A super-Earth and a sub-Neptune orbiting the bright, quiet M3 dwarf TOI-1266
B.-O. Demory, F.J. Pozuelos, Y. Gomez Maqueo Chew, L. Sabin, R. Petrucci, U. Schroffenegger, S.L. Grimm, M. Sestovic, M. Gillon, J. McCormac, K. Barkaoui, W. Benz, A. Bieryla, F. Bouchy, A. Burdanov, K.A. Collins, J. de Wit, C.D. Dressing, L.J. Garcia, S. Giacalone, P. Guerra, J. Haldemann, K. Heng, E. Jehin, E. Jofre, S.R. Kane, J. Lillo-Box, V. Maigne, C. Mordasini, B. M. Morris, P. Niraula, D. Queloz, B.V. Rackham, A.B. Savel, A. Soubkiou, G. Srdoc, K.G. Stassun, A.H.M.J. Triaud, R. Zambelli, G. Ricker, D.W. Latham, S. Seager, J.N. Winn, J.M. Jenkins, T. Calvario-Velasquez, J.A. Franco Herrera, E. Colorado, E.O. Cadena Zepeda, L. Figueroa, A.M. Watson, E.E. Lugo-Ibarra, L. Carigi, G. Guisa, J. Herrera, G. Sierra Diaz, J.C. Suarez, D. Barrado, N.M. Batalha, Z. Benkhaldoun, A. Chontos, F. Dai, Z. Essack, M. Ghachoui, C.X. Huang, D. Huber, H. Isaacson, J.J. Lissauer, M. Morales-Calderon, P. Robertson, A. Roy, J.D. Twicken, A. Vanderburg, L.M. Weiss
AAstronomy & Astrophysics manuscript no. TOI1266 c (cid:13)
ESO 2020September 10, 2020
A super-Earth and a sub-Neptune orbiting the bright, quiet M3dwarf TOI-1266
B.-O. Demory , F.J. Pozuelos , , Y. Gómez Maqueo Chew , L. Sabin , R. Petrucci , , , U. Schro ff enegger ,S.L. Grimm , M. Sestovic , M. Gillon , J. McCormac , , K. Barkaoui , , W. Benz , A. Bieryla , F. Bouchy ,A. Burdanov , , K.A. Collins , J. de Wit , C.D. Dressing , L.J. Garcia , S. Giacalone , P. Guerra ,J. Haldemann , K. Heng , , E. Jehin , E. Jofré , , , S.R. Kane , J. Lillo-Box , V. Maigné , C. Mordasini ,B. M. Morris , P. Niraula , D. Queloz , B.V. Rackham , , A.B. Savel , , A. Soubkiou , G. Srdoc ,K.G. Stassun , A.H.M.J. Triaud , R. Zambelli , G. Ricker , D.W. Latham , S. Seager , , , J.N. Winn ,J.M. Jenkins , T. Calvario-Velásquez , J.A. Franco Herrera , E. Colorado , E.O. Cadena Zepeda , L. Figueroa ,A.M. Watson , E.E. Lugo-Ibarra , L. Carigi , G. Guisa , J. Herrera , G. Sierra Díaz , J.C. Suárez , , D. Barrado ,N.M. Batalha , Z. Benkhaldoun , A. Chontos , F. Dai , Z. Essack , , M. Ghachoui , C.X. Huang , D. Huber ,H. Isaacson , , J.J. Lissauer , M. Morales-Calderón , P. Robertson , A. Roy , J.D. Twicken , ,A. Vanderburg , and L.M. Weiss (A ffi liations can be found after the references) Accepted for publication on 20 July 2020.
ABSTRACT
We report the discovery and characterisation of a super-Earth and a sub-Neptune transiting the bright ( K = . R = . + . − . R ⊕ and anorbital period of 10.9 days. The outer, smaller planet has a radius of R = . + . − . R ⊕ on an 18.8-day orbit. The data are found to be consistentwith circular, co-planar and stable orbits that are weakly influenced by the 2:1 mean motion resonance. Our TTV analysis of the combined datasetenables model-independent constraints on the masses and eccentricities of the planets. We find planetary masses of M p = . + . − . M ⊕ ( < . ⊕ at 2- σ ) for TOI-1266 b and 2 . + . − . M ⊕ ( < . ⊕ at 2- σ ) for TOI-1266 c. We find small but non-zero orbital eccentricities of 0 . + . − . ( < .
21 at2- σ ) for TOI-1266 b and 0 . ± .
03 ( < .
10 at 2- σ ) for TOI-1266 c. The equilibrium temperatures of both planets are of 413 ±
20 K and 344 ±
16 K,respectively, assuming a null Bond albedo and uniform heat redistribution from the day-side to the night-side hemisphere. The host brightness andnegligible activity combined with the planetary system architecture and favourable planet-to-star radii ratios makes TOI-1266 an exquisite systemfor a detailed characterisation.
Key words.
Planets and satellites – Techniques: photometric – Methods: numerical
1. Introduction
The science of exoplanets has been historically driven by dedi-cated astronomical observations. Currently, the Transiting Exo-planet Survey Satellite (TESS; Ricker et al. 2015) is leading thediscovery of multi-planetary transiting systems with relativelysmall planets (i.e. sub-Neptune or smaller), orbiting aroundbright M-dwarf stars in the solar neighbourhood (e.g. Güntheret al. 2019; Jenkins et al. 2019; Kostov et al. 2019; Cloutier et al.2020). Their brightness allows for a detailed characterisation ofsmall planets, and, in the near future, a glimpse into their at-mospheric composition with the James Webb Space Telescope(JWST). Furthermore, when multiple transit-like signals are de-tected from a single star, the signals are likely to be genuine asopposed to false positives such as eclipsing binaries (Lathamet al. 2011; Lissauer et al. 2012; Morton et al. 2016). In somecases, in particular where the planets are near resonant orbits,time-series photometry alone not only allows for the measure-ment of the planet size, but also places dynamical constraintson the planet mass (Holman 2005; Agol et al. 2005). Measuringthe planet mass and radius allows for the derivation of the bulk density, thus constraining planetary structure models (e.g. Dornet al. 2017).There are more than 3000 transiting exoplanets known todate , including 499 planetary systems with more than one de-tected transiting planet. This large sample of transiting exo-planets allows for in-depth exploration of the distinct exoplanetpopulations. One such study by Fulton et al. (2017) identifieda bi-modal distribution for the sizes of super-Earth and sub-Neptune Kepler exoplanets, with a peak at ∼ ⊕ and anotherat ∼ ⊕ . The interval between the two peaks is called theradius valley and it is typically attributed to the stellar irradi-ation received by the planets, with more irradiated planets be-ing smaller due to the loss of their gaseous envelopes. Study-ing more than one super-Earth or sub-Neptune planet in a singlesystem allows for tighter constraints on formation models (e.g.Owen & Campos Estrada 2020; Kubyshkina et al. 2019) and thusthe exploration of the e ff ects of other physical processes such asthe core and envelope mass distribution (e.g. Modirrousta-Galianet al. 2020). http://exoplanet.eu/ retrieved on 10 Aug 2020Article number, page 1 of 22 a r X i v : . [ a s t r o - ph . E P ] S e p & A proofs: manuscript no. TOI1266
Here we present the discovery and characterisation of theplanetary system TOI-1266, which was first identified from theTESS photometry. We confirmed the planetary nature of thetransits through ground-based follow-up observations, includingtime-series photometry, high-angular resolution images, spec-troscopy, and archival imagery.The paper is structured as follows. Section 2 describes allobservations. The stellar characterisation of the planet host isdescribed in §3. The validation of the transit signals in the lightcurves is presented in §4. The search for transit signals and theanalysis of the light curves to derive physical properties are pre-sented in §5. We also include a stability analysis and mass con-straints from a dynamical analysis in §5.2. Finally, in §6, wediscuss the implications for the formation and evolution of theTOI-1266 planetary system given the measured planet radii, or-bital periods, and constraints on the masses, as well as prospectsfor atmospheric characterisation. A summary of our results andtheir implications is presented in §7.
2. Observations
In this section, we present all the observations of TOI-1266 ob-tained with TESS and ground-based facilities. A summary of allground-based time-series photometric observations of TOI-1266is shown in Table 1.
TOI-1266 is a late-type star with a measured parallax that ispart of the TESS Candidate Target List (Stassun et al. 2018). Itwas observed by TESS with 2-min-cadence in sectors 14–15 (18July to 11 Sep 2019) and 21–22 (21 Jan to 18 Mar 2020). TOI-1266’s astrometric and photometric properties from the literatureare reported in Table 2. The time-series observations of TOI-1266 were processed with the TESS Science Processing Opera-tions Center (SPOC) pipeline (Jenkins 2002; Jenkins et al. 2016,2017), which resulted in the detection of two periodic transit sig-nals: TOI-1266.01 and .02, the latter being at the detection limitusing sectors 14-15 data alone, thus requiring additional data tostrengthen that signal.We retrieved the Presearch Data Conditioning Simple Aper-ture Photometry (PDC-SAP) (Stumpe et al. 2012; Smith et al.2012; Stumpe et al. 2014) from the Mikulski Archive for SpaceTelescopes and removed all datapoints flagged as ‘bad qual-ity’. We identified 819 / / / / Gaia
DR2 sources su-perimposed.
We obtained ground-based photometric time-series observationsof TOI-1266 from the SAINT-EX Observatory (Search AndcharacterIsatioN of Transiting EXoplanets), which was commis-sioned in March 2019. SAINT-EX is a 1-m F / https://github.com/jlillo/tpfplotter de San Pedro Mártir in Baja California, México (31.04342 N,115.45476 W) at 2780 m altitude. The telescope is installedon an ASTELCO equatorial NTM-1000 mount equipped withdirect-drive motors, which enables operations without meridianflip. The telescope is installed in a 6.25-m wide dome built by theGambato company. In terms of mount performance, SAINT-EXtypically achieves a RMS better than 3 (cid:48)(cid:48) relative to the pointingmodel and a tracking accuracy – without autoguiding – betterthan 2 (cid:48)(cid:48) over 15-min timescales. To improve this figure further,SAINT-EX uses the DONUTS autoguiding software (McCor-mac et al. 2013), which increases the guiding precision to 0.2 (cid:48)(cid:48) RMS or better that is less than a pixel. SAINT-EX is equippedwith an Andor iKon-L camera that integrates a deep-depletione2v 2K ×
2K CCD chip with a BEX2-DD coating that is opti-mised for the near infrared (NIR). The filter wheel includes theSloan ugriz (cid:48) broad-band filters, as well as special blue-blocking(transmittance >
90% beyond 500 nm) and NIR (transmittance >
95% beyond 705 nm) filters. The detector gives a field of viewof 12 (cid:48) × (cid:48) with 0.34 (cid:48)(cid:48) per pixel.SAINT-EX operations are robotic and the data reduction andanalysis are automated by a custom pipeline PRINCE (Photo-metric Reduction and In-depth Nightly Curve Exploration) thatingests the raw science and calibration frames and produces lightcurves using di ff erential photometry. The PRINCE pipeline per-forms standard image reduction steps, applying bias, dark, andflat-field corrections. Astrometric calibration is conducted usingAstrometry.net (Lang et al. 2010) to derive correct world coordi-nate system (WCS) information for each exposure. Photutils star detection (Bradley et al. 2019) is run on a median imageof the whole exposure stack to create a pool of candidate starsin the field of view. Stars whose peak value in the largest aper-ture is above the background by a certain threshold, defined byan empirical factor times the median background noise of thenight, are kept as reference stars for the di ff erential photomet-ric analysis. From the WCS information and the detected stars’coordinates, the pipeline runs centroiding, aperture and annulusphotometry on each detected star from the common pool, usingLMFit (Newville et al. 2014) and Astropy (Astropy Collabora-tion et al. 2013; Price-Whelan et al. 2018), and repeats this foreach exposure to obtain the measured lightcurves for a list ofapertures. The measured lightcurves for each aperture are cor-rected for systematics using either a PCA approach (Pedregosaet al. 2011) or a simple di ff erential photometry approach thatcorrects a star’s lightcurve by the median lightcurve of all starsin the pool except for the target star.SAINT-EX observed one transit of each planet of the TOI-1266 system in early 2020. The observing strategy was to use the z (cid:48) filter with a slightly-defocused 12-s exposure time to mitigateshutter noise and scintillation. A partial transit of TOI-1266.02was observed on 29 January 2020 from 7:36 to 12:05 UT. A fulltransit of TOI-1266.01 was then observed on 29 February 2020from 6:16 to 11:03 UT. We reduced both datasets with PRINCEusing di ff erential aperture photometry. We corrected our di ff er-ential light curves for variations in both the airmass and the fullwidth at half maximum (FWHM) along both horizontal and ver-tical axes on the detector. This correction is performed simul-taneously to the transit fit in our MCMC framework detailed inSection 5.1.2. We used the 60-cm TRAPPIST-North telescope located atOukaimeden Observatory in Morocco (Jehin et al. 2011; Gillonet al. 2013; Barkaoui et al. 2019) to observe one full and one par-
Article number, page 2 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266
Date (UT) Filter Facility Exp. time [s] Notes25 Dec 2019 Ic OAA-0.4m 160 b full29 Jan 2020 z (cid:48) SAINT-EX-1m 12 c partial29 Feb 2020 z (cid:48) SAINT-EX-1m 12 b full21 Mar 2020 z (cid:48) TRAPPIST-N-0.6m 15 b full21 Mar 2020 r (cid:48) Artemis-1m 10 b partial01 Apr 2020 V TRAPPIST-N-0.6m 60 b partial23 Apr 2020
T ES S
Kotizarovci-0.3m 50 b full23 Apr 2020 clear ZRO-0.4m 200 b full
Table 1.
Ground-based time-series photometric observations of TOI-1266.
628 630 632 634 636 638
Pixel Column Number P i x e l R o w N u m b e r EN TIC 467179528 - Sector 14 m = -2.0 m = 0.0 m = 2.0 m = 5.0 m = 8.01 2 3456 0.000.020.040.060.080.100.12 F l u x × ( e )
554 556 558 560 562 564
Pixel Column Number P i x e l R o w N u m b e r E N
TIC 467179528 - Sector 15 m = -2.0 m = 0.0 m = 2.0 m = 5.0 m = 8.01 234 56 0.000.020.040.060.080.100.120.140.16 F l u x × ( e )
980 982 984 986 988 990
Pixel Column Number P i x e l R o w N u m b e r EN TIC 467179528 - Sector 21 m = -2.0 m = 0.0 m = 2.0 m = 5.0 m = 8.012 3 45 6 0.0000.0250.0500.0750.1000.1250.1500.175 F l u x × ( e )
860 862 864 866 868 870
Pixel Column Number P i x e l R o w N u m b e r EN TIC 467179528 - Sector 22 m = -2.0 m = 0.0 m = 2.0 m = 5.0 m = 8.012 3 456 0.00.20.40.60.81.01.21.4 F l u x × ( e ) Fig. 1.
TESS target pixel files (TPFs) of the four sectors that observed TOI-1266. The plots were created with tpfplotter (Aller et al. 2020).The apertures used to extract the photometry (Twicken et al. 2010; Morris et al. 2017) by the SPOC pipeline are shown as red shaded regions. The Gaia
DR2 catalogue (Gaia Collaboration et al. 2018) is overplotted, with all sources up to 8 magnitudes in contrast with TOI-1266 are shown asred circles. We note that the symbol size scales with the magnitude contrast. tial transit of TOI-1266.01. TRAPPIST-North is equipped witha thermoelectrically cooled 2 K × K Andor iKon-L BEX2-DDCCD camera with a pixel scale of 0.6 (cid:48)(cid:48) and a field of view of20 (cid:48) × (cid:48) . We used the TESS Transit Finder tool, which is a cus-tomised version of the Tapir software package (Jensen 2013), toschedule the photometric time-series. Data reduction and photo-metric analysis were performed with the TRAPPHOT pipelinedeveloped in
IRAF as described in Gillon et al. (2013). The firsttransit was observed on 21 March 2020 in the Sloan- z (cid:48) filter withan exposure time of 15 seconds. We took 476 raw images andperformed aperture photometry in an uncontaminated apertureof 6.5 pixels (4.0 (cid:48)(cid:48) ) and a FWHM of 2.6 (cid:48)(cid:48) . The second transitwas observed on 01 April 2020 in the Johnson- V filter with anexposure time of 60 seconds. We took 338 raw images and weperformed aperture photometry in an uncontaminated apertureof 8.1 pixels (5.0 (cid:48)(cid:48) ) and a FWHM of 3.4 (cid:48)(cid:48) . During that secondobservation of TOI-1266, the telescope underwent a meridianflip at HJD 2458941.5431, and we noticed the presence of thinclouds during the ingress. One partial transit of TOI-1266.01 was acquired on 21March 2020 with the Artemis telescope, which constitutes theSPECULOOS-North facility located at the Teide Observatory(Canary Islands, Spain). The Artemis telescope is a twin of theSPECULOOS-South and SAINT-EX telescopes, which are alloperated similarly and utilise Andor iKon-L cameras with e2v2K ×
2K deep-depletion CCDs. We acquired 668 images in theSloan- r (cid:48) filter with an exposure time of 10 seconds. Data reduc-tion consisted of standard calibration steps and subsequent aper-ture photometry with the TRAPPHOT pipeline. Best comparisonstars and optimum aperture size were selected on the basis of theminimisation of the out-of-transit scatter of the light curve.
A full transit of TOI-1266 b was observed in I C band on 25 Dec2019 from Observatori Astronòmic Albanyà (OAA) in Girona,Spain. The 0.4 m telescope is equipped with a 3056 × (cid:48)(cid:48) .
44 pixel − , re-sulting in a 36 (cid:48) × (cid:48) field of view. The images were calibratedand the photometric data were extracted using the AstroImageJ ( AIJ ) software package (Collins et al. 2017).
A full transit of TOI-1266 b was observed in Baader R long-pass 610 nm band on 23 Apr 2020 from Kotizarovci Observatorynear Viskovo, Croatia. The 0.3 m telescope is equipped with a765 ×
510 SBIG ST7XME camera with an image scale of 1 (cid:48)(cid:48) . − resulting in a 15 . (cid:48) × . (cid:48) field of view. The images werecalibrated and the photometric data were extracted using AIJ . A full transit of TOI-1266 b was observed without filter on 23Apr 2020 from the Zambelli Roberto Observatory (ZRO) in Lig-uria, Italy. The 0.4-m telescope is equipped with a 3072 × (cid:48)(cid:48) .
16 pixel − resulting in a 49 (cid:48) × (cid:48) field of view. The images were calibratedand the photometric data were extracted using AIJ . We obtained two ‘reconnaissance’ spectra with the TillinghastReflector Echelle Spectrograph (TRES; Furesz 2008) instrumentmounted on the Fred Lawrence Whipple Observatory’s 1.5-mtelescope on 25 January 2020 and 30 January 2020. The TRESwavelength coverage spans 385 to 910 nm and the resolvingpower is 44000. The purpose of these spectra is to discard ob-
Article number, page 3 of 22 & A proofs: manuscript no. TOI1266
Parameter Value Source
Target designations
TIC 467179528 12MASS J13115955 + Gaia
DR2 1678074272650459008 4
PhotometryT ES S ± B ± V ± Gaia ± u ± g ± r ± i ± z ± J ± H ± K ± µ m 8.72 ± µ m 8.61 ± µ m 8.50 ± µ m 8.23 ± Astrometry
RA (J2000) 13 11 59.56 4DEC (J2000) +
65 50 01.70 4RA PM (mas / yr) -150.652 ± / yr) -25.368 ± ± Table 2.
TOI-1266 stellar astrometric and photometric properties. 1.Stassun et al. (2018), 2. Cutri et al. (2003), 3. Zacharias et al. (2013), 4.Brown et al. (2018), 5. Alam et al. (2015), 6. Cutri & et al. (2013). vious false positive scenarios and provide basic constraints onthe stellar host. The two TRES spectra were extracted usingthe procedures outlined in Buchhave et al. (2010). Radial ve-locities were determined using special procedures developed byJonathan Irwin for the analysis of spectra of M dwarfs, ratherthan the standard pipeline analysis, which was optimised forSolar-type stars, and uses the wavelength region near the Mg bfeatures at 519 nm and a library of calculated templates to yieldabsolute velocities. Irwin’s tools use an observed spectrum ofBarnard’s star as the template, and the wavelength region near715 nm that contains TiO features rich in radial-velocity infor-mation. For M dwarfs, the S / N per resolution element is signif-icantly stronger at 715 nm, in this case 30, compared to 12 at519 nm. The two TRES observations were obtained at phases16.79 and 17.25 of the TESS ephemeris for the inner planet (i.e.at opposite quadratures for a circular orbit), and yielded absolutevelocities of -41.511 and -41.662 km / s, thus ruling out a stellarcompanion or brown dwarf orbiting TOI-1266, as the source ofthe transits for the inner planet. We obtained a single spectrum with the HIRES (Vogt et al. 1994)instrument mounted on the Keck-I 10-m telescope on 15 Decem-ber 2019. HIRES has a wavelength coverage of 390 to 900 nmand a resolving power of 50 000. The spectrum with which weconducted these analyses has a S / N per resolution element of 80.
We used high-angular resolution imaging to rule out false-positive signals caused by unresolved blended stars in the time-series photometry. This is particularly important for the TESSlight curves, given that the TESS pixels are ∼ (cid:48)(cid:48) . TOI-1266 was observed on 30 October 2019 with the AstraLuxinstrument (Hormuth et al. 2008), a high-spatial resolution cam-era installed at the 2.2 m telescope of the Calar Alto Observa-tory (Almería, Spain). This fast-readout camera uses the lucky-imaging technique (Fried 1978) by obtaining thousands of short-exposure frames to subsequently select a small percentage ofthem showing the best Strehl ratio (Strehl 1902), and combin-ing them into a final image. We observed this target using theSloan Digital Sky Survey z filter (SDSSz), which provides thebest resolution and contrast capabilities for the instrument (Hor-muth et al. 2008), and obtained 35 000 frames with 20 ms expo-sure time and a 6 (cid:48)(cid:48) × (cid:48)(cid:48) field-of-view. The datacube was subse-quently reduced using the observatory pipeline (Hormuth et al.2008), and we used a 10% selection rate for the best frames toobtain a final high-resolution imaging with a total exposure timeof 70 s. We then computed the sensitivity curve by using ourown astrasens package , following the procedure described inLillo-Box et al. (2012, 2014). The image allows us to discardstellar companions with magnitude contrasts down to ∆ m = (cid:48)(cid:48) (corresponding to 7.2 au at the distance of this system), andhence, establish a maximum contamination in the planet transitbetter than 3%. The AstraLux contrast curve is shown in Fig. 2. TOI-1266 was observed on 12 November 2019 with theadaptive-optics-assisted ShARCS camera (McGurk et al. 2014;Gavel et al. 2014) on the Shane 3-m telescope at Lick Observa-tory. We collected observations in both the K s and J filters withexposure times of 6 s and 12 s, respectively. Observations wereperformed with a four-point dither pattern, with the distance be-tween subsequent exposures being 4.00 (cid:48)(cid:48) on a side.We reduced our data with SImMER (Savel, Hirsch et al., inprep), an open-source,
Python -based pipeline . Prior to align-ing images, the pipeline implements standard dark-subtractionand flat-fielding. To align our science images for each target, weadapted methods from Morzinski et al. (2015), performing ro-tations about points within a search radius and minimising thesummed residuals from the original image. To determine oursensitivity to undetected stellar companions to TOI-1266, wecalculated the minimum detectable companion brightness at in-creasing angular separations from the target. We performed thisstep by constructing concentric annuli centred on TOI-1266 anddetermining the mean and standard deviation of the flux within https://github.com/jlillo/astrasens https://github.com/arjunsavel/SImMER Article number, page 4 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266 . . . . . . C o n t r a s t ( m a g )
10% cont.5% cont.2% cont. TOI-1266 (AstraLux - SDSSz)
Angular separation (arcsec) C o n t r a s t ( m a g ) TOI-1266 (ShARCS K s )TOI-1266 (ShARCS J ) Fig. 2.
Contrast curves for TOI-1266 resulting from high-angular res-olution imaging.
Top: σ contrast curve of the AstraLux image andcontamination levels (horizontal dotted lines) obtained in SDSS z filter. Bottom: σ contrast curves computed from ShARCS images of TOI-1266 taken in the K s (solid line) and J (dashed line) filters. each annulus (e.g. Marois et al. 2006, Nielsen et al. 2008, Jansonet al. 2011, Wang et al. 2015). We subsequently took our con-trast curve to be 5 σ above the mean. Through this method, wefind that we are sensitive in the K S band to companions 4 mag-nitudes fainter than the host beyond a separation of 0.51 (cid:48)(cid:48) andcompanions 8 magnitudes fainter than the host beyond a separa-tion of 1.67 (cid:48)(cid:48) . The full contrast curves are shown in Figure 2.
3. Stellar characterisation
We used the TRES spectra to derive initial stellar param-eters employing the method described in Maldonado et al.(2015). Briefly, the e ff ective temperature, spectral type and ironabundance were computed from the measurements of pseudo-equivalent widths of several spectral features. This analysisyields T e ff = ±
100 K, spectral type M3, and [ Fe / H ] = − . ± .
18 dex. We also used the derived temperature andmetallicity as inputs in the empirical relations by Maldonadoet al. (2015) to derive the stellar mass ( M (cid:63) = . ± . M (cid:12) ),the radius ( R (cid:63) = . ± . R (cid:12) ), and the surface gravity (log g = . ± .
10 dex).
We analysed the HIRES spectrum with SpecMatch-Empirical(Yee et al. 2017), which classifies stars by comparing their op-tical spectra to a library of spectra of well-characterised stars.With this technique, we recovered T e ff = ±
70 K, [Fe / H] = − . ± .
09 dex, and R (cid:63) = . ± . R (cid:12) , confirming the dwarf nature of the host star. Using the spectrum, we also ruledout double-lined spectroscopic binaries with contamination ra-tios down to 1% (Kolbl et al. 2014), greatly constraining the pa-rameter space within which false positive scenarios can exist. As an independent check on the derived stellar parameters, weperformed an analysis of the broadband spectral energy distri-bution (SED) together with the
Gaia
DR2 parallax in order todetermine an empirical measurement of the stellar radius, fol-lowing the procedures described in Stassun & Torres (2016);Stassun et al. (2017, 2018). We obtained the
BVgri magnitudesfrom APASS, the
JHK S magnitudes from , the W1–W4 magnitudes from WISE , and the GG BP G RP magnitudes from Gaia (see Table 2). In addition, we obtained the NUV flux from
GALEX in order to assess the level of chromospheric activity,if any. Together, the available photometry spans the full stellarSED over the wavelength range 0.2–22 µ m (see Figure 3).We performed a fit using NextGen stellar atmosphere mod-els (Hauschildt et al. 1999), with the fitted parameters being thee ff ective temperature ( T e ff ) and metallicity ([Fe / H]). We set theextinction ( A V ) to zero due to the star being nearby. We usedthe T e ff from the TIC (Stassun et al. 2018) as an initial guess.The broadband SED is largely insensitive to the surface grav-ity (log g ), thus we simply adopted the value from the TIC. Theresulting fit is satisfactory (Figure 3) with a reduced χ of 1.9.The best-fit parameters are T e ff = ±
150 K and [Fe / H] = − . ± . F bol = . ± . × − erg s − cm − . Taking the F bol and T e ff together with the Gaia
DR2 parallax, adjusted by + .
08 mas to account for the system-atic o ff set reported by Stassun & Torres (2018), gives the stellarradius as R = . ± .
037 R (cid:12) . Finally, estimating the stellarmass from the empirical relations of Mann et al. (2019) gives M = . ± . M (cid:12) , which with the empirical radius measure-ment gives the mean stellar density as ρ (cid:63) = . ± . − .In a separate global fit, we used the EXOFASTv2 analy-sis package (Eastman et al. 2019) to derive the stellar parame-ters. EXOFASTv2 simultaneously utilises the SED, MIST stel-lar models (Dotter 2016; Choi et al. 2016), Gaia
DR2 parallaxand enforces an upper limit on the extinction of A V = . T e ff and [Fe / H] from the spectral anal-ysis, presented in Section 3.1. The resulting EXOFASTv2 fit pro-vides values for T e ff = ± R = . ± . R (cid:12) , and M = . ± . M (cid:12) .In Table 3, we present a summary of the values of the stellarparameters obtained from the di ff erent instruments and methodspreviously described. We also added stellar properties derived inthis work. We adopt the mass and metallicity values from theSED + Mann analysis as priors in our global analysis, because itassumes only a simple Gaussian prior on the
Gaia parallax, andthus, is completely empirical.Additionally, using the radial velocity determined from theHIRES data ( − ± − ), and the proper motion andparallax from Gaia
DR2, we derived Galactic space-velocitycomponents (U, V, W) = (3.99 ± − ± − ± − , following the procedure detailed in Jofré et al.(2015). From the space-velocity components and the member-ship formulation by Reddy et al. (2006), we find that TOI-1266 https://github.com/jdeast/EXOFASTv2 Article number, page 5 of 22 & A proofs: manuscript no. TOI1266 λ ( μ m)-14-13-12-11-10 l og λ F λ ( e r g s - c m - ) Fig. 3. Spectral energy distribution (SED) of TOI-1266.
Red symbolsrepresent the observed photometric measurements, where the horizontalbars represent the e ff ective width of the passband. Blue symbols are themodel fluxes from the best-fit NextGen atmosphere model (black). has a probability of ∼
96% of belonging to the thin disc popula-tion.
We first searched for signs of stellar variability in the TESSPDC-SAP data from Sect. 2.1, as one might expect given theprevalence of activity in M dwarfs (e.g. Newton et al. 2016,2018). We performed a visual inspection of the light curve andfound no hints of rotational modulation nor evidence of flaringactivity. We then used the tools provided by the
Lightkurve
Python package (Lightkurve Collaboration et al. 2018) to com-pute the Lomb-Scargle periodogram (Scargle 1982) for all thephotometric data and for the data of each sector, without detect-ing any significant peak that might indicate periodic variabil-ity. To check that the variability was not removed by the PDCpipeline, we also performed an independent data reduction fromthe TESS Target Pixel Files (TPFs). We used a circular aperture,tracking the star on each image, and we stitched the observa-tions from sectors 14, 15, 21 and 22 together to produce a newlightcurve. We computed a Lomb-Scargle periodogram, and weadditionally fit a Gaussian process model with a quasi-periodickernel (see e.g. Aigrain et al. 2016). We did not find any peri-odic variation consistent with stellar variability, however. Thiscould result from a rotation period much longer than the 120 dayobservation period, or a small spot coverage.Within the total ∼
120 days of TESS observations across allfour sectors, we did not observe any flares from the star, con-sistent with an inactive early M dwarf (Hawley et al. 2014).We note that the radius and inferred mass are compatible withan uninflated early M-dwarf, and the NUV photometry is con-sistent with an unspotted photosphere and negligible chromo-spheric activity. In summary, TOI-1266 appears to be an old,inactive, slightly metal-poor early M dwarf.
4. Target vetting tests
As a first step in the false-positive vetting, we closely examinedthe data validation (DV) report (Twicken et al. 2018; Li et al. Parameter Value Source T e ff / K ±
70 HIRES ± SED + Mann3533 ±
45 EXOFASTv23570 ±
100 TRES[Fe / H] -0.24 ± -0.5 ± SED + Mann-0.03 ± M ∗ / M (cid:12) ± Mann0.447 ± ± R ∗ / R (cid:12) ± ± + Mann0.428 ± ± ± This worklog g / dex 4.85 ± + Mann4.826 ± ± ± This work ρ ∗ / g cm − ± + Mann8 . + . − . EXOFASTv2 ± This workSpectral Type M3 TRES F bol / erg s − cm − (6 . ± . × − SED + Mann
Table 3.
Stellar Characterisation. SED + Mann use the empirical rela-tions of Mann et al. (2019). Parameters in bold are the adopted stellarvalues. We use the SED + Mann mass and metallicity as priors in ourglobal analysis presented in Sect. 5.1.2, where we also derive the otherparameters that appear in bold. ff erenceimage centroid test to ensure that the source of the transit occurson the target star, as well as, a ‘ghost diagnostic test’ to discardscattered light as a source for the observed signal. These conclu-sive tests encouraged us to conduct further analysis to validateboth planet candidates. In the context of the TESS Follow-up Observing Program, weused SAINT-EX to perform observations of the transit of eachplanet to eliminate possible contamination from nearby starsincluded in the large TESS aperture. We identified five suchsources located between 36 and 132 (cid:48)(cid:48) from TOI-1266 within the
Gaia
DR2 catalogue (Brown et al. 2018), with measured deltamagnitudes ranging between 4.6 and 7.1 in the z (cid:48) band. Us-ing AstroImageJ (Collins et al. 2017), we estimated that eclipsedepths between 0.064 and 0.2 occurring on these stars would Article number, page 6 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266 be necessary to create the 0.0015 deep transit observed on TOI-1266 for the c planet candidate. Visual inspection of the lightcurves did not show transit signatures with the predicted depthson the nearby stars but revealed a 0.0015 deep transit on thetarget star as expected. We repeated the same analysis for thedeeper transit of the b planet candidate, and confirmed boththe lack of deep transits on the other stars and the detection ofa ∼ Gaia
DR2 sources. We also detected no wave-length dependence of the transit depths between the TESS, z (cid:48) , r (cid:48) , I C , and V bandpasses (see Sect. 5.1.2). Archival images are useful for investigating the background con-tamination of stars with non-negligible proper motion (PM),such as TOI-1266. None of the blue and red POSS1 images from1953 at the current target location show the presence of a sourcethat would be blended with the target at the epoch of the TESSobservations (Fig. 4). TOI-1266’s PM, combined with the mod-erate spatial resolution of ground-based all-sky surveys, does notallow us to constrain background sources from more recent op-tical imagery such as POSS2, Pan-STARRS and SDSS.
As an additional vetting step, we calculated the false positiveprobabilities of these TOIs using triceratops (Tool for Rat-ing Interesting Candidate Exoplanets and Reliability Analysis ofTransits Originating from Proximate Stars; Giacalone & Dress-ing 2020a,b) and vespa (Validation of Exoplanet Signals usinga Probabilistic Algorithm; Morton 2012, 2015). To tighten theconstraints we obtain from these calculations, we incorporatedthe contrast curves obtained from our high-resolution AO imag-ing. With triceratops , we compute false positive probabili-ties of 0.00310 and 0.08287 for TOI-1266.01 and TOI-1266.02,respectively, and with vespa , we compute false positive proba-bilities of 0.00002 and 0.00993, respectively. Because this is amulti-planet system, we were able to apply additional priors tothese probabilities using the results of Lissauer et al. (2012). Thisstudy uses data from the
Kepler mission to estimate the fractionof planet candidates that are false positives when in systems withmultiple planet candidates. This is done by assuming that the ex-pected number of targets with k false positives, E ( k ), is given bythe Poisson distribution E ( k ) = λ k e − λ k ! N ≈ ( R FP nN ) k k ! N , (1)where R FP is the false positive rate, n is the number of planetcandidates, and N is the number of targets from which the sam-ple is drawn. The sample used in Lissauer et al. (2012) contained n =
230 planet candidates in candidate two-planet systems from N = R FP = .
5. Thus, the ex-pected number of candidate two-planet systems in which both Discrepancies in these false positive probabilities are due to di ff er-ences in the calculations performed by the two tools. At the time ofthis writing, triceratops estimated probability using maximum like-lihood estimation, while vespa determines probability by calculatingmarginal likelihoods. In addition, triceratops considers more falsepositive scenarios in its procedure. Regardless, both tools require a falsepositive probability < .
05 to validate a planet candidate. planet candidates are false positives is E ( k = ≈ − R FP ) nN × E ( k = ≈
2. Therefore, the prior probability that a planet candidate ina candidate two-planet system is a false positive is (1 + / ≈ .
01 (see also Guerrero et al., submitted). Multiplying the prob-abilities above by this prior, we find a false positive probability < .
01 for both TOIs using both triceratops and vespa .These probabilities are su ffi ciently low to rule out astro-physical false positives originating from both resolved nearbystars, and unresolved stars blended within the photometric aper-ture. In conclusion, the combination of TESS photometry, high-resolution spectroscopy, high-precision ground-based photome-try, and archival imagery enable us to rule out false-positive sce-narios for the observed transit signals of TOI-1266 b and c. Thanks to our data, we can place some limited constraints on thepresence of a binary companion. Our high-resolution imaging inFig. 2 limits any object with a ∆ m > z -band at a distance > . (cid:48)(cid:48) (corresponding to a semi-major axis of 7.2 au, and or-bital period of 25 years). Using the Bara ff e et al. (2015) models,and assuming a system age of 5 Gyr, we can exclude any binarycompanion with a mass > .
10 M (cid:12) . Using the K -band obser-vations, we can exclude the presence of any Hydrogen-burningobject beyond 1 (cid:48)(cid:48) ( > .
07 M (cid:12) ).Inside of 7.2 au, we have to rely on spectroscopy to placeany constraints. A companion could in principle be detected asan extra set of lines, which requires two conditions: it is brightenough, and its orbital velocity is distinct enough from the TOI-1266 A, the primary star. Our HIRES spectrum reached a S / N of80. Using models from Bara ff e et al. (2015) once more, stellarcompanions with masses > .
15 M (cid:12) could be detectable withS / N =
5. The velocity resolution of HIRES is ∼ − . Allcompanions with orbital velocity <
12 km s − would see theirabsorption lines blending with the primary’s for the majority oftheir orbital motion, meaning they would likely remain unno-ticed. An orbital velocity di ff erence of >
12 km s − , correspondsto orbital separations of < . ∼ . .
15 M (cid:12) , and sin i = < . > .
05 M (cid:12) , eccentricities of 0.3, and orbital periodsof 1000 years ( ∼
82 au), would induce cycles in the eccentricityof TOI-1266 c, on timescales much shorter than the age of thesystem (21 Myr for the parameters we quote), but only if thatcompanion has an orbital inclination between 40 and 140 ◦ .In summary, we can exclude detecting the presence withinthe data of most stellar companions, except at orbital separa-tions between 3.8 and 7.2 au. However, we cannot exclude anycompanion should that object be within the line of sight (i.e.high-angular resolution imaging does not detect it, and with arelative radial velocity near 0 km / s). Radial velocities would notdetect face-on orbits, however those are ruled out using dynami-cal arguments. Article number, page 7 of 22 & A proofs: manuscript no. TOI1266
POSS I Blue: 1953 ′′ POSS II Blue: 1993 ′ Pan − STARRS i: 2012 ′ TESS Sector 14: 2019 ′ Fig. 4.
Archival images of TOI-1266 to assess for current, unresolved blending. POSS I (1953), II (1993) and Pan-STARRS (2012) archivalimages around TOI-1266 with TESS field of view for sectors 14, 15, 21 and 22 superimposed. The red cross marks TOI-1266’s location at the2020 epoch.
5. Results
As mentioned previously, TOI-1266 was observed by TESSin sectors 14, 15, 21 and 22. The TESS Science O ffi ce is-sued two alerts for this object based on SPOC DV reports;TOI 1266.01 and TOI 1266.02 correspond to planetary candi-dates with periods of 10.8 d and 18.8 d respectively. We per-formed our own search for candidates using the SHERLOCK ( S earching for H ints of E xoplanets f R om L ightcurves O fspa C e-based see K ers) pipeline presented in Pozuelos et al.(2020). This pipeline makes use of the Lightkurve package(Lightkurve Collaboration et al. 2018), which downloads thePDC-SAP flux data from the
NASA
Mikulski Archive for SpaceTelescope (MAST), and removes outliers defined as data points > σ above the running mean. In order to remove stellar noiseand instrumental drifts, our pipeline uses wotan (Hippke et al.2019) with two di ff erent detrending methods: bi-weight andGaussian process with a Matérn 3 / ffi ciency(SDE) of the transit search, which was performed by means ofthe transit least squares package (Hippke & Heller 2019). The transit least squares uses an analytical transit model basedon the stellar parameters, and is optimised for the detectionof shallow periodic transits. We properly recovered the twoaforementioned candidates, where the best systematics modelcorresponded to the bi-weight method with a window-size of0.4149 d. In addition to these two signals, we found a threshold-crossing event with a period of 12.5 d. However, after an in-depth vetting process (Heller et al. 2019), we discarded this sig-nal, which we attributed to systematics in the data set. We showin Fig. 5 the PDC-SAP flux, the best systematics model, and thefinal detrended lightcurve with the two planet candidates.In order to assess the detectability of other planets in the dataset available from TESS, we performed an injection-recoverytest, where we injected synthetic planetary signals into the PDC-SAP fluxes corresponding to planets with di ff erent radii and pe-riods. We then detrended the lightcurve using the best methodfound previously that is the bi-weight approach with a windowsize of 0.4149 d. Before searching for planets, we masked thetwo known candidate planets with periods of 10.8 d and 18.8 d. SHERLOCK code is available upon request.
We explored the R planet – P planet parameter space in the ranges of0.8–3.0 R ⊕ with steps of 0.05 R ⊕ , and 1–30 d with steps of 1 d,for a total of 1305 di ff erent scenarios. In this test, we definedan injected signal as being recovered when a detected epochmatched the injected epoch within one hour, and if a detectedperiod matched any half-multiple of the injected period to bet-ter than 5%. It is important to note that since we injected thesynthetic signals directly in the PDC-SAP lightcurve, they werenot a ff ected by the PDC-SAP systematic corrections. Therefore,the detection limits found correspond to the most optimistic sce-nario (see e.g. Pozuelos et al. 2020; Eisner et al. 2020). The re-sults are shown in Fig. 6, and we reached several conclusionsfrom this test: (1) We can rule out the presence of planets withsizes larger than ∼ ⊕ with orbits shorter than 10 d. However,such planets might reside in orbits with longer periods and, thus,remain undetected, as a longer period yields a lower detectabil-ity. In fact, for periods greater than 10 d, we obtained a recoveryrate ranging from 30 to 70 %. (2) For the full set of investigatedperiods, planets with sizes smaller than 1.5 R ⊕ would remain un-detected, with recovery rates lower than 30%, and close to 0%for 1.0 R ⊕ . We used the full photometric dataset described in Sect. 2 alongwith the transit signals detected in the previous step as input pa-rameters to a global analysis of the TOI-1266 system. We alsoincluded the stellar mass and e ff ective temperature derived inSect. 3 as Gaussian priors to convert the transit fitted parametersinto physical values.We used the MCMC algorithm implementation already pre-sented in the literature (e.g. Gillon et al. 2012; Demory et al.2012; Gillon et al. 2014). The inputs to the MCMC are the pho-tometric time-series obtained during the data reduction describedabove. For each light curve, we fit simultaneously for the instru-ment baseline model and a transit model of two Keplerian orbitscorresponding to TOI-1266 b and c. This approach ensures thatinstrumental systematic noise is properly propagated to the sys-tem parameters of interest. The photometric baseline model co-e ffi cients used for detrending for each instrument are determinedat each step of the MCMC procedure using a singular valuedecomposition method (Press et al. 1992). The resulting coef-ficients are then used to correct the raw photometric lightcurves.Such an approach is necessary because the input data originatefrom multiple instruments with di ff erent sources of systematics.We show in Table 4 the baseline model used for each light curve. Article number, page 8 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266
Fig. 5.
TESS data of TOI-1266 from the four sectors in which it was observed. In all cases, the black line corresponds to the PDC-SAP fluxesobtained from SPOC pipeline, the solid-orange line corresponds to the best-detrended model, and the teal line is the final detrended lightcurve.The red dtriangles mark the 10.8 d period planetary candidate, while the blue triangles mark the 18.8 d candidate.
Fig. 6.
Injection-and-recovery test performed to check the detectabilityof extra planets in the system. We explored a total of 1305 di ff erent sce-narios. Larger recovery rates are presented in green and yellow colours,while lower recovery rates are shown in blue and darker hues. Planetssmaller than 1.5 R ⊕ would remain undetected for almost the full set ofperiods explored. To derive accurate uncertainties on the system parameters, wecomputed two scaling factors, β w and β r , following Winn et al.(2008), to account for over- or under-estimated white noise andcorrelated noise (Pont et al. 2006) in each dataset (these valuesare computed over 10 to 240-min timescales).We computed the quadratic limb-darkening (LD) coe ffi cients u and u in the TESS , z (cid:48) , r (cid:48) , I C , and Johnson V filters, usingthe PyLDTk code (Parviainen & Aigrain 2015) and a libraryof PHOENIX high-resolution synthetic spectra (Husser et al.2013). We placed Gaussian priors on each of the quadratic LD parameters, with a 5-fold inflation of the uncertainties computedfrom model interpolation. All LD parameters used in this analy-sis are shown in Table 5. For each of the two planets, we fitted for(1) the transit depth (planet-to-star area ratio) R P R (cid:63) for each instru-ment to assess transit depth chromaticity, (2) the transit duration T , (3) the orbital period P , (4) the transit centre T , and (5) theimpact parameter b = a cos iR (cid:63) , where a is the orbital semi-majoraxis and i the orbital inclination. For this MCMC fit, we assumedcircular orbits, and fixed √ e cos ω and √ e sin ω values to 0. Weran two chains of 100 000 steps (including 20% burn-in) each,and checked their e ffi cient mixing and convergence by visuallyinspecting the autocorrelation functions of each chain, and byusing the Gelman & Rubin (1992) statistical test, ensuring thatthe test values for all fitted parameters were < . σ credible intervalsof the system parameter’s posterior distribution functions. Thecorresponding light curves for both planets are shown in Fig. 7,8, 9, and 10.Our analysis shows a good agreement between the combinedstellar density value of ρ (cid:63) = . ± .
25 g cm − derived from thephotometry alone, and (1) the ρ (cid:63) = . ± . − derived fromthe SED + Mann analysis, as well as, (2) the ρ (cid:63) = . + . − . g cm − derived from the EXOFASTv2 analysis described in Sect. 3. Thetransit depths measured in four di ff erent bandpasses (TESS, z (cid:48) , r (cid:48) , and V ) for TOI-1266 b are all in agreement at the ∼ σ level.We find a good agreement as well for the transit depth of TOI-1266 c albeit with only two bandpasses ( TESS and z (cid:48) ). We alsorepeated the same MCMC analysis, this time allowing √ e cos ω and √ e sin ω to vary, but did not find evidence for eccentric or-bits for any of TOI-1266 b and c, using transit photometry alone. Article number, page 9 of 22 & A proofs: manuscript no. TOI1266
Planet Facility T0 [
BJD
TDB ] Baseline model functional form Residual RMS (exp. time) β w β r b TESS 8691.0063 flux o ff set 0.00165 (120 s) 0.44 1.188701.9011 flux o ff set 0.00186 (120 s) 0.50 1.108712.7959 flux o ff set 0.00176 (120 s) 0.81 1.168723.6907 flux o ff set 0.00173 (120 s) 0.68 1.538734.5855 flux o ff set 0.00190 (120 s) 0.84 1.118876.2179 flux o ff set 0.00188 (120 s) 0.91 1.008887.1127 flux o ff set 0.00174 (120 s) 0.84 1.228908.9023 flux o ff set 0.00178 (120 s) 0.78 1.188919.7971 flux o ff set 0.00180 (120 s) 0.79 1.08OAA 8843.5335 flux o ff set + airmass ff set + airmass + FWHM ff set + airmass + FWHM ff set + airmass + FWHM ff set + airmass + FWHM ff set + airmass + airmass ff set 0.00189 (120 s) 0.51 1.048708.7625 0.00190 (120 s) 0.49 1.008727.5638 0.00185 (120 s) 0.77 1.338877.9741 0.00174 (120 s) 0.84 1.008896.7754 0.00180 (120 s) 0.87 1.00SAINT-EX 8877.9741 flux o ff set + airmass + FWHM Table 4.
Baseline model functional forms, residual RMS, and scaling factors of each transit light curve used in the photometric global analysis.For each baseline, a polynomial is used with the indicated variables as parameters.
Filter u u Notes
TESS . ± .
09 0 . ± .
10 used as well for Kotizarovci z (cid:48) . ± .
08 0 . ± . r (cid:48) . ± .
10 0 . ± . V . ± .
10 0 . ± . Ic . ± .
09 0 . ± . . ± .
09 0 . ± .
09 ZRO, QE >
50% between 480 and 800 nm
Table 5.
Quadratic limb-darkening coe ffi cients used in the photometric global analysis for each instrument. -0.10 -0.05 0.00 0.05 0.10T-T0 [days]0.9940.9960.9981.0001.0021.0041.006 R e l a t i v e F l u x -0.10 -0.05 0.00 0.05 0.10T-T0 [days]0.9940.9960.9981.0001.0021.0041.006 R e l a t i v e F l u x Fig. 7.
TESS phase-folded transits of TOI-1266 b (left) and TOI-1266 c (right) from the global analysis. Grey circles are un-binned data pointswhile 15-min bins are shown as black circles. The best-fit model is shown in red.Article number, page 10 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266
Parameter TOI-1266 b TOI-1266 cTransit fitted parameters
Transit depth, ( R p / R (cid:63) ) . + . − . . ± . T (days) 0 . + . − . . + . − . Impact parameter, b . ± .
12 0 . + . − . Mid-transit time, T (BJD TDB ) 2458821 . + . − . . + . − . Orbital period, P (days) 10 . + . − . . + . − . Tr. depth di ff ., δ TESS − SAINT − EX , z (cid:48) . + . − . . ± . ff ., δ TESS − TRAPPIST − N , z (cid:48) . + . − . Tr. depth di ff ., δ TESS − TRAPPIST − N , V . + . − . Tr. depth di ff ., δ TESS − ARTEMIS , r (cid:48) . ± . ff ., δ TESS − OAA , Ic − . + . − . Tr. depth di ff ., δ TESS − ZRO , clear . + . − . Tr. depth di ff ., δ TESS − Kotizarovci , TESSband . + . − . Physical and orbital parameters
Planet radius, R p (R ⊕ ) 2 . + . − . . + . − . Semi-major axis, a p (au) 0 . + . − . . + . − . Orbital inclination, i p (deg) 89 . + . − . . + . − . Irradiation, S p ( S ⊕ ) 4 . + . − . . + . − . Equilibrium temperature, T eq (K) 413 ±
20 344 ± M p (M ⊕ ) 13 . + . − . ( < . σ ) 2 . + . − . ( < . σ )Orbital eccentricity (TTV), e . + . − . ( < .
21 at 2- σ ) 0 . ± .
03 ( < .
10 at 2- σ ) Table 6.
Global model fitted results along with mass and eccentricity estimates from the TTV analysis (see Sect. 5.2.1). For each parameter, weindicate the median of the posterior distribution function, along with the 1- σ credible intervals. The equilibrium temperature corresponds to a casewith null Bond albedo and no heat recirculation from the day side to the nightside hemispheres of the planet. R e l a t i v e F l u x R e l a t i v e F l u x Fig. 8.
SAINT-EX detrended transits of TOI-1266 b (left) and TOI-1266 c (right) from the global analysis, both observed in z (cid:48) . Grey circles areun-binned data points while 15-min bins are shown as black circles. The best-fit model is shown in red. As the system is within 6% of the second order 5:3 mean motionresonance (MMR) and within 14% of the stronger first order 2:1MMR, we attempt to constrain planet masses from the transittiming variations (Agol et al. 2005; Holman 2005; Agol & Fab- rycky 2017) measured in our combined photometric dataset. Wehave in total 13 transits of planet b and five transits of planet c(Table 7). We computed TTVs using a similar MCMC setup asin Sect. 5.1.2, but allowing each transit timing to vary, using thesame tests as the ones described in Sect. 5.1.2 to ensure that thechains have converged. We derived posterior distribution func-tions for each transit timing that we use for our TTV analysis
Article number, page 11 of 22 & A proofs: manuscript no. TOI1266 R e l a t i v e F l u x R e l a t i v e F l u x R e l a t i v e F l u x Fig. 9.
Single, detrended transits of TOI-1266 b obtained with TRAPPIST-N in z (cid:48) (left), V (centre), and with ARTEMIS in r (cid:48) (right) from theglobal analysis. Grey circles are un-binned data points while 15-min bins are shown as black circles. The best-fit model is shown in red. R e l a t i v e F l u x R e l a t i v e F l u x R e l a t i v e F l u x Fig. 10.
Single, detrended transits of TOI-1266 b obtained with OAA (left), Kotizarovci (centre), and with ZRO (right) from the global analysis.Grey circles are un-binned data points while 15-min bins are shown as black circles. The best-fit model is shown in red. described in this section. While our observations provide onlya partial sampling of the TTV libration periods (Ste ff en 2006;Lithwick et al. 2012) of ∼
106 and 68 days for the 5:3 and 2:1MMR respectively, we can still place upper limits on the massescomputed from N-body simulations.We used the integrator GENGA (Gravitational Encountersin N-body simulations with Graphics processing unit Accelera-tion) (Grimm & Stadel 2014) together with a di ff erential evolu-tion Markov chain Monte Carlo (DEMCMC) method (Ter Braak2006; Vrugt et al. 2009), as described in Grimm et al. (2018),to perform a TTV analysis of the transit timings reported in Ta-ble 7. The TTV signal is shown in Figure 11 together with 1000samples from the MCMC calculations. We find planetary massesof M p = . + . − . M ⊕ ( < . ⊕ at 2- σ ) for TOI-1266 b, and2 . + . − . M ⊕ ( < . ⊕ at 2- σ ) for TOI-1266 c. We constrain theorbital eccentricities to 0 . + . − . ( < .
21 at 2- σ ) for TOI-1266 b,and 0 . ± .
03 ( < .
10 at 2- σ ) for TOI-1266 c. The posteriordistributions of the derived masses and eccentricities are shownin Figure 12. We note that the arguments of periastron remainunconstrained. A visual inspection of Fig. 11 shows that the li-bration period favoured by the fit is ∼
70 days, which suggeststhat the system dynamics are more influenced by the 2:1 MMRthan the 5:3 MMR. The small number of TOI-1266 c transitscombined with their shallow depth causes the derived mass forTOI-1266 b to be less constrained by the data. During our explo-ration of the parameter space, we found another, lower statisticalsignificance solution, yielding a similar mass for c but highermass and smaller eccentricity for b. Further high-precision tran-sits are, thus, required to improve these preliminary mass andeccentricity constraints. It is also worth mentioning that the ex-pected radial-velocity semi-amplitude of approximately 4 m / s Fig. 11.
TTV signal of the two planets. In green are shown the observedtransit times with the corresponding uncertainties, in black are shownthe transit times from 1000 random MCMC samples. would enable mass measurements of TOI-1266 b with Dopplerspectroscopy, thus, complementing the TTV technique for theinnermost planet.
With the current set of data, we found as a likely planetary ar-chitecture a system composed by two eccentric planets: a moremassive inner planet, TOI-1266 b, at 0.0736 au, and a lighter
Article number, page 12 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266
Predicted timing Observed di ff erence SourceBJD TDB -2450000 days
TOI-1266 b − . + . − . TESS8701.90112 − . + . − . TESS8712.79593 − . + . − . TESS8723.69073 0 . + . − . TESS8734.58553 0 . + . − . TESS8843.53357 0 . + . − . OAA8876.21798 0 . + . − . TESS8887.11278 0 . + . − . TESS8908.90239 − . + . − . TESS + SAINT-EX8919.79719 0 . + . − . TESS8930.69199 0 . + . − . ARTEMIS + TRAPPIST-N8941.58680 0 . + . − . TRAPPIST-N8963.37640 0 . + . − . Kotizarovci + ZRO
TOI-1266 c . + . − . TESS8708.76250 − . + . − . TESS8727.56379 0 . + . − . TESS8877.97410 0 . + . − . TESS + SAINT-EX8896.77539 0 . + . − . TESS
Table 7.
Transit timings used in the TTV analysis. one, TOI-1266 c, at 0.1058 au. Unfortunately, due to the largeuncertainties in their masses, the nature of these planets remainsunknown (see Table 6). In this section, we seek to constrain themasses and eccentricities of the planets by exploring the globalstability of the system. To achieve this, we made use of the MeanExponential Growth factor of Nearby Orbits, Y ( t ) (MEGNO;Cincotta & Simó 1999, 2000; Cincotta et al. 2003) parameter.This chaos index has been widely used to explore the stabil-ity of both the Solar System, and extrasolar planetary systems(e.g. Jenkins et al. 2009; Hinse et al. 2015; Wood et al. 2017;Horner et al. 2019). In short, MEGNO evaluates the stability ofa body’s trajectory after a small perturbation of its initial con-ditions through its time-averaged mean value, (cid:104) Y ( t ) (cid:105) , which am-plifies any stochastic behaviour, thereby allowing one to distin-guish between chaotic and quasi-periodic trajectories during theintegration time: if (cid:104) Y ( t ) (cid:105) → t → ∞ , the motion is quasi-periodic; while if (cid:104) Y ( t ) (cid:105) → ∞ for t → ∞ , the system is chaotic.To investigate this, we used the MEGNO implementation with anN-body integrator rebound (Rein & Liu 2012), which employsthe Wisdom-Holman WHfast code (Rein & Tamayo 2015).We performed two suites of simulations to explore if the sys-tem could actually be fully stable in the range of the 2- σ un-certainties obtained for the masses and the eccentricities (seeSection 5.2.1). To address this question, we constructed two-dimensional MEGNO-maps in the M b – M c and e b – e c parame-ter spaces following Jenkins et al. (2019). Hence, in the firstcase, we explored planet masses ranging from 1 to 37 M ⊕ forTOI-1266 b, and from 1 to 6 M ⊕ for TOI-1266 c. In the sec-ond case, we explored planet eccentricities in the ranges of0.0–0.21 and 0.0–0.1 for TOI-1266 b and TOI-1266 c, respec- tively. In both sets of simulations, we took 100 values from eachrange, meaning that the size of the obtained MEGNO-maps were100 ×
100 pixels. Thus, we explored the M b – M c and e b – e c param-eter spaces up to 10,000 times in total. In each case, we fixed theother parameters to the nominal values given in Table 6. The in-tegration time was set to 1 million orbits of the outermost planet,and the time-step was set to 5% of the orbital period of the inner-most planet. We found that, concerning the masses, the system isfully stable in the range of values studied here; hence we cannotset extra constraints on the planetary masses. On the other hand,we found that the full set of eccentricities explored is not permit-ted, and we identified regions with di ff erent behaviours wherethe system transitions from stable to unstable gradually towardsthe upper-right region of the e b – e c parameter space (see Fig. 13).This allowed us to clearly identify three di ff erent regions (A, B,and C). First, where the system is fully stable (A), and where themutual eccentricities follow the relationship given by: e b + . e c < . . (2)Then, the second is a transitional region where the system isstill stable, but some instabilities appear (B). This region spansfrom the limit given by Eq. 2, and the upper limit given by: (cid:40) e b < .
140 if e c < . , e b + . e c < .
17 if e c > . . (3)Finally, region C, where the aforementioned relationships areviolated, and instability is more likely. We found that the nom-inal values are stable in the transition region of the parameterspace (i.e. region B), which may hint that these values could be Article number, page 13 of 22 & A proofs: manuscript no. TOI1266
Fig. 12.
Posterior distribution for TOI-1266 b and c masses (left), and eccentricities (right) from the TTV analysis. The histograms show themedian (dashed lines) and the 1- σ credible intervals (solid lines). We show in blue the posterior distributions with the 1- and 2- σ contour lines. more appropriately considered as upper limits to stability, wherelarger values would rapidly turn into unstable scenarios. Thisencouraged us to favour the hypothesis of low eccentricities forboth planets in terms of long-term stability, with the most re-strictive condition given by Eq. 2. Hereafter, for our dynamicalpurposes, we have adopted the nominal planetary masses andeccentricities given in Table 6, which, as we demonstrated, arestable and, in the case of the eccentricities, may represent a real-istic upper limits of their real values.Using the stellar parameters given in Table 2, the plane-tary parameters provided in Table 6, and the derived planetarymasses described above, we conducted a dynamical analysis ofthe system with the goal of testing for the potential existenceof additional planets, especially in the region where the TESSphotometry is not accurate enough to detect them, as the casefor planets smaller than 1.5 R ⊕ with periods longer than 4 days(see Fig. 6). For this purpose, we used the mercury IntegratorPackage (Chambers 1999) to perform the N-body integrations.The adopted methodology is similar to that used by Kane (2015,2019), where a grid of initial conditions is used to explore thevalid parameter space for possible additional planets within thesystem. The innermost planet has an orbital period of ∼ years, equivalent to 2 × orbits of the outer planet, demonstrated the intrinsic stability ofthe system described in Table 6. We then inserted an Earth-massplanet in a circular orbit at several hundred locations within thesemi-major axis range of 0.05–0.20 au to test for possible loca-tions of additional planets within the system. These simulationswere executed for 10 years each, and the results were evaluatedbased on the survival of all planets. Non-survival means that oneor more of the planets were ejected from the system or lost tothe potential well of the host star. The results of this simulationare shown in Fig. 14, where the semi-major axis (bottom) andorbital period (top) are shown on the x -axis, and the percentageof the simulation time during which all three planets survived Fig. 13.
Dynamical analysis of the TOI-1266 system based on aMEGNO-map. The size of the map is 100 ×
100 pixels, which exploresthe e b – e c parameter space at the 2- σ uncertainty level. When (cid:104) Y ( t ) (cid:105) → (cid:104) Y ( t ) (cid:105) → e b and e c is shown by the bluemarker, while the 1- σ uncertainty region is shown by the red box. Thethree areas, A (stable region), B (transition region), and C (unstable re-gion) have been labelled, and are delimited by the solid black lines,which represent the conditions given by Eqs. 2 and 3. is shown on the y -axis. These results show that the semi-majoraxis range of 0.058–0.138 au is a largely unstable region where,given an additional planet, it is highly unlikely that orbital in-tegrity of the system may be retained. However, outside of thisrange, the viability of orbits is rapidly regained and so there ispotential for numerous other locations where additional transit- Article number, page 14 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266
Fig. 14.
Survival rate of an additional Earth-mass planet in the TOI-1266 system. The results of a dynamical stability analysis that placedan Earth-mass within the system in the semi-major axis range of 0.05–0.20 au and evaluated the overall system stability for a period of 10 years (see description in Section 5.2.2). These results demonstrate thatthere are few viable orbits allowed in the range 0.064–0.131 au, butthat additional terrestrial planets may exist in the system outside of thatrange. ing or non-transiting planets may contribute to the overall systemarchitecture. TOI-1266 b and TOI-1266 c are close-in exoplanets, which, dueto their proximity to their host star, may be a ff ected by tides.While the size and maximum mass face values of TOI-1266 cpoint to a terrestrial composition, the large uncertainty in themass of TOI-1266 b prevents us from making any definitive as-sertions regarding its nature. Therefore, in this section we onlyfocus on the tidal evolution of TOI-1266 c. To quantify the influ-ence of tides on this planet, we made use of the constant time-lag model (CTL), where a planet is considered as a weakly vis-cous fluid that is deformed due to gravitational e ff ects (see e.g.Mignard 1979; Hut 1981; Eggleton et al. 1998; Leconte et al.2010). Tides a ff ect each orbital parameter over a di ff erent time-scale: the obliquity and rotational period are the first to be al-tered, while the eccentricity and the semi-major axis are a ff ectedover longer periods of time (see e.g. Bolmont et al. 2014; Barnes2017). To study the e ff ects of tides, we made use of posidonius (Blanco-Cuaresma & Bolmont 2017). The main free parametersthat define the tidal dissipation of a given planet are the degree-2potential Love number k and its constant time lag ∆ τ , wherek can have values between 0 and 1.5, and ∆ τ can span ordersof magnitudes (Barnes 2017). Observations have revealed thatthe Earth’s dissipation is completely dominated by the frictioninduced by its topography on tidal gravito-inertial waves thatpropagate in the oceans (Mathis 2018). Therefore, when explor-ing terrestrial exoplanets under the influence of tides, the Earth’sreference value k , ⊕ ∆ τ ⊕ =
213 s (Neron de Surgy & Laskar 1997)is commonly adopted. Typically, 0.1 × k , ⊕ ∆ τ ⊕ is used for plan-ets without oceans, and 10 × k , ⊕ ∆ τ ⊕ for volatile-rich planets (seee.g. Bolmont et al. 2014, 2015). This strategy allowed us to iden-tify a range of possible tidal behaviours.For a close-in exoplanet, it is expected that tidal torques fixthe rotation rate to a specific frequency, in a process called tidal Fig. 15.
Obliquity and rotational period evolution due to the e ff ectsof tides for planet TOI-1266 c for the case of 1 × k , ⊕ ∆ τ ⊕ . Each set ofline-style curves represents a di ff erent initial spin-rate, and each set ofcoloured curves represents a di ff erent initial obliquity. It is seems thatfor any possible combination of the initial conditions, within only ashort time scale (compared with the age of the star), the planet is tidallylocked. locking. A tidally-locked planet in a circular orbit will rotate syn-chronously, and the same side of the planet will always face thestar. On the other hand, for a fluid planet, the rotation is pseu-dosynchronous, which means that its rotation tends to be as fastas the angular velocity at periapse (hence, the same side does notalways face the star). Planets that are solid, like Mercury, can belocked because of a permanent deformation into a specific reso-nance (see e.g. Bolmont et al. 2015; Hut 1981; Barnes 2017).To ascertain which of these scenarios applies to TOI-1266 c,we followed the aforementioned strategy: we studied the evolu-tion of the obliquity ( (cid:15) ) and rotational period (P rot ) by consider-ing a number of cases with: di ff erent initial planetary rotationalperiods of 10 hr, 100 hr, and 1000 hr, combined with obliquitiesof 15 ◦ , 45 ◦ , and 75 ◦ , for the three cases concerning tidal dissipa-tion: (0.1, 1, and 10) × k , ⊕ ∆ τ ⊕ .We found that in all cases, the planet is tidally locked rapidly:10 yr for 0.1 × k , ⊕ ∆ τ ⊕ , 10 yr for 1 × k , ⊕ ∆ τ ⊕ , and 10 yr for10 × k , ⊕ ∆ τ ⊕ . The results for the particular case of 1 × k , ⊕ ∆ τ ⊕ aredisplayed in Fig. 15. We note that the presence of a relativelylarge moon orbiting the planet may provoke chaotic fluctuationsof its obliquity, or even impart it with another value (see e.g.Laskar & Robutel 1993; Lissauer et al. 2012). However, it hasbeen found that compact planetary systems are unlikely to havemoons (Lissauer & Cuzzi 1985; Kane 2017), which encouragesus to tentatively consider that TOI-1266 c is tidally locked andfairly well aligned with the host star.Circularisation of the orbits due to the e ff ects of tides is aslow process, which may last from hundreds to billion years (seee.g. Bolmont et al. 2015; Barnes 2017; Pozuelos et al. 2020). In Mercury’s case, it’s the 3:2, and because of Mercury’s large e, thatis near pseudosynchronous, but if Mercury had a smaller e, it could havegotten trapped into synchronous orbit. Article number, page 15 of 22 & A proofs: manuscript no. TOI1266
From our results of the global model, we found that the planetTOI-1266 c may have a certain level of eccentricity with a me-dian value of 0.04. This may be provoked by the lack of timeto circularise the orbit by tides (which is not explored in thisstudy) or due to the architecture of the system, where the planetsare close to the 5:3 and 2:1 MMRs, which can excite the orbitsand consequently induce a marginal level of eccentricity. Hence,both planets might be experiencing some level of tidal heating.In this context, we computed for TOI-1266 c the tidal heatingfor the nominal eccentricity of 0.04 for (0.1, 1, and 10) × k , ⊕ ∆ τ ⊕ configurations. We found that the planet is heated by 0.5 W m − for 10 × k , ⊕ ∆ τ ⊕ , 0.05 W m − for 1 × k , ⊕ ∆ τ ⊕ , and 0.005 W m − for 0.1 × k , ⊕ ∆ τ ⊕ .Taken together, our results suggest that it is likely thatthe outermost planet TOI-1266 c is tidally locked, but due toits small but non-zero eccentricity, which may persist throughMMR excitations, it may not have the same side always facingthe star. In a recent paper by Pozuelos et al. (2020), the authorsadapted the general description of the flux received by a planetgiven by Kane & Torres (2017) for the configuration found here,for a tidally-locked planet on a non-circular orbit. It was foundthat in such a configuration, the orbital phase is no longer rel-evant, and the distribution of flux along the latitude ( β ) is thesame for the whole orbit, which depends only on the planet’s ec-centricity. In our case, assuming the nominal value of eccentric-ity found in our models (i.e. 0.04) we found 3805–3242 W m − (2.79–2.37 F ⊕ ) at the equator, 2691–2293 W m − (1.97–1.68 F ⊕ )at β = ± ◦ , and ∼ − (0.0 F ⊕ ) at the poles. These valuessuggest that the stellar flux received by the planet may vary by ∼
15% along its orbit. Based on dynamical arguments, this vari-ation of ∼
15% may be considered as an upper limit. Indeed, wedemonstrated that the nominal values of the eccentricities mightbe considered as upper limits, where the system tends to morestable scenarios for low eccentricities (see Fig. 13). At the 1- σ uncertainty level, the minimum eccentricity of TOI-1266 c is0.01. In such a case, the variation of the flux along the orbit isonly ∼
6. Discussion
In this section, we use the mass and radii constraints on TOI-1266 b and c derived from the transit photometry to investi-gate the location of these planets in the mass-radius diagram.We emphasise that the mass constraints will be improved onceadditional transit timings, or precise radial-velocity timeseriesbecome available. However, Figure 16 provides a first assess-ment on whether the derived planet properties are consistent withusual mass-radius relationships. In this figure, the compositioncurves were calculated with model B of Michel et al. (2020). Weused for iron the equation of state of Hakim et al. (2018), forrock the model of Sotin et al. (2007) and for water the equationof state of Mazevet et al. (2019).
With radii of about 2.4 and 1.6 R ⊕ , TOI-1266 b and c span theso-called radius valley (Fulton et al. 2017). Since atmosphericevaporation is a possible explanation for the origin of the valley(Owen & Wu 2013; Lopez & Fortney 2013a; Jin et al. 2014),this feature is also known as the ‘evaporation valley’. We note,however, that the origin for the radius valley feature is currently unconstrained and that other studies advocate, for instance, forcore-powered mass loss as the driving mechanism for this pattern(Ginzburg et al. 2018; Gupta & Schlichting 2020). The recentdiscovery of a change in the fraction of planets above and belowthe valley over ∼ Gyr timescales has indeed been interpreted infavour of the core-powered mass loss scenario for some solar-type stars (Berger et al. 2020), although there is evidence that theformation pathway may be di ff erent in low-mass stars (Cloutier& Menou 2020).Planets in multiple systems with dissimilar radii, like TOI-1266 b & c, Kepler-36 b & c (Carter et al. 2012) or TOI-402 b& c (Dumusque et al. 2019), are of particular interest to un-derstand the origin of the radius valley, as they allow to studythe di ff erential evolutionary history of the planets, and to checkwhether evaporation can self-consistently explain all the planetsin a system (Lopez et al. 2012; Lopez & Fortney 2013b; Owen& Campos Estrada 2020).To understand the implication of the hypothesis that evap-oration has shaped the distinct radii of TOI-1266 b & c, wesimulated their long-term thermodynamical evolution (cooling,contraction, atmospheric escape) with the Bern evolution model completo21 (Mordasini et al. 2012; Jin et al. 2014; Jin & Mor-dasini 2018).The model simulates the long-term evolution of the planetsafter the dissipation of the protoplanetary disc by solving the in-ternal structure equations of the planets. It includes XUV-drivenatmospheric photoevaporation in the radiation-recombinationand energy-limited regimes (Murray-Clay et al. 2009).The planets consist of a solid core and a H / He envelope, andwe assumed that their cores have an Earth-like 2:1 silicate:ironcomposition described by the polytropic equation of state (EOS)of Seager et al. (2007).The gaseous envelope consists of H / He, described by theEOS of Saumon et al. (1995), and the opacity corresponds toa condensate-free solar-composition gas (Freedman et al. 2014).As in Mordasini (2020), we simulated the evolution of 6 000planets on a grid of semi-major axis and mass. The initial con-ditions (i.e. the post-formation envelope — core mass ratio andluminosity) are the same as in the nominal case considered inMordasini (2020), but the stellar mass is now 0.5 M (cid:12) . The stellarXUV luminosity as a function of time was taken from McDonaldet al. (2019).Figure 17 shows the result in the plane of orbital distanceversus planet radius at an age of 10 Gyr, where the evapora-tion valley is apparent. Planets above this threshold retain someH / He, while those below become bare rocky cores. In the topleft corner, the region devoid of planets corresponds to the sub-Neptunian desert (Lundkvist et al. 2016; Mazeh et al. 2016;Bourrier et al. 2018).TOI-1266 b & c are also shown as black squares. Planet b islocated clearly above the valley, while planet c’s median radiussits just underneath. This position corresponds to the most mas-sive (and largest) cores at a given semi-major axis that have losttheir H / He.The interesting property of TOI-1266 is that the inner planetis larger than the outer one. In the context of evaporation, thiscan be explained if the inner planet is also more massive thanthe outer one. The higher mass allows for the planet to keep itsH / He envelope even at a higher XUV flux. We thus studied themasses of model planets that are compatible with TOI-1266 b& c in terms of orbital distance and radius in Figure 17, andfind that these model planets have masses of about 10 ± . M ⊕ for planet b, and 6 + − M ⊕ for planet c, which is consistent withthe masses derived using our TTV measurements (Sect. 5.2.1). Article number, page 16 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266
Mass [M E ] R a d i u s [ R E ] % H O % F e + % R o c k1 6 % F e + % R o c k + % H O % F e VE U N
TOI-1266 bTOI-1266 c
VenusEarthUranusNeptune
Fig. 16.
TOI-1266 b and c on the mass-radius diagram based on the radii and masses derived from the transit photometry and TTV analyses.Alongside, we show mass radius curves for pure iron (brown), an earth like composition of 32% iron, and 68% rock (red), a mixture of 50% waterwith an earth like core (grey blue), and for pure water (blue). The data of the background planets were taken from the NASA Exoplanet Archive(retrieved on 2020 July 15). We show only those planets that have a relative mass and radius uncertainty of less than 20%.
These specific numbers depend on model assumptions, such asthe core and envelope composition, the initial conditions, or theevaporation model. But the general result, namely that the innerplanet should be more massive, is robust.We note that Figure 17 has been obtained with an evapora-tion model that assumes a constant evaporation e ffi ciency in theenergy limited domain. It is known (Owen & Wu 2017) that thisyields a steeper slope (R vs a) for the evaporation valley than theone found in models which calculate the evaporation e ffi ciencyself-consistently (Owen & Jackson 2012).This shallower slope is also in better agreement with ob-servations (Mordasini 2020). This a ff ects the prediction for themass ratios of the two planets; in particular, a shallow slopemeans that the two masses can be more similar than estimatedabove. If we assume that the slope of the valley is instead thesame as the slope observed for FGK stars (Van Eylen et al. 2018;Cloutier & Menou 2020), and not the one predicted in the model,then we can estimate that the inner planet must have a mass thatis at least 25% higher than the mass of the outer planet (Mor-dasini 2020). Then, the inner planet can keep some H / He.
The potential for atmospheric characterisation of an exoplane-tary system relates directly to the size and brightness of the host:the smaller and brighter the host, the larger the signal in trans- R [ R e ] a [AU] 0 5 10 15 20 25 M a ss [ M e ] Fig. 17.
Comparison of TOI-1266 b & c with evaporation models. Thecoloured dots show the position in the plane of semi-major axis versusradius of simulated planets evolving under the e ff ect of cooling, contrac-tion, and atmospheric escape around a 0.5 M (cid:12) star at an age of 10 Gyr.One sees the radius valley and the sub-Neptunian desert. The coloursshow the planet mass. Black symbols show TOI-1266 b & c. mission and photon count (i.e. S / N), all other parameters be-ing equal. TOI-1266’s relatively small size and proximity makes
Article number, page 17 of 22 & A proofs: manuscript no. TOI1266 it a remarkably good host for the atmospheric study of super-Earth-sized and larger planets. In order to quantify and contex-tualise its prospect for atmospheric study, we followed the sameapproach as in Gillon et al. (2016), focusing here on temper-ate sub-Neptune-sized planets following the NASA ExoplanetArchive . Figure 18 reports the planets’ signal in transmission,which we derive as follows: S = R p h e ff R ∗ , with h e ff = kT µ g , (4)where R p is the planetary radius, R ∗ is the stellar radius, h e ff is thee ff ective atmospheric height, µ is the atmospheric mean molec-ular mass, T is the atmospheric temperature, and g is the localgravity. We assume h e ff to cover seven atmospheric scale heights,assuming atmospheres down to ∼ R ⊕ , which we model as sub-Neptunes, and 20 amu forthe smaller planets, which we model as terrestrial. We assumethe atmospheric temperature to be the equilibrium temperaturefor a Bond albedo of 0. For the planets with missing masses,we estimated g using the statistical model from Chen & Kipping(2017).TOI-1266 b and c’s projected signals in transmission are ∼
220 and ∼
100 ppm, which are significantly above
JWST ’s plau-sible noise floor level (20–50 ppm; Greene et al. 2016). In orderto quantify this further, we also report in Figure 18 a relativeS / N scaling the signal amplitude with the hosts’ brightness in theJ band and using TRAPPIST-1 b’s S / N as a reference. We findthat TOI-1266’s planets compare favourably to TRAPPIST-1bin terms of potential for atmospheric exploration. In fact, assess-ing the presence of a clear hydrogen-dominated atmosphere asassumed for the purpose of this discussion would require 1 and4 transits for planet b and c, respectively, with JWST NIRSpecPrism mode.However, this preliminary assessment could be complicatedby at least two factors. A first obstacle of transmission spec-troscopy is refraction, which bends starlight away from the lineof the sight to the observer. In a transmission spectrum, thishas a similar e ff ect to an opaque cloud with a ‘cloud-top pres-sure’ (Sidis & Sari 2010), which introduces a spectral contin-uum that mutes the strength of spectral features. To determineif this e ff ect is significant, we use equation (14) and Table 1of Robinson et al. (2017) to estimate the pressure correspond-ing to this refraction continuum. For nitrogen-dominated atmo-spheres, we estimate this pressure to be 1.3 and 0.8 bar for TOI-1266 b and TOI-1266 c, respectively, if we assume g ∼ cms − and T ∼ T eq . For carbon dioxide-dominated atmospheres,we estimate this pressure to be 0.7 and 0.4 bar for TOI-1266 band TOI-1266 c, respectively. Since transmission spectroscopyprobes pressures ∼ ff ect on the shape of the transmis-sion spectra for TOI-1266 b and TOI-1266 c. Given the low equi-librium temperatures, a second obstacle may be the presence ofclouds or hazes that are likely to strongly shape the transmissionspectra of these weakly-irradiated exoplanets (see e.g. Crossfield& Kreidberg 2017, and references therein).We finally note that the planets of TOI-1266 are attractivetargets for transmission spectroscopy due to the small geomet-ric size of and lack of activity of the host star. More active M https: // exoplanetarchive.ipac.caltech.edu dwarfs like TRAPPIST-1 pose significant challenges to transmis-sion spectroscopy, since the stellar surface features emit di ff er-ent spectra from the mean photosphere, introducing a degeneratesignal that one must disentangle to correctly identify the signalfrom the exoplanet atmosphere (Morris et al. 2018b,c,a; Ducrotet al. 2018; Wakeford et al. 2019). TOI-1266 has no photometricevidence of these confounding starspot signatures, and therefore,makes a clean case for transmission spectroscopy. Radial velocities (RVs) are likely to become available for thistarget in the future. It is critical to obtain precise masses and thusbulk densities for planets with sub-Neptune radii to identify ifthey are evaporated giants or giant rocks, so that we may identifymodel atmospheres to apply to the transmission spectroscopy.This requirement for a reliable mass constraint will be one ofthe fundamental limitations in choosing sub-Neptune targets forobservations with JWST (Batalha et al. 2017). For this system,we might have some certainty about whether or not these areevaporated giants, which will strengthen our interpretations ofthe transmission spectra.In addition, we might we be able to measure the Rossiter-McLaughlin e ff ect for this system, due to its brightness andlack of confounding stellar activity. The obliquity of the systemwould be a valuable addition to the recent observation by Hiranoet al. (2020) that the TRAPPIST-1 planets are well-aligned withthe host star’s spin.We finally note that as of writing, TOI-1266 will not be ob-served by TESS during Sectors 23-26 nor during Extended Mis-sion 1.
7. Conclusions
This study reports on the discovery and preliminary characterisa-tion of the TOI-1266 system that hosts a super-Earth and a sub-Neptune around a M3 dwarf. Our analysis combines photometryobtained from space- and ground-based facilities with a care-ful treatment of instrumental systematics and correlated noisefor each dataset. The resulting data enable us to compute pre-liminary mass measurements for both planets, investigate theirtidal evolution and search for additional companions in the sys-tem. Along with other recently discovered TESS exoplanets (e.g.Cloutier et al. 2020; Cloutier & Menou 2020), TOI-1266 willlikely become a key system to better understand the nature ofthe radius valley around early to mid-M dwarfs. First, its or-bital architecture, influenced by the 2:1 mean-motion resonance,will facilitate the measurement of precise planetary masses withhigh-precision photometry (TTV) and Doppler spectroscopy (ra-dial velocities). Second, the host brightness is such that the sys-tem will be observable in most JWST modes, hence providinga large wavelength coverage. Third, the outer planet TOI-1266 chas an irradiation level that is similar to that of Venus and isalso a favourable target for atmospheric characterisation. Wealso note that TOI-1266 c may be tidally-locked but with a non-circular orbit, resulting in incident stellar flux varying at a fewpercent level only along its orbit. Such a configuration wouldalso lead to more homogeneous longitudinal temperature di ff er-ences, in stark contrast with the bulk of small transiting exoplan-ets discovered so far. Acknowledgements.
We warmly thank the entire technical sta ff of the Observa-torio Astronómico Nacional at San Pedro Mártir in México for their unfailing Article number, page 18 of 22emory et al.: A super-Earth and a sub-Neptune orbiting the M3V TOI-1266
150 200 250 300 350 400
Equilibrium Temperature (K) E x p ec t e d T r a n s m i ss i o n S i gn a l ( pp m ) Kepler-62 f Kepler-62 eKepler-150 fKepler-186 f Kepler-296 eKepler-1652 b Kepler-438 bKepler-436 bKepler-1653 b Kepler-69 cKepler-1649 bKepler-441 b K2-72 eKepler-61 b EPIC 212737443 cK2-3 d Kepler-446 dK2-72 cKepler-445 dKepler-22 b Kepler-437 b K2-118 bKepler-296 f K2-72 dK2-239 dKepler-296 d K2-239 cK2-264 c EPIC 211822797 bK2-152 bK2-286 bTRAPPIST-1 gTRAPPIST-1 h TRAPPIST-1 f L 98-59 dTRAPPIST-1 e Kepler-445 cK2-18 bK2-288 B b K2-3 cTRAPPIST-1 d TRAPPIST-1 c LTT 1445 A bTOI-270 d GJ 143 bLP 791-18 cLHS 1140 b R ⊕ R ⊕ TRAPPIST-1 b
TOI-1266 c TOI-1266 b − . − . − . . . L o g o f R e l a t i v e S / N Fig. 18.
Most promising sub-Neptune-sized planets for atmospheric characterisation. Point colours illustrate the S / N of a
JWST / NIRSPEC ob-servation relative to TRAPPIST-1 b. S / N below 1 / JWST within ∼ JWST ’s threshold of ∼
50 ppm. The size of the circle is proportional to the size of the planet. support to SAINT-EX operations, namely: U. Ceseña, A. Córdova, B. García,C.A. Guerrero, F. Guillén, J.A. Hernández, B. Hernández, E. López, B. Martínez,G. Melgoza, F. Montalvo, S. Monrroy, J.C. Narvaez, J.M. Nuñez, J.L. Ochoa,I. Plauchú, F. Quiroz, H. Serrano, T. Verdugo. We gratefully acknowledge thesupport from the Embassy of Mexico in Bern to the SAINT-EX project. Wealso thank the past members of the SAINT-EX team B. Courcol, E. Rose andK. Housen for their help in the course of the project. We are grateful to theanonymous referee for a thorough and helpful review of our paper. We thankJonathan Irwin for his help on the TRES data analysis. B.-O.D. acknowledgessupport from the Swiss National Science Foundation (PP00P2-163967). Thiswork has been carried out within the frame of the National Centre for Compe-tence in Research PlanetS supported by the Swiss National Science Foundation.Y.G.M.C acknowledges support from UNAM-PAPIIT IN-107518. R.P. and E.J.acknowledge DGAPA for their postdoctoral fellowships. The research leading tothese results has received funding from the ARC grant for Concerted ResearchActions, financed by the Wallonia-Brussels Federation. TRAPPIST is fundedby the Belgian Fund for Scientific Research (Fonds National de la RechercheScientifique, FNRS) under the grant FRFC 2.5.594.09.F, with the participationof the Swiss National Science Fundation (SNF). TRAPPIST-North is a projectfunded by the University of Liege, and performed in collaboration with CadiAyyad University of Marrakesh. MG and EJ are F.R.S.-FNRS Senior ResearchAssociates. J.C.S. acknowledges funding support from Spanish public funds forresearch under projects ESP2017-87676-2-2 and RYC-2012-09913 (Ramón yCajal programme) of the Spanish Ministry of Science and Education. This paperincludes data collected by the TESS mission. We acknowledge the use of publicTOI Release data from pipelines at the TESS Science O ffi ce and at the TESS Sci-ence Processing Operations Center. Funding for the TESS mission is provided bythe NASA Explorer Program. Resources supporting this work were provided bythe NASA High-End Computing (HEC) Program through the NASA AdvancedSupercomputing (NAS) Division at Ames Research Center for the productionof the SPOC data products. This work is based upon observations carried outat the Observatorio Astronómico Nacional on the Sierra de San Pedro Mártir (OAN-SPM), Baja California, México. This research has been partly funded bythe Spanish State Research Agency (AEI) Projects No.ESP2017-87676-C5-1-Rand No. MDM-2017-0737 Unidad de Excelencia "María de Maeztu"- Centrode Astrobiología (INTA-CSIC). This paper is based on observations collectedat Centro Astronómico Hispano en Andalucía (CAHA) at Calar Alto, operatedjointly by Instituto de Astrofísica de Andalucía (CSIC) and Junta de Andalucía.The research leading to these results has received funding from the EuropeanResearch Council under the European Union’s Seventh Framework Programme(FP / o Antoine de Saint-Exupéry Youth Foundation through their involvementin the educational programme of the SAINT-EX Observatory.
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Postal 877, 22800, Ensenada, B.C., México Universidad Nacional de Córdoba - Observatorio Astronómico deCórdoba, Laprida 854, X5000BGR, Córdoba, Argentina Consejo Nacional de Investigaciones Científicas y Técnicas (CON-ICET), Argentina Department of Physics, University of Warwick, Gibbet Hill Road,Coventry CV4 7AL, UK Centre for Exoplanets and Habitability, University of Warwick, Gib-bet Hill Road, Coventry CV4 7AL, UK Oukaimeden Observatory, High Energy Physics and AstrophysicsLaboratory, Cadi Ayyad University, Marrakech, Morocco Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street,Cambridge, MA, 02138, USA Observatoire astronomique de l’Université de Genève, 51 chemindes Maillettes, 1290 Versoix, Switzerland Department of Earth, Atmospheric and Planetary Sciences, Mas-sachusetts Institute of Technology, Cambridge, MA 02139, USA Instituto de Astrofísica de Canarias, Vía Láctea s / n, 38205 La La-guna, Tenerife, Spain Department of Astronomy, 501 Campbell Hall, University of Cali-fornia at Berkeley, Berkeley, CA 94720, USA Observatori Astronòmic Albanyà, Camí de Bassegoda S / N, Albanyà17733, Girona, Spain Department of Earth and Planetary Sciences, University of Califor-nia, Riverside, CA 92521, USA Centro de Astrobiología (CAB, CSIC-INTA), Dpto. de Astrofísica,ESAC campus 28692 Villanueva de la Cañada (Madrid), Spain Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6,CH 3012 Bern, Switzerland Cavendish Laboratory, J.J. 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