±
120 0 . ± .
061 0 . ± .
12 1 . ± .
070 0 . . − .
08 4 .
80 128WASP-103b 0 .
926 1 . ± .
088 1 . . − .
047 2508+75 −
70 6110 ±
160 0 . . − .
055 0 . ± .
13 1 . . − .
036 2 . . − .
56 5 .
25 118WASP-104b 1 .
755 1 . ± .
047 1 . ± .
037 1516 ±
39 5450 ±
130 1 . ± .
099 0 . ± .
09 1 . ± .
049 1 . . − .
13 12 .
10 121WASP-106b 9 .
290 1 . ± .
076 1 . . − .
028 1140 ±
29 6000 ±
150 0 . . − . − . ± .
09 1 . ± .
054 3 . . − .
52 6 .
30 121WASP-10b 3 .
093 3 . . − .
110 1 . ± .
020 1119+26 −
28 4675 ±
100 3 . ± .
088 0 . ± .
20 0 . . − .
028 4 . . − .
04 19 .
95 26,36,57WASP-117b 10 .
022 0 . ± .
009 1 . . − .
065 1024+30 −
26 6040 ±
90 0 . ± . − . ± .
14 1 . ± .
029 2 . . − .
71 7 .
40 120WASP-119b 2 .
500 1 . ± .
080 1 . ± .
200 1600 ±
80 5650 ±
100 0 . ± .
250 0 . ± .
10 1 . ± .
060 5 . . − .
75 8 .
90 155WASP-120b 3 .
611 5 . ± .
260 1 . ± .
083 1890 ±
50 6450 ±
120 0 . ± . − . ± .
07 1 . ± .
110 2 . ± .
18 3 .
20 147WASP-121b 1 .
275 1 . . − .
062 1 . ± .
044 2358 ±
52 6459 ±
140 0 . . − .
013 0 . ± .
09 1 . . − .
079 1 . . − .
36 4 .
05 146WASP-122b 1 .
710 1 . ± .
051 1 . . − .
062 1960 ±
50 5774+75 −
74 0 . . − .
025 0 . . − .
06 1 . . − .
043 4 . . − .
29 6 .
35 147,149WASP-123b 2 .
978 0 . ± .
050 1 . ± .
074 1510 ±
40 5740 ±
130 0 . ± .
080 0 . ± .
08 1 . ± .
089 4 . . − .
74 8 .
20 147WASP-124b 3 .
373 0 . ± .
070 1 . ± .
030 1400 ±
30 6050 ±
100 1 . ± . − . ± .
11 1 . ± .
050 0 . . − .
04 7 .
45 155WASP-126b 3 .
289 0 . ± .
040 0 . . − .
050 1480 ±
60 5800 ±
100 0 . . − .
170 0 . ± .
08 1 . ± .
060 4 . . − .
63 8 .
00 155WASP-12b 1 .
091 1 . ± .
100 1 . ± .
090 2516 ±
36 6300+200 −
100 0 . ± .
042 0 . . − .
15 1 . ± .
140 1 . . − .
40 4 .
05 27WASP-130b 11 .
551 1 . ± .
040 0 . ± .
030 833 ±
18 5600 ±
100 1 . ± .
130 0 . ± .
10 1 . ± .
040 0 . . − .
03 10 .
60 158WASP-131b 5 .
322 0 . ± .
020 1 . ± .
050 1460 ±
30 5950 ±
100 0 . ± . − . ± .
08 1 . ± .
060 5 . . − .
62 7 .
20 158WASP-132b 7 .
134 0 . ± .
030 0 . ± .
030 763 ±
16 4750 ±
100 2 . . − .
200 0 . ± .
13 0 . ± .
040 3 . . − .
92 19 .
95 158WASP-133b 2 .
176 1 . ± .
090 1 . ± .
050 1790 ±
40 5700 ±
100 0 . ± .
040 0 . ± .
12 1 . ± .
080 4 . . − .
54 6 .
75 155WASP-135b 1 .
401 1 . ± .
080 1 . ± .
090 1717+46 −
40 5680 ±
60 1 . ± .
210 0 . ± .
13 1 . ± .
070 2 . . − .
11 10 .
70 160WASP-13b 4 .
353 0 . . − .
050 1 . . − .
120 1417+62 −
58 5826 ±
100 0 . . − .
140 0 . ± .
20 1 . . − .
090 4 . . − .
70 6 .
65 17,100WASP-140b 2 .
236 2 . ± .
070 1 . . − .
180 1320 ±
40 5300 ±
100 1 . ± .
250 0 . ± .
10 0 . ± .
040 2 . . − .
22 15 .
10 158WASP-141b 3 .
311 2 . ± .
150 1 . ± .
080 1540 ±
50 6050 ±
120 0 . ± .
099 0 . ± .
09 1 . ± .
060 2 . . − .
50 5 .
65 158WASP-142b 2 .
053 0 . ± .
090 1 . ± .
080 2000 ±
60 6060 ±
150 0 . ± .
056 0 . ± .
12 1 . ± .
080 2 . . − .
43 4 .
50 158WASP-14b 2 .
244 7 . . − .
496 1 . . − .
082 1866+37 −
42 6475 ±
100 0 . . − .
085 0 . ± .
20 1 . . − .
122 0 . . − .
40 4 .
30 35,39WASP-157b 3 .
952 0 . ± .
093 1 . ± .
044 1339 ±
93 5840 ±
140 1 . ± .
320 0 . ± .
09 1 . ± .
120 0 . . − .
04 7 .
65 157WASP-15b 3 .
752 0 . ± .
050 1 . ± .
077 1652 ±
28 6300 ±
100 0 . ± . − . ± .
11 1 . ± .
120 2 . . − .
32 4 .
80 21WASP-16b 3 .
119 0 . . − .
076 1 . . − .
060 1280+35 −
21 5700 ±
150 1 . . − .
250 0 . ± .
10 1 . . − .
129 0 . . − .
04 10 .
35 30WASP-17b 3 .
735 0 . ± .
032 1 . ± .
081 1771 ±
35 6650 ±
80 0 . ± . − . ± .
09 1 . ± .
026 1 . . − .
19 3 .
75 87WASP-18b 0 .
941 10 . ± .
380 1 . ± .
057 2384+58 −
30 6400 ±
100 0 . ± .
088 0 . ± .
09 1 . ± .
069 0 . . − .
33 5 .
15 33,38WASP-19b 0 .
789 1 . ± .
023 1 . ± .
032 2050 ±
40 5500 ±
100 1 . . − .
059 0 . ± .
09 0 . ± .
020 6 . . − .
39 13 .
65 44,78WASP-1b 2 .
520 0 . . − .
090 1 . . − .
047 1811+34 −
27 6110 ±
45 0 . . − .
059 0 . ± .
08 1 . . − .
047 2 . . − .
23 5 .
30 8,11,82WASP-20b 4 .
900 0 . ± .
018 1 . ± .
057 1379 ±
32 5950 ±
100 0 . ± . − . ± .
06 1 . ± .
040 4 . . − .
45 6 .
75 130WASP-21b 4 .
323 0 . ± .
010 1 . . − .
030 1321+30 −
26 5800 ±
100 0 . . − . − . ± .
10 0 . ± .
040 9 . . − .
58 13 .
00 41,88WASP-22b 3 .
533 0 . ± .
017 1 . . − .
038 1466 ±
34 6000 ±
100 0 . . − . − . ± .
08 1 . ± .
026 3 . . − .
60 7 .
45 43,69WASP-23b 2 .
944 0 . . − .
099 0 . . − .
056 1119+22 −
21 5150 ±
100 2 . . − . − . ± .
13 0 . . − .
120 1 . . − .
78 18 .
85 65WASP-24b 2 .
341 1 . . − .
037 1 . . − .
057 1660+44 −
42 6075 ±
100 1 . . − .
100 0 . ± .
10 1 . . − .
025 1 . . − .
46 6 .
55 53WASP-25b 3 .
765 0 . ± .
040 1 . . − .
050 1212 ±
35 5703 ±
100 1 . ± . − . ± .
10 1 . ± .
030 1 . . − .
85 11 .
00 86WASP-26b 2 .
757 1 . ± .
021 1 . ± .
075 1637 ±
45 5950 ±
100 0 . ± . − . ± .
09 1 . ± .
028 4 . . − .
42 7 .
00 42,69WASP-28b 3 .
409 0 . ± .
043 1 . ± .
042 1468 ±
37 6150 ±
140 1 . ± . − . ± .
10 1 . ± .
050 2 . . − .
81 7 .
20 130
AT-P-65b and HAT-P-66b 31
Table 8 — Continued
Planet Period
Mp Rp T eq T eff ⋆ ρ⋆ [Fe / H] M⋆ Age t tot Refs.(d) ( M J) ( R J) (K) (K) (g cm −
3) ( M ⊙ ) (Gyr) (Gyr)WASP-29b 3 .
923 0 . ± .
020 0 . . − .
035 980 ±
40 4800 ±
150 2 . . − .
320 0 . ± .
14 0 . ± .
033 11 . . − .
10 19 .
95 54WASP-2b 2 .
152 0 . . − .
093 1 . . − .
083 1304 ±
54 5200 ±
200 2 . . − .
150 0 . ± .
05 0 . ± .
120 4 . . − .
38 17 .
65 7,11,82,110WASP-30b 4 .
157 60 . ± .
890 0 . ± .
021 1474 ±
25 6100 ±
100 0 . ± . − . ± .
10 1 . ± .
026 3 . . − .
51 6 .
50 76WASP-31b 3 .
406 0 . ± .
030 1 . ± .
060 1568 ±
33 6203 ±
98 0 . ± . − . ± .
09 1 . ± .
026 2 . . − .
53 6 .
55 67WASP-32b 2 .
719 3 . ± .
070 1 . ± .
070 1560 ±
50 6100 ±
100 1 . ± . − . ± .
10 1 . ± .
030 1 . . − .
69 7 .
15 62WASP-34b 4 .
318 0 . ± .
010 1 . . − .
080 1250 ±
30 5700 ±
100 1 . . − . − . ± .
10 1 . ± .
070 0 . . − .
05 10 .
75 64WASP-35b 3 .
162 0 . ± .
060 1 . ± .
030 1450 ±
20 6050 ±
100 1 . ± . − . ± .
09 1 . ± .
020 2 . . − .
72 7 .
75 73WASP-36b 1 .
537 2 . ± .
068 1 . ± .
030 1700+42 −
44 5800 ±
150 1 . . − . − . ± .
12 1 . ± .
032 2 . . − .
30 10 .
60 93WASP-37b 3 .
577 1 . . − .
128 1 . . − .
051 1325+25 −
15 5800 ±
150 0 . . − . − . ± .
12 0 . . − .
040 9 . . − .
09 12 .
10 72WASP-38b 6 .
872 2 . ± .
065 1 . . − .
044 1261+24 −
23 6150 ±
80 0 . ± . − . ± .
07 1 . ± .
041 3 . . − .
30 6 .
10 63WASP-39b 4 .
055 0 . ± .
030 1 . ± .
040 1116+33 −
32 5400 ±
150 1 . . − . − . ± .
10 0 . ± .
030 5 . . − .
17 15 .
40 66WASP-3b 1 .
847 1 . . − .
036 1 . . − .
120 1960+33 −
76 6400 ±
100 0 . . − .
070 0 . ± .
20 1 . . − .
110 0 . . − .
44 4 .
60 9,14,49WASP-41b 3 .
052 0 . ± .
070 1 . ± .
070 1235 ±
50 5450 ±
150 1 . ± . − . ± .
09 0 . ± .
030 4 . . − .
78 14 .
30 90WASP-42b 4 .
982 0 . ± .
035 1 . ± .
057 995 ±
34 5200 ±
150 1 . ± .
200 0 . ± .
13 0 . . − .
081 4 . . − .
27 16 .
90 91WASP-43b 0 .
813 1 . ± .
100 0 . . − .
090 1370 ±
70 4400 ±
200 3 . . − . − . ± .
17 0 . ± .
050 6 . . − .
61 19 .
95 70WASP-44b 2 .
424 0 . . − .
066 1 . . − .
140 1343 ±
64 5400 ±
150 1 . . − .
423 0 . ± .
10 0 . ± .
034 2 . . − .
11 13 .
65 101WASP-45b 3 .
126 1 . ± .
053 1 . . − .
140 1198 ±
69 5100 ±
200 1 . ± .
381 0 . ± .
12 0 . . − .
000 8 . . − .
22 18 .
05 101WASP-46b 1 .
430 2 . ± .
073 1 . ± .
058 1654 ±
50 5600 ±
150 1 . ± . − . ± .
13 0 . ± .
034 6 . . − .
37 14 .
45 101WASP-47b 4 .
159 1 . ± .
091 1 . ± .
039 1220 ±
20 5400 ±
100 1 . ± .
013 0 . ± .
07 1 . ± .
037 9 . . − .
04 14 .
95 102,142,144WASP-47d 9 .
031 0 . . − .
011 0 . ± .
012 943+17 −
17 5400 ±
100 1 . ± .
013 0 . ± .
07 1 . ± .
037 9 . . − .
01 14 .
95 102,142WASP-47e 0 .
790 0 . ± .
012 0 . ± .
006 2126+39 −
39 5400 ±
100 1 . ± .
013 0 . ± .
07 1 . ± .
037 9 . . − .
86 15 .
00 102,142,144WASP-48b 2 .
144 0 . ± .
090 1 . ± .
080 2030 ±
70 6000 ±
150 0 . ± . − . ± .
12 1 . ± .
040 4 . . − .
18 5 .
50 73WASP-49b 2 .
782 0 . ± .
027 1 . ± .
047 1369 ±
39 5600 ±
150 1 . ± . − . ± .
07 0 . . − .
076 7 . . − .
97 14 .
55 91WASP-4b 1 .
338 1 . ± .
064 1 . ± .
021 1650 ±
30 5500 ±
100 1 . . − . − . ± .
09 0 . ± .
040 3 . . − .
28 13 .
45 15,20WASP-50b 1 .
955 1 . . − .
086 1 . ± .
048 1393 ±
30 5400 ±
100 2 . . − . − . ± .
08 0 . . − .
074 3 . . − .
42 15 .
55 68WASP-52b 1 .
750 0 . ± .
020 1 . ± .
030 1315 ±
35 5000 ±
100 2 . ± .
110 0 . ± .
12 0 . ± .
030 4 . . − .
23 19 .
95 105WASP-54b 3 .
694 0 . ± .
023 1 . . − .
180 1742+49 −
69 6100 ±
100 0 . . − . − . ± .
08 1 . . − .
036 4 . . − .
44 5 .
80 106WASP-55b 4 .
466 0 . ± .
040 1 . . − .
030 1290 ±
25 5900 ±
100 1 . . − . − . ± .
08 1 . ± .
040 4 . . − .
03 9 .
80 102WASP-56b 4 .
617 0 . . − .
035 1 . . − .
033 1216+25 −
24 5600 ±
100 1 . ± .
060 0 . ± .
06 1 . ± .
024 6 . . − .
98 11 .
30 106WASP-57b 2 .
839 0 . . − .
046 0 . . − .
014 1251+21 −
22 5600 ±
100 2 . . − . − . ± .
10 0 . ± .
027 0 . . − .
51 13 .
60 106WASP-58b 5 .
017 0 . ± .
070 1 . ± .
200 1270 ±
80 5800 ±
150 0 . ± . − . ± .
09 0 . ± .
100 10 . . − .
11 12 .
75 105WASP-59b 7 .
920 0 . ± .
045 0 . ± .
068 670 ±
35 4650 ±
150 4 . ± . − . ± .
11 0 . ± .
035 0 . . − .
03 19 .
95 105WASP-5b 1 .
628 1 . ± .
082 1 . ± .
057 1706+52 −
48 5700 ±
100 1 . ± .
110 0 . ± .
09 1 . ± .
063 4 . . − .
94 10 .
20 15,37,89WASP-60b 4 .
305 0 . ± .
034 0 . ± .
120 1320 ±
75 5900 ±
100 1 . ± . − . ± .
09 1 . ± .
035 3 . . − .
68 8 .
50 105WASP-61b 3 .
856 2 . ± .
170 1 . ± .
030 1565 ±
35 6250 ±
150 0 . . − . − . ± .
12 1 . ± .
070 2 . . − .
53 5 .
35 102WASP-62b 4 .
412 0 . ± .
040 1 . ± .
060 1440 ±
30 6230 ±
80 0 . ± .
085 0 . ± .
06 1 . ± .
050 1 . . − .
36 5 .
85 102WASP-63b 4 .
378 0 . ± .
030 1 . . − .
060 1540 ±
40 5550 ±
100 0 . . − .
035 0 . ± .
07 1 . ± .
050 7 . . − .
71 8 .
00 102WASP-64b 1 .
573 1 . ± .
068 1 . ± .
039 1689 ±
49 5550 ±
150 1 . . − . − . ± .
11 1 . ± .
028 7 . . − .
08 13 .
30 109WASP-65b 2 .
311 1 . ± .
160 1 . ± .
059 1480 ±
10 5600 ±
100 1 . . − . − . ± .
07 0 . ± .
140 7 . . − .
44 13 .
65 113WASP-66b 4 .
086 2 . ± .
130 1 . ± .
090 1790 ±
60 6600 ±
150 0 . . − . − . ± .
10 1 . ± .
070 2 . . − .
23 3 .
35 102WASP-67b 4 .
614 0 . ± .
040 1 . . − .
200 1040 ±
30 5200 ±
100 1 . ± . − . ± .
09 0 . ± .
040 9 . . − .
28 19 .
95 102WASP-68b 5 .
084 0 . ± .
030 1 . . − .
060 1488+49 −
32 5910 ±
60 0 . . − .
071 0 . ± .
08 1 . ± .
030 3 . . − .
23 4 .
95 119WASP-69b 3 .
868 0 . ± .
017 1 . ± .
047 963 ±
18 4700 ±
50 2 . ± .
180 0 . ± .
08 0 . ± .
029 18 . . − .
04 19 .
95 129WASP-6b 3 .
361 0 . . − .
038 1 . . − .
052 1194+58 −
57 5450 ±
100 1 . . − . − . ± .
09 0 . . − .
080 5 . . − .
83 16 .
05 16WASP-70Ab 3 .
713 0 . ± .
022 1 . . − .
102 1387 ±
40 5700 ±
80 0 . . − . − . ± .
06 1 . ± .
042 7 . . − .
10 11 .
40 129WASP-71b 2 .
904 2 . ± .
072 1 . ± .
110 2066 ±
67 6050 ±
100 0 . ± .
030 0 . ± .
07 1 . ± .
062 2 . . − .
17 3 .
00 108WASP-72b 2 .
217 1 . . − .
045 1 . . − .
080 2064+90 −
62 6250 ±
100 0 . . − . − . ± .
09 1 . . − .
035 2 . . − .
27 4 .
15 109WASP-73b 4 .
087 1 . . − .
060 1 . . − .
080 1790+75 −
51 6030 ±
120 0 . . − .
056 0 . ± .
14 1 . . − .
040 2 . . − .
29 3 .
25 119WASP-74b 2 .
138 0 . ± .
060 1 . ± .
060 1910 ±
40 5990 ±
110 0 . ± .
025 0 . ± .
13 1 . ± .
120 2 . . − .
35 4 .
90 136WASP-75b 2 .
484 1 . ± .
050 1 . ± .
048 1710 ±
20 6100 ±
100 0 . ± .
060 0 . ± .
09 1 . ± .
070 2 . . − .
53 6 .
20 113WASP-76b 1 .
810 0 . ± .
030 1 . . − .
040 2160 ±
40 6250 ±
100 0 . . − .
025 0 . ± .
10 1 . ± .
070 2 . . − .
25 3 .
95 152WASP-77Ab 1 .
360 1 . ± .
060 1 . ± .
020 1669+24 −
24 5500 ±
80 1 . . − .
028 0 . ± .
11 1 . ± .
045 4 . . − .
20 13 .
45 117WASP-78b 2 .
175 0 . ± .
080 1 . ± .
110 2350 ±
80 6100 ±
150 0 . ± . − . ± .
14 1 . ± .
090 3 . . − .
38 4 .
10 92WASP-79b 3 .
662 0 . ± .
080 2 . ± .
140 1900 ±
50 6600 ±
100 0 . ± .
040 0 . ± .
10 1 . ± .
070 1 . . − .
16 2 .
90 92WASP-7b 4 .
955 0 . . − .
180 0 . . − .
040 1379+35 −
23 6400 ±
100 0 . . − .
179 0 . ± .
10 1 . . − .
190 0 . . − .
37 5 .
00 24WASP-80b 3 .
068 0 . . − .
039 0 . . − .
027 814+19 −
19 4145 ±
100 4 . . − . − . ± .
16 0 . ± .
050 15 . . − .
17 19 .
95 107WASP-82b 2 .
706 1 . ± .
040 1 . . − .
050 2190 ±
40 6500 ±
80 0 . . − .
020 0 . ± .
11 1 . ± .
080 1 . . − .
14 2 .
55 152WASP-83b 4 .
971 0 . ± .
030 1 . . − .
050 1120 ±
30 5480 ±
110 1 . . − .
180 0 . ± .
12 1 . ± .
090 3 . . − .
13 12 .
20 136WASP-88b 4 .
954 0 . ± .
080 1 . . − .
070 1772+54 −
45 6430 ±
130 0 . . − . − . ± .
12 1 . ± .
050 2 . . − .
19 2 .
80 119WASP-89b 3 .
356 5 . ± .
400 1 . ± .
040 1120 ±
20 4955 ±
100 1 . ± .
099 0 . ± .
14 0 . ± .
080 10 . . − .
64 19 .
95 136WASP-8b 8 .
159 2 . . − .
074 1 . . − .
079 951+21 −
28 5600 ±
80 1 . . − .
160 0 . ± .
07 1 . . − .
050 1 . . − .
88 11 .
10 40WASP-90b 3 .
916 0 . ± .
070 1 . ± .
090 1840 ±
50 6440 ±
130 0 . ± .
028 0 . ± .
14 1 . ± .
100 1 . . − .
26 2 .
90 152WASP-94Ab 3 .
950 0 . . − .
032 1 . . − .
050 1604+25 −
22 6153+75 −
76 0 . . − .
028 0 . ± .
15 1 . ± .
090 2 . . − .
39 4 .
60 122WASP-95b 2 .
185 1 . . − .
040 1 . ± .
060 1570 ±
50 5830 ±
140 1 . . − .
180 0 . ± .
16 1 . ± .
090 2 . . − .
12 7 .
90 128WASP-96b 3 .
425 0 . ± .
030 1 . ± .
060 1285 ±
40 5500 ±
150 1 . ± .
100 0 . ± .
19 1 . ± .
090 4 . . − .
51 11 .
60 128WASP-97b 2 .
073 1 . ± .
050 1 . ± .
060 1555 ±
40 5670 ±
110 1 . ± .
130 0 . ± .
11 1 . ± .
060 2 . . − .
95 9 .
75 128WASP-98b 2 .
963 0 . ± .
070 1 . ± .
040 1180 ±
30 5550 ±
140 2 . ± . − . ± .
19 0 . ± .
060 2 . . − .
73 16 .
00 128WASP-99b 5 .
753 2 . ± .
130 1 . . − .
050 1480 ±
40 6150 ±
100 0 . . − .
056 0 . ± .
15 1 . ± .
100 2 . . − .
33 4 .
05 128
Table 8 — Continued
Planet Period
Mp Rp T eq T eff ⋆ ρ⋆ [Fe / H] M⋆ Age t tot Refs.(d) ( M J) ( R J) (K) (K) (g cm −