Draft version February 8, 2017 PreprinttypesetusingLATEXstyleemulateapjv.01/23/15 STELLAR & PLANETARY PARAMETERS FOR K2’S LATE TYPE DWARF SYSTEMS FROM C1 TO C5 Arturo O. Martinez1,2,3, Ian J. M. Crossfield4,5,6, Joshua E. Schlieder7,8,9, Courtney D. Dressing10,6, Christian Obermeier11,12, John Livingston13, Simona Ciceri14, Sarah Peacock4, Charles A. Beichman8, Sébastien Lépine2, Kimberly M. Aller15, Quadry A. Chance16, Erik A. Petigura13,17 Andrew W. Howard18, Michael W. Werner19 Draft version February 8, 2017 ABSTRACT The NASA K2 mission uses photometry to find planets transiting stars of various types. M dwarfs 7 are of high interest since they host more short-period planets than any other type of main-sequence 1 stars and transiting planets around M dwarfs have deeper transits compared to other main-sequence 0 stars. In this paper, we present stellar parameters from K and M dwarfs hosting transiting planet 2 candidates discovered by our team. Using the SOFI spectrograph on the European Southern Ob- b servatory’s New Technology Telescope, we obtained R ≈ 1000 J-, H-, and K-band (0.95 - 2.52 µm) e spectraof34late-typeK2planetandcandidateplanethostsystemsand12brightK4-M5dwarfswith F interferometrically measured radii and effective temperatures. Out of our 34 late-type K2 targets, we identify 27 of these stars as M dwarfs. We measure equivalent widths of spectral features, derive 7 calibration relations using stars with interferometric measurements, and estimate stellar radii, effec- tive temperatures, masses, and luminosities for the K2 planet hosts. Our calibrations provide radii ] R and temperatures with median uncertainties of 0.059 R(cid:12) (16.09%) and 160 K (4.33%), respectively. We then reassess the radii and equilibrium temperatures of known and candidate planets based on S our spectroscopically derived stellar parameters. Since a planet’s radius and equilibrium temperature . h depend on the parameters of its host star, our study provides more precise planetary parameters for p planets and candidates orbiting late-type stars observed with K2. We find a median planet radius - and an equilibrium temperature of approximately 3R and 500 K, respectively, with several systems o ⊕ (K2-18b and K2-72e) receiving near-Earth-like levels of incident irradiation. r t s Subject headings: methods: data analysis – stars: fundamental parameters – stars: late-type – plane- a tary systems – techniques: spectroscopic [ 2 1. INTRODUCTION There are still significant discrepancies between theoret- v ical models and observations of M dwarf spectra (e.g. 8 Small, low-luminosity M dwarfs are the most common Hoeijmakers et al. 2015), and we are still uncertain as 8 type of star in the Galaxy, but their properties are less to why the occurrence rate of small, short-period plan- 5 well understood than those of hotter solar-type stars. ets is higher for M dwarfs and the occurrence rate of a 0 0 1Department of Astronomy, San Diego State University, 5500 gas giants (on both close and wide orbits) is lower for . CampanileDrive,SanDiego,CA,USA M dwarfs when compared to solar-like stars, as shown 1 2DepartmentofPhysicsandAstronomy,GeorgiaStateUniver- in studies of the Kepler field (Dressing & Charbonneau 0 sity,GA,USA 2013; Gaidos et al. 2014; Morton & Swift 2014; Dressing 7 3Visiting Researcher, Steward Observatory, University of Ari- & Charbonneau 2015; Muirhead et al. 2015) and other 1 zona,Tucson,AZ,USA 4Lunar&PlanetaryLaboratory,UniversityofArizona,Tucson, surveys (Shields et al. 2016). There are a few exceptions : v AZ,USA tothelowoccurrencerateofgasgiantsaroundMdwarfs; 5Astronomy and Astrophysics Department, UC Santa Cruz, i there has been at least one confirmed gas giant orbiting X SantaCruz,CA,USA 6NASASaganFellow an M dwarf (Johnson et al. 2012). r 7NASAAmesResearchCenter,MoffettField,CA,USA Fortunately, the discovery of exoplanets around M a 8NASA Exoplanet Science Institute, California Institute of dwarfsismucheasierwhencomparedtofindingexoplan- Technology,Pasadena,CA,USA etsaroundSun-likestars. Forexample,whileatransiting 9NASAPostdoctoralProgramFellow 10Division of Geological and Planetary Sciences, California In- 2R⊕ planet would have a transit depth of 0.03% when stituteofTechnology,Pasadena,CA,USA orbiting the Sun, that same planet would have a transit 11MaxPlanckInstitutfürAstronomie,Heidelberg,Germany depth of 0.5% for an M5 dwarf. Using planet candidates 12Max-Planck-Institute for Extraterrestrial Physics, Garching, from the original Kepler mission, Howard et al. (2012) Germany 13Department of Astronomy, Graduate School of Science, The and Mulders et al. (2015a,b) showed that the occur- UniversityofTokyo,7-3-1Bunkyo-ku,Tokyo113-0033,Japan rence rates of small planets are higher for M dwarf than 14Department of Astronomy, Stockholm University, SE-106 91 for any other main-sequence star. Other surveys, such Stockholm,Sweden 15InstituteforAstronomy,UniversityofHawai’iatM¯anoa,Hon- as MEarth (Charbonneau et al. 2009; Berta-Thompson olulu,HI,USA et al. 2015) and Transiting Planets and Planetesimals 16StewardObservatory,UniversityofArizona,Tucson,AZ,USA SmallTelescope,havealsosuccessfullyidentifiedinterest- 17HubbleFellow ing new planets transiting M dwarfs (Gillon et al. 2016). 18DepartmentofAstronomy,CaliforniaInstituteofTechnology, Additionally,Mdwarfsprovideourbestchancestoiden- Pasadena,CA91125,USA 19JetPropulsionLaboratory,Pasadena,CA,USA 2 Martinez et al. tify nearby potentially habitable planets since the hab- 2. TARGET SELECTION AND PLANET itable zone around M dwarfs, when compared to those CANDIDATE SEARCH around other main-sequence stars, is closer to the M We initially selected our K2 M dwarf candidates from dwarf due to the its lower luminosity. This is exempli- Campaigns1through5. Ourteamselectedandproposed fied by the discovery of Proxima Centauri b, a small, late-typedwarftargetstotheK2missionasdescribedby likely temperate planet orbiting the closest star to the Crossfield et al. (2016). In brief, we selected targets as Sun (Anglada-Escudé et al. 2016; Damasso & Del Sordo being likely low-mass dwarfs by a combined color and 2016). proper motion cut with (V −J) > 2.5, V + 5 logµ + Host star properties must be well understood in order 5 < 10, and (6V - 7J - 3) < 5 logµ (where µ is the tobeabletoderiveplanetproperties. Unfortunately,the proper motion; Crossfield et al. 2015). The combination stellar properties of M dwarfs are challenging to predict ofthecolorandpropermotioncutgreatlyreducesgiants from photometry (due to M dwarfs being intrinsically from our sample and further narrows down the M dwarf faint and the modeling uncertainties as described above candidate list. Finally, we imposed a magnitude limit of andbyMannetal.2015). Themostaccurateparameters Kp < 16.5 mag (Crossfield et al. 2016). of M dwarfs are derived from interferometric data (Boy- We further identify likely low-mass planet-hosting ajian et al. 2012b) or photometric and spectroscopic ob- dwarf stars, as explained in Crossfield et al. (2016). In servationsofdouble-linedeclipsingbinaries(Torresetal. brief,weusedtheTERRAalgorithm(Petiguraetal.2013) 2010). to search for planet transits that have a signal-to-noise For systems where such observations are not feasi- ratio (S/N) > 12, which are called threshold-crossing ble,severalauthorshavedevelopedacalibrationmethod events (TCEs). TCEs are required to have orbital pe- basedonmedium-resolution, near-infraredspectrainor- riods of P ≥ 1 day and to have at least three transits. der to inferthe stellar properties of these Mdwarfsfrom These restrictions, along with the diagnostic tests that empirical observations (Mann et al. 2015; Newton et al. TERRA provides, show whether the object is a candidate 2015;Terrienetal.2015)andstellarmodels(Rojas-Ayala transiting planet, binary star system, another variable et al. 2012), while others have applied similar empirical object, or noise. If a planet candidate is found, TERRA is calibrationtechniquestotheopticalpartofthespectrum iteratively repeated after removing the identified transit (Nevesetal.2014;Maldonadoetal.2015). Bymeasuring signals(describedbySinukoffetal.2016)toseewhether theequivalentwidths(EWs),orthestrengthofanygiven there are any additional planets in the system. absorption feature one can calculate stellar parameters by calibrating from a reference sample with previously 3. OBSERVATIONS measured parameters of interest. Since the EW of an absorption feature varies with photospheric temperature We acquired our infrared spectra at the 3.58 m Eu- and surface gravity, this approach allows these parame- ropean Southern Observatory (ESO) New Technology ters(andrelatedquantities, likestellarradiusandmass) Telescope (NTT) using the SOFI spectrograph (Moor- to be calculated. wood et al. 1998) as part of program 194.C-0443 (PI: Using the repurposed Kepler spacecraft, the K2 mis- I. J. M. Crossfield). We observed through 13 full or par- sion is continuing to observe many stars in the Galaxy tialusablenightsin2015and2016. Weusedtwogrisms, in the search for more exoplanets (Howell et al. 2014). red and blue, to produce a total spectrum for each ob- However, K2 has some limitations. With just two (out ject spanning a continuous wavelength range from 0.95 offour)operatingreactionwheels,thespacecraftcanob- to2.52µm20 ataresolutionofR≈1000. Domeflatsand serve only along the ecliptic plane with observation win- lamps were either taken at the start or the end of each dowsof80dayspercampaign. Nonetheless, K2haspro- observing night. Our observation sample comprises 34 vided astronomers with powerful data enabling a large starsobservedbyK2infields1through5, alongwith12 number of candidate and confirmed exoplanets (Vander- brightKandMdwarfswithinterferometricallymeasured burg & Johnson 2014; Crossfield et al. 2015; Foreman- stellar parameters (refer to Table 1 for our calibration Mackeyetal.2015;Huangetal.2015;Montetetal.2015; sample). Sanchis-Ojedaetal.2015;Sinukoffetal.2015;Crossfield For all observations, we used an ABBA nodding pat- et al. 2016). tern to obtain the spectrum of the object, while remov- In this paper we analyze medium-resolution, near- ing the spectrum of the background, including sky emis- infraredspectraofcandidateplanetarysystemsdetected sionlinesanddarkcurrent. Theexposuretimesforeach by K2 to provide updated stellar and planetary param- frame range from the minimum allowed exposure time eters. We measure EWs to infer stellar radii and effec- (1.182 s) to 120 s. We typically took at least six sepa- tive temperatures, and subsequently planetary radii and rate spectra (for each grism) for all the targets. Either equilibrium temperatures. In §2, we briefly explain our immediately before or after each M dwarf candidate, we target selections and how we compiled our planet candi- observed a nearby A0V star for telluric corrections. If datelist. In§3,wedescribeourobservationaltechniques, the observation for one grism took more than 10 min- data reduction, and various calibration samples. In §4, utes, its A0V calibrator would be taken before the start we explain the process by which we obtain our stellar of the first grism and then taken again after the second and planetary parameters and compare our derived stel- grism exposure had finished, for their respective grisms. larparameterswiththoseofpreviouslyspectroscopically and interferometrically measured stellar parameters. In 20 Thebluegrismspansthewavelengthrangefrom0.95to1.64 §5, we summarize our results and describe future work µm while the red grism spans the wavelength range from 1.53 to 2.52 µm. Note, there is a small overlap from both grisms in the relevant to this paper. H-band,thusallowingthefully-reducedspectraofallofourstars tobecontinuous. Stellar & Planetary Parameters for Late Type Dwarf Systems 3 WeidentifiedsuitableA0VstarsusingtheIRTF’sonline tool21. 3.1. Data Reduction TherawdatatakenattheNTTwerereducedbyusing acombinationofPython,ImageReductionandAnalysis Facility(IRAF)software,22 andusingvariousInteractive Data Language (IDL) programs. We flat-fielded the raw spectra in order to correct for any pixel-to-pixel vari- ation. Wavelength calibrations were done by taking Xe arcspectrumforbothgrismseitheratthebeginningorat theendofthenight. UsingIRAF,emissionlinesfromthe taken Xe arc frames were manually selected by compar- ing them to the SOFI manual23. One-dimensional spec- tra were then extracted for identifying the star’s spec- trum. IRAF had difficulty tracing the 2D spectra of our fainter targets, so for these stars we used brighter stars Fig. 1.— Sample spectrum of one of our K2 targets (EPIC 201367065orK2-3)thatcoversacontinuouswavelengthfrom0.95 during that night to define a static extraction aperture. to2.52µmandisnormalizedtothemedianfluxvalue. Notethat We subsequently used the IDL routines of Vacca et al. we ignore regions heavily contaminated by telluric features (e.g., (2003) to process our spectra. First, with xcombspec wavelengthrangesthatarewithin1.35-1.45µmand1.80-1.95µm). Afterdatareductioniscomplete,wetrimanapproximate0.01-0.02 (from the SpeXtool software package by Cushing et al. µmofftheedgesofthewavelengthranges. Spectraofallourstars 2004), wecombinedmultipleexposuresforagivengrism areavailableaselectronicsupplementstothispaper. ofanobjectintoonespectrum. Anyspectrathatarenot shown to have similar spectral features with the other fit various functions for a variety of EW ratios, and Ter- exposures for that star and grism were excluded. rien et al. (2015), which measured H-band atomic fea- We corrected for telluric absorption by using our A0V tures, to stars with previously measured radii and/or spectra with the xtellcor general routine. Spectra of effective temperatures. However, stars that are inter- A0V stars were used since these stars are mostly com- ferometrically measured are preferred to these samples posedoffeaturelessspectra,withtheexceptionofhydro- since measurements from interferometry are more accu- gen absorption. Differences between the hydrogen lines rate and precise when compared to spectroscopic, EW- in the A0V and a model Vega spectrum were corrected based methods. Although most interferometrically mea- for, and then the object’s spectrum was divided by the sured stars lie too far north to be observed with SOFI, resulting telluric spectrum of the A0V; the observations wemanagedtoobtainspectraof12starswithpreviously for the telluric calibrator were usually taken within a interferometrically determined stellar radii and effective shorttime(approximately15minutes)andhaveasimilar temperatures. These stars form our calibration sample, airmass (within 0.3 airmass) to the object (Rojas-Ayala and their properties are summarized in Table 1. et al. 2012). We note that for some of the observations, the telluric calibrator’s spectrum was sufficiently differ- 4. SPECTRAL ANALYSIS ent from that of Vega that some residual H lines remain in the M dwarf candidate’s spectrum. Additionally, the Mould (1976) was the first to use infrared absorption large differences in airmass left residual telluric features line strengths to estimate the radii and effective temper- in some of the spectra, and any spectra that were con- atures of low-mass dwarfs. The strengths of absorption taminated were removed from our analysis. featurescorrespondingtoagivenelementormoleculede- Thelaststepforthereductionprocesswastocombine pend on the effective temperatures of the star. Chang- the two different grisms using xmergexd. We then used ing the temperature of the star then changes the elec- several strong absorption features in each spectrum to tronic (or vibrational) population levels of the element correct for radial velocity (RV) shifts and/or offsets in (ormolecule)in theM dwarf atmosphere. M dwarf radii our wavelength calibration. Finally, we interpolated all are related to their effective temperatures so that they spectra to put them on the same wavelength scale. All roughly follow a linear relation from 4700 K & 0.7 R(cid:12) of the objects in our sample have a S/N that ranged down to at least 3300 K & 0.3 R(cid:12). Some of the ab- from 20 (for the faint K2 targets)24 to over 200 (for the sorption features in the spectrum can also present in- brighter, interferometriccalibration targets). Weshowa formation about the stellar surface gravity. The lines of representative reduced spectrum in Figure 1. alkalielements,forexample,areaffectedbysurfacegrav- ity and can then be used to distinguish old dwarf stars, young dwarf stars, and giants with similar temperatures 3.2. Calibration Sample (Spinrad 1962; Steele & Jameson 1995; Lyo et al. 2004; We applied the relations from a variety of works, such Schlieder et al. 2012). asNevesetal.(2014)andMaldonadoetal.(2015),which The EW is defined by the following equation: 21 http://irtfweb.ifa.hawaii.edu/cgi-bin/spex/find_a0v. (cid:90) λ2(cid:20) F(λ)(cid:21) cgi22 DevelopedattheNationalOpticalAstronomyObservatory EWλ = λ1 1− Fc(λ) dλ (1) 23 ProvidedbyESO. 24K2targetsthathadaS/Nof20wereremovedfromthelikely where F(λ) is the flux of the absorption feature between low-massdwarflist,thusmakingourfinal34starsample. λ1 and λ2, and Fc(λ) is the continuum flux. We inves- 4 Martinez et al. tigate the features used by Cushing et al. (2005), Rojas- information criterion (BIC) value and the lowest scat- Ayala et al. (2012), Newton et al. (2014), and Newton ter in the fit residuals. We use a Monte Carlo approach et al. (2015) for our work. The features, shown in Table to estimate the uncertainties on the fit coefficients and 2,areslightlyadjustedowningtodifferencesinresolution inferred stellar parameters. Random gaussian distribu- ofthespectrographs-typicallyourintegrationrangesare tions are then used to generate synthetic data sets of slightlywiderthanthosepreviouslypresented. Addition- EWs,stellarradii,andeffectivetemperatures. Atotalof ally,anyspectrallinedoubletsandmolecularbandsused 1000 trials are used for calculating the uncertainties for in our empirical indices are treated as single features in each parameter. the the EW calculations. The blue continuum and red continuum of each feature are also adjusted such that 4.3. Calibration Relations and Literature Comparison theywouldnotoverlapwithanynearbyfeaturewindows. Because some of our spectra contain residual system- In the following sections, we describe the steps that are aticsnearprominentHlines,wefindonlypoorfitsusing taken to infer the stellar and planetary parameters us- EWs located near these lines (Brackett 11-21). Viewing ing these EW measurements of our K2 and calibration all possible combinations of the remaining EWs, we de- samples. termine that the optimal fits for calculating our param- eters are determined by having a low BIC value for the 4.1. Spectral Classification fit and comparing it to the median uncertainty of all the Wevisuallyestimatedthespectraltypes(SpT)ofeach uncertaintiesinagivencombinationofEWs. Wepresent of our stars by comparing our SOFI spectra to spectra the following equations for calculating stellar radius and of standard stars in the IRTF Spectral Library (Cush- effective temperature: ing et al. 2005; Rayner et al. 2009). Then, we convolved (cid:18) (cid:19) (cid:18) (cid:19) T Mg Al the library spectra from G8V to M7V down to the res- eff =a+b 1.57 +c 1.67 (2) olution of SOFI and plotted these against each of our K Al1.31 Ca I1.03 SOFIspectra. WeestimatedeachSpTandacorrespond- (cid:18) (cid:19) R CO ing uncertainty three times by independently comparing ∗ =a+b(Mg )+c 2.29 . (3) spectra in the J-, H-, and K- bandpasses. The final un- R(cid:12) 1.57 Na I1.14 certaintyoneachSpTcorrespondstotheuncertaintyon Table 3 lists the best-fitting coefficients and the covari- theweightedmeanandthusrepresentsourbestestimate ance matrix for each fit. Note that some coefficients ex- of the error on this quantity. We then compute a single hibit significant correlations, suggesting that uncertain- SpT for each star using a weighted mean. The SpT and ties would be underestimated if these correlations were uncertainty, rounded to the nearest tenth of a type, are neglected. listed in Table 4. Out of the 34 stars in our K2 sample, Based on the range of our calibration sample, we re- we identify 27 as M dwarfs. strict ourselves to stars in the range 3000 K < T < Duringourvisualspectralinspection,wecomparedour eff 4500 K and 0.2 < R /R < 0.7. There is overall ex- spectra to the library spectra of giant stars in order to ∗ (cid:12) cellent agreement between our derived values for radius remove giants as early as possible in our analysis pro- and effective temperature, while four stars (GJ 551, GJ cess. We identified only one star as a likely giant: EPIC 699, GJ 526, GJ 876) have somewhat larger deviations 202710713,whichHuberetal.(2016)andDressingetal. in stellar radius and/or effective temperature. Figures (2017) also classified as an evolved star. 2 and 3 compare the inferred and literature values for ourcalibratedsample. Themiddleandbottompanelsof 4.2. Stellar Parameters these two figures show that the dispersions of the resid- For each absorption feature and stellar parameter (ra- uals are 0.059R (16.09%) and 160 K (4.33%) for stel- (cid:12) dius and effective temperature), we use least-squares fit- lar radius and effective temperature, respectively. All of ting to determine the dependence of those parameters the stars in our calibration sample, with the exception on the EWs calculated from the spectra. Various func- of GJ 526, have published luminosities (calculated using tional forms of EWs are used to fit the calibration sam- theStefan-Boltzmannlaw)within1σ ofourinferredval- ple’sparameters. Theyincludeallcombinationsoflinear, ues. Finally, we estimate each star’s mass by inverting quadratic,andaratioofEWsoftwodifferentabsorption the mass-radius relationship of Maldonado et al. (2015). features. For example, in the simplest linear case, one The full set of stellar values is listed in Table 4 and the lets the EW for the chosen absorption feature be the in- K2 stellar parameters are plotted in Figure 4. dependent variable, while stellar radius or effective tem- Wealsoindependentlycompareourstellarparameters peratureisthedependentvariable. Aftercalculatingthe to those of Dressing et al. (2017). Out of our 34-star linear term and the offset, one then uses all the EWs to K2 sample (as referenced in Table 4), we share 21 stars calculate the stellar radius for all the stars in our sam- in common with their sample. While this work calcu- ple. This process is then repeated for all the absorption lates stellar parameters using the spectra acquired with features in the spectra, all the stellar parameters, each NTT/SOFI, Dressing et al. (2017) use two different in- calibration sample, and each functional combination of struments in their work. The SpeX instrument, on the EWs. To account for intrinsic scatter in stellar proper- NASA Infrared Telescope Facility, provides wavelength ties, we include an additional noise term, tuned to give coverage from 0.7 to 2.55 µm at a resolution of R ≈ χ2 ≈ 1 in the best cases. We find that scatter terms of 2000 (Rayner et al. 2003). The other instrument used red 100 K and 0.05R fulfill this criterion. was TripleSpec on the Palomar 200", providing wave- (cid:12) Inordertofindtheoptimalfitforeachcalibrationsam- length coverage from 1.0 to 2.4 µm at a resolution of R ple, we then select the model giving the lowest Bayesian ≈ 2500-2700 (Herter et al. 2008). Dressing et al. (2017) Stellar & Planetary Parameters for Late Type Dwarf Systems 5 0.8 Boyajian et al. (2012) ]0.8 ] K2 stars Rsun0.6 sun0.7 [0.4 R Rstar0.2 COablsceurlvaetedd s [0.6 0.0 u ]0.15 Rsun0.10 σ=0.059 di0.5 [0.05 a C 0.00 R - 0.05 r 0.4 O0.10 a ) / O %]200 σ=16.09% tell0.3 C S - [20 0.2 O 40 ( GJ570AGJ845GJ702BGJ205 GJ880 GJ526 GJ436 GJ176 GJ876 GJ581 GJ699 GJ551 450E0ffecti4v0e00 Temp3e5r00ature 3[0K0]0 Fig. 2.— Stellar radius for the stars in our interferometric Fig. 4.— Weshowstellarradiusandeffectivetemperaturefor calibration sample, from the literature (blue circles) and derived allourK2targetstars(blackpointswitherrorbars)derivedusing usingEq.3(redcircles). Themiddleandbottompanelsshowthe Eqs. 2 and 3. The red squares and dashed line show the average absolute and fractional deviations for each star. The dispersion valuesforeachSpTascalculatedbyBoyajianetal.(2012b). of the residuals is 0.059R(cid:12) and 16.09%, respectively. Our sample spansfrom0.2to0.7R(cid:12). the validity the of our approach. Additionally, our stel- ]5000 K4500 Observed lar parameters are consistent with those from a number [4000 Calculated of previous publications (Crossfield et al. 2015; Montet eff3500 etal.2015;Petiguraetal.2015;Mannetal.2016;Ober- T3000 meier et al. 2016; Schlieder et al. 2016). 2500 ThemosthighlydiscrepantsystemevidentinFigure6 ] 400 K 300 σ=160 seemstobetheeffectivetemperatureofEPIC211770795. [ 200 C 100 Our estimate is significantly lower than the 4750 K es- - 1000 timated by Dressing et al. (2017). Their value is larger O 200 than the 4500 K upper limit determined from our cali- 300 / O 1068 σ=4.33% bthraattioonursarmelpalteio(nseseaFriegunroet2)w,epllrocvaidliibnrgatfeudrthbeeryoevniddetnhcies - C) [%] 2024 rtiavnegete.mFpuerrtahteurrmeovrael,uweseasneedatnhoosffesreetpboerttwedeebnyoDurreesffsiencg- (O 864 et al. (2017), demonstrating that systematic calibration GJ845GJ570AGJ702BGJ205GJ880GJ176GJ526GJ581GJ581GJ436GJ699GJ876GJ551 eyrsreosr.s Amsaysesetnillwpiltahytahreoliendinexo-bnaesoerdbroetlahtioofntsheosfeMananaln- Fig. 3.— Stellar effective temperature for the stars in our in- et al. (2015), our EW-based relations also start to satu- terferometric calibration sample, from the literature (blue circles) rate around 4000 K and could systematically effect any andderivedusingEq.2(redcircles). Themiddleandbottompan- derived planetary parameters, such as equilibrium tem- elsshowtheabsoluteandfractionaldeviationsforeachstar. The dispersion of the residuals is 160 K and 4.33%, respectively. Our peratures. samplespansfrom3000to4500K. Metallicity could be a factor for some stars and could cause a shift in effective temperature and stellar radius. The larger uncertainties in our stellar parameters when compared to those of Dressing et al. (2017) may result derive and compare stellar parameters using EW-based from a range of stellar metallicities. relations developed by Newton et al. (2015) and index- Additionally, we compare all 34 of our stellar parame- based relations from Mann et al. (2013). Both sets of ters with the photometrically derived stellar parameters relations were calibrated using a set of stars with in- fromHuberetal.(2016), showninFigures7and8. Fig- terferometrically determined parameters from Boyajian ure 7 shows that there is a median increase of 0.15R etal.(2012b). Ultimately, effectivetemperatures, stellar (cid:12) whencomparingourstellarradiitothoseofHuberetal. radii, and luminosities were derived using the Newton et al. (2015) relations, stellar masses25 and metallicity (2016). Figure 8 shows a general agreement in effective temperature between both of our works with the excep- were calculated using the Mann et al. (2013) relations, tion of EPIC 204489514 and EPIC 205145448. and surface gravities were calculated from masses and We note that the analysis done in Huber et al. (2016) stellar radii. is subject to the limitations of broadband photometry. Comparing the parameters derived by Dressing et al. (2017)withthoseshowninFigures5and6,wefindχ2 Furthermore, Huber et al. (2016) note that model-based red estimatestendtounderpredictstellarradiiby20%(Boy- < 1 in both cases. This indicates that there is an ex- ajian et al. 2012a) and encourage the use of empirical cellent agreement between our two methods and verifies calibrations for estimating the stellar parameters in cool 25UsingtheeffectivetemperaturesfromtheNewtonetal.(2015) dwarfs. Lastly,ourempiricallycalculatedparametersare relation in agreement with those in Dressing et al. (2017) for the 6 Martinez et al. )0.9 )0.9 ork0.8 ork0.8 w0.7 w0.7 s0.6 i s0.6 h i t0.5 h ( t0.5 n0.4 ( RSu0.3 Sun0.4 /0.2 R0.3 Star0.1 /ar0.2 R St0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 R R /R (Dressing et al. 2017) 0.0 Star Sun 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 R /R (Huber et al. 2016) Star Sun Fig. 5.— Comparison of our stellar radii to those of Dressing et al. (2017). The dotted line shows a 1:1 agreement, while any Fig. 7.— Comparison of our stellar radii to those of Huber deviation from the dotted line presents the small discrepancies. et al. (2016). The dotted line shows a 1:1 agreement, while any Overall,thereisageneralagreementbetweenourworksinderiving deviationfromthedottedlinepresentsthesmalldiscrepancies. As ourstellarradii. indiscussedin§4.3,wefindthatthemajorityoftheobjectsinthe samplearelargerinourworkandfinda0.15R(cid:12) medianincrease. 5000 ) 5000 k 4500 r o ) w k 4500 s 4000 or hi w (t 3500 s 4000 K hi / t eff3000 ( 3500 T K / f 25020500 3000 3500 4000 4500 5000 ef3000 T T /K (Dressing et al. 2017) eff 2500 Fig. 6.— Comparisonofoureffectivetemperaturestothoseof 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 Dressingetal.(2017). Thedottedlineshowsa1:1agreement,while Teff/K (Huber et al. 2016) anydeviationfromthedottedlinepresentsthesmalldiscrepancies. Overall,thereisageneralagreementbetweenourworksinderiving Fig. 8.— Comparisonofourineffectivetemperaturestothoseof oureffectivetemperatures. Weaddresssmallcaveatsin§4.3forthe Huberetal.(2016). Thedottedlineshowsa1:1agreement,while outlier,EPIC211770795. anydeviationfromthedottedlinepresentsthesmalldiscrepancies. See§4.3foradiscussion. points where we disagree with the values of Huber et al. (2016), giving us further confidence in our results. a comparison to our own Earth-Sun system: 4.4. Planetary Parameters (cid:18) T (cid:19)(cid:18)(cid:20)R (cid:21)(cid:20)1AU(cid:21)(cid:19)1/2 T =(270K) eff ∗ (5) Radiiandequilibriumtemperaturesoftransitingplan- eq T R a eff,(cid:12) (cid:12) etsarecalculatedusingthestellarparametersofitshost where T is the effective temperature of the star, R star. Using the transit depths and periods measured us- eff ∗ is the radius of the star, and a is the semi-major axis ingK2photometry(Crossfieldetal.2016)andournewly of the planet orbiting its parent star. Here we calculate calculatedstellarparameters,planetradiiaredetermined thesemi-majoraxisoftheplanetbyusingKepler’sthird with the following equation: law. The 270 K equilibrium temperature scaling factor (cid:18)R (cid:19)2 correspondstoaBondalbedoof0.3,whichiscomparable ∆L= p (4) to that inferred for gas giants more highly irritated than R ∗ Earth. All uncertainties are propagated through the en- where ∆L is the transit depth of the planet candidate tire calculation for planet radii. We present the derived with respect to its host star. values for our K2 planets and planet candidates in Ta- Calculating the equilibrium temperature of a planet ble 5 and plot these derived values (along with incident candidate requires more parameters from the planet and irradiation) in Figure 9. its host star. The following equation calculates the equi- Our sample shown in Figure 9 includes 18 validated librium temperatures for each K2 planet or candidate as planets and 19 remaining planet candidates. While Stellar & Planetary Parameters for Late Type Dwarf Systems 7 Equilibrium Temperature [K] 1000 700 500 300 200 64 256 ] ] h Crossfield et al. 2015 Earth32 Eart128 This work R R 64 [16 [ s s 32 diu 8 iu 16 d a R 4 a 8 R et t 4 n 2 e a n 2 Pl 1 V E Pla 1 0.5 0.5 10-1 100 101 102 103 104 102 101 100 Insolation [S ] Insolation [S ] ⊕ ⊕ Fig. 9.— Planet radii, incident irradiation, and equilibrium Fig. 10.— PlanetradiiandincidentirradiationfortheK2plan- temperaturesofallK2planetsandcandidatesobservedinourpro- etsandplanetcandidatesthatappearinbothourworkandCross- gram. Venus and Earth are indicated by single letters. Plus red field et al. (2016). Black circles indicate the K2 objects reported signs indicate validated planets, and gray squares indicate planet byCrossfieldetal.(2016),whilethedarkredsquaresindicatethe candidates, as reported by Crossfield et al. (2016). The shaded K2objectsinthiswork. Thedarkgraylinesconnectourupdated region represents the approximate location of the cloud-free hab- parametervaluestotheoriginalestimatespublishedbyCrossfield itable zone for an early-type M dwarf (Kopparapu et al. 2013). etal.(2016). See§4.4fordetails. That zone was defined for planets with masses 0.3–10 times that of Earth. The larger of those masses corresponds to the upper, lightlyshadedarea(Wolfgangetal.2016). ado et al. (2015), and Terrien et al. (2015) by measuring EWs in the near-infrared part of the spectrum. Interfer- ometric calibration samples are used from Demory et al. fitting for the light-curve parameters of these remain- (2009), von Braun et al. (2011, 2012), Boyajian et al. ing candidates, degeneracies (such as impact parameters (2012b), and von Braun et al. (2014) in order to provide nearunity)arosethatprecludeanyprecisedetermination a more precise baseline to calculate the stellar radii and of R /R . The candidates have much larger uncertain- p ∗ effective temperatures of the stars in our sample. Var- ties on their size, which typically makes statistical vali- ious functions (whether they are linear, quadratic, or a dationmuchmoredifficult. Basedonthepaucityoflarge ratio of EWs) are tested, and we use the functions with (>6R ) planets orbiting M dwarfs (Johnson et al. 2007, ⊕ the best BIC value and the lowest residuals to calculate 2010), the (cid:38) 9 candidates larger than this size are likely stellar parameters. false positives; since planet validation is not the aim of Our spectroscopically derived stellar radii improve on this work, we retain the previously assigned designation previously reported values that relied on stellar models of planet candidate. poorlycalibratedtotheselow-massstars. Wefindame- Inadditiontotheselikelyfalsepositives,ourvalidated dian increase of 0.15R when comparing our measure- planets include several hot Neptunes and two planets (cid:12) ments to those of Huber et al. (2016), consistent with (K2-18bandK2-72e)thatlienearthehabitablezone. Of themedianincreaseinsizefoundbyNewtonetal.(2015) our whole K2 sample, only eight planets (three of which whenrevisingthephotometricallybasedstellarradiuses- are still planet candidates) are smaller than 1.6 Earth timates determined by Dressing & Charbonneau (2013) radii. According to Rogers (2015), planets smaller than forcooldwarfsobservedduringtheprimeKeplermission. 1.6Earthradiiarelikelytohavecompositionsdominated Finally, we calculate the K2 planet or planet candidate by rock or iron, while larger planets are more likely to radius and equilibrium temperature. be volatile-rich. However, there may still be rocky plan- Sinceourteamalsoobtainedopticalspectra,usingthe ets larger than this limit. For example, Buchhave et al. EFOSC2spectrograph(Buzzonietal.1984)ontheNTT, (2016)foundthatKepler-20b,a1.9R planet,hasaden- ⊕ in a future work we will apply the same techniques in sity consistent with a rocky composition even though it order to cross-check our stellar properties. Furthermore, is beyond the rocky-to-gaseous transition. thisworkdoesnotcalculatestellarmetallicities;however, Wecompareourcalculationsoftheinsolationfluxfrom we plan to so in later works. our K2 sample to those from Crossfield et al. (2016) in Our work paves the way for future exoplanet surveys. Figure 10. The discrepancies between our values and Otherspectroscopicandphotometricsurveysfocusingon thoseinCrossfieldetal.(2016)highlighttheimportance M dwarfs are currently underway or are being planned of using spectroscopically derived stellar parameters in for the near future. SPECULOOS, a 1 m near-infrared order to compute planet parameters. telescope, will observe approximately 500 of the nearest M and brown dwarfs in the southern hemisphere (Gillon 5. CONCLUSION AND FUTURE PROSPECTS et al. 2013). CARMENES will provide high-resolution In this paper, we derive stellar and planetary param- (R = 82,000) spectra between 0.5 and 1.7 µm for late- eters for K2 K and M dwarf systems. We adopt similar type M dwarfs and search for Earth-like planets in the calibration techniques from Neves et al. (2014), Maldon- habitablezone(Quirrenbachetal.2012). TheHabitable 8 Martinez et al. Zone Planet Finder (HZPF) will also provide spectra for the K2 team for all the assistance and interesting con- M dwarfs and will attempt to find planets through the versationsthroughoutthiswork. A.W.H.acknowledges Doppler effect (Mahadevan et al. 2010). Yet another RV support for our K2 team through a NASA Astrophysics survey,SPIRou,aimstofindexoplanetsaroundlow-mass Data Analysis Program grant. A. W. H. and I. J. M. C. starsusinghigh-resolutionspectrabetween0.98and2.35 acknowledge support from the K2 Guest Observer Pro- µm (Santerne et al. 2013). gram. Finally, we thank the anonymous referee for the FuturetransitsurveyswilldetectmanynewEarth-like insightful comments that improved the quality of this planets around M dwarfs, just like previous and ongoing manuscript. photometric surveys such as Kepler and K2. Although This material is based on work supported by the the current Gaia mission (Lindegren 2010) focuses more National Science Foundation under Award nos. AST- on astrometry (for which stellar mass is a key input), 1322432, a PAARE Grant for the California-Arizona its two photometers can provide light curves for exo- Minority Partnership for Astronomy Research and Ed- planetdetection. TheTransitingExoplanetSurveySatel- ucation (CAMPARE), and DUE-1356133, an S-STEM lite (TESS; Ricker et al. 2009) and PLAnetary Transits GrantfortheCal-BridgeCSU-UCPhDBridgeProgram. andOscillationsofstars(PLATO;Raueretal.2014)will This work was funded in part by Spitzer GO 11026 (PI alsofindplanets,someofwhichwillbehigh-prioritytar- Werner),managedbyJPL/Caltechunderacontractwith gets for the James Webb Space Telescope (JWST; Gard- NASA and locally by the University of Arizona. This ner et al. 2006). The recent announcement of a roughly work was performed in part under contract with the Earth-mass planet candidate orbiting Proxima Centauri California Institute of Technology/Jet Propulsion Lab- (Anglada-Escudé et al. 2016) adds yet more urgency to oratory funded by NASA through the Sagan Fellowship theneedtosearchformoreplanetsandcharacterizetheir Program executed by the NASA Exoplanet Science In- low-masshoststars. Thecombinationofallofthesesur- stitute. TravelcostswerepartiallysupportedbytheNa- veys will yield many new M dwarf systems in need of tional Geographic Society. Any opinions, findings, and stellar and planetary parameters and of a large, precise conclusions or recommendations expressed in this ma- calibration sample. terial are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. A. O. 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TABLE 2 J-, H-, and K-band equivalent width features Feature Featurewindow Bluecontinuum Redcontinuum µm µm µm CaI(1.03µm) 1.0320 1.0365 1.0280 1.0315 1.0368 1.0377 NaI(1.14µm) 1.1361 1.1432 1.1270 1.1327 1.1478 1.1572 Al(1.31µm) 1.3125 1.3180 1.3060 1.3090 1.3180 1.3220 Mg(1.48µm) 1.4865 1.4905 1.4810 1.4850 1.4920 1.4960 Mg(1.50µm) 1.5002 1.5075 1.4910 1.4983 1.5090 1.5163 Mg(1.57µm) 1.5725 1.5797 1.5665 1.5720 1.5810 1.5865 Si(1.58µm) 1.5875 1.5925 1.5820 1.5865 1.5930 1.5975 CO(1.62µm) 1.6178 1.6280 1.6048 1.6150 1.6300 1.6402 Al(1.67µm) 1.6698 1.6790 1.6558 1.6650 1.6800 1.6892 Mg(1.71µm) 1.7089 1.7139 1.7000 1.7050 1.7149 1.7199 NaI(2.20µm) 2.2020 2.2120 2.1890 2.1990 2.2125 2.2225 CaI(2.26µm) 2.2586 2.2696 2.2480 2.2570 2.2700 2.2800 CO(2.29µm) 2.292 2.315 2.286 2.290 2.315 2.320 Note. —Allthewavelengthsarepresentedattheirrestwavelength. TABLE 3 Equivalent Width Formulae Quantity Formula a b c Teff a+b(Mg1.57/Al1.31)+c(Al1.67/CaI1.03) 2989.5 -577.05 53.804 uncertainties: 78.56147 52.42034 10.44419 Covariance: 6171.9 -3355.2 -493.87 -3355.2 2747.9 265.68 -493.87 265.68 109.08 R∗ a+b(Mg1.57)+c(CO2.29/NaI1.14) 0.18552 1265.2 0.010852 uncertainties: 0.02569482 117.2119 0.005063553 Covariance: 0.00066022 -1.8673 -0.00003695 -1.8673 13739 -0.2305 -0.00003695 -0.2305 0.00002564