Confirming known planetary trends using a photometrically selected Kepler sample
Jonah T. Hansen, Luca Casagrande, Michael J. Ireland, Jane Lin
MMNRAS , 1–10 (2020) Preprint 18 September 2020 Compiled using MNRAS L A TEX style file v3.0
Confirming known planetary trends using a photometrically selected
Kepler sample
Jonah T. Hansen, (cid:63) Luca Casagrande, Michael J. Ireland and Jane Lin Research School of Astronomy and Astrophysics, The Australian National University, Canberra, ACT 2611, Australia
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Statistical studies of exoplanets and the properties of their host stars have been critical toinforming models of planet formation. Numerous trends have arisen in particular from the rich
Kepler dataset, including that exoplanets are more likely to be found around stars with a highmetallicity and the presence of a “gap” in the distribution of planetary radii at 1.9 R ⊕ . Here wepresent a new analysis on the Kepler field, using the APOGEE spectroscopic survey to builda metallicity calibration based on
Gaia , 2MASS and Strömgren photometry. This calibration,along with masses and radii derived from a Bayesian isochrone fitting algorithm, is used totest a number of these trends with unbiased, photometrically derived parameters, albeit with asmaller sample size in comparison to recent studies. We confirm that planets are indeed morefrequently found around higher metallicity stars: planetary frequencies are 0 . ± .
12 percentfor [Fe/H] < 0 and 1 . ± .
16 percent for [Fe/H] ≥
0. We also recover the planet radius gap,along with a slight positive correlation with stellar mass. We conclude that this method showspromise to derive robust statistic of exoplanets. We also remark that spectrophotometry from
Gaia
DR3 will have an effective resolution similar to narrow band filters and allow to overcomethe small sample size inherent in this study.
Key words: planets and satellites: fundamental parameters – catalogues – stars: planetarysystems – stars: fundamental parameters
Since the release of
Kepler ’s (Borucki et al. 2010) rich collectionof over 4000 exoplanet transits, the study of exoplanet statisticshas blossomed into a thriving field. Exoplanet demographic stud-ies have led to many interesting results, including the preferenceof large exoplanets ( R p > R ⊕ ) to form around high metallicitystars (Santos et al. 2004; Fischer & Valenti 2005; Zhu 2019) andthat close, multiple planet systems form preferentially around metalpoor stars (Brewer et al. 2018). However, perhaps one of the mostimportant results to have come out of these studies it that of theplanet radius “gap” - a decrease in the number of planets with radiiaround 1.5-2.0 R ⊕ (e.g., Owen & Wu 2013; Fulton et al. 2017).This particular radius is significant, as it separates the classificationof “super-Earths” from “sub-Neptunes”. Reasons for the presenceof this gap are numerous, ranging from UV photoevaporation ofa planet’s atmosphere (Owen & Wu 2013, 2017; Lopez & Rice2018) to core-powered mass loss (Ginzburg et al. 2018; Gupta &Schlichting 2020).Recently, more separate studies have found evidence for thisgap, using both the Kepler (Van Eylen et al. 2018; Berger et al.2020b) and K2 surveys (Hardegree-Ullman et al. 2020; Cloutier & (cid:63)
E-mail: [email protected]
Menou 2020) and a handful have also identified the gap follows atrend with stellar mass: the drop in occurrence is found at smallerradii around less massive stars (Fulton & Petigura 2018; Bergeret al. 2020b). The radius gap still has ambiguity in the strength ofthis deficiency, with studies such as the seminal Fulton et al. (2017)revealing a shallow gap, whereas Van Eylen et al. (2018), with amuch smaller sample but with very precise parameters from aster-oseismology, find a gap nearly devoid of planets. There is hence aquestion whether the strength of this gap is due to more precise pa-rameters, small number statistics, selection effects or a combinationof the three.Part of the ambiguity around these planetary trends, includingthe radius gap, stem from the imprecise nature of the
Kepler inputcatalogue (KIC). The KIC was a compilation of 13 million stars withoptical photometry and stellar parameters created for the purposeof choosing
Kepler targets, of which approximately 200,000 werechosen (Batalha et al. 2010; Brown et al. 2011). However, the pa-rameters for these stars were lacking in precision and some criticalparameters, such as the age and mass of these stars, were missingentirely. To investigate exoplanet demographics, precise stellar pa-rameters are required which has led to many follow-up studies ofthe stars in the KIC (e.g., Bruntt et al. 2012; Molenda-Żakowiczet al. 2013; Huber et al. 2014; Petigura et al. 2017; Furlan et al.2018; Berger et al. 2020a). Many of these studies rely on spec- © 2020 The Authors a r X i v : . [ a s t r o - ph . E P ] S e p Hansen et al. troscopy, for which sample selection effects are usually quite strongand observations are biased towards the brightest targets.In this paper, we derive stellar parameters for a photometricallyunbiased sample of confirmed
Kepler transiting planets to studysome of the known trends concerning exoplanetary demographics.We assemble our sample starting from the Strömgren survey forAsteroseismology and Galactic Archaeology (SAGA, Casagrandeet al. 2014) and complementing it with photometry from
Gaia
DR2(Gaia Collaboration et al. 2018) and 2MASS (Skrutskie et al. 2006).Metallicity of the
Kepler host stars is derived through a photometriccalibration based on the APOGEE survey (Majewski et al. 2017),and effective temperatures are calculated through the Infra-Red FluxMethod (IFRM; e.g., Blackwell & Shallis 1977; Casagrande et al.2010) We then calculate the masses and radii of
Kepler host starsthrough
Gaia parallaxes and isochrone fitting by using the Bayesianisochrone fitting algorithm Elli (Lin et al. 2018). This results inus obtaining a similar planet radius-mass trend to that of Fulton &Petigura (2018) and Berger et al. (2020b), as well as finding largeplanets preferentially form around metal rich stars and a slight trendthat multiple exoplanet systems form around metal poor stars.
Multiple stellar catalogues were combined to leverage finding an ap-propriate metallicity index for our planet host star sample. Foremostof these was the aforementioned
Kepler
Input Catalogue (KIC), acatalogue of stars that lie in the
Kepler field (Brown et al. 2011).Not all the stars present in the KIC contain useful data on their prop-erties and so a subset of the catalogue was used: all KIC objectsviewed in Quarter 15 of the
Kepler mission that had long cadencedata. This is a sample collected before
Kepler ’s reaction wheel hadfailed, and after stars with faulty data had been removed.The KIC catalogue was matched with the
Gaia
DR2 catalogue(Gaia Collaboration et al. 2018) to obtain
Gaia photometry andparallaxes for these stars. We remark that for the isochrone fittingdescribed in Section 5 we use distances from Bailer-Jones et al.(2018). The
Gaia data for these KIC stars was combined with otherphotometric catalogues, including the 2MASS catalogue’s J , H and K band photometry and the Strömgren catalogue’s u , v , b and y bandphotometry produced by Casagrande et al. (2014). These catalogueswere cross-matched so that all stars contained the photometry fromeach survey; resulting in our catalogue of multi-band photometryencompassing around 30,000 stars. We note here that this is a smallfraction of the KIC, primarily due to to the small fraction of starsin the Kepler field currently with Strömgren photometry.The photometry was corrected for reddening using the Schlegelet al. (1998) reddening map. This map is known to overestimatereddening along the galactic plane (see e.g., Arce & Goodman1999; Schlafly & Finkbeiner 2011). Hence, it was re-scaled by thefollowing formula where b is the galactic latitude: E ( B − V ) res = E ( B − V ) + . (| b | − ) − .
16 (1)which is appropriate for the range 5 (cid:46) b (cid:46)
20 encompassed bythe
Kepler field, and whose derivation is explained in Kunder et al.(2017) and Casagrande et al. (2019). Magnitudes were de-reddenedusing extinction coefficients from Casagrande & VandenBerg (2014,2018).The photometric stellar catalogue was finally combined withthe list of
Kepler
Objects of Interest (KOI). This is a list of allcandidate exoplanets found in the
Kepler field, provided by theNASA Exoplanet Archive ( https://exoplanetarchive.ipac. [ F e / H ] Figure 1.
Metallicity against the second principle component from the PCA.A linear regression line is shown in red. caltech.edu/ ). Objects with a koi disposition flag of false pos-itive were removed and the remaining entries were paired with thephotometric data from their host star, producing a separate KOIcatalogue of about 800 exoplanets and their host stars.
In order to derive homogeneous metallicities for all stars in our cat-alogue, we devise a metallicity calibration using the photometry as-sembled in Section 2. The largest sample of stars with spectroscopicmetallicities in the
Kepler field is from APOGEE (APO GalacticEvolution Experiment; e.g., Majewski et al. 2017), an infrared spec-troscopic mission that was designed to measure the radial velocitiesand, more importantly, chemical abundances of over 100,000 redgiants withing the Milky Way. We used the [M/H] metallicity fromAPOGEE DR14 (Abolfathi et al. 2018) to calibrate our photome-try; removing stars with the star_bad label and combining this datawith the photometric catalogue compiled above to obtain a total of2415 stars in the KIC with known metallicities. These stars werethen used to derive a metallicity relation for the KIC as a whole.To derive the best relation a Principle Component Analysis(hereafter referred to as PCA) decomposition was performed over84 linear combinations of colour indices. PCA can greatly reduce thedimensionality of the given data; in this case, reducing the dimen-sionality of the 84 candidate colour indices and their combinationsup to second order. The colour indices chosen were those sug-gested to be sensitive to metallicity, including the well established m = ( v − b ) − ( b − y ) from the Strömgren photometric system, aswell as u − b , G − K , v − G , R p − K , and ( B p − R p ) − ( R p − K ) .A singular value decomposition was performed on the collec-tion of 84 colour indices for our APOGEE cross-matched photo-metric catalogue; outputting linear combinations of the input di-mensions called “Principle Components”. The first of these vectorsdescribes the linear combination of variables that produces the mostvariance in the data, the second giving the combination that pro-duces the second most variance and so forth. Through an analysisof these principle components, we identified that the first principlecomponent corresponded to the effective temperature of the star.The second component was the desired parameter - the metallicity.The correspondence between the second principle component andthe APOGEE metallicity can be seen in Fig. 1.With the metallicity principle component identified, we ran aniterative process to reduce the number of input parameters so thatthe resulting calibration was not over determined. The process is MNRAS000
Kepler field is from APOGEE (APO GalacticEvolution Experiment; e.g., Majewski et al. 2017), an infrared spec-troscopic mission that was designed to measure the radial velocitiesand, more importantly, chemical abundances of over 100,000 redgiants withing the Milky Way. We used the [M/H] metallicity fromAPOGEE DR14 (Abolfathi et al. 2018) to calibrate our photome-try; removing stars with the star_bad label and combining this datawith the photometric catalogue compiled above to obtain a total of2415 stars in the KIC with known metallicities. These stars werethen used to derive a metallicity relation for the KIC as a whole.To derive the best relation a Principle Component Analysis(hereafter referred to as PCA) decomposition was performed over84 linear combinations of colour indices. PCA can greatly reduce thedimensionality of the given data; in this case, reducing the dimen-sionality of the 84 candidate colour indices and their combinationsup to second order. The colour indices chosen were those sug-gested to be sensitive to metallicity, including the well established m = ( v − b ) − ( b − y ) from the Strömgren photometric system, aswell as u − b , G − K , v − G , R p − K , and ( B p − R p ) − ( R p − K ) .A singular value decomposition was performed on the collec-tion of 84 colour indices for our APOGEE cross-matched photo-metric catalogue; outputting linear combinations of the input di-mensions called “Principle Components”. The first of these vectorsdescribes the linear combination of variables that produces the mostvariance in the data, the second giving the combination that pro-duces the second most variance and so forth. Through an analysisof these principle components, we identified that the first principlecomponent corresponded to the effective temperature of the star.The second component was the desired parameter - the metallicity.The correspondence between the second principle component andthe APOGEE metallicity can be seen in Fig. 1.With the metallicity principle component identified, we ran aniterative process to reduce the number of input parameters so thatthe resulting calibration was not over determined. The process is MNRAS000 , 1–10 (2020) onfirming Planetary Trends as follows: the decomposition was completed with n colour indexdimensions and the parameter with the weakest contribution to thesecond principle component was removed. The decomposition wasthen performed again with n − u − b index from the Strömgren photometricsystem and the G − K index combining the G band from Gaia ’sphotometry and the K band from 2MASS. A second round of PCAwas conducted with these two indices, as well as the APOGEEmetallicity itself, resulting in a linear calibration of the form [ Fe / H ] cal = a ( G − K ) + a ( u − b ) + a (2)This calibration still had some residual trends, particularly inthe G − K colour index. To correct this, we further fitted a 5th orderpolynomial to the residuals and subtracted this from the metallicity.Hence, our final calibration was of the form: [ Fe / H ] cal = c ( G − K ) + c ( G − K ) + c ( G − K ) + c ( G − K ) + c ( G − K ) + c ( u − b ) + c (3)with calibration parameters: c = − . c = . c = − . c = . c = − . c = . c = . G − K vs u − b plane is shown in the up-per panel of Fig. 2, where stars are colour coded by their APOGEEmetallicity. Also shown in the bottom panels is the residual ofour photometric metallicity calibration as function of spectroscopic[Fe/H] and G − K . The standard deviation of the residuals (shownin red) is 0.18 dex. It should be noted that for [Fe/H] (cid:46) −
1, our cal-ibration systematically overestimates the true metallicity. However,this is of little concern for the sake of our study, since the bulk ofplanets lie well above this limit.Especially when looking at the G − K residual plot, we can seeby eye that this calibration does not hold well everywhere. As wewill describe in the following section, we performed multiple colourand magnitude cuts to determine a selection for which the sampleof KOI host stars is representative of the larger KIC population, aswell as such that the metallicity callibration is well behaved. Wedetermined that this range is:1 . ≤ u − b ≤ . . ≤ G − K ≤ . Kepler follow-up survey. The comparisons are shownin Fig. 3, with a mean difference (Our metallicity - Petigura et al.(2017)) of − . ± .
14 dex, and a difference (Our metallicity -Furlan et al. (2018)) of 0 . ± .
10 dex. Both of these are wellwithin the quoted uncertainty of our metallicity calibration.
Table 1.
KS statistic, Wilcoxon rank-sum statistic and resulting p-values ofthe distribution of colours and magnitudes between all KOIs and the fullphotometric sample when the cuts discussed in Section 4 are applied.
Parameter KS Statistic D KS p Wilcoxon Statistic U Wilcoxon pG − K u − b G In comparing the metallicity distribution of the KOI sample tothe KIC sample, it is important to understand the extend of anydifferences in brightness or colour distributions, which could biasconclusions about planetary demographics. These differences couldbe potentially caused by a strong stellar-mass dependent planetaryfrequency (e.g., as is know for rare Jovian planets Bowler et al.2010), or a strong effect of instrumental noise in planet detectabilityat fainter included KIC stars. However, if the samples are verysimilar in apparent magnitude and colour distributions, then we cancompare metallicities of the KOI and KIC samples without needingto re-sample a subset of the KIC stars.Since our sample is drawn from photometric catalogues, we canperform well defined magnitude and colour cuts and ensure the KOIsample represents the underlying sample of stars found in the KICcatalogue. This is very different from spectroscopically selectedsamples, where stars and KOI might be preferentially picked fortheir properties. We took our collection of KOIs and analysed theirdistribution in the colours ( G − K ) and ( u − v ) , as well as the G apparent magnitude. We then iteratively restricted colours andmagnitudes, performing Kolmogorov-Smirnov (KS) tests betweenthe KOI sample and the full photometric catalogue we assembleduntil the two samples were consistent with the null hypothesis thatthey are drawn from the same population. The resultant colour andmagnitude cuts we determine are as follows:1 . ≤ u − b ≤ . . ≤ G − K ≤ . . ≤ G ≤ . parent population when restricted to theabove colour and magnitude ranges. The KS statistic and resultantp-value for the relevant parameters can be found in Table 1. AWilcoxon rank sum test was also computed and the results can alsobe found in Table 1. Finally, both tests were completed for the subsetof KOIs that have a confirmed disposition according to the NASAExoplanet database. The results are in Table 2.From this, it is evident that all three parameters for both samplesdo not have statistically significant low p-values. Hence we cannotreject the null hypothesis that the samples are drawn from the sameparent population and we can therefore use the photometricallycalibrated list of KOI host stars as a representative population ofthe full photometric catalogue. An HR diagram of the colour-cutphotometric sample is shown in Fig. 4. One trend we aimed to investigate was the “Planet-Radius gap”, afeature where there is a relative absence of planets with radii around1.9 R ⊕ (e.g., Owen & Wu 2013; Fulton et al. 2017), with somestudies showing that the depression follows a slight dependence on MNRAS , 1–10 (2020)
Hansen et al. u - b Calibration [Fe/H] = 0Calibration [Fe/H] = -0.25Calibration [Fe/H] = 0.25 10 A p o g ee [ F e / H ] (a) [ F e / H ] (b) [ F e / H ] (c) Figure 2.
Comparison of our photometric metallicity calibration against that of APOGEE. a) The G − K , u − b colour plane coloured by the APOGEE [M/H]metallicity index. Our photometric metallicity calibration is shown by the lines for a given metallicity. b) Metallicity residuals (our metallicity - APOGEE)against APOGEE metallicity. Red plots the full catalogue of stars, whereas blue only plots stars that fall within the colour cut discussed in the text. c) Same asb, but against the G − K colour index. Table 2.
KS statistic, Wilcoxon rank-sum statistic and resulting p-valuesof the distribution of colours and magnitudes between all confirmed KOIsand the full photometric sample when the cuts discussed in Section 4 areapplied.
Parameter KS Statistic D KS p Wilcoxon Statistic U Wilcoxon pG − K u − b G the mass of the host star (e.g., Fulton & Petigura 2018; Berger et al.2020b). We derived stellar masses and radii using the Bayesianisochrone fitting algorithm Elli (Lin et al. 2018), which is builtupon the MIST isochrones (Choi et al. 2016). The input parametersused by Elli are effective temperatures ( T eff ), 2MASS K magni-tudes, reddening, Gaia
DR2 parallaxes, surface gravities log ( g ) andour photometric metallicities. In the following, we describe in detailour procedure.To obtain effective temperatures we run the InfraRed FluxMethod (IRFM) for all our KOIs. The IRFM is an almost modelindependent photometric technique originally devised to obtain an-gular diameters to a precision of a few per cent, and capable ofcompeting against intensity interferometry should a good flux cal- MNRAS000
DR2 parallaxes, surface gravities log ( g ) andour photometric metallicities. In the following, we describe in detailour procedure.To obtain effective temperatures we run the InfraRed FluxMethod (IRFM) for all our KOIs. The IRFM is an almost modelindependent photometric technique originally devised to obtain an-gular diameters to a precision of a few per cent, and capable ofcompeting against intensity interferometry should a good flux cal- MNRAS000 , 1–10 (2020) onfirming Planetary Trends [H] L i t e r a t u r e [ F e / H ] Petigura 2017Furlan 2018 0.6 0.4 0.2 0.0 0.2 0.4Literature [Fe/H]0.250.000.25 [ F e / H ] T eff (K)0.250.000.25 [ F e / H ] [ F e / H ] Figure 3.
Comparison of our photometric metallicity against that of Petigura et al. (2017) and Furlan et al. (2018), with residuals plotted against the literaturevalues of metallicity, effective temperature and surface gravity. G Parent PopulationAll KOIConfirmed KOI ( R p <4 R )Confirmed KOI ( R p R ) Figure 4.
HR Diagram of the representative colour-cut photometric sample.The colours represent the different subsets of the full photometric catalogue. ibration be achieved (e.g., Blackwell & Shallis 1977; Blackwellet al. 1980). We used the implementation described in Casagrandeet al. (2010) which employs
Gaia and 2MASS photometry to de-rive effective temperatures and angular diameters for stars of knownmetallicity and surface gravity. We adopted our photometric metal-licities, and log ( g ) from the KOI catalogue. Effective temperaturesderived from the IRFM were then fed into Elli along the otherparameters needed to derive stellar radii and masses. A new esti-mate of log ( g ) was computed, iterating between the IRFM and Elli.Because of the mild dependence of the IRFM on the adopted metal-licity and surface gravity (see e.g., Alonso et al. 1995; Casagrandeet al. 2006) only a couple of iterations were necessary to convergeon a final mass and radius for each star.First, we compared our T eff against those published in Petiguraet al. (2017) and Furlan et al. (2018), showing excellent agreement, with a mean difference of 30 K and a standard deviation of 90 K (Fig.5). Since T eff from the IRFM are sensitive to reddening (wherea change of ± .
01 in E ( B − V ) has an impact of ±
50 K), thiscomparison suggests that reddening is well under control.In addition to stellar radii obtained from isochrone fitting, theavailability of angular diameters and
Gaia distances (Bailer-Joneset al. 2018) for all our targets allowed us to derive radii independentlyof stellar isochrones. We dub these "empirical radii" since they arevirtually free from any stellar modelling assumption. Finally, theplanet radius was determined by applying the planet to star radiusratio provided in the KOI catalogue; a parameter estimated from thetransit depth.Fig. 6 compares the stellar radii derived by Elli against theempirical ones, showing relative residuals (Elli radius - empiricalradius)/Elli radius with a mean of 0 . ± .
03 solar radii and afractional error of 2 percent. This gives confidence that the radiiand other stellar quantities derived from Elli are robust. It shouldbe noted that an outlier was removed, due to having abnormallylarge uncertainties on its parallax. From this point on, we adopt theempirical radius as our accepted stellar radius.The empirical radii also have good relative uncertainties, with amean of 3.4 percent, which is on par with that of Berger et al. (2020a)and Fulton & Petigura (2018). When multiplied by the
Kepler planetto star radius ratio, we find our planet radii have uncertainties witha mean of 6.2 percent, highlighting that uncertainties in the
Kepler radius ratio carry a significant contribution to the uncertainties inthe planetary radius.Finally, we tested our stellar parameters against those derivedby Berger et al. (2020a), in particular the stellar luminosity (Fig. 7)and stellar radius (Fig. 8). Both of these parameters had extremelygood agreement, with luminosity residuals of − . ± . L (cid:12) andradius residuals of 0 . ± . R (cid:12) . We also tested our masses againsttheir catalogue, finding a mean difference and standard deviation of MNRAS , 1–10 (2020)
Hansen et al. L i t e r a t u r e T e ff ( K ) Petigura 2017Furlan 20184500 4750 5000 5250 5500 5750 6000 6250 6500IRFM T eff (K)2000200 T e ff ( K ) Figure 5.
Comparison of our effective temperatures from the IRFM (ab-scissa) with those of Petigura et al. (2017) and Furlan et al. (2018). E m p i r i c a l R s t a r ( R ) R star ( R )505 R e l a t i v e R s t a r R e s i d u a l s ( % ) Figure 6.
Comparison of Elli produced stellar radii with empirical radiiderived from the Bailer-Jones et al. (2018) distance and our angular diame-ters. − ± We first investigated trends concerning metallicity between the KOIhost stars and the parent population (ref. Section 4). The subset ofKOIs which have been labelled as confirmed by the NASA Ex-oplanet Database was also extracted and compared, before finallysplitting the confirmed KOIs between large ( R p ≥ R ⊕ ) and small( R p < R ⊕ ) planetary radii. The use of the confirmed sub-samplewas to ensure that we were not affected by non-planetary compan-ions, with the trade off of a smaller sample size. If a star had multipleplanets, then it was classified according to the radius of the largestone. Histograms and cumulative distribution functions (CDFs) ofthese populations are shown in Fig. 9. B e r g e r L s t a r ( L ) L star ( L )0.50.00.5 L s t a r ( L ) Figure 7.
Comparison of our stellar luminosities with those of Berger et al.(2020a). B e r g e r R s t a r ( R ) R star ( R )0.250.000.25 R s t a r ( R ) Figure 8.
Comparison of our stellar radii with those of Berger et al. (2020a).
Table 3.
KS tests of the metallicities of the different subsets against themetallicies of the full photometric sample in the same colour and magnituderanges.
Sample KS Statistic D KS p Wilcoxon Statistic U Wilcoxon p All KOI host stars 0.081 0.087 -1.629 0.103All confirmed KOI host stars 0.155 0.004 -2.879 0.004Confirmed KOI ( R p < R ⊕ ) 0.141 0.025 -2.112 0.035Confirmed KOI ( R p ≥ R ⊕ ) 0.308 0.035 -2.389 0.017 The mean metallicity of the KOIs ([Fe/H] = -0.01) and espe-cially that of the confirmed KOIs ([Fe/H] = 0.02) is different fromthat of the parent population of stars as a whole ([Fe/H] = -0.03).This suggests that the exoplanet host stars are more metal rich thanthe rest of the candidate KOIs. To confirm this deviation, KS andWilcoxon rank-sum tests were undertaken using the full metallicitydistribution function (MDF), with each subset being tested againstthe parent population. The results are shown in Table 3.With a p (cid:39) parent population cannot be rejected. MNRAS000
Sample KS Statistic D KS p Wilcoxon Statistic U Wilcoxon p All KOI host stars 0.081 0.087 -1.629 0.103All confirmed KOI host stars 0.155 0.004 -2.879 0.004Confirmed KOI ( R p < R ⊕ ) 0.141 0.025 -2.112 0.035Confirmed KOI ( R p ≥ R ⊕ ) 0.308 0.035 -2.389 0.017 The mean metallicity of the KOIs ([Fe/H] = -0.01) and espe-cially that of the confirmed KOIs ([Fe/H] = 0.02) is different fromthat of the parent population of stars as a whole ([Fe/H] = -0.03).This suggests that the exoplanet host stars are more metal rich thanthe rest of the candidate KOIs. To confirm this deviation, KS andWilcoxon rank-sum tests were undertaken using the full metallicitydistribution function (MDF), with each subset being tested againstthe parent population. The results are shown in Table 3.With a p (cid:39) parent population cannot be rejected. MNRAS000 , 1–10 (2020) onfirming Planetary Trends C D F C o un t C o un t C o un t Parent PopulationAll KOIAll Confirmed KOIConfirmed KOI ( R p < 4 R )Confirmed KOI ( R p R ) Figure 9.
Histograms and cumulative distribution functions of the metallicity distribution of various exoplanet subsets. Confirmed KOI are those with a NASAExoplanet Database designated disposition of confirmed, whereas “All KOI” refer to those with a disposition of confirmed or candidate.
However, when restricting ourselves to the sample of confirmedKOIs, the significance drops to a mere 0 . K O I F r a c t i o n All Confirmed KOIConfirmed KOI ( R p <4 R E )Confirmed KOI ( R p R E )Multiple exoplanet systems Figure 10.
Fraction of the parent population that host exoplanets for a givenmetallicity bin. Different colours refer to the different planet sizes of theKOI, or whether they are present in a system with multiple objects. Errorbars are drawn from the Poisson statistic. oplanets form around stars with a wide range of metallicities, largeexoplanets form around primarily metal rich stars. We show thatwhile the smaller exoplanets have a weaker trend than their largercounterparts, they still have a bias towards metallicities around andabove solar metallicity.
MNRAS , 1–10 (2020)
Hansen et al.
Table 4.
Percentage of stars in our representative sample of the
Kepler field hosting KOIs for high ([Fe/H] ≥
0) and low ([Fe/H] < 0) metallicities.Uncertainties are drawn from the Poisson statistic.
Sample Metal Poor [Fe/H] < 0 (%) Metal Rich [Fe/H] > 0 (%)
All confirmed KOI host stars 0.88 ± ± R p < R ⊕ ) 0.77 ± ± R p ≥ R ⊕ ) 0.11 ± ± ± ± We summarise these findings in Table 4, which shows the per-centage of stars in our representative sample of the
Kepler field thathost exoplanets for metallicities above and below solar metallicity.Here, large exoplanets are more than twice as likely to be foundaround metal rich stars, while smaller exoplanets are 1.5 times aslikely. We thus find that all exoplanets are more likely to be observedat higher metallicities, with the size of the exoplanet influencing thestrength of this trend.Furthermore, multiple planet systems follow the trend sup-ported by Brewer et al. (2018), which while also having a peak atsolar luminosity as seen in Fig. 10, has an upwards trend at lowmetallicities. This indicates that the multiple exoplanet systems de-tected by
Kepler are likely to be compact, small exoplanet systemsof the type described by Brewer et al. (2018), which favour lowermetallicity stars.
As mentioned previously, one aim of this work was to study theplanet-radius gap. With the stellar mass and planet radius we recov-ered through the processes outlined in Section 5, we generated a2D density plot through a Monte Carlo (MC) simulation. We drew10,000 samples assigning each time normal errors in stellar massand planet radius for each of our confirmed KOI data points, andplotted the density distribution as contours in Fig. 11. We also plot1000 random samples from the MC simulation. We chose not toinclude the KOIs with a candidate disposition due to the potentialpresence of false positives in this sample (examined in Section 6.1).What is particularly clear is the presence of a “gap” with apositive slope around 1.8-2.0 R (cid:12) . This highlights a weak trend withstellar mass, similar to what was found by Fulton & Petigura (2018)and Berger et al. (2020b). To confirm this, we overplotted the bestfit line to the radius gap from Berger et al. (2020b) with a slope of d log R p / d log M star = .
26 in Fig. 11. This line fits the data well,again supporting the conclusions of previous studies.To view the gap more clearly, we contracted this plot overmass and normalised the data, creating a simple histogram of planetradii. This is shown in solid red in Fig. 12. We also show in solidblue the histogram of planet radii when KOI with a dispositionof candidate are included. The most notable feature is a veryclear bimodal distribution, with a gap again at 1.9 R ⊕ , supportingthe conclusions of e.g Fulton & Petigura (2018) and Berger et al.(2020b). The restriction of only including confirmed KOI influencesthe distribution by increasing the side of the second peak at ∼ . R ⊕ and decreasing the width of the first at ∼ . R ⊕ , but the locationof the gap does not change.Following the work of Berger et al. (2020b), we also looked athow the radius histogram was affected by the incident stellar fluxfalling on the planet. We chose the separating flux value of 150 F ⊕ from Berger et al. (2020b), to test to see whether we identifieda similar trend; our sample had 114 planets designated as cool.This is plotted in Fig. 13, where again we have chosen to only plot confirmed KOI. We recover that planets with higher incident fluxexhibit smaller radii than their cooler counterparts, possibly due toevaporation of the atmospheres of these planets. As with Bergeret al. (2020b), we caution that these results may be a result of smallnumber statistics and are likely fraught with Kepler selection effects.
We have compiled a photometric catalogue of stars in the
Kepler field utilising photometry from
Gaia , Strömgren and 2MASS cat-alogues. We created a metallicity calibration based on APOGEEspectroscopy to obtain a metallicity for our photometric sample,and then performed well defined colour and magnitude cuts toensure our dataset was a representative sample of the underlyingpopulation of stars. We then derived temperatures and angular di-ameters using the IFRM, which were then used to derive stellar radiiand stellar mass through Bayesian isochrone fitting. The resultantparameters were compared favourably with previous results fromthe literature, especially giving stellar radii with relative uncertain-ties around 3.4 percent. Planetary radii uncertainties of 6.2 percenthence indicate a major uncertainty contribution from the
Kepler planet to star ratio.The main findings from our analysis are as follows: • We find that the stars hosting confirmed KOIs have a statisti-cally different metallicity distribution than the parent population ofstars in the
Kepler field. We also find that this statistical claim is notvalid for the sample of KOIs that include those with a dispositionof candidate, consequences of the undetected false positives in thelist of KOIs. • We quantify the metallicity distribution differences betweenKOI and the larger sample of KIC stars, finding that KOI hosts tendto be more metal rich than their non-planet hosting counterparts.While holding especially true for large exoplanets larger than 4 R ⊕ ,which has been known about in literature for some time (e.g, Buch-have et al. 2012), we also find this holds for smaller exoplanets albeitto a weaker extent. This follows the conclusions of (e.g, Zhu 2019).Finally, we also find that Kepler stars with more than one exoplanetfavour metal rich planets to a lesser degree than those with a singledetection, supporting the conclusions of Brewer et al. (2018). Inparticular, we find an increase in the number of multiple exoplanetsystems at the lowest metallicity bin in our sample. • In a two dimensional histogram of planetary radius and stellarmass, we recover the planet radius gap at ∼ . R ⊕ . We find that thegap exhibits a weak positive trend with stellar mass, corroboratingthe findings of Fulton & Petigura (2018) and Berger et al. (2020b).We also tentatively find that there is a trend that planets with a highincident flux (>150 F ⊕ ) tend to have smaller radii.We note that our sample size is relatively small, especiallycompared to recent studies such as that of Fulton & Petigura (2018)and Berger et al. (2020b). The major reason for this is the limitednumber of stars in the Kepler field for which we had Strömgrenphotometry for. However, we anticipate that with the upcoming
Gaia
DR3 release we can obtain a larger sample of e.g., Strömgrenphotometry (or other suitable metallicity sensitivity indices) directlyfrom the BP and RP spectra. With this larger sample, we believe thatthe methods described in this paper will be limited solely by Kepler uncertainties, thus allowing for more robust statistics and deeperinsight into the demographics of
Kepler ’s exoplanet population.
MNRAS000
MNRAS000 , 1–10 (2020) onfirming Planetary Trends M star ( M )1.02.03.04.0 P l a n e t R a d i u s R p ( R ) Figure 11.
2D Monte Carlo distribution of the stellar mass and planetary radius of KOI with a confirmed disposition. Density contours are shown behind arandom selection of 1000 samples. Note the presence of a gap around R p = . R ⊕ . Also plotted in red is the best fit line to the radius gap from Berger et al.(2020b), with their slope of d log R p / d log M st ar = .
26. It can be seen that our data also fits this line well, showing that the radius gap has a slight positivecorrelation with stellar mass. R p ( R )0.00.10.20.30.40.5 N o r m a li s e d F r e q u e n c y All KOIConfirmed KOI
Figure 12.
Normalised histograms of the planetary radius of all KOI (blue)and only the confirmed KOI (red).
ACKNOWLEDGEMENTS
L.C. is the recipient of the ARC Future Fellowship FT160100402.M.I. acknowledges support from the ARC Discovery Scheme(DP170102233). This research has also made use of the NASAExoplanet Archive, which is operated by the California Insti-tute of Technology, under contract with the National Aeronau-tics and Space Administration under the Exoplanet ExplorationProgram. This work has made use of data from the European R p ( R )0.00.20.40.60.8 N o r m a li s e d F r e q u e n c y All planets F planet FF planet > 150 F Figure 13.
Normalised histograms of the planetary radius of confirmed KOI,separated by host star luminosities. All confirmed KOI are shown in black,whereas the red and blue histograms represent the subset with a planetaryflux of less than and greater than 150 F ⊕ respectively. Space Agency (ESA) mission
Gaia ( ), processed by the Gaia
Data Processing and Analy-sis Consortium (DPAC, ). Funding for the DPAC has been pro-vided by national institutions, in particular the institutions partici-pating in the
Gaia
Multilateral Agreement.
MNRAS , 1–10 (2020) Hansen et al.
DATA AVAILABILITY
The data underlying this article are available in the article and in itsonline supplementary material.
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