Characterisation of 92 Southern TESS Candidate Planet Hosts and a New Photometric [Fe/H] Relation for Cool Dwarfs
Adam D. Rains, Maruša Žerjal, Michael J. Ireland, Thomas Nordlander, Michael S. Bessell, Luca Casagrande, Christopher A. Onken, Meridith Joyce, Jens Kammerer, Harrison Abbot
MMNRAS , 1–22 (2015) Preprint 17 February 2021 Compiled using MNRAS L A TEX style file v3.0
Characterisation of 92 Southern TESS Candidate Planet Hosts and a NewPhotometric [Fe/H] Relation for Cool Dwarfs
Adam D. Rains, ★ Maruša Žerjal, Michael J. Ireland, Thomas Nordlander, , Michael S. Bessell, Luca Casagrande, , Christopher A. Onken, , Meridith Joyce, , Jens Kammerer, , and Harrison Abbot Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D) Centre for Gravitational Astrophysics, Research Schools of Physics, and Astronomy and Astrophysics, Australian National University European Southern Observatory, Karl-Schwarzschild-Str 2, 85748, Garching, Germany
Last updated 2015 May 22; in original form 2013 September 5
ABSTRACT
We present the results of a medium resolution optical spectroscopic survey of 92 cool (3 , (cid:46) 𝑇 eff (cid:46) ,
500 K) southern TESScandidate planet hosts, and describe our spectral fitting methodology used to recover stellar parameters. We quantify modeldeficiencies at predicting optical fluxes, and while our technique works well for 𝑇 eff , further improvements are needed for [Fe/H].To this end, we developed an updated photometric [Fe/H] calibration for isolated main sequence stars built upon a calibrationsample of 69 cool dwarfs in binary systems, precise to ± .
19 dex, from super-solar to metal poor, over 1 . < Gaia ( 𝐵 𝑃 − 𝑅 𝑃 ) < .
3. Our fitted 𝑇 eff and 𝑅 ★ have median precisions of 0.8% and 1.7%, respectively and are consistent with our sample of standardstars. We use these to model the transit light curves and determine exoplanet radii for 100 candidate planets to 3.5% precision andsee evidence that the planet-radius gap is also present for cool dwarfs. Our results are consistent with the sample of confirmedTESS planets, with this survey representing one of the largest uniform analyses of cool TESS candidate planet hosts to date. Key words: stars: low-mass, stars: fundamental parameters, planets and satellites: fundamental parameters, techniques: spec-troscopic,
Low mass stars are the most common kind of star in the Galaxy,comprising more than two thirds of all stars (Chabrier 2003), anddominating the Solar Neighbourhood population (e.g. Henry et al.1994, 2006; Winters et al. 2015; Henry et al. 2018). This abundancealone makes them prime targets for planet searches, with microlens-ing surveys, which have very little bias on host star masses, revealingthat there is at least one bound planet per Milky Way star (Cas-san et al. 2012). Results from the Kepler Mission (Borucki et al.2010) also bear this out, showing that a large number of planets re-main undiscovered around cool dwarfs (Morton & Swift 2014), andthat such cool stars are actually more likely to host small planets(2 < 𝑅 𝑃 < 𝑅 ⊕ , where 𝑅 𝑃 and 𝑅 ⊕ are the planet and earth ra-dius respectively) than their hotter counterparts (Howard et al. 2012;Dressing & Charbonneau 2015).However, the inherent faintness of these stars complicates the studyof both them and their planets. While we now know of over 4,000confirmed planets orbiting stars other than our own (overwhelm-ingly discovered by transiting exoplanet surveys), almost an equalnumber await confirmation . Exoplanet transit surveys like Keplerand TESS (Ricker et al. 2015) are able to place tight constraints on ★ E-mail: [email protected] (ADR) https://exoplanetarchive.ipac.caltech.edu/ planetary radii given a known stellar radius, but follow-up precisionradial velocity observations are required to provide planetary massconstraints. This is the second reason why planet searches aroundlow mass stars are critical: their smaller radii and lower masses makethe transit signals and radial velocities of higher amplitudes for anyplanets they host as compared to the same planets around more mas-sive host stars. This is especially important when looking for planetswith terrestrial radii or masses respectively.Many planet host stars have never been targeted by a spectroscopicsurvey, leaving their properties to be estimated through photometryalone. For instance, the TESS input catalogue (Stassun et al. 2018,2019) based its stellar parameters primarily on photometry, havingspectroscopic properties for only about 4 million stars of the nearly700 million with photometrically estimated equivalents. While starswarmer than 4,000 K are well suited to bulk estimation of propertiesfrom photometry (see e.g. Carrillo et al. 2020), special care mustbe taken for cool dwarfs whose faintness and complex atmospheresmake such relations more complex to develop and implement (e.g.see Muirhead et al. 2018 for the K and M dwarf specific approachtaken from the TESS input catalogue).NASA’s TESS Mission, by virtue of being all sky, has given us awealth of bright candidates which are now being actively followedup by ground based spectroscopic surveys.While multi-epoch radialvelocity observations are required to determine planetary masses,these surveys are typically biased towards the brightest stars and © a r X i v : . [ a s t r o - ph . E P ] F e b Adam D. Rains et al. smallest planets. As such, there remains a need for single-epochspectroscopic follow-up of fainter targets to provide reliable host starproperties (primarily 𝑇 eff , log 𝑔 , [Fe/H], and the stellar radius 𝑅 ★ ) andallow radial constraints to be placed on transiting planet candidates.Indeed, the LAMOST Survey (Zhao et al. 2012) undertook targetedlow resolution spectroscopic follow-up of stars in the Kepler field(De Cat et al. 2015) with the goal of deriving spectroscopic stellarproperties. Considering the goal of planet radii determination specif-ically, Dressing et al. (2019) used medium-resolution near-infrared(NIR) spectra, and Wittenmyer et al. (2020) high-resolution opticalspectra to follow-up K2 (Howell et al. 2014) transiting planet can-didate hosts and place radius constraints on both planets and theirhosts.Even without mass estimates, much can be learned about exoplanetdemographics from their radii alone. As demonstrated by Fulton et al.(2017), Fulton & Petigura (2018), Van Eylen et al. (2018), Kruseet al. (2019), Hardegree-Ullman et al. (2020), and (Hansen et al.2020), having a large sample of precise planet radii allows insightinto the exoplanet radius distribution, which appears to be bimodalwith an observable gap in the super-Earth regime ( ∼ . 𝑅 ⊕ ). This isthought to be the result of physical phenomena like photoevaporation(where flux from the parent star strips away weakly held atmospheres,e.g. Owen & Wu 2013; Lee et al. 2014; Lopez & Fortney 2014;Lee & Chiang 2016; Owen & Wu 2017; Lopez & Rice 2018), orcore-powered mass loss (where a cooling rocky core erodes lightplanetary atmospheres via its cooling luminosity, e.g. Ikoma & Hori2012; Ginzburg et al. 2018; Gupta & Schlichting 2019, 2020), and itslocation likely has a dependence on stellar host mass (e.g. Cloutier& Menou 2020). As such, improving the sample of planets withradius measurements allows us to place observational constraints onplanet formation channels and the mechanisms that sculpt planetsthroughout their lives.The scientific importance of searching for planets around low-mass stars to study their demographics is thus clear. However, theexact approach for understanding the stars themselves is less obvi-ous, as cool dwarfs are not as well understood as their prevalencewould suggest. Their inherent faintness and atmospheric complex-ity has lead to long standing issues observing representative sets ofstandard stars, generating synthetic spectra accounting for molecularabsorption as well as consistently modelling their evolution (see e.g.Allard et al. 1997; Chabrier 2003).Analysis of spectra from warmer stars is made simpler by theexistence of regions of spectral continuum where atomic or molec-ular line absorption is minimal, allowing one to disentangle withinreasonable uncertainties the effect of [Fe/H] and 𝑇 eff on an emerg-ing spectrum.This is not the case for cool dwarfs for which there isno continuum at shorter wavelengths, with the deepest absorptioncaused by most notably TiO in the optical and water in the NIR,but also various other oxides or hydrides. The strength of these fea-tures is a function of both temperature and [Fe/H], making it difficultto ascribe a unique 𝑇 eff -[Fe/H] pair to a given star. This was pre-dicted by theory (see e.g. Allard et al. 1997, Baraffe et al. 1998, andChabrier & Baraffe 2000 for summaries), and borne out observation-ally (Bonfils et al. 2005; Woolf & Wallerstein 2006; Johnson & Apps2009; Schlaufman & Laughlin 2010; Neves et al. 2012; Hejazi et al.2015) (albeit for the limited [Fe/H] space covered by the calibrationsample), and through colour-temperature relations (Casagrande et al.2008).The last decade has seen a number of studies using low-mediumresolution (mostly NIR) spectra, often focused on the developmentof [Fe/H] relations based on spectral indices (e.g. optical-NIR: Mannet al. 2013b,c, 2015; Kuznetsov et al. 2019; NIR: Newton et al. 2014; H band: Terrien et al. 2012; K band: Rojas-Ayala et al. 2010, 2012).Other studies have opted to use high-resolution spectra which givesaccess to unblended atomic lines that are not accessible to lowerresolution observations (e.g. optical: Bean et al. 2006a,b; Rajpurohitet al. 2014; Passegger et al. 2016; Y band: Veyette et al. 2017; optical-NIR: Passegger et al. 2018; J band: Önehag et al. 2012; H band: Soutoet al. 2017).Finally, on the point of M-dwarf evolutionary models (and low-mass, cool main sequence stars more generally), there has long beencontention between model radii and observed radii (e.g. Kraus et al.2015). This is often attributed to magnetic fields (and/or the mixinglength parameter, which simplistically parameterizes the effects ofmagnetic fields among other energy transport mechanisms in 1D stel-lar structure and evolution programs) and is related to the difficultyin accurately modelling convection (e.g. Feiden & Chaboyer 2012;Joyce & Chaboyer 2018). Fortunately, due to the aforementionedinsensitivity of NIR photometry (particularly K band) to [Fe/H], em-pirical mass and radius relations have been developed and calibratedon interferometric diameters and dynamical masses (e.g. Henry &McCarthy 1993; Delfosse et al. 2000; Benedict et al. 2016; Mannet al. 2015, 2019).Here we conduct a moderate resolution spectroscopic survey of 92southern cool ( 𝑇 eff (cid:46) ,
500 K) TESS candidate planet hosts with theWiFeS instrument (Dopita et al. 2007) on the ANU 2.3 m Telescopeat Siding Spring Observatory (NSW, Australia). We combine ourspectroscopic observations with literature optical photometry andtrigonometric parallaxes from Gaia DR2 (Gaia Collaboration et al.2016; Brown et al. 2018), infrared photometry from 2MASS (Skrut-skie et al. 2006), optical photometry from SkyMapper DR3 (Kelleret al. 2007, Onken et al. 2019, DR3 DOI: 10.25914/5f14eded2d116),empirical relations from (Mann et al. 2015, 2019), and syntheticMARCS model atmospheres (Gustafsson et al. 2008) in order toproduce stellar 𝑇 eff , log 𝑔 , [Fe/H], bolometric flux ( 𝑓 bol ), 𝑅 ★ , andstellar mass ( 𝑀 ★ ). By modelling the transit light curves of these hoststars, we are additionally able to produce precision planetary radii for100 candidate planets, which represents one of the largest uniformanalyses of cool TESS hosts to date. Our observations and data re-duction are described in Section 2, our photometric [Fe/H] relation inSection 3, our host star characterisation methodology and resultingparameters in Section 4, our transit light curve fitting and results inSection 5, discussion of results in Section 6, and concluding remarksin Section 7. Our initial target selection of southern cool dwarf TOIs was done inAugust 2019, including stars with 𝑇 eff (cid:54) of < .
4, as recommended by the Gaia team . Adding extra targets sourcedin August 2020, and removing those identified as false-positives Expected to be approximately 1.0 in case where the single star modelprovides a good fit for the astrometric data. See: https://gea.esac.esa.int/archive/documentation/GDR2/Gaia_archive/chap_datamodel/sec_dm_main_tables/ssec_dm_ruwe.html Though we do accept TIC 158588995 with a marginal RUWE ∼ , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts B P R P M G ScienceStandard
Figure 1.
Gaia DR2 𝑀 𝐺 versus ( 𝐵 𝑝 − 𝑅 𝑝 ) colour magnitude diagram forscience targets (filled blue circles) and cool dwarf standards (orange opencircles). through community follow-up observations (as listed on NASA’sExoplanet Follow-up Observing Program for TESS, ExoFOP-TESS,website ), we are left with a sample of 92 southern candidate planethosts spread across the sky with 8 . < apparent Gaia 𝐺 < . 𝐺 , 𝐵 𝑃 , 𝑅 𝑃 , and 2MASS 𝐽 , 𝐻 , 𝐾 𝑆 photometry, and most have at least one of SkyMapper DR3 𝑟 , 𝑖 , 𝑧 (noting that the survey is still ongoing, so not all bands are availablefor all targets). We calculate distances from Gaia DR2 parallaxes,incorporating the systematic parallax offset of − ± 𝜇 as foundby Stassun & Torres (2018).To correct for reddening we use the 3D dust map of Leike et al.(2020), implemented within the python package dustmaps (Green2018). Targeting bright, cool dwarfs as we do here automaticallymeans our stars will be relatively close, and we take those withinthe Local Bubble, two thirds of our sample, to be unreddened ( (cid:46)
70 pc, e.g. Leroy 1993; Lallement et al. 2003) so long as the Gaia 𝐺 band extinction reported by the dust map is consistent with zero( 𝐴 𝐺 < . 𝐽𝐻𝐾 𝑆 bands andCasagrande et al. (2019) for SkyMapper 𝑢𝑣𝑔𝑟𝑖𝑧 , with Gaia 𝐺 , 𝐵 𝑃 ,and 𝑅 𝑃 coefficients computed from the relation given in Casagrandeet al. (2020) for 𝐵 𝑃 − 𝑅 𝑃 = .
03, the median value for our sample. https://exofop.ipac.caltech.edu/tess/ MNRAS000
03, the median value for our sample. https://exofop.ipac.caltech.edu/tess/ MNRAS000 , 1–22 (2015) A da mD . R a i n s e t a l . Table 1.
Science targetsTOI 𝑎 TIC 𝑏 𝑐 Gaia DR2 𝑑 RA 𝑑 DEC 𝑑 𝐺 𝑑 𝐵 𝑝 − 𝑅 𝑝𝑑 Plx 𝑑 ruwe 𝑑 E( 𝐵 − 𝑉 ) N 𝑒 pc (hh mm ss.ss) (dd mm ss.ss) (mag) (mag) (mas)741 359271092 09213761-6016551 5299440441521812992 09 21 35.86 -61 43 07.68 8.68 2.03 95.63 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Notes: 𝑎 TESS Object of Interest ID, 𝑏 TESS Input Catalogue ID (Stassun et al. 2018, 2019), 𝑐 𝑐 Gaia (Brown et al. 2018) - note that Gaia parallaxes listed here have been correctedfor the zeropoint offset, 𝑑 Number of candidate planets, NASA Exoplanet Follow-up Observing Program for TESS M N R A S , ( ) ha r a c t e r i s a ti ono f C oo l T E SS C and i da t e P l an e t H o s t s Table 1 – continued Science targetsTOI 𝑎 TIC 𝑏 𝑐 Gaia DR2 𝑑 RA 𝑑 DEC 𝑑 𝐺 𝑑 𝐵 𝑝 − 𝑅 𝑝𝑑 Plx 𝑑 ruwe 𝑑 E( 𝐵 − 𝑉 ) N 𝑒 pc (hh mm ss.ss) (dd mm ss.ss) (mag) (mag) (mas)875 14165625 05120890-3742313 4820828591913853696 05 12 08.93 -38 17 29.40 12.12 1.51 9.39 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± M N R A S , ( ) Adam D. Rains et al.
Given the complexities involved in determining the properties ofcool dwarfs, we also observed a set of 136 well characterised lateK/M-dwarf standards from the literature. Broadly these standardshave parameters from at least one of the following sources:(i) [Fe/H] from an FGK companion,(ii) [Fe/H] from low resolution NIR spectra,(iii) 𝑇 eff from interferometry.With the exception of available interferometric 𝑇 eff standards, weadditionally wanted to source standards from large uniform cata-logues due to the known problem of systematics between differentspectroscopic techniques (e.g. Lebzelter et al. 2012; Hinkel et al.2016). With this in mind, the bulk of our M/late-K dwarf standardscome from the works of Rojas-Ayala et al. (2012) and Mann et al.(2015), with interferometric targets from von Braun et al. (2012),Boyajian et al. (2012), von Braun et al. (2014), Rabus et al. (2019),and Rains et al. (2020); and FGK companion [Fe/H] compiled byNewton et al. (2014) from Valenti & Fischer (2005), Sousa et al.(2006) and Sozzetti et al. (2009). Our mid-K dwarf calibrators donot come from a single uniform catalogue; they are instead pulledfrom the works of Woolf & Wallerstein (2005), Sousa et al. (2008),Prugniel et al. (2011), Sousa et al. (2011), Tsantaki et al. (2013),Luck (2017), Luck (2018) and Montes et al. (2018).These stars were observed with the same instrument settings asour science targets (but at higher SNR), with the intent to providechecks against our analysis techniques for this notoriously complexset of stars. Observations were conducted using the WiFeS instrument (Wide-Field Spectrograph, Dopita et al. 2007) on the ANU 2.3 m Telescopeat Siding Spring Observatory, Australia between August 2019 andSeptember 2020. WiFeS, a dual camera integral field spectrograph,is an effective stellar survey instrument due to its high throughputand broad wavelength coverage. Using the B3000 and R7000 grat-ings, and RT480 beam splitter, we obtain low resolution blue spectra(3500 (cid:54) 𝜆 (cid:54) 𝜆 / Δ 𝜆 ∼ (cid:54) 𝜆 (cid:54) 𝜆 / Δ 𝜆 ∼ 𝐺 .Target observations were bracketed hourly with NeAr Arc lampexposures, telluric standards were observed every few hours, andflux standards were observed several times throughout each night.Data reduction was done using the standard PyWiFeS pipeline (Chil-dress et al. 2014) with the exception of custom flux calibration dueto PyWiFeS’ poor performance with R7000 spectra. Science targetobservations are listed in Table A1, and standard star observations inTable B1. Radial velocities of the WiFeS R7000 spectra were determined froma least squares minimisation of a set of synthetic template spectravarying in temperature (see Section 4.1 for details of model grid).We use a coarsely sampled version of this grid, computed at R ∼ (cid:54) 𝜆 (cid:54) (cid:54) 𝑇 eff (cid:54) 𝑔 = .
5, and [Fe/H] = .
0, with 𝑇 eff steps of 100 K for radial velocity R V , W i F e S ( k m s ) TESSStandard75 50 25 0 25 50 75 100 125RV, Gaia DR2 (kms )10010 R e s i d u a l s Figure 2.
Comparison between those stars with radial velocities in Gaia DR2and our work here, from which we determine a scatter of ∼ . − . determination. For further information on our RV fitting formalism,see Žerjal et al. (2020) .Statistical uncertainties on this approach are median ∼
410 m s − ,though comparison to Gaia DR2 in Figure 2 reveals a larger scat-ter with standard deviation ∼ . − , computed from a medianabsolute deviation, which we add in quadrature with our statisti-cal uncertainties. Higher uncertainties are consistent with the workof Kuruwita et al. (2018) who found that WiFeS varies on shortertimescales than our hourly arcs can account for. While they ad-ditionally improved precision by calibrating using oxygen B-bandabsorption, RV uncertainties of ∼ . − are sufficient for thiswork. Our final values are reported in Table A1 for science targets,and Table B1 for standards. As established earlier, cool dwarf metallicities are notoriously dif-ficult to determine, particularly when working with optical spectra.Delfosse et al. (2000) initially proposed empirical calibrations todetermine [Fe/H] from a star’s position in 𝑀 𝐾 − ( 𝑉 − 𝐾 ) space, atechnique which was later iterated on by Bonfils et al. (2005), John-son & Apps (2009), Schlaufman & Laughlin (2010), and Neves et al.(2012). Such relations are based on the fact that once on the main se-quence, low mass stars do not evolve (and hence change in brightnessand temperature) appreciably on moderate timescales as comparedto their higher mass and faster evolving counterparts. Thus, assum-ing no extra scatter from unresolved binaries and standard heliumenrichment (e.g. Pagel & Portinari 1998), a star’s position above orbelow the mean main sequence is directly correlated with its chemicalcomposition (Baraffe et al. 1998). Our RV fitting code, along with all other code for this project, can be foundat https://github.com/adrains/plumage
MNRAS , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts These relations are benchmarked on what is considered the goldstandard for M-dwarf metallicites: [Fe/H] from a hotter FGK com-panion taken to have formed at the same time and thus have thesame chemical composition (e.g. Desidera et al. 2004; Hawkinset al. 2020). The process of determining which stars on the skyare likely associated has now been greatly simplified with the releaseof Gaia DR2, which has provided precision parallax measurementsand proper motions for nearly all nearby M-dwarfs, with our sampleof secondaries having median 0 .
17 % parallax precision.We take as input the sample of FGK-KM-dwarf pairs compiled byMann et al. (2013a) and Newton et al. (2014). These combine primarystar [Fe/H] measurements from high resolution spectra sourced froma variety of previous surveys (Mishenina et al. 2004; Luck & Heiter2005; Valenti & Fischer 2005; Bean et al. 2006a; Ramírez et al.2007; Robinson et al. 2007; Fuhrmann 2008; Casagrande et al. 2011;da Silva et al. 2011; Mann et al. 2013a), with Mann et al. (2013a)correcting for inter-survey systematics to place them on a common[Fe/H] scale. To this set we add the metal-poor, cool subdwarf VB12to extend our metallicity coverage, taking the [Fe/H] reported byRamírez et al. (2007) for its primary HD 219617 AB (and correctingfor the systematic reported by Mann et al. 2013a). This provided 128total pairs, which was reduced to 69 after crossmatching with bothGaia DR2 and 2MASS, and removing those stars with missing orpoor photometry (2MASS Qflg ≠ ‘AAA’, where ‘AAA’ is the highestphotometric quality rating and corresponds to 𝐽𝐻𝐾 𝑆 respectively);those flagged on SIMBAD as spectroscopic binaries; those withpoor Gaia astrometry (Gaia dup flag=1, RUWE > . − . < [ Fe / H ] < + . 𝑀 𝐾 𝑆 − colour space, though using ( 𝐵 𝑃 − 𝐾 𝑆 ) instead of ( 𝑉 − 𝐾 𝑆 ) . For our main sequence fit, we usethe complete Mann et al. (2015) sample of cool dwarfs with Gaiaparallaxes, which spans a wider range in ( 𝐵 𝑃 − 𝐾 𝑆 ) and is lesssparse than the assembled sample of M-dwarf secondaries. We findthe following third order polynomial sufficient to describe the mainsequence: ( 𝐵 𝑃 − 𝐾 𝑆 ) = 𝑎 𝑀 𝐾 𝑆 + 𝑎 𝑀 𝐾 𝑆 + 𝑎 𝑀 𝐾 𝑆 + 𝑎 (1)where 𝑎 = . 𝑎 = − . 𝑎 = . 𝑎 = − . ( 𝐵 𝑃 − 𝐾 𝑆 ) from thispolynomial (as a colour offers greater discriminatory power than 𝑀 𝐾 𝑆 , Schlaufman & Laughlin 2010), and use least squares to findthe best fitting linear relation for [Fe/H]: [ Fe / H ] = 𝑏 Δ ( 𝐵 𝑃 − 𝐾 𝑆 ) + 𝑏 (2)where 𝑏 and 𝑏 are the linear polynomial coefficients. After correct-ing for a remaining trend in the residuals, our adopted coefficientsare 𝑏 = . 𝑏 = − . . < ( 𝐵 𝑃 − 𝑅 𝑃 ) < . ± .
19 dex (fromthe standard deviation in the residuals). We stress that the relationshould only be used for stars that pass the same quality cuts we use tobuild the relation: unsaturated photometry, not flagged as a duplicatesource in Gaia, RUWE < .
4, and not a known/suspected spectro-scopic binary or pre-main sequence star. Our [Fe/H] recovery andfits can be seen in Figure 3. http://simbad.u-strasbg.fr/simbad/ The TESS candidate planet host observing program described heredeveloped from an ANU 2.3 m/WiFeS survey of potential youngstars (Žerjal et al. 2020) to identify signs of youth (via Balmer Seriesand Ca II H&K emission, and Li 6708Å absorption) and determineRVs to enable kinematic analysis with
Chronostar (Crundall et al.2019) when combined with Gaia astrometry. While their spectraltype coverage (1 . < 𝐵 𝑃 < .
6) was relatively similar to ourown, instrument setup however prioritised higher spectral resolutionfor improved velocity precision and coverage of the key wavelengthregions of interest. These regions are firmly in the optical, where M-dwarf spectral features are strongly blended and heavily dominatedby molecular absorption from hydrides (e.g. MgH, CaH, SiH) andoxides (e.g. TiO, VO, ZrO). This is in contrast to most of the previouslow-medium resolution studies of M-dwarfs which work in the NIRwhere the absorption is less severe and many more [Fe/H] sensitivefeatures are available.Here we describe our attempts to derive reliable atmospheric pa-rameters from our spectra using a model based approach. Our inves-tigation ultimately revealed substantial systematics and degeneracieswhen fitting to model optical spectra, resulting in our inability torecover log 𝑔 or [Fe/H]. While the spectra are included in our tem-perature fitting routine, they are primarily used for RV determination,identification of peculiarities (such as signs of youth), and for test-ing model fluxes. The details of our findings are covered below, andwe await follow-up work to explore a standard-based or data-drivenapproach (e.g. similar to the work of Birky et al. 2020, but in theoptical) to take full advantage of the information in our now largelibrary of optical cool dwarf spectra. While synthetic spectra show better agreement for FGK stars, theonset of strong molecular features such as TiO and H O in the atmo-spheres of late K and M dwarf atmospheres make the task of mod-elling their spectra far more complex. There are known historicalissues, for instance, when computing optical colours from syntheticspectra (e.g. difficulties in computing accurate 𝑉 band magnitudes,Leggett et al. 1996), and the line lists required are considerably morecomplicated. Thus, before using models in our automatic fitting rou-tine, we first investigate their performance at different wavelengthsto flag regions requiring special consideration. For the purposes ofthis comparison, we check the MARCS grid of stellar atmospheresagainst the BT-Settl grid (Allard et al. 2011), both of which aredescribed in detail below.Our template grid of 1D LTE MARCS spectra was previouslydescribed by Nordlander et al. (2019) and computed using the TUR-BOSPECTRUM code (v15.1; Alvarez & Plez 1998; Plez 2012) andMARCS model atmospheres (Gustafsson et al. 2008). The spectraare computed with a sampling resolution of 1 km s − , correspond-ing to a resolving power of 𝑅 ∼
300 000, with a microturbulentvelocity of 1 km s − . We adopt the solar chemical composition andisotopic ratios from Asplund et al. (2009), except for an alpha en-hancement that varies linearly from [ 𝛼 / Fe ] = [ Fe / H ] (cid:62) 𝛼 / Fe ] = + . [ Fe / H ] (cid:54) −
1. We use a selection of atomiclines from VALD3 (Ryabchikova et al. 2015) together with roughly15 million molecular lines representing 18 different molecules, themost important of which for this work are CaH (Plez, priv. comm.),MgH (Kurucz 1995; Skory et al. 2003), and TiO (Plez 1998, withupdates via VALD3).MARCS model fluxes were developed for usage over a range of
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Adam D. Rains et al. B P K S )5678 M K S . . . . . . ( B P K S )1.51.00.50.00.5 [ F e / H ] Fit (uncorrected)Fit (adopted) [ F e / H ] ( f i t ) [ Fe / H ]=0.02±0.19 [ F e / H ] ( B P R P ) ( B P R P ) [ F e / H ] R e s i d Figure 3. Left: [Fe/H] calculated from our calibration vs [Fe/H] from the primary star, colour coded by Gaia ( 𝐵 𝑃 − 𝑅 𝑃 ) . The standard deviation of the residuals,and our adopted uncertainty for the relation, is ± .
19 dex.
Top Right: 𝑀 𝐾 𝑆 − ( 𝐵 𝑃 − 𝐾 𝑆 ) colour magnitude diagram for our sample of cool dwarf secondariescolour coded by host star [Fe/H]. The dashed red line is a third order polynomial representing the main sequence, fitted to the Mann et al. (2015) sample of cooldwarfs. Bottom Right:
Fitted [Fe/H] as a function Δ ( 𝐵 𝑃 − 𝐾 𝑆 ) offset from the mean main sequence polynomial. The dashed red line is the initial uncorrectedlinear least squares fit, and the dash-dotted blue line is the adopted fit after correcting for the remaining trend in the residuals spectral types including both cool giants and, critically for our workhere, cool dwarfs. Recent work fitting cool dwarf stellar atmosphereshowever have mostly used high-resolution NIR spectra (J band: Öne-hag et al. 2012; Lindgren et al. 2016; Lindgren & Heiter 2017; Hband: Souto et al. 2017, 2018) rather than the medium resolutionoptical spectra we use here.For BT-Settl, we use the most recently published grid (Allard et al.2012a,b; Baraffe et al. 2015) which uses abundances from Caffauet al. (2011) and covers 1200 < 𝑇 eff < . < log 𝑔 < . = .
0. Note that while older grids have a wider range of [M/H],they are also less complete in terms of physics and line lists, so weopt for the newest grid for our comparison here, and limit ourselvesto testing on stars with approximately Solar [Fe/H].BT-Settl atmospheres have been developed with a focus on cooldwarf atmospheres and have a strong history of use for studying cooldwarfs at a variety of wavelengths and resolutions (e.g. Rojas-Ayalaet al. 2012; Muirhead et al. 2012; Mann et al. 2012; Rajpurohit et al.2013; Lépine et al. 2013; Gaidos et al. 2014; Mann et al. 2013c,2015; Veyette et al. 2016, 2017; Souto et al. 2018). Most noteworthyfor our comparison are tests by Reylé et al. (2011) and Mann et al.(2013c), which examined model performance at optical wavelengthregions > < 𝜆 < 𝑇 eff , log 𝑔 , and [Fe/H], aswell as the BT-Settl equivalent for those with close to Solar [Fe/H].Given our large library of standards we were able to observe modelperformance as a function of both stellar parameters and wavelength.A representative comparison (with overplotted filter bandpasses) isshown in Figure 4, and our main conclusions are summarised asfollows: • Both MARCS and BT-Settl models severely overpredict (wors- https://phoenix.ens-lyon.fr/Grids/BT-Settl/CIFIST2011_2015/ ening with decreasing 𝑇 eff ) flux blueward of ∼ • BT-Settl additionally underpredicts flux at ∼ • Synthetic photometry generated in SkyMapper 𝑣 , 𝑔 , 𝑟 , and Gaia 𝐵 𝑃 is thus systematically brighter than the observed equivalents forreasonable assumptions of 𝑇 eff , log 𝑔 , and [Fe/H] for the star underconsideration.We are able to quantify these systematics by integrating photom-etry from our flux calibrated observed spectra and comparing to theMARCS synthetic equivalents generated at the literature parametersfor each star. Our wavelength coverage allows us to check the mag-nitude offsets Δ 𝑣 , Δ 𝑔 , Δ 𝑟 and Δ 𝐵 𝑃 , corresponding to 𝑣 , 𝑔 , 𝑟 , and 𝐵 𝑃 respectively. We note that for the purpose of this comparison we donot account for inaccuracies in our flux calibration, telluric absorp-tion, nor for WiFeS not covering the bluest ∼
200 Å of 𝐵 𝑃 . However,checks with synthetic spectra show that this region accounts for lessthan 0 .
25 % of 𝐵 𝑃 flux at 3000 K where our correction is greatest,and remains less than 0 . 𝑔 , 𝑟 , and 𝐵 𝑃 in Figure5, and fit separately for each filter by the following linear relation inobserved Gaia DR2 ( 𝐵 𝑃 − 𝑅 𝑃 ) : Δ 𝑚 𝜁 = 𝑎 ( 𝐵 𝑃 − 𝑅 𝑃 ) + 𝑎 (3)where Δ 𝑚 𝜁 is the magnitude offset in filter 𝜁 ; 𝑎 equals 0.116, 0.084,and 0.034 for 𝑔 , 𝑟 , and 𝐵 𝑃 fits respectively; and 𝑎 equals -0.072,-0.069, and -0.037 for 𝑔 , 𝑟 , and 𝐵 𝑃 fits respectively. Computingthe standard deviation for the residuals shows 0.10, 0.05, and 0.02uncertainties in magnitude (equivalent to roughly 10%, 5%, and 2%uncertainties in flux) for 𝑔 , 𝑟 , and 𝐵 𝑃 respectively. From this weconclude that while the corrections to 𝑟 , and 𝐵 𝑃 are modest, 𝑔 islikely too affected to prove useful.Following this both qualitative and quantitative investigation com- MNRAS , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts paring model fluxes to our library of standard star spectra, we makethe following decisions for our synthetic fitting methodology: • Given similar observed systematics for both MARCS and BT-Settl model fluxes, we adopt the MARCS grid to enable fitting for[Fe/H] as well as 𝑇 eff and log 𝑔 . • Only use our R7000 spectra (5400 (cid:54) 𝜆 (cid:54) • Apply an observed ( 𝐵 𝑃 − 𝑅 𝑃 ) dependent systematic offset toour generated synthetic 𝐵 𝑃 and 𝑟 photometry per Equation 3. • Given the widespread historical use and success of studying M-dwarfs at NIR wavelengths, we use 𝑅 𝑃 , 𝑖 , 𝑧 , 𝐽 , 𝐻 , and 𝐾 𝑆 photometryassuming no substantial model systematics. • However, to account for remaining model uncertainties, we addconservative ± .
011 magnitude (1% in flux) uncertainties in quadra-ture with the observed uncertainties for 𝑅 𝑃 , 𝑖 , 𝑧 ; and the fitted ± . 𝑟 , and ± .
05 for 𝐵 𝑃 . Our approach to spectral fitting was developed specifically to workwith the complicated spectra of our cool star sample and incorpo-rates nine distinct sources of information. While it was hoped thatthis methodology would be sufficient to disentangle the strong de-generacy between 𝑇 eff and [Fe/H] and accurately recover distant-independent [Fe/H] for our standard sample, this ultimately provednot to be the case. While we are able to tightly constrain 𝑇 eff , we mustresort to using the photometric [Fe/H] relation developed in Section3 to fix [Fe/H] during the fit. The information included in our fit isas follows:(i) Medium resolution R7000 optical spectra from WiFeS,(ii) Observed Gaia 𝐵 𝑃 , 𝑅 𝑃 ; 2MASS 𝐽 , 𝐻 , and 𝐾 𝑆 ; and SkyMap-per DR3 𝑟 , 𝑖 , 𝑧 photometry,(iii) Empirical cool dwarf radius relations from Mann et al. (2015)- valid for K7-M7 stars, and used to estimate log 𝑔 ,(iv) Empirical cool dwarf mass relations from Mann et al. (2019)- valid for 0 . 𝑀 (cid:12) < 𝑀 ★ < . 𝑀 (cid:12) , and used to estimate log 𝑔 ,(v) Synthetic MARCS model spectra (for spectral fitting, interpo-lated to the resolution and wavelength grid of WiFeS)(vi) MARCS model fluxes (for photometric fitting),(vii) Stellar parallaxes from Gaia DR2,(viii) The interstellar dust map from Leike & Enßlin (2019),(ix) A set of reference stellar standards with known parametersfor testing and validation purposes (see Section B for details).We found that least squares fitting between real and syntheticspectra alone consistently underestimated expected log 𝑔 values ofour sample by up to 0 . 𝑔 using the absolute 𝐾 𝑆 band radius and massrelations of Mann et al. (2015) and Mann et al. (2019) respectively,and fix it during fitting. We then use a two step iterative procedure,with the first fit fixing log 𝑔 to the value from empirical relations,and a second and final fit using our interim measured radius and amass from Mann et al. (2019). All of our TESS targets fall withinthe stated 4 < 𝑀 𝐾 𝑆 <
11 limits for the mass relation. Althoughthe relation is only valid for main sequence stars, we employ it with Calculated using the Python code available at: https://github.com/awmann/M_-M_K- caution for two suspected young stars TOI 507 (TIC 348538431) andTOI 142 (425934411), both discussed in more detail in Section 6.5,on the assumption that the resulting value of log 𝑔 will still be moreaccurate than an unconstrained synthetic fit. Additionally, we suspectTOI 507 of being a near-equal mass binary, and as such treat it as0 .
75 magnitudes fainter (or half as bright) for the purpose of usingthe relation, equivalent to determining the mass for only a singlecomponent.While this now solves the log 𝑔 issue, we are still left with twoissues arising from the spectra themselves. The first is that certainwavelength regions of our MARCS model spectra are a poor matchcompared to our reference sample with known 𝑇 eff , log 𝑔 , and [Fe/H]- particularly at cooler temperatures. As discussed in Section 4.1, weaccount for this by using only spectra from the red arm of WiFeSwith 𝜆 > 𝑇 eff and [Fe/H] when fitting spectra. This effect is caused by both thetemperature and metallicity influencing the strength of atmosphericmolecular absorbers or opacity sources (predominantly TiO in theoptical, but also various hydrides). What this means in practice isthat there often isn’t a single minimum or optimal set of atmosphericparameters when fitting synthetic spectra, but instead there exists arange of good fits (or even multiple minima) at different combinationsof 𝑇 eff and [Fe/H] - possibly separated by several 100 K in 𝑇 eff orseveral 0.1 dex in [Fe/H].In an attempt to overcome this, we include photometry from red-der wavelengths that are less dominated by absorption than opticalwavelengths, meaning that 𝑇 eff and [Fe/H] are less degenerate. Whilewe do not have NIR spectra for our science or reference sample, wedo have Gaia, SkyMapper, and 2MASS photometry in the form of 𝐵 𝑃 , 𝑅 𝑃 , 𝑟 , 𝑖 , 𝑧 , 𝐽 , 𝐻 , and 𝐾 𝑆 which together give us almost contin-uous wavelength coverage out to nearly 2.4 𝜇 m and covers the bulkof stellar emission for our cool stars.We thus modified our fitting methodology to also compute the un-certainty weighted residuals between observed and synthetic stellarphotometry. In order to compare synthetic photometry to its observedequivalent we formulate the fit as follows: 𝑚 𝜁 ,𝑚 = BC 𝜁 ( 𝑇 eff , log 𝑔, [ Fe / H ]) + 𝑚 bol (4)where 𝑚 𝜁 ,𝑚 is the model magnitude in filter 𝜁 ; BC 𝜁 is the bolomet-ric correction (i.e. the total flux outside of a filter 𝜁 ) as a functionof 𝑇 eff , log 𝑔 , and [Fe/H] in filter 𝜁 ; and 𝑚 bol is the apparent bolo-metric magnitude (i.e. the apparent magnitude of the star over allwavelengths). In this implementation 𝑚 bol serves as a physicallymeaningful free parameter used to scale synthetic magnitudes totheir observed equivalents and ultimately allow computation of theapparent bolometric flux 𝑓 bol . This is done using the well tested bolometric-corrections software (Casagrande & VandenBerg2014, 2018a,b) to interpolate a grid of bolometric corrections fromMARCS fluxes in different filters for the stellar parameters at eachfitting call. By fitting for 𝑚 bol and using bolometric corrections,we are thus directly able to compare an observed magnitude, 𝑚 𝜁 ,𝑜 ,from Gaia, SkyMapper, or 2MASS directly with its MARCS syn-thetic equivalent. With log 𝑔 fixed, we now have a three term fit interms of 𝑇 eff , [Fe/H], and 𝑚 bol , the latter of which allows for directcomputation of the bolometric flux (and thus the stellar radius).This fitting procedure is equivalent to minimising the following https://github.com/casaluca/bolometric-corrections MNRAS , 1–22 (2015) Adam D. Rains et al. f ( N o r m a li s e d ) Observed MARCS BT-Settl v g r B P R P Figure 4.
Observed WiFeS B3000 and R7000 spectra for GJ 447, along with a MARCS synthetic spectrum interpolated to the parameters from Mann et al.2015 ( 𝑇 eff = 𝑔 = .
04, [Fe/H] = − . 𝑇 eff = 𝑔 = .
0, [Fe/H] = . 𝑣 , 𝑔 , 𝑟 , and Gaia 𝐵 𝑃 and 𝑅 𝑃 filters are overplotted for reference. Note the severe model disagreement below 5400 Å. B P R P m r integrated r =0.034( B P R P ) 0.037,[ r =0.02] B P integrated B P =0.084( B P R P ) 0.069,[ B P =0.05] g integrated g =0.116( B P R P ) 0.072,[ g =0.10] Figure 5.
Gaia 𝐵 𝑃 , and SkyMapper 𝑔𝑟 systematic offsets between integratedflux calibrated WiFeS spectra and MARCS model integrated spectra at liter-ature parameters for our standard stars, plotted as a function of observed Gaia 𝐵 𝑃 − 𝑅 𝑃 . Stars redder in 𝐵 𝑃 − 𝑅 𝑃 have systematically more flux at bluerwavelengths, with the best fit linear magnitude offset plotted for each filter,and the standard deviation in magnitude noted. relation (performed using the least_squares function from scipy ’soptimize module): 𝑅 ( 𝜃 ) = 𝑀 ∑︁ 𝑖 = (cid:32) 𝐶 √︃ 𝜒 𝑓 𝑓 𝑜,𝑖 − 𝑓 𝑚,𝑖 𝜎 𝑓 𝑜,𝑖 (cid:33) + 𝑁 ∑︁ 𝜁 = (cid:32) √︃ 𝜒 𝑚 𝑚 𝜁 ,𝑜 − ( 𝑚 𝜁 ,𝑚 + Δ 𝑚 𝜁 ) 𝜎 𝑚 𝜁 (cid:33) (5)with model uncertainties taken into account via: 𝜎 𝑚 𝜁 = √︃ 𝜎 𝑚 𝜁 ,𝑜 + 𝜎 𝑚 𝜁 ,𝑚 (6)where 𝑅 ( 𝜃 ) are the combined spectral and photometric squaredresiduals as a function of 𝜃 , a vector of 𝑇 eff , log 𝑔 , [Fe/H], 𝑚 bol ); 𝑀 is the total number of spectral pixels, 𝑖 is the spectral pixel index, 𝑓 o , i and 𝑓 m , i are the observed and model spectral fluxes respec-tively at pixel 𝑖 , normalised by their respective medians in the range6200 (cid:54) 𝜆 (cid:54) 𝜎 𝑓 o , i is the observed flux uncertainty at pixel 𝑖 ; 𝑁 is the total number of photometric filters; 𝜁 is the filter index, 𝑚 𝜁 ,𝑜 and 𝑚 𝜁 ,𝑚 are the observed and model magnitudes respectivelyin filter 𝜁 ; Δ 𝑚 𝜁 is the systematic model magnitude offset in filter 𝜁 (per Equation 3 for 𝑟 and 𝐵 𝑃 , and 0 for all other filters); 𝜎 𝑚 𝜁 ,𝑜 and 𝜎 𝑚 𝜁 ,𝑚 are the uncertainties on the observed and model magnitudesrespectively, added in quadrature to give the total magnitude uncer-tainty 𝜎 𝑚 𝜁 ; 𝜒 𝑓 and 𝜒 𝑚 are the global minimum 𝜒 values computedfrom the spectral and photometry residuals respectively (i.e. global fitusing only R7000 spectra, without photometry, and a separate globalphotometric fit without spectra) used to normalise the two sets ofresiduals in the case of poor fits and place them on a similar scale;and 𝐶 , set to 20, is a constant used to account for the spectra havingmany more pixels than the number of photometric points. This valueof 𝐶 was chosen by visually inspecting the residuals of our spectralfits and means that we assume, on average, every 20 spectral pixelsare correlated and do not contain unique information.We test the accuracy of our fitted [Fe/H] using a set of cool starstellar standards in Figure 6. It is immediately clear that, despitethe tight constraint on 𝑇 eff that our broad wavelength coverage fromphotometry allows, we are unable to recover [Fe/H] for our standardsample to better precision than our photometric [Fe/H] relation fromSection 3. Our fits systematically overpredict [Fe/H] for the cooleststars in our sample, which might be similar to what was observed inFigure 3 of Rojas-Ayala et al. 2012 (using BT-Settl models), wherethey find even metal-rich models fail to reproduce the depth of certainfeatures. This has also previously been observed for cool, metal-poorclusters when using evolutionary models (e.g. Joyce & Chaboyer2015), and observed for isochrones (e.g. Joyce & Chaboyer 2018).From this we conclude that a simple least squares fit to our mediumresolution optical spectra, unweighted to [Fe/H] sensitive regions,and using models with both known and unknown systematics is notsufficient to accurately determine [Fe/H] for cool dwarfs.Given this, it is clear a three parameter fit to 𝑇 eff , [Fe/H], and 𝑚 bol is unreasonable. Our final reported parameters are thus a twoparameter fit to 𝑇 eff , and 𝑚 bol , fixing [Fe/H] to the value from ourrelation in Section 3 for those stars falling within the ( 𝐵 𝑃 − 𝑅 𝑃 ) range, and the mean value for the Solar Neighbourhood of [Fe/H] = − .
14 (Schlaufman & Laughlin 2010) for stars outside this range,or suspected of binarity or being young. To further account for bothmodel and zeropoint uncertainties, we add a 1% flux uncertaintyin quadrature with our fitted statistical uncertainties on 𝑚 bol . Ourstandard star 𝑇 eff recovery for the two parameter fit is shown inFigure 7. MNRAS , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts We compute the apparent bolometric flux 𝑓 bol from our fitted valueof 𝑚 bol using Equation 3 from Casagrande & VandenBerg (2018a),from which we then compute the stellar radius 𝑅 ★ . Figure 8 showsa comparison between our radii and those from our interferometricstandard sample, and final values for TESS science targets and stellarstandards are reported in Tables 2 and B2 respectively. We now present results for all TOIs not ruled out as false positives(e.g. due to background stars, or eclipsing binaries) by the TESSTeam and exoplanet community, as listed on the NASA ExoFOP-TESS website.Transit light curves for targets across all TESS sectors weredownloaded from NASA’s Mikulski Archive for Space Telescopes(MAST) service. For all high-cadence data, we used the Pre-searchData Conditioning Simple Aperture Photometry (PDCSAP) fluxes,which have already had some measure of processing to remove sys-tematics.All light curves were downloaded and manipulated using thepython package
LightKurve (Lightkurve Collaboration et al. 2018).Many stars in our sample show some amount of stellar variability,with periods ranging from days to many weeks. We remove this us-ing
LightKurve ’s flatten function, which applies a Savitzky-Golayfilter (Savitzky & Golay 1964) to the data to remove low frequencytrends. When applying the filter we mask out all planetary transits byknown TOIs. Once flattened, the light curves are then phase foldedusing either the period provided by NASA ExoFOP-TESS (for moststars), or our own fitted period (for stars revisited in the TESS ex-tended mission whose long time baseline reveals the ExoFOP-TESSperiod to be incorrect). We use the provided measurement of transitduration to select only photometry from the transit itself, plus 10%of a duration either side for use in model fitting.Model fitting is implemented using the python package
BATMAN (Kreidberg 2015), which is capable of generating model transit lightcurves for a given set of orbital elements (scaled by the stellar ra-dius 𝑅 ★ ) and limb darkening coefficients. We use a four term limbdarkening law, interpolating the PHOENIX grid provided by Claret(2017) using values of 𝑇 eff and log 𝑔 from Table 2. The resultingcoefficients are in Table D1.Transit photometry alone is not sufficient to uniquely constrain theplanet orbit and radius when fitting for the scaled semi-major axis 𝑎 𝑅 ★ = 𝑎𝑅 ★ , the planetary radius ratio 𝑅 𝑃,𝑅 ★ = 𝑅 𝑃 𝑅 ★ , the inclination 𝑖 ,the eccentricity 𝑒 , and the longitude of periastron 𝜔 (Kipping 2008).While we can use our measurements of 𝑀 ★ , 𝑅 ★ , and 𝑇 to constrainthe semi-major axis of a circular orbit (Equation 7), we do not havethe precision required to fit for eccentric orbits. As such, we fix 𝑒 = 𝜔 = 𝑎 𝑅 ★ ,𝑐 -the value 𝑎 𝑅 ★ assuming a circular orbit, as a prior during fitting. Incases where 𝑒 ∼
0, we expect the fitted semi-major axis 𝑎 𝑅 ★ , 𝑓 toapproach 𝑎 𝑅 ★ ,𝑐 . For cases with a discrepancy between the two, weflag the planet as an indication of a possibly eccentric orbit in Table3. This measured semi-major axis, calculated using our Mann et al.(2015) absolute 𝐾 𝑆 band 𝑀 ★ , and 𝑇 from NASA ExoFOP, can beconstrained as follows: 𝑎 = √︄ 𝐺 𝑀 ★ 𝑇 𝜋 (7) where 𝑎 is the semi-major axis, 𝐺 is the gravitational constant, 𝑀 ★ is the stellar mass (with 𝑀 ★ >> 𝑀 𝑝 , the planetary mass), and 𝑇 isthe planet orbital period - all of which we assume are independentquantities.Now with a prior on the semi-major axis, we again use theleast_squares function from scipy ’s optimize module to performleast squares fitting to minimise the following expression: 𝑅 𝑡 = (cid:32) 𝑎 𝑅 ★ ,𝑚 − 𝑎 𝑅 ★ , 𝑓 𝜎 𝑎 𝑅★,𝑚 + 𝑁 ∑︁ 𝑗 𝑡 obs , j − 𝑡 model , j 𝜎 𝑡 obs , j (cid:33) (8)where 𝑅 𝑡 are the light curve and prior residuals (as a function of 𝑅 𝑝,𝑅 ★ , 𝑎 𝑅 ★ , 𝑓 , and 𝑖 ), 𝑎 𝑅 ★ ,𝑚 the measured scaled semi-major axis, 𝑎 𝑅 ★ , 𝑓 the fitted scaled semi-major axis, 𝜎 𝑎 𝑅★,𝑚 the uncertaintyon the measured scaled semi-major axis, 𝑗 is the time step, 𝑁 thetotal number of epochs, 𝑡 obs , j is the observed flux at time step 𝑗 , 𝑡 model , j the model flux at time step 𝑗 , and 𝜎 𝑡 obs , j is the measured fluxuncertainty at time step 𝑗 .Results from this fitting procedure are presented in Table 3, a com-parison with confirmed planets in Figure 11, and a histogram of theresulting planet candidate radii in Figure 12. Note that we do not fitthe light curves for some candidates: TOIs 256.01 and 415969908.02have only two and one transits respectively; TOI 507.01 is a suspectedequal mass binary; TOIs 302.01 and 969.01 do not have PDCSAPtwo minute cadence data; and TOIs 203.01, 253.01, 285.01, 696.02,785.01, 864.01, 1216.01, 260417932.02, and 98796344.02 have tran-sits observed only at low SNR. Just over half our TESS sample have radial velocities in Gaia DR2,with the remaining 42 therefore having an incomplete set of positionaland kinematic data. Our RVs are consistent with Gaia DR2 for ouroverlap sample and accurate to within ∼ . − (Section 2.4), thusproviding RVs for the remainder and enabling insight into Galacticpopulation, or kinematic analysis using tools such as Chronostar (Crundall et al. 2019) to determine ages for those that are foundto be members of stellar associations. These results are especiallyinteresting given the planet-hosting nature of these stars.
Comparing our 𝑇 eff results to those of Mann et al. (2015) revealsexcellent agreement for our two parameter fit (Figure 7), with thescatter on our residuals being smaller than their mean reported un-certainty of 60 K and only a relatively small systematic of ∼
30 Kobserved. Such consistency is encouraging given that this representsour largest uniform set of comparison stars, a set whose temperatureshave already been successfully benchmarked against those from in-terferometry and should be much less sensitive to model limitationsthan our own.When comparing to Rojas-Ayala et al. (2012), the results are lessconsistent, though we observe a similar effect to Mann et al. (2015)in that Rojas-Ayala et al. (2012) overestimates temperatures for thewarmest stars. These temperatures, however, come solely from mea-surement of the H O-K2 index in the 𝐾 band in conjunction withBT-Settl model atmospheres - much more limited in wavelength cov-erage than Mann et al. (2015) or our work here.The interferometric sample shows good agreement, though we ob-serve a ∼
70 K temperature systematic of the same sign as for the
MNRAS000
MNRAS000 , 1–22 (2015) Adam D. Rains et al.
Table 2.
Final results for TESS candidate exoplanet hostsTOI TIC 𝑇 eff log 𝑔 [Fe/H] 𝑀 𝑅 𝑚 bol 𝑓 bol EW(H 𝛼 ) log 𝑅 (cid:48) HK (K) ( 𝑀 (cid:12) ) ( 𝑅 (cid:12) ) (10 − ergs s − cm − ) Å136 410153553 2988 ±
30 5.06 ± ± ± ± ± ±
30 5.07 ± ± ± ± ± ±
30 5.01 ± ± ± ± ± ±
30 5.01 ± ± ± ± ± ±
30 4.76 ± ± ± ± ± ±
30 4.97 ± ± ± ± ± ±
30 4.90 ± ± ± ± ± ±
30 4.86 ± ± ± ± ± ±
30 4.97 ± ± ± ± ± ±
30 4.83 ± ± ± ± ± ±
30 4.77 ± ± ± ± ± ±
30 4.83 ± ± ± ± ± ±
30 4.94 ± ± ± ± ± ±
30 4.81 ± ± ± ± ± ±
30 4.82 ± ± ± ± ± ±
30 4.86 ± ± ± ± ± ±
30 4.77 ± ± ± ± ± ±
30 4.82 ± ± ± ± ± ±
30 4.88 ± ± ± ± ± ±
30 4.81 ± ± ± ± ± ±
30 4.80 ± ± ± ± ± ±
30 4.80 ± ± ± ± ± ±
30 4.83 ± ± ± ± ± ±
30 4.80 ± ± ± ± ± ±
30 4.88 ± ± ± ± ± ±
30 4.92 ± ± ± ± ± ±
30 4.83 ± ± ± ± ± ±
30 4.88 ± ± ± ± ± ±
30 4.76 ± ± ± ± ± ±
30 4.77 ± ± ± ± ± ±
30 4.75 ± ± ± ± ± ±
30 4.71 ± ± ± ± ± ±
30 4.69 ± ± ± ± ± ±
30 4.70 ± ± ± ± ± ±
30 4.76 ± ± ± ± ± ±
30 4.74 ± ± ± ± ± ±
30 4.55 ± ± ± ± ± ±
30 4.72 ± ± ± ± ± ±
30 4.70 ± ± ± ± ± ±
30 4.70 ± ± ± ± ± ±
30 4.67 ± ± ± ± ± ±
30 4.72 ± ± ± ± ± ±
30 4.77 ± ± ± ± ± ±
30 4.60 ± ± ± ± ± ±
30 4.60 ± ± ± ± ± ±
30 4.67 ± ± ± ± ± ±
30 4.65 ± ± ± ± ± ±
30 4.71 ± ± ± ± ± ±
30 4.73 ± ± ± ± ± ±
30 4.86 ± ± ± ± ± ±
30 4.63 ± ± ± ± ± ±
30 4.67 ± ± ± ± ± ±
30 4.63 ± ± ± ± ± ±
30 4.67 ± ± ± ± ± ±
30 4.63 ± ± ± ± ± ±
30 4.62 ± ± ± ± ± ±
30 4.69 ± ± ± ± ± ±
30 4.65 ± ± ± ± ± ±
30 4.69 ± ± ± ± ± ±
30 4.63 ± ± ± ± ± ±
30 4.62 ± ± ± ± ± ±
30 4.66 ± ± ± ± ± ±
30 4.65 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts [ F e / H ] ( f i t ) r e s i d T e ff K ( f i t ) Figure 6. [Fe/H] recovery for our 3 parameter fit in 𝑇 eff , [Fe/H], 𝑚 bol for our four sets of [Fe/H] standards: Mann et al. 2015, Rojas-Ayala et al. 2012, primarystar [Fe/H] for cool dwarfs in binaries, and mid-K dwarfs. The median and standard deviation of each set of residuals is annotated. Note the inability of the 3parameter fit to reliably recover [Fe/H], with the scatter on our recovered [Fe/H] for the binary sample (the most reliable set of [Fe/H] standards) being largerthan the scatter on our photometric [Fe/H] relation. T e ff ( K , f i t ) T eff (K, Mann+15)1500150 r e s i d T eff (K, Rojas-Ayala+12)3001500150300 0.40.20.00.23000 3500 4000 4500 5000 T eff (K, interferometric)3001500150 0.300.250.200.150.100.050.00 [ F e / H ] ( p h o t ) T eff (K, other)1500150 Figure 7. 𝑇 eff recovery for our 2 parameter fit in 𝑇 eff , and 𝑚 bol for our four sets of 𝑇 eff standards: Mann et al. 2015, Rojas-Ayala et al. 2012, interferometry,and mid-K dwarfs. [Fe/H] is from our photometric [Fe/H] relation where appropriate, or fixed to the mean Solar Neighbourhood [Fe/H] if not. The median andstandard deviation of each set of residuals is annotated. Table 2 – continued Final results for TESS candidate exoplanet hostsTOI TIC 𝑇 eff log 𝑔 [Fe/H] 𝑀 𝑅 𝑚 bol 𝑓 bol EW(H 𝛼 ) log 𝑅 (cid:48) HK (K) ( 𝑀 (cid:12) ) ( 𝑅 (cid:12) ) (10 − ergs s − cm − ) Å1082 261108236 4096 ±
30 4.65 ± ± ± ± ± ±
30 4.70 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± ±
30 4.71 ± ± ± ± ± ±
30 4.68 ± ± ± ± ± ±
30 4.61 ± ± ± ± ± ±
30 4.59 ± ± ± ± ± ±
30 4.58 ± ± ± ± ± ±
30 4.55 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± ±
30 4.66 ± ± ± ± ± ±
30 4.62 ± ± ± ± ± ±
30 4.59 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± ±
30 4.63 ± ± ± ± ± ±
30 4.59 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± ±
30 4.59 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± ±
30 4.61 ± ± ± ± ± ±
30 4.62 ± ± ± ± ± ±
30 4.59 ± ± ± ± ± ±
30 4.59 ± ± ± ± ± ±
30 4.58 ± ± ± ± ± ±
30 4.57 ± ± ± ± ± ±
30 4.61 ± ± ± ± ± ±
30 4.57 ± ± ± ± ± ±
30 4.60 ± ± ± ± ±000
30 4.60 ± ± ± ± ±000 , 1–22 (2015) Adam D. Rains et al.
Table 3.
Final results for TESS candidate exoplanetsTOI TIC Sector/s Period 𝑅 𝑝 / 𝑅 ★ 𝑎 / 𝑅 ★ 𝑒 flag 𝑖 𝑅 𝑝 (days) ( ◦ ) ( 𝑅 ⊕ )122.01 231702397 1,27-28 5.07803 † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± Notes:
Periods denoted by † are not as reported by ExoFOP, and have been refitted here. These are overwhelmingly systems with TESS extended mission data,thus having longer time baselines with which to constrain orbital periods. Our fitted periods however are generally consistent within uncertainties of theirExoFOP values, and as such we do not report new uncertainties here. Additionally, our least squares fits to 7 of our light curves proved insenstive to non-edge-oninclinations. As such, we report conservative uncertanties of ± ° for these planets.MNRAS , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Table 3 – continued Final results for TESS candidate exoplanetsTOI TIC Sector/s Period 𝑅 𝑝 / 𝑅 ★ 𝑎 / 𝑅 ★ 𝑒 flag 𝑖 𝑅 𝑝 (days) ( ◦ ) ( 𝑅 ⊕ )702.01 237914496 1-4,7,11,27,29-31 3.56809 † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± † ± ± ± ± ± ± ± ± ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± † ± ± ± ± † ± ± ± ± ± ± ± ± † ± ± ± ± ± ± ± ± † ± ± ± ± † ± ± ± ± ± ± ± ± † ± ± ± ± ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± † ± ± ± ± Mann et al. (2015) sample. However, due to the bias of interferome-try towards close and thus bright targets, these are also the brighteststars we observe and they have correspondingly high photometric un-certainties due to saturation. This is particularly acute in the 2MASSbands, where less than half the sample have the photometric qualityflag (Qflg) of ‘AAA’, in contrast to the rest of the standard samplewhere all but two of 117 stars has Qflg ‘AAA’, and the entirety of theTESS sample. Nonetheless, our derived radii for the interferomet-ric standards (Figure 8) are consistent when allowing for additionalscatter from poor quality photometry on bright stars that will not bepresent for our science targets. Encouragingly however Mann et al.(2015), which we are in agreement with, integrated their own pho-tometry from low resolution flux calibrated spectra and found a goodmatch between their results and their own interferometric sample.Finally, our results are consistent with our sample of mid-K-dwarfsin the temperature range of our warmest science targets. The observedhigher scatter (than e.g. the Mann et al. 2015 sample) is to be expecteddue to inter-study systematics, as these targets were not pulled froma single uniform catalogue.While the exact cause of the Mann et al. (2015) and interferometric systematic is unclear, its appearance in both samples suggests it isnot an artefact. As such, we apply a -30 K correction to the observedtemperature systematic. Although our remaining scatter is consistentwith the scatter in our external reference catalogues, we add a further ±
30 K 𝑇 eff uncertainty in quadrature with our statistical uncertaintiesto account for the unknown origin of the observed systematic. Giventhese corrections, we are confident our fitting methodology is able torecover both accurate and precise stellar temperatures and radii forstars in the range 3000 K (cid:46) 𝑇 eff (cid:46) The inability of cool dwarf atmospheric models to reproduce opticalfluxes is significant. Such wavelengths are among the most easilyaccessible, and understanding them is required to take full advantageof photometry from surveys like Gaia and SkyMapper. Thus anyonerelying directly (e.g. spectral fitting) or indirectly (e.g. isochronefitting with colours) on models for cool stellar atmospheres mustdo so with caution (for specifics on isochone systematics, see e.g.
MNRAS000
MNRAS000 , 1–22 (2015) Adam D. Rains et al. R a d i u s ( R , f i t ) R , Interferometric)0.050.000.05 2.53.03.54.04.55.05.56.0 K S Figure 8.
Radius comparison for those targets with interfometric radii tobetter than 5% precision. The median distance precision for these targets is0 .
04 %. We find generally good agreement between literature measurementsand our own, though noting that the brightness of this sample (see apparent2MASS 𝐾 𝑆 magnitude on the colour bar) results in photometry that is eithersaturated or has lower precision and thus may be the cause of some of thescatter observed. VandenBerg et al. 2006 for the Victoria-Regina models, Dotter et al.2008 and Joyce & Chaboyer 2018 for DSEP, and Dotter 2016 forMIST). That said, there is an ever increasing empirical knowledgeof M-dwarfs meaning that, even in the absence of accurate models,empirical or data driven approaches should be possible (e.g. seeBirky et al. 2020 which demonstrates that a data driven approach, atleast in the 𝐻 band, is possible for M-dwarfs). The very small rateof evolution for these low-mass stars means we can rely on mass andchemical composition to derive the fundamental parameters of thestar, thus making for a more tractable problem. The TESS Input Catalogue is often the first stellar parameter refer-ence for newly alerted TOIs. As these parameters are mostly derivedfrom empirical relations using literature photometry, we thought ituseful to compare these predictions with our fits to inspect for re-maining catalogue systematics. Figure 9 displays this comparison for 𝑇 eff and 𝑅 ★ , and while the TIC temperatures are broadly consistent,TIC radii for the warmest stars in our sample appear systematicallylarge. This stellar radii systematic is noteworthy as it would bias anypredicted exoplanet radii around mid-K dwarfs. While model limitations prevented us from taking full advantage ofour spectra during fitting, our wide wavelength coverage allows usto look for spectral peculiarities. In the current study, these take theform of emission in the Hydrogen Balmer Series or Ca II H&K (bothsigns of stellar activity and youth), as well as absorption in the Li6 ,
708 Å (another sign of youth). While none of our TESS planethosts show detectable Lithium absorption, we report H 𝛼 equivalentwidths and log 𝑅 (cid:48) HK in Table 2, calculated using the methodology ofŽerjal et al. (2020). 53 stars in our sample have EWH 𝛼 > − . T e ff ( K , f i t ) R ( R , f i t ) T eff (K, TIC)5002500250500 r e s i d R ( R , TIC)0.20.10.00.10.2 r e s i d Figure 9.
Comparison of 𝑇 eff and 𝑅 ★ as reported here compared to thosefrom the TESS Input Catalogue. The median and standard deviation of eachset of residuals is annotated. strongly dependent on 𝑇 eff and thus somewhat approximate), and 35have log 𝑅 (cid:48) HK > − .
75 (the lower bound for active stars used in Grayet al. 2006).Of particular note are our two most active stars, the first of whichis TOI 507 (TIC 348538431). TOI 507 appears substantially over-luminous in Figure 1, and presents with strong emission across theBalmer Series and in Ca II H&K. Visual inspection of its spec-trum, along with comparison to the cool dwarf standard HIP 103039which is very similar in 𝑇 eff , indicates that it is actually a double-linedspectroscopic binary. Transit depths appear similar for both primaryand secondary eclipses, which points to the system being composedof roughly equal mass components. Taking a ∼ 𝑚 bol , and flux reported in Table 2 have been de-rived for a single component of this binary system, assuming equalmass and brightness.The second star is TOI 142 (425934411) which is also overlumi-nous and shows displays strong emission features. Interestingly, itappears to host a giant planet ( 𝑅 𝑃 = . ± . 𝑅 ⊕ ) on a shortperiod ( 𝑇 ≈ .
85 day) - see Figure 10. While this is unusual for sucha cool star, it is not unheard of, such as K2 32b which is a knownshort period super-Neptune orbiting a pre-main sequence star (Davidet al. 2016; Mann et al. 2016). Further characterisation of the systemhowever, whilst scientifically interesting, is likely to be hampered bythe faintness of the host star ( 𝐺 ∼ . Table 4 collates literature parameters for previously characterisedplanets in our sample. These planets have typically had follow-up ra-dial velocity observations which not only allows for planetary massdetermination, but helps constrain their orbits when combined withthe TESS light curves we use here (or additional time series photo-metric follow up). Figure 11 compares these results to our own for 𝑅 𝑃 / 𝑅 ★ , 𝑎 / 𝑅 ★ , 𝑖 , and 𝑅 𝑃 . We find our results consistent with theliterature, aside from a few exceptions discussed below. MNRAS , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Phase0.951.001.05 F l u x [ e s ] transit modelfolded light curve (2 min binning)folded light curve (10 min binning)0.100 0.075 0.050 0.025 0.000 0.025 0.050 0.075 0.100Phase0.050.000.05 r e s i d u a l s Figure 10.
Phase folded light curve with best fitting transit model for TOI 142.01. R P / R * ( f i t ) a / R * ( f i t ) i ( f i t ) R P ( f i t ) R P / R * (literature)0.0100.0050.0000.0050.010 r e s i d
20 40 60 80 a / R * (literature)42024 r e s i d
81 82 83 84 85 86 87 88 89 90 91 i (literature)1.500.750.000.751.50 r e s i d R P (literature)1.00.50.00.51.0 r e s i d Figure 11.
Comparison of 𝑅 𝑃 / 𝑅 ★ , 𝑎 / 𝑅 ★ , 𝑖 , and 𝑅 𝑃 to literature results in Table 4. Our two largest literature planets, TOIs 129.01 and 551.01, are hot Jupitersin a grazing configuration which leaves their radii poorly constrained. As such, they have been left off for clarity, though our results are consistent withinuncertainties. The median and standard deviation of each set of residuals is annotated and excludes these two planets. Vanderspek et al. (2019) reports a larger value of 𝑅𝑝 / 𝑅 ★ for LHS3844 b (TOI 136.01) than we do here, a difference we can attributeto our access to an extra sector of TESS data. While they also haveground based data, the extra TESS sector amounts to some 60 extratransits, which should give us improved precision. Comparison with HATS-48 A b (TOI 1067.01) from Hartman et al.(2020) shows an inconsistent value of 𝑅 𝑃 / 𝑅 ★ , indicating a differencein how we have modelled the light curves. While we have access toan additional sector of TESS data, the difference primarily appearsto come from a) including RVs in their fit, and b) their use of anadditional ‘dilution factor’ when fitting to account for nearby unre-solved stars. Such nearby stars have the effect of diluting the transitand making the transit appear shallower than it would were only theflux from the host star observed. Our transit fits, by comparison, relyon the quality of the detrending and correction for crowding alreadydone by the TESS team and provided in their PDCSAP fluxes.Leleu et al. (2021) reports parameters for six planets orbiting TOI178, of which only three were alerted on as TOIs. Our parametersare consistent for all but two of these, TOI 178 b (not alerted on)and TOI 178.03, both of which are relatively low SNR detections byTESS. Although our analysis includes an additional TESS sector ofdata, they employ higher precision data from CHEOPS to which weattribute the difference.The analysis of LHS 1140 c (TOI 256.02) by Ment et al. (2019)results in a value of 𝑅 𝑃 / 𝑅 ★ discrepant with our own. While ouranalysis makes use of an additional sector of TESS data, we con- sider their results more reliable as they conducted a joint RV andtransit photometry analysis, including additional ground based dataalongside high precision Spitzer data.
We find a consistent 𝑅 𝑃 / 𝑅 ★ with Esposito et al. (2017) for WASP-43b (TOI 656.01), though our value of 𝑅 𝑃 is smaller. This difference isattributable to their larger and less precise stellar 𝑇 eff , with which theyobtain a smaller stellar radius - resulting in a smaller planetary radii.As discussed, we are confident with our 𝑇 eff and 𝑅 ★ recovery, andconsider the difference the result of differing approaches to stellarparameter determination.For HATS-6 b (TOI 468.01) we find our 𝑅 𝑃 / 𝑅 ★ and 𝑇 eff con-sistent, but a different value for 𝑅 𝑃 as compared to Hartman et al.(2015). This difference again arises from a smaller literature valueof 𝑅 ★ . We consider our approach to radius determination using stel-lar fluxes more direct than the modelling based approach used here,especially given our access to precision Gaia parallaxes. We plot a histogram of our candidate planet radii in Figure 12, whichclearly shows the existence of the planet radius gap, first identified byFulton et al. (2017), at ∼ . − . 𝑅 ⊕ at a ∼ 𝜎 level. As we remainlimited by our small sample size, we do not perform any additionalanalysis and leave such investigations for future studies based ona larger sample of TESS planets. Our results however do providefurther evidence for the gap being present at low stellar masses. MNRAS000
We find a consistent 𝑅 𝑃 / 𝑅 ★ with Esposito et al. (2017) for WASP-43b (TOI 656.01), though our value of 𝑅 𝑃 is smaller. This difference isattributable to their larger and less precise stellar 𝑇 eff , with which theyobtain a smaller stellar radius - resulting in a smaller planetary radii.As discussed, we are confident with our 𝑇 eff and 𝑅 ★ recovery, andconsider the difference the result of differing approaches to stellarparameter determination.For HATS-6 b (TOI 468.01) we find our 𝑅 𝑃 / 𝑅 ★ and 𝑇 eff con-sistent, but a different value for 𝑅 𝑃 as compared to Hartman et al.(2015). This difference again arises from a smaller literature valueof 𝑅 ★ . We consider our approach to radius determination using stel-lar fluxes more direct than the modelling based approach used here,especially given our access to precision Gaia parallaxes. We plot a histogram of our candidate planet radii in Figure 12, whichclearly shows the existence of the planet radius gap, first identified byFulton et al. (2017), at ∼ . − . 𝑅 ⊕ at a ∼ 𝜎 level. As we remainlimited by our small sample size, we do not perform any additionalanalysis and leave such investigations for future studies based ona larger sample of TESS planets. Our results however do providefurther evidence for the gap being present at low stellar masses. MNRAS000 , 1–22 (2015) Adam D. Rains et al.
Table 4.
Summary of literature properties for already confirmed planetsTOI TIC Name 𝑅 𝑃 / 𝑅 ∗ 𝑎 / 𝑅 ∗ i 𝑅 𝑃 Reference ° 𝑅 ⊕ . + . − . . + . − . . + . − . . + . − . Waalkes et al. (2020)129.01 201248411 HIP 65A b 0 . + . − . . + . − . . + . − . . + . − . Nielsen et al. (2020)136.01 410153553 LHS 3844 b 0 . + . − . . + . − . . + . − . . + . − . Vanderspek et al. (2019)175.01 307210830 L 98-59 c 0 . + . − . . + . − . . + . − . . + . − . Kostov et al. (2019)175.02 307210830 L 98-59 d 0 . + . − . . + . − . . + . − . . + . − . Kostov et al. (2019)175.03 307210830 L 98-59 b 0 . + . − . . + . − . . + . − . . + . − . Kostov et al. (2019)178.01 251848941 TOI-178 d 0 . + . − . . + . − . . + . − . . + . − . Leleu et al. (2021)178.02 251848941 TOI-178 g 0 . + . − . . + . − . . + . − . . + . − . Leleu et al. (2021)178.03 251848941 TOI-178 e 0 . + . − . . + . − . . + . − . . + . − . Leleu et al. (2021)- 251848941 TOI-178 b 0 . + . − . . + . − . . + . − . . + . − . Leleu et al. (2021)- 251848941 TOI-178 c 0 . + . − . . + . − . . + . − . . + . − . Leleu et al. (2021)- 251848941 TOI-178 f 0 . + . − . . + . − . . + . − . . + . − . Leleu et al. (2021)237.01 305048087 TOI 237 b 0 . + . − . . + . − . . + . − . . + . − . Waalkes et al. (2020)256.02 92226327 LHS 1140 c 0 . + . − . . + . − . . + . − . . + . − . Ment et al. (2019)270.01 259377017 TOI-270 c 0 . + . − . . + . − . . + . − . . + . − . Günther et al. (2019)270.02 259377017 TOI-270 d 0 . + . − . . + . − . . + . − . . + . − . Günther et al. (2019)270.03 259377017 TOI-270 b 0 . + . − . . + . − . . + . − . . + . − . Günther et al. (2019)442.01 70899085 LP 714-47 b 0 . + . − . . + . − . . + . − . . + . − . Dreizler et al. (2020)455.01 98796344 LTT 1445 A b 0 . + . − . . + . − . . + . − . . + . − . Winters et al. (2019)468.01 33521996 HATS-6 b 0 . + . − . . + . − . . + . − . . + . − . Hartman et al. (2015)551.01 192826603 NGTS-1 b 0 . + . − . . + . − . . + . − . . + . − . Bayliss et al. (2018)562.01 413248763 GJ 357 b 0 . + . − . . + . − . . + . − . . + . − . Luque et al. (2019)656.01 36734222 WASP-43 b 0 . + . − . . + . − . . + . − . . + . − . Esposito et al. (2017)700.01 150428135 TOI-700 c 0 . + . − . . + . − . . + . − . . + . − . Gilbert et al. (2020)700.02 150428135 TOI-700 d 0 . + . − . . + . − . . + . − . . + . − . Gilbert et al. (2020)700.03 150428135 TOI-700 b 0 . + . − . . + . − . . + . − . . + . − . Gilbert et al. (2020)1067.01 201642601 HATS-48 A b 0 . + . − . . + . − . . + . − . . + . − . Hartman et al. (2020)1073.01 158297421 HATS-47 b 0 . + . − . . + . − . . + . − . . + . − . Hartman et al. (2020)1130.01 254113311 TOI-1130 b 0 . + . − . . + . − . . + . − . . + . − . Huang et al. (2020)1130.02 254113311 TOI-1130 c 0 . + . − . . + . − . . + . − . . + . − . Huang et al. (2020) R )0246810121416182022 P l a n e t s Figure 12.
Histogram of candidate planet radii with 𝑅 𝑃 < 𝑅 ⊕ , with0 . 𝑅 ⊕ width bins and Poisson uncertainties. Note that we detect the exo-planet radius gap at approximately a ∼ 𝜎 level, though remain limited by oursmall sample size. In the work presented above, we have described our ANU2.3 m/WiFeS observing program to characterise 92 southern TESScandidate planet hosts with 3 , (cid:46) 𝑇 eff (cid:46) ,
500 K in order toprecisely determine the radii of 100 transiting planets they host. Inthe process of doing so we investigated cool dwarf model atmo- sphere systematics, as well as developed a new photometric [Fe/H]calibration. The main conclusions from our work are as follows: • Cool dwarf MARCS model atmospheres systematically overes-timate flux in the optical relative to the well produced spectral regions5585 − ( 𝐵 𝑃 − 𝑅 𝑃 ) colour, enabling the correction of synthetic Gaia 𝐵 𝑃 , andSkyMapper 𝑔 and 𝑟 magnitudes. • Using the same models, a general least squares fitting approachto medium resolution optical spectra and literature photometry is notsufficient to accurately recover [Fe/H] for cool dwarfs. We insteaddevelop an updated photometric [Fe/H] calibration for cool dwarfs,built using a sample of 69 M and K dwarfs with FGK binary compan-ions having reliable [Fe/H] measurements. By relating the positionof these isolated main sequence KM stars in 𝑀 𝐾 𝑆 − ( 𝐵 𝑃 − 𝐾 𝑆 ) space to the FGK companion, and thus system, [Fe/H], our relationcan determine metallicity to a precision of ± .
19 dex for stars with1 . < ( 𝐵 𝑃 − 𝑅 𝑃 ) < .
3. This relation expands on the work ofBonfils et al. (2005), Johnson & Apps (2009), and Schlaufman &Laughlin (2010), and takes advantage of precision Gaia parallaxes(for precise distances) and kinematics (for binary identification) forthe first time. • We determine 𝑇 eff and 𝑅 ★ for our 92 TESS candidate planethosts with a median precision of 0.8% and 1.7% respectively, aswell as radial velocities to ∼ . − . 42 of these targets did notpreviously have radial velocities from Gaia DR2, thus completingcompleting the kinematics for these stars. MNRAS , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts • We report H 𝛼 equivalent widths and Ca II H&K log 𝑅 (cid:48) HK for oursample, both signs of activity and youth. None of our stars displaydetectable Lithium 6708 Å absorption. • We use our derived stellar parameters to fit the TESS light curvesfor our 100 planet candidates in order to determine 𝑅 𝑃 with a medianprecision of 3.5%. Our planet properties are consistent with the 30already confirmed by other studies. We additionally see evidence ofthe planet radius gap at a ∼ 𝜎 level for our low-mass stellar sample,with the robustness of the detection only limited by the small samplesize. • We report the existence of two likely young systems based onstellar emission and location above the main sequence: TOI 507 (TIC348538431) and TOI 142 (425934411). The former appears to be anear-equal mass, double-lined eclipsing binary with 𝑇 eff ≈ 𝑅 𝑃 = . ± . 𝑅 ⊕ ) on a short period ( 𝑇 ≈ .
85 day) orbit.This is one of the largest uniform analyses of cool TESS candidateplanet hosts to date, and the first cool dwarf photometric [Fe/H]calibration based on Gaia data. Given the major difficulties encoun-tered using model atmospheres for [Fe/H] determination, we plan toconduct follow-up work investigating empirical or data driven ap-proaches built upon our now large collection of cool dwarf standardspectra.
ACKNOWLEDGEMENTS
We acknowledge the traditional owners of the land on which theANU 2.3 m Telescope stands, the Gamilaraay people, and pay ourrespects to elders past, present and emerging. We also acknowledgehelpful early conversations with George Zhou about target selectionand observing strategy, as well as the efforts of Andy Casey in de-veloping a prototype data-driven model which ultimately proved outof scope for this study.ADR acknowledges support from the Australian Government Re-search Training Program, and the Research School of Astronomy &Astrophysics top up scholarship. MŽ and MJI acknowledge fundingfrom the Australian Research Council (grant DP170102233). LC isthe recipient of the ARC Future Fellowship FT160100402. MJ wassupported the Research School of Astronomy and Astrophysics atthe Australian National University and funding from Australian Re-search Council grant No. DP150100250. Parts of this research wereconducted by the Australian Research Council Centre of Excellencefor All Sky Astrophysics in 3 Dimensions (ASTRO 3D), throughproject number CE170100013.This research has made use of the Exoplanet Follow-up Observa-tion Program website, which is operated by the California Institute ofTechnology, under contract with the National Aeronautics and SpaceAdministration under the Exoplanet Exploration Program. This paperincludes data collected by the TESS mission. Funding for the TESSmission is provided by the NASA Explorer Program. This work hasmade use of data from the European Space Agency (ESA) mission
Gaia ( ), processed by the Gaia
Data Processing and Analysis Consortium (DPAC, ). Fund-ing for the DPAC has been provided by national institutions, in par-ticular the institutions participating in the
Gaia
Multilateral Agree-ment. This publication makes use of data products from the TwoMicron All Sky Survey, which is a joint project of the Universityof Massachusetts and the Infrared Processing and Analysis Cen-ter/California Institute of Technology, funded by the National Aero- nautics and Space Administration and the National Science Foun-dation. The national facility capability for SkyMapper has beenfunded through ARC LIEF grant LE130100104 from the AustralianResearch Council, awarded to the University of Sydney, the Aus-tralian National University, Swinburne University of Technology, theUniversity of Queensland, the University of Western Australia, theUniversity of Melbourne, Curtin University of Technology, MonashUniversity and the Australian Astronomical Observatory. SkyMap-per is owned and operated by The Australian National University’sResearch School of Astronomy and Astrophysics. The survey datawere processed and provided by the SkyMapper Team at ANU. TheSkyMapper node of the All-Sky Virtual Observatory (ASVO) ishosted at the National Computational Infrastructure (NCI). Devel-opment and support the SkyMapper node of the ASVO has beenfunded in part by Astronomy Australia Limited (AAL) and the Aus-tralian Government through the Commonwealth’s Education Invest-ment Fund (EIF) and National Collaborative Research InfrastructureStrategy (NCRIS), particularly the National eResearch CollaborationTools and Resources (NeCTAR) and the Australian National DataService Projects (ANDS). This research made use of Lightkurve, aPython package for Kepler and TESS data analysis.Software:
Astropy (Astropy Collaboration et al. 2013), batman (Kreidberg 2015), iPython (Perez & Granger 2007), dustmaps (Green 2018), lightkurve (Lightkurve Collaboration et al. 2018),
Matplotlib (Hunter 2007),
NumPy (Harris et al. 2020),
Pandas (McKinney 2010),
SciPy (Jones et al. 2016).
DATA AVAILABILITY
All fitted stellar and planetary results are available in the article and inits online supplementary material, and stellar spectra will be sharedon reasonable request to the corresponding author. All other dataused is publicly available.
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APPENDIX A: OBSERVATIONSAPPENDIX B: STELLAR STANDARDSAPPENDIX C: PHOTOMETRIC [FE/H] DATAAPPENDIX D: LIMB DARKENING
This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Table A1.
Observing log for TESS candidate exoplanet host starsTIC UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)219338557 19-08-25 1.1 120 36.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±000
Observing log for TESS candidate exoplanet host starsTIC UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)219338557 19-08-25 1.1 120 36.00 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±000 , 1–22 (2015) Adam D. Rains et al.
Table A1 – continued Observing log for TESS candidate exoplanet host starsTIC UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)141527579 20-02-03 1.4 900 24.59 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Table B1.
Observing log for cool dwarf standardsGaia DR2 UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)19316224572460416 19-07-22 1.5 5 20.65 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±000
Observing log for cool dwarf standardsGaia DR2 UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)19316224572460416 19-07-22 1.5 5 20.65 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±000 , 1–22 (2015) Adam D. Rains et al.
Table B1 – continued Observing log for cool dwarf standardsGaia DR2 UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)3902785109124370432 20-02-03 1.4 300 20.95 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Table B1 – continued Observing log for cool dwarf standardsGaia DR2 UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)2848646203058386560 20-09-13 1.7 450 -48.92 ± ± ± ± ± ± ± ± ± ±000
Table B1 – continued Observing log for cool dwarf standardsGaia DR2 UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)3902785109124370432 20-02-03 1.4 300 20.95 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Table B1 – continued Observing log for cool dwarf standardsGaia DR2 UT Date airmass exp RV SNR(sec) (km s − ) (B) (R)2848646203058386560 20-09-13 1.7 450 -48.92 ± ± ± ± ± ± ± ± ± ±000 , 1–22 (2015) Adam D. Rains et al.
Table B2.
Final results for cool dwarf standardsGaia DR2 𝑇 eff log 𝑔 [Fe/H] 𝑀 𝑅 𝑚 bol 𝑓 bol (K) ( 𝑀 (cid:12) ) ( 𝑅 (cid:12) ) (10 − ergs s − cm − )5853498713160606720 2885 ±
30 5.14 ± ± ± ± ± ±
30 5.20 ± ± ± ± ± ±
30 5.03 ± ± ± ± ± ±
30 5.10 ± ± ± ± ± ±
30 5.03 ± ± ± ± ± ±
30 5.08 ± ± ± ± ± ±
30 5.13 ± ± ± ± ± ±
30 4.99 ± ± ± ± ± ±
30 5.09 ± ± ± ± ± ±
30 5.06 ± ± ± ± ± ±
30 4.91 ± ± ± ± ± ±
30 5.04 ± ± ± ± ± ±
30 4.98 ± ± ± ± ± ±
30 5.06 ± ± ± ± ± ±
30 4.72 ± ± ± ± ± ±
30 5.08 ± ± ± ± ± ±
30 4.94 ± ± ± ± ± ±
30 4.98 ± ± ± ± ± ±
30 4.98 ± ± ± ± ± ±
30 4.97 ± ± ± ± ± ±
30 5.06 ± ± ± ± ± ±
30 4.83 ± ± ± ± ± ±
30 5.06 ± ± ± ± ± ±
30 4.97 ± ± ± ± ± ±
30 4.98 ± ± ± ± ± ±
30 4.92 ± ± ± ± ± ±
30 4.98 ± ± ± ± ± ±
30 4.97 ± ± ± ± ± ±
30 4.92 ± ± ± ± ± ±
30 4.88 ± ± ± ± ± ±
30 5.01 ± ± ± ± ± ±
30 4.78 ± ± ± ± ± ±
30 4.81 ± ± ± ± ± ±
30 4.89 ± ± ± ± ± ±
30 4.82 ± ± ± ± ± ±
30 4.95 ± ± ± ± ± ±
30 4.90 ± ± ± ± ± ±
30 4.96 ± ± ± ± ± ±
30 5.01 ± ± ± ± ± ±
30 4.76 ± ± ± ± ± ±
30 4.91 ± ± ± ± ± ±
30 4.89 ± ± ± ± ± ±
30 4.81 ± ± ± ± ± ±
30 4.96 ± ± ± ± ± ±
30 4.83 ± ± ± ± ± ±
30 4.90 ± ± ± ± ± ±
30 4.69 ± ± ± ± ± ±
30 4.92 ± ± ± ± ± ±
30 4.97 ± ± ± ± ± ±
30 4.84 ± ± ± ± ± ±
30 4.88 ± ± ± ± ± ±
30 4.69 ± ± ± ± ± ±
30 4.79 ± ± ± ± ± ±
30 4.89 ± ± ± ± ± ±
30 4.93 ± ± ± ± ± ±
30 4.84 ± ± ± ± ± ±
30 4.77 ± ± ± ± ± ±
30 4.76 ± ± ± ± ± ±
30 4.76 ± ± ± ± ± ±
30 4.83 ± ± ± ± ± ±
30 4.48 ± ± ± ± ± ±
30 4.79 ± ± ± ± ± ±
30 4.79 ± ± ± ± ± ±
30 4.81 ± ± ± ± ± , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Table B2 – continued Final results for cool dwarf standardsGaia DR2 𝑇 eff log 𝑔 [Fe/H] 𝑀 𝑅 𝑚 bol 𝑓 bol (K) ( 𝑀 (cid:12) ) ( 𝑅 (cid:12) ) (10 − ergs s − cm − )4519789081415296128 3541 ±
30 4.94 ± ± ± ± ± ±
30 4.94 ± ± ± ± ± ±
30 4.65 ± ± ± ± ± ±
30 4.75 ± ± ± ± ± ±
30 4.76 ± ± ± ± ± ±
30 4.73 ± ± ± ± ± ±
30 4.71 ± ± ± ± ± ±
30 4.75 ± ± ± ± ± ±
30 4.72 ± ± ± ± ± ±
30 4.91 ± ± ± ± ± ±
30 4.77 ± ± ± ± ± ±
30 4.81 ± ± ± ± ± ±
30 4.71 ± ± ± ± ± ±
30 4.71 ± ± ± ± ± ±
30 4.72 ± ± ± ± ± ±
30 4.79 ± ± ± ± ± ±
30 4.81 ± ± ± ± ± ±
30 4.70 ± ± ± ± ± ±
30 4.79 ± ± ± ± ± ±
30 4.74 ± ± ± ± ± ±
30 4.75 ± ± ± ± ± ±
30 4.77 ± ± ± ± ± ±
30 4.85 ± ± ± ± ± ±
30 4.72 ± ± ± ± ± ±
30 4.90 ± ± ± ± ± ±
30 4.67 ± ± ± ± ± ±
30 4.58 ± ± ± ± ± ±
30 4.75 ± ± ± ± ± ±
30 4.69 ± ± ± ± ± ±
30 4.79 ± ± ± ± ± ±
30 4.92 ± ± ± ± ± ±
30 4.67 ± ± ± ± ± ±
30 4.66 ± ± ± ± ± ±
30 4.68 ± ± ± ± ± ±
30 4.70 ± ± ± ± ± ±
30 4.65 ± ± ± ± ± ±
30 4.61 ± ± ± ± ± ±
30 4.74 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± ±
30 4.80 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± ±
30 4.66 ± ± ± ± ± ±
30 4.66 ± ± ± ± ± ±
30 4.68 ± ± ± ± ± ±
30 4.64 ± ± ± ± ± ±
30 4.62 ± ± ± ± ± ±
30 4.55 ± ± ± ± ± ±
30 4.66 ± ± ± ± ± ±
30 4.66 ± ± ± ± ± ±
30 4.61 ± ± ± ± ± ±
30 4.61 ± ± ± ± ± ±
30 4.58 ± ± ± ± ± ±
30 4.60 ± ± ± ± ± ±
30 4.66 ± ± ± ± ± ±
30 4.58 ± ± ± ± ± ±
30 4.72 ± ± ± ± ± ±
30 4.58 ± ± ± ± ± ±
30 4.61 ± ± ± ± ± ±
30 4.63 ± ± ± ± ± ±
30 4.67 ± ± ± ± ± ±
30 4.53 ± ± ± ± ± ±
30 4.58 ± ± ± ± ± ±
30 4.54 ± ± ± ± ± ±
30 4.61 ± ± ± ± ±000
30 4.61 ± ± ± ± ±000 , 1–22 (2015) Adam D. Rains et al.
Table B2 – continued Final results for cool dwarf standardsGaia DR2 𝑇 eff log 𝑔 [Fe/H] 𝑀 𝑅 𝑚 bol 𝑓 bol (K) ( 𝑀 (cid:12) ) ( 𝑅 (cid:12) ) (10 − ergs s − cm − )5378886891122066560 4611 ±
30 4.66 ± ± ± ± ± ±
30 4.57 ± ± ± ± ± ±
30 4.61 ± ± ± ± ± ±
30 4.70 ± ± ± ± ± ±
30 4.57 ± ± ± ± ± ±
30 4.53 ± ± ± ± ± ±
30 4.56 ± ± ± ± ± ±
30 4.57 ± ± ± ± ± , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Table C1.
Stellar pairs and primary [Fe/H] used for photometric [Fe/H] relationGaia DR2 ID (s) 𝐵 𝑃 − 𝑅 𝑃 Gaia DR2 ID (p) [Fe/H] ref [Fe/H] adopted853820948481913472 1.66 853819947756949120 Valenti & Fischer 2005 − . ± . . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . . ± . . ± . − . ± . . ± . − . ± . . ± . . ± . . ± . . ± . − . ± . − . ± . − . ± . . ± . . ± . . ± . − . ± . . ± . . ± . . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . − . ± . . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . . ± . − . ± . − . ± . . ± . − . ± . − . ± . . ± . − . ± . − . ± . − . ± .000
Stellar pairs and primary [Fe/H] used for photometric [Fe/H] relationGaia DR2 ID (s) 𝐵 𝑃 − 𝑅 𝑃 Gaia DR2 ID (p) [Fe/H] ref [Fe/H] adopted853820948481913472 1.66 853819947756949120 Valenti & Fischer 2005 − . ± . . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . . ± . . ± . − . ± . . ± . − . ± . . ± . . ± . . ± . . ± . − . ± . − . ± . − . ± . . ± . . ± . . ± . − . ± . . ± . . ± . . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . − . ± . . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . . ± . − . ± . − . ± . . ± . − . ± . − . ± . . ± . − . ± . − . ± . − . ± .000 , 1–22 (2015) Adam D. Rains et al.
Table C1 – continued Stellar pairs and primary [Fe/H] used for photometric [Fe/H] relationGaia DR2 ID (s) 𝐵 𝑃 − 𝑅 𝑃 Gaia DR2 ID (p) [Fe/H] ref [Fe/H] adopted1034999982042706048 2.53 1035000055055287680 Mishenina et al. 2004 − . ± . . ± . − . ± . − . ± . . ± . . ± . − . ± . . ± . − . ± . , 1–22 (2015) haracterisation of Cool TESS Candidate Planet Hosts Table D1.
Nonlinear limb darkening coefficients from Claret (2017)TIC 𝑎 𝑎 𝑎 𝑎 Table D1 – continued Limb darkening coefficientsTIC 𝑎 𝑎 𝑎 𝑎000