A planetary system with two transiting mini-Neptunes near the radius valley transition around the bright M dwarf TOI-776
R. Luque, L. M. Serrano, K. Molaverdikhani, M. C. Nixon, J. H. Livingston, E. W. Guenther, E. Pallé, N. Madhusudhan, G. Nowak, J. Korth, W. D. Cochran, T. Hirano, P. Chaturvedi, E. Goffo, S. Albrecht, O. Barragán, C Briceño, J. Cabrera, D. Charbonneau, R. Cloutier, K. A. Collins, K. I. Collins, K. D. Colón, I. J. M. Crossfield, Sz. Csizmadia, F. Dai, H. J. Deeg, M. Esposito, M. Fridlund, D. Gandolfi, I. Georgieva, A. Glidden, R. F. Goeke, S. Grziwa, A. P. Hatzes, C. E. Henze, S. B. Howell, J. Irwin, J. M. Jenkins, E. L. N. Jensen, P. Kábath, R. C. Kidwell Jr., J. F. Kielkopf, E. Knudstrup, K. W. F. Lam, D. W. Latham, J. J. Lissauer, A. W. Mann, E. C. Matthews, I. Mireles, N. Narita, M. Paegert, C. M. Persson, S. Redfield, G. R. Ricker, F. Rodler, J. E. Schlieder, N. J. Scott, S. Seager, J. Šubjak, T. G. Tan, E. B. Ting, R. Vanderspek, V. Van Eylen, J. N. Winn, C. Ziegler
AAstronomy & Astrophysics manuscript no. main © ESO 2020December 1, 2020
A planetary system with two transiting mini-Neptunes near theradius valley transition around the bright M dwarf TOI-776 (cid:63)
R. Luque , , L. M. Serrano , K. Molaverdikhani , , M. C. Nixon , J. H. Livingston , E. W. Guenther , E. Pallé , ,N. Madhusudhan , G. Nowak , , J. Korth , W. D. Cochran , T. Hirano , P. Chaturvedi , E. Go ff o , S. Albrecht ,O. Barragán , C Briceño , J. Cabrera , D. Charbonneau , R. Cloutier , K. A. Collins , K. I. Collins ,K. D. Colón , I. J. M. Crossfield , Sz. Csizmadia , F. Dai , H. J. Deeg , , M. Esposito , M. Fridlund , ,D. Gandolfi , I. Georgieva , A. Glidden , , R. F. Goeke , S. Grziwa , A. P. Hatzes , C. E. Henze , S. B. Howell ,J. Irwin , J. M. Jenkins , E. L. N. Jensen , P. Kábath , R. C. Kidwell Jr. , J. F. Kielkopf , E. Knudstrup ,K. W. F. Lam , D. W. Latham , J. J. Lissauer , A. W. Mann , E. C. Matthews , I. Mireles , N. Narita , , , ,M. Paegert , C. M. Persson , S. Redfield , G. R. Ricker , F. Rodler , J. E. Schlieder , N. J. Scott ,S. Seager , , , J. Šubjak , T. G. Tan , E. B. Ting , R. Vanderspek , V. Van Eylen , J. N. Winn , and C. Ziegler (A ffi liations can be found after the references) Received 17.09.2020 / Accepted 30.11.2020
ABSTRACT
We report the discovery and characterization of two transiting planets around the bright M1 V star LP 961-53 (TOI-776, J = . M = . ± . M (cid:12) ) detected during Sector 10 observations of the Transiting Exoplanet Survey Satellite ( TESS ). Combining the
TESS photometry withHARPS radial velocities, as well as ground-based follow-up transit observations from MEarth and LCOGT telescopes, we measured for the innerplanet, TOI-776 b, a period of P b = .
25 d, a radius of R b = . ± . R ⊕ , and a mass of M b = . ± . M ⊕ ; and for the outer planet, TOI-776 c,a period of P c = .
66 d, a radius of R c = . ± . R ⊕ , and a mass of M c = . ± . M ⊕ . The Doppler data shows one additional signal,with a period of ∼
34 d, associated with the rotational period of the star. The analysis of fifteen years of ground-based photometric monitoringdata and the inspection of di ff erent spectral line indicators confirm this assumption. The bulk densities of TOI-776 b and c allow for a wide rangeof possible interior and atmospheric compositions. However, both planets have retained a significant atmosphere, with slightly di ff erent envelopemass fractions. Thanks to their location near the radius gap for M dwarfs, we can start to explore the mechanism(s) responsible for the radius valleyemergence around low-mass stars as compared to solar-like stars. While a larger sample of well-characterized planets in this parameter space isstill needed to draw firm conclusions, we tentatively estimate that the stellar mass below which thermally-driven mass loss is no longer the mainformation pathway for sculpting the radius valley is between 0.63 and 0.54 M (cid:12) . Due to the brightness of the star, the TOI-776 system is also anexcellent target for the James Webb Space Telescope, providing a remarkable laboratory to break the degeneracy in planetary interior models andto test formation and evolution theories of small planets around low-mass stars. Key words. planetary systems – techniques: photometric – techniques: radial velocities – stars: individual: LP 961-53 – stars: low-mass
1. Introduction
Exoplanets with masses between those of Earth and Uranus arecharacterized by a broad range of measured bulk densities (e.g.,Hatzes & Rauer 2015). A low density suggests the presence of anextended H / He-envelope around a solid core. On the contrary, ifthe density is high, the exoplanet is considered to be fully rockyor enriched in light elements (e.g., water, methane, ammonia).In a nutshell, the absence of an envelope might be the result oftwo opposite scenarios: the planet is born without it or the planetloses it over time. In the first case, the planet forms in a gas-poor inner proto-planetary disk without a thick H / He-envelope(e.g., Lee et al. 2014; Lee & Chiang 2016). For the second casedi ff erent mechanisms have been proposed in the last years, suchas slow atmospheric escape powered by the planetary core’s pri-mordial energy reservoir from formation (Ginzburg et al. 2018;Gupta & Schlichting 2019, 2020), impact erosion by planetesi-mals (Shuvalov 2009; Schlichting et al. 2015; Wyatt et al. 2020),or erosion processes driven by the stellar X-ray + EUV (XUV)- (cid:63)
Based on observations made with ESO Telescopes at the La SillaObservatory under programs ID 1102.C-0923 and 60.A-9709. radiation (e.g., Murray-Clay et al. 2009; Lammer et al. 2012;Owen & Jackson 2012; Owen & Wu 2013; Kislyakova et al.2013, 2014; Lopez & Fortney 2014; Jin et al. 2014; Chen &Rogers 2016; Osborn et al. 2017; Jin & Mordasini 2018; Lopez& Rice 2018; Wu 2019; Mordasini 2020).For the latter, the erosion rate becomes faster if the plane-tary surface gravity decreases and the amount of XUV-radiationthat the planet receives increases. In addition, the intensity ofXUV-radiation depends on the orbital semi-major axis and onthe stellar activity level. The XUV-radiation is particularly highat young ages and then it declines as a result of age, mass andstellar rotation (Walter et al. 1988; Briceno et al. 1997; Tu et al.2015). A star that begins its life rapidly rotating will su ff er amore rapid decline in rotation than a star that was initially a slowrotator. Thus, for a several Gyr old star, understanding its orig-inal activity level is challenging. The presence, or absence, of ahydrogen-rich envelope in a system containing just one planetcan thus be equally explained by assuming that the host star waseither a slow or rapid rotator when it was young. Systems con-taining more than one planet are necessary to test the theory ofatmospheric erosion, because the origin of all the planets of a Article number, page 1 of 26 a r X i v : . [ a s t r o - ph . E P ] N ov & A proofs: manuscript no. main system should be explained with a unique evolutionary historyof the host’s XUV-radiation (Owen & Campos Estrada 2020).On the other hand, the amount of XUV-radiation also de-pends on the stellar type. The XUV luminosities of young G-and M-stars are similar to each other. The average X-ray lumi-nosity of G-stars is 10 erg s − , while in the case of M dwarfs,the 50 Myr stars in α -Per, for example, have luminosities of10 erg s − (France et al. 2016). The main di ff erence is that Mdwarfs remain in the high activity phase for up to 2 Gyr (John-stone et al. 2015), a much longer time compared to the 300 Myrof G-stars (Güdel et al. 2004). This makes M dwarfs preferredtargets to study planetary systems that have experienced signif-icant stellar XUV irradiation. Another advantage of M dwarfsis their small size, which makes it easier to detect smaller tran-siting planets. The paucity of close-in planets around mid-K tomid-M dwarfs between approximately 1.4 and 1 . R ⊕ (Cloutieret al. 2020), known as the radius valley, marks the transition be-tween rocky planets and sub-Neptunes orbiting low-mass stars.As such, M dwarfs multi-planetary systems which include sub-Neptunes and / or rocky planets represent an ideal benchmark fortesting the theory of atmospheric erosion.Gas-poor formation provides an alternative to explain the ab-sence of H / He envelopes in some low-mass planets, since theerosion scenario presents some issues. For instance, if a close-in 10 M ⊕ rocky planet forms while there is still a gaseous disk,its mass is high enough to undergo runaway accretion and be-come a Jupiter-type planet. The detection of close-in Jupiter-mass planets, at least in A-stars, shows that it is hard to re-construct a mechanism which transforms a Jupiter into a rockysuper-Earth since any working physical process should be ableto completely strip o ff the H / He atmosphere. On the other hand,stars hosting hot Jupiters have high metallicities, while rockyplanets are equally distributed between metal-poor and metal-rich stars (Winn et al. 2017). Thus, there are two alternative sce-narios within gas-poor formation models that could explain theexistence of rocky super-Earths. Either the dust-to-gas ratio ofthe inner disk is 20 times higher than solar, or the gas accretionis delayed until just before the disk disperses (Lee et al. 2014;Lee & Chiang 2016).Lopez & Rice (2018) proposed a statistical test that could al-low us to understand the most likely formation history for super-Earths. If a high percentage of rocky planets are the evaporatedcores of sub-Neptunes, the transition radius from rocky to sub-Neptune planets should decrease for longer orbital periods. Onthe contrary, if the gas-poor formation scenario is correct, thetransition radius should increase with orbital period. Anothermethodology to test the formation theory of super-Earths re-quires studying the position of the radius valley for stars withdi ff erent masses, thus of di ff erent stellar types. If the photo-evaporation scenario is correct, the radius valley shifts towardsplanets of smaller radii for stars of lower mass. If, on the con-trary, the gas-poor formation scenario is at work, the valley posi-tion is not a ff ected by the stellar mass (Cloutier & Menou 2020).However, since the radius valley represents the range of radiiin which the transition between rocky planets and sub-Neptunesoccurs, it is necessary to accurately determine the mass and ra-dius of the planets to calculate the mass-fraction of their en-velope and unveil their nature. Therefore, the ideal test to un-derstand which model is more realistic between the gas-poorformation and the photo-evaporation consists of measuring themasses and radii of the planets close to, or inside, the radiusvalley, preferably in a multi-planetary system around low-massstars. In this way, we can also constrain these models in a muchbetter way than through the radius distribution alone. As of today, there is a limited number of known multi-planetary systems which orbit M-dwarfs (3000 K < T e ff < M p < M ⊕ ) required to test the two men-tioned formation theories. There are only two systems with threetransiting planets with measured dynamical masses, Kepler-138(Almenara et al. 2018) and L 98-59 (Cloutier et al. 2019), andfour systems with two transiting planets: LHS 1140 (Lillo-Boxet al. 2020), LTT 3780 (Nowak et al. 2020; Cloutier et al. 2020),K2-146 (Lam et al. 2020; Hamann et al. 2019), and Kepler-26(Jontof-Hutter et al. 2016). This paucity of systems is inadequatefor understanding the formation and evolution of planetary sys-tems around M dwarfs. The discovery of each new system is thusimportant, especially if the host star is bright and the planets areclose to the radius valley.In this paper, we present the discovery of two transiting plan-ets orbiting an M1 V star. The inner one has a period of 8.2 dand a radius of ∼ . R ⊕ ; thus, it is close to the radius valley.The outer planet has a period of 15.7 d and a radius of 2 . R ⊕ ,in the sub-Neptune regime. By measuring their masses, we ex-plore whether these new planets are characterized by extendedH / He envelopes. Since they orbit a relatively bright, nearby Mdwarf, these new objects represent ideal targets for follow-up at-mospheric studies. TESS photometry
400 402 404 406 408 410
Pixel Column Number P i x e l R o w N u m b e r E N
TIC 306996324 - Sector 10 m = -2 m = 0 m = 2 m = 4 m = 6 m = 8 12 34 567 89 1011 1213 141516 1718 19202122 23 1.52.02.53.03.54.04.55.0 F l u x × ( e ) Fig. 1.
TESS target pixel file image of LP 961-53 in Sector 10 (createdwith tpfplotter , Aller et al. 2020). The electron counts are color-coded. The red bordered pixels are used in the simple aperture photom-etry. The size of the red circles indicates the
TESS magnitudes of allnearby stars and LP 961-53 (label × "). Positions are cor-rected for proper motions between Gaia
DR2 epoch (2015.5) and
TESS
Sector 10 epoch (2019.2). The
TESS pixel scale is approximately 21 (cid:48)(cid:48) . LP 961-53 (TIC 306996324) was observed with
TESS inSector 10 (Camera https://mast.stsci.edu Article number, page 2 of 26. Luque et al.: A multi-planetary system around TOI-776 R e l a t i v e f l u x R e s i d u a l s ( pp m ) Fig. 2.
TESS
PDC-corrected SAP transit photometry from SPOC pipeline with the best-fit juliet model (black line; see Sect. 5.2.1 for details onthe modeling). Purple and orange ticks above the light curve mark the transits of the candidates TOI–776.01 (purple) and TOI–732.02 (orange). on June 1, 2019. SPOC provided for this target simple aperturephotometry (SAP) and systematics-corrected photometry, a pro-cedure consisting of an adaptation of the Kepler Presearch DataConditioning algorithm (PDC, Smith et al. 2012; Stumpe et al.2012, 2014) to
TESS . Figure 1 shows the
TESS pixels includedin the computation of the SAP and PDC-corrected SAP data. Forthe remainder of this work we make use of the latter photometricdata, shown in Fig. 2.On June 11, 2019, two transiting candidates orbiting LP 961-53 were announced in the
TESS data public website underthe TESS
Object of Interest (TOI) number 776. TOI-776.01 isa planet candidate with a period of 15.65 d, a transit depth of1484 ±
127 ppm, and an estimated planet radius of 2 . ± . R ⊕ ;while TOI-776.02 is a planet candidate with a period of 8.24 d,a transit depth of 1063 ±
104 ppm, and an estimated planet ra-dius of 1 . ± . R ⊕ . Both candidates passed all the tests from theTCE (Threshold Crossing Event) Data Validation Report (DVR;Twicken et al. 2018; Li et al. 2019): even-odd transits compari-son, eclipsing binary (EB) discrimination tests, ghost diagnostictests to help rule out scattered light, or background EB, amongothers. However, the vetting team at the TESS
Science O ffi ceproposed the possibility that TOI-776.01 could be an EB, wherethe secondary transit is the primary transit of TOI-776.02 can-didate. The ground-based follow-up observations discussed inthe next Section refuted this scenario and confirmed the two an-nounced candidates as bona-fide planets.
3. Ground-based observations
We observed the TOI-776 candidates as part of the
TESS
Follow-up Observing Program (TFOP) . The goals of these ground-based photometric follow-up observations were to verify thatthe transits observed by TESS are on target, and to refine thetransit ephemeris and depth measurements. We used the
TESSTransit Finder , a customized version of the
Tapir software https://tev.mit.edu/data/ https://tess.mit.edu/followup package (Jensen 2013), to schedule photometric time-seriesfollow-up observations. We observed two transits of TOI-776.01and three transits of TOI-776.02, as summarized in Table 1 anddiscussed further below. A single transit of TOI-776.01 was observed with the 40 cmMEarth-South telescope array (Irwin et al. 2015) at Cerro TololoInter-American Observatory (CTIO), Chile on June 1, 2019.Seven telescopes observed continuously from evening twilightuntil the target star set below airmass 2, using an exposure timeof 10 s with all telescopes in focus. The target star was west ofthe meridian throughout the observation to avoid meridian flips.Data were reduced following the standard procedures in Ir-win et al. (2007) and Berta et al. (2012) with a photometricextraction aperture radius of r = (cid:48)(cid:48) on sky given thepixel scale of 0 (cid:48)(cid:48) .
84 pix − ). The light curve is shown in Fig. 3,lower right. Due to the large variation in airmass and relativelyred target star compared to the available field comparison stars,we found the light curve exhibited a small amount of resid-ual second-order (color-dependent) atmospheric extinction, sothe transit model was fitted including an extinction term (lineardecorrelation against airmass). One transit of TOI-776.01 and two transits of TOI-776.02 wereobserved with the 1.0 m telescopes in the Las Cumbres Ob-servatory (LCOGT) telescope network (Brown et al. 2013).The 4096 × (cid:48)(cid:48) .
389 pix − , resulting in a 26 (cid:48) × (cid:48) field ofview. The images were calibrated using the standard LCOGT BANZAI pipeline, and photometric data were extracted with
AstroImageJ (Collins et al. 2017).An ingress of TOI-776.01 was observed from the LCOGTnode at CTIO on July 1, 2019 in the i (cid:48) filter, simultaneous withthe MEarth-South observations mentioned above (Fig. 3, middleright). Transits of TOI-776.02 were observed from the LCOGT Article number, page 3 of 26 & A proofs: manuscript no. main
Table 1.
TESS Follow-up Program transit observations.
Observatory Date Filter Exposure Total Aperture Pixel scale FOV[UTC] [s] [h] [m] [arcsec] [arcmin]
TOI-776.01 = TOI-776 c
MEarth-South, CTIO, Chile Jul 1, 2019 RG715 10 4.2 7 × . × i (cid:48)
20 3.4 1.0 0.39 26 . × . TOI-776.02 = TOI-776 b
LCOGT, SAAO, South Africa Feb 29, 2020 z s
45 4.7 1.0 0.39 26 . × . z s
45 4.1 1.0 0.39 26 . × . R C
60 3.6 0.3 1.23 31 × z s filter, with the tele-scopes defocused. A full transit of TOI-776.02 was observed with the 30 cm PerthExoplanet Survey Telescope (PEST) on May 22, 2020. Thesedata have a scatter that is too large to reliably detect the transit.For this reason, we did not include them in the global fit. We compiled ground-based, long baseline photometric seriesfrom automated surveys. The following public surveys ob-served TOI-776: the All-Sky Automated Survey for Supernovae(ASAS-SN; Kochanek et al. 2017), All-Sky Automated Sur-vey (ASAS; Pojmanski 2002), Northern Sky Variability Survey(NSVS; Wo´zniak et al. 2004), and the Catalina surveys (Drakeet al. 2014). The telescope location, instrument configurations,and photometric bands of each public survey were summarizedin Table 1 of Díez Alonso et al. (2019). All together, the mea-surements span a period of 15 yr.Additionally, TOI-776 is a candidate of the Super-Wide An-gle Search for Planets (SuperWASP; Pollacco et al. 2006). Su-perWASP acquired more than 11 000 photometric observations,using a broad-band optical filter spanning three consecutive sea-sons from May to July 2006, January to June 2007, and Januaryto June 2008. In order to detect long-term photometric modula-tions associated with the stellar rotation, we binned the data intoone day intervals, resulting in 201 epochs.
The large pixel size of
TESS increase the possibility of contam-ination by nearby sources that are not detected in the seeing-limited photometry or in
Gaia
DR2. Close companions can di-lute the transit depth and thus alter the measured planet radius,or lead to false positives if the companion is itself an EB (e.g.Ciardi et al. 2015). We thus searched for companions by collect-ing adaptive optics (AO) and speckle images of TOI-776 using 4and 8 m class telescopes, providing robust limits on the presenceof companions and the level of photometric dilution. http://pestobservatory.com/ On June 15, 2019, TOI-776 was observed usingthe adaptive optics near-infrared imager (NIRI) mounted on the8.1 m Gemini North telescope at Mauna Kea, Hawai’i. We col-lected a total of 9 × γ filter centered on2 . µ m. We dithered the telescope between exposures, so thatthe sky background can be constructed from the science framesthemselves. After removing bad pixels, flat-fielding, and sub-tracting the sky background, we aligned the stellar position be-tween frames and co-added the images. The sensitivity of ourobservations was calculated as a function of radius by inject-ing fake companions, and scaling their brightness such that theycould be detected at 5 σ . The contrast curve and image are shownin Fig. 4. Only the central 4 (cid:48)(cid:48) × (cid:48)(cid:48) are shown, but no compan-ions are seen anywhere in the field, which has a field of view ∼ (cid:48)(cid:48) × (cid:48)(cid:48) . VLT/NaCo
On July 4, 2019, TOI-776 was observed in Br γ us-ing the NAOS-CONICA AO instrument (NaCo), mounted at theNasmyth A port of the 8 m UT1 Very Large Telescope (VLT)in Paranal, Chile. We collected a total of 9 ×
10 s Br γ images.Data were reduced and analyzed using the same procedures asdescribed above for the NIRI data, and no companions werefound in the reduced image. The NaCo contrast curve is shownin Fig. 4. On December 12, 2019, TOI-776 was ob-served in I band with a pixel scale of 0.01575 (cid:48)(cid:48) pix − using theHRCam imager, mounted on the 4.1 m Southern AstrophysicalResearch (SOAR) telescope at Cerro Tololo Inter-American Ob-servatory, Chile. The data were acquired and reduced followingthe procedures described in Tokovinin (2018) and Ziegler et al.(2020). The resulting reconstructed image achieved a contrast of ∆ mag = . (cid:48)(cid:48) (see top panel of Fig. 5). Gemini/Zorro
On March 15, 2020, TOI-776 was observed us-ing the Zorro speckle imager (Scott 2019), mounted on the 8.1 mGemini South telescope in Cerro Pachón, Chile. Zorro uses highspeed electron-multiplying CCDs (EMCCDs) to simultaneouslyacquire data in two bands centered at 562 nm and 832 nm. Thedata were collected and reduced following the procedures de-scribed in Howell et al. (2011). The resulting reconstructed im-age achieved a contrast of ∆ mag = . (cid:48)(cid:48) inthe 832 nm band (see bottom panel of Fig. 5). We note that at the Article number, page 4 of 26. Luque et al.: A multi-planetary system around TOI-776 R e l a t i v e f l u x Phase R e s i dua l s ( pp m ) R e l a t i v e f l u x Phase R e s i dua l s ( pp m ) R e l a t i v e f l u x Phase R e s i dua l s ( pp m ) R e l a t i v e f l u x Phase R e s i dua l s ( pp m ) R e l a t i v e f l u x Phase R e s i dua l s ( pp m ) R e l a t i v e f l u x Phase R e s i dua l s ( pp m ) Fig. 3.
Phase-folded light curves of TOI-776 b and c. First column: transits of TOI-776 b observed with
TESS (top) in Sector 10, LCO-SAAO(middle) on Feb 29, 2020, and LCO-SSO (bottom) on May 22, 2020. Second column: transits of TOI-776 c observed with
TESS (top) in Sector10, and LCO-CTIO (middle) and MEarth-South (bottom) on July 2, 2020.
TESS and MEarth-South photometry binned every 10 min are markedwith blue diamonds to improve visualization. In all panels, the black lines and shaded areas indicate the detrended best fit model from Sect. 5.2.3and its 1 σ confidence interval. Below each panel are represented the residuals after the subtraction of the median best fit model. distance of TOI-776, our Zorro speckle images cover a spatialrange of 0.46 to 32 au around the star with contrasts between 5to 8 mag. We obtained 29 high-resolution (R ≈ Article number, page 5 of 26 & A proofs: manuscript no. main m a g n i t u d e ( B r ) Gemini/NIRIVLT/NaCo [ a r c s e c ] Fig. 4.
Contrast curves from NIRI (orange) and NaCo (blue), andthe central 4 (cid:48)(cid:48) × (cid:48)(cid:48) of the NIRI image (inset). We rule out companions6 mag fainter than TOI-776 beyond 250 mas, and 7.5 mag fainter be-yond 900 mas. The NaCo observations have a slightly tighter innerworking angle, while the NIRI observations reach a deeper sensitivitybeyond 0.5 (cid:48)(cid:48) . serval (Zechmeister et al. 2018) and TERRA (Anglada-Escudé& Butler 2012). Both programs employ a template-matching al-gorithm that is better suited to derive precise radial velocities forM dwarfs, if compared to the cross-correlation function (CCF)technique implemented in the DRS. In the CCF technique, theline lists of M dwarfs used to define the binary mask are in-complete and they thus produce a CCF which is often a poormatch for cool stars. The RVs have a median internal uncer-tainty of 1 . − (1 . − ) and a root mean square of 5 . − (3 . − ) around the mean value for the serval ( TERRA ) ex-tractions, respectively. We report in Tables B.1 and B.2 of theAppendix the HARPS measurements, the extracted RVs andthe associated uncertainties, Na i D, Na ii D, and H α line indicesfrom both programs together with the chromatic index (CRX)and di ff erential line width (dLW) computed by serval , and theMount Wilson S-index computed by TERRA .
4. Stellar properties
TOI-776 belongs to the Catalog Of Nearby Cool Host-Stars forHabitable ExopLanets and Life (CONCH-SHELL) compiled byGaidos et al. (2014). For an all-sky sample of approximately3000 M- or late K-type stars, the authors provide spectroscop-ically determined values of the spectral type, e ff ective tempera-ture and metallicity, which combined with empirical relations forcool stars, allow to estimate stellar radius, luminosity and mass.In particular, they measure that TOI-776 is a relatively inactiveM1 V dwarf star with the stellar properties shown in Table 2. arcsec m a g n i t u d e ( I - b a n d ) [arcsec] -202 [ a r c s e c ] SOAR Speckle ACF
TIC306996324 m
562 nm832 nm
TOI776
Fig. 5.
Top : SOAR contrast curve and 6 (cid:48)(cid:48) × (cid:48)(cid:48) reconstructed image (in-set). Bottom : Gemini / Zorro contrast curves and 1.2 (cid:48)(cid:48) × (cid:48)(cid:48) reconstructedimages (inset). We carried out an independent analysis to improve the pho-tospheric and fundamental parameters of TOI-776. We used
SpecMatch-Emp (Yee et al. 2017) to empirically estimate thee ff ective temperature, metallicity, and stellar radius by compar-ing the co-added HARPS high-resolution spectrum with a spec-troscopic library of well-characterized stars. The results of thisanalysis are in agreement with the values of Gaidos et al. (2014)within the errors. Then, we derived the stellar radius and lumi-nosity combining Gaia G , G BP , G RP photometry and 2MASS J , H , K s magnitudes with the spectroscopic parameters from the SpecMatch-Emp analysis and the
Gaia parallax. We correctedthe Gaia G photometry for the magnitude dependent o ff set us-ing Eq. 3 from Casagrande & VandenBerg (2018), and adopted aminimum uncertainty of 0.01 mag for the Gaia magnitudes to ac-count for additional systematic uncertainties. We added 0.06 masto the nominal
Gaia parallax to account for the systematic o ff setfound by Stassun & Torres (2018); Riess et al. (2018); Zinn et al.(2019). Our best estimate of the stellar radius is consistent withthe value from Gaidos et al. (2014) and in agreement with eachof the radius estimates obtained independently using only one of Article number, page 6 of 26. Luque et al.: A multi-planetary system around TOI-776
Table 2.
Stellar parameters of TOI-776.Parameter Value ReferenceName and identifiersName LP 961-53 Luyten (1974)TOI 776
TESS
Science O ffi ceTIC 306996324 Stassun et al. (2018)Coordinates and spectral type α Gaia
DR2 δ − Gaia
DR2SpT M1 V Gaidos et al. (2014)Magnitudes V [mag] 11 . ± .
04 UCAC4 g [mag] 12 . ± .
12 UCAC4 G [mag] 10 . ± . Gaia
DR2 r [mag] 10 . ± .
03 UCAC4 i [mag] 10 . ± .
09 UCAC4 J [mag] 8 . ± .
018 2MASS H [mag] 7 . ± .
040 2MASS K s [mag] 7 . ± .
020 2MASSParallax and kinematics π [mas] 36 . ± . Gaia
DR2 d [pc] 27 . ± . Gaia
DR2 µ α cos δ [mas yr − ] + . ± . Gaia
DR2 µ δ [mas yr − ] − . ± . Gaia
DR2 V r [km s − ] 49.34 ± Gaia
DR2 U [km s − ] 60.71 ± a V [km s − ] − ± a W [km s − ] 18.73 ± a Photospheric parameters T e ff [K] 3709 ±
70 This work3766 ±
100 Gaidos et al. (2014)log g . ± .
025 This work[Fe / H] − . ± .
12 This workPhysical parameters R [ R (cid:12) ] 0 . + . − . This work0 . ± .
05 Gaidos et al. (2014) L [ L (cid:12) ] 0 . ± .
002 This work0 . ± .
013 Gaidos et al. (2014) M [ M (cid:12) ] 0 . + . − . This work0 . ± .
07 Gaidos et al. (2014)Age [Gyr] 7 . + . − . This work
References.
Gaia
DR2: Gaia Collaboration et al. (2018); UCAC4:Zacharias et al. (2013); 2MASS: Skrutskie et al. (2006).
Notes. ( a ) Computed in the local standard of rest. the magnitudes. Finally, we computed the mass using the mass-radius relations for M dwarfs from Schweitzer et al. (2019).We also applied the methods of Reddy et al. (2006) to
Gaia
DR2 astrometry for TOI-776 to compute galactic U , V , W ve-locities in the local standard of rest and the probabilities of kine-matic membership in galactic stellar populations. We found thatTOI-776 has a probability of 96.3% of belonging to the thindisk population, which is in excellent agreement with the galac-tic population probabilities for this star in the recent catalog ofCarrillo et al. (2020). Additionally, using the code isochrones (Morton 2015), we estimated the age of TOI-776 to be looselyconstrained between 2 to 10 Gyr. From the metallicity, age andkinematics given in Table 2, we can conclude that TOI-776 is arelatively old member of the galactic thin disk population. To determine the rotational period of the star, we used the pub-licly available photometric data for TOI-776. Using juliet (seemore details about the algorithm in Sect. 5.2) we modeled theASAS-SN, ASAS, NSVS, Catalina, and daily binned Super-WASP data with Gaussian processes (GPs). In particular, weadopted the quasi-periodic GP kernel introduced in Foreman-Mackey et al. (2017) of the form k i , j ( τ ) = B + C e − τ/ L (cid:34) cos (cid:32) πτ P rot (cid:33) + (1 + C ) (cid:35) , where τ = | t i − t j | is the time-lag, B and C define the amplitude ofthe GP, L is a timescale for the amplitude-modulation of the GP,and P rot is the rotational period of the modulations. As in Luqueet al. (2019), we considered each of the five data-sets to havedi ff erent values of B and C , in order to account for the possibilitythat di ff erent bands could have di ff erent GP amplitudes, whilewe imposed the timescale of the modulation and the rotationalperiod as common parameters for all the data sets. In addition,we fitted for an extra jitter term for each photometric time series.We considered wide uninformative priors for the jitter, B , C , L ,and a uniform rotation period prior between 10 and 100 d.Figure 6 shows the posterior samples of the GP hyperparam-eter P rot after fitting all the long-term monitoring ground-basedphotometry. The distribution is bimodal with peaks at 33 ± ± P rot can be explained as a consequence of thestellar di ff erential rotation coupled with the activity cycle (Rüdi-ger et al. 2014; Küker et al. 2019). For early M dwarfs with ro-tational periods similar to TOI-776, the expected dynamo cycletime is between 3 to 6 yr (Küker et al. 2019), thus detectable inour data. Additionally, assuming that this star is a solar-like ro-tator, the rotational velocity of the star decreases as the latitudeincreases. The two peaks correspond to two di ff erent groups ofactivity features, a bigger one, closer to the equator, which gen-erates the first peak of the posterior distribution, and a smallerone, at a higher latitude, which produces the second peak. Theopposite situation, with an anti-solar like rotator, is less likely,considering that TOI-776 is an adult star, still belonging to themain sequence.
5. Analysis
We performed a frequency analysis of the HARPS serval / TERRA extracted measurements to search for theDoppler reflex motion induced by the two transiting planetsdiscovered in the
TESS light curve and to unveil the presence ofadditional signals associated with the star and / or other orbitingplanets.Figure 7 shows the generalized Lomb Scargle (GLS; Zech-meister et al. 2009) periodograms of the HARPS RVs and ac-tivity indicators extracted with serval (blue lines) and with TERRA (red lines). The horizontal dashed lines mark the GLSpowers corresponding to the 0.1, 1, and 5% false alarm prob-ability (FAP). The vertical dashed lines mark the orbital fre- Following the bootstrap method described, e.g., in Murdoch et al.(1993) and Hatzes (2016), we estimated the FAP by computing the GLSArticle number, page 7 of 26 & A proofs: manuscript no. main
20 25 30 35 40 45 50 55 60P rot , phot (d)0.000.050.100.150.200.250.30 P r o b a b ili t y d e n s i t y PhotometryservalTERRA
Fig. 6.
Probability density of the samples of the P rot parameter from theGP fit of the ground-based, long-term photometric monitoring (grey)from Sect. 4.2 and of the period of the additional sinusoidal signal fromthe RV fit from Sect. 5.2.2 using serval (blue) or TERRA (red) reduc-tions. quencies of the two transiting planets detected in the
TESS lightcurve (f b = − and f c = − ) and the stellar signal at ∼ − (see below).The upper panel of Fig. 7 displays the GLS periodogram ofthe HARPS RVs in the frequency range 0 - 0.42 d − . The high-est peak is found at 0.055 d − (FAP ≈ c = − ). Taking intoaccount our frequency resolution of 0.021 d − , the two frequen-cies are indistinguishable. This suggests that the highest peakseen in the periodogram of the HARPS RVs is the stellar reflexmotion induced by the outer transiting planet TOI-776 c. Thesecond highest peak is found at 0.129 d − (Fig. 7, upper panel),which is close to the orbital frequency of TOI-776 b. However,this signal is an alias of the signal at 0.055 d − . The periodogramof the window function indeed shows a peak at 0.074 d − (high-lighted with an arrow in the bottom panel of Fig. 7), which isequal to the frequency spacing between the two highest peaksseen in the periodogram of the HARPS RVs.We used the code pyaneti (Barragán et al. 2019)(Sect. 5.2.3) to subtract the Doppler signal of TOI-776 c from theHARPS RVs. We assumed a circular model (see also Sect. 5.2.2),fixing period and time of first transit to the TESS ephemeris,while allowing for the systemic velocity and RV semi-amplitudeto vary. The periodogram of the RV residuals shows a broad peakcentered around ∼ − with a FAP of about 10 %. Althoughthe Doppler signal is not significant, the GLS periodograms ofthe CRX, dLW, H α , and S-index activity indicators show alsopeaks at ∼ − , suggesting that this signal is caused by thepresence of active regions appearing and disappearing from thevisible stellar disk as the star rotates around its axis. It is worthnoting that the peak at 0.130 d − is not observed in the GLS pe-riodogram of the RV residuals, corroborating the interpretationthat this peak is an alias of the dominant frequency detected inthe periodogram of the HARPS data. periodogram of 10 time series obtained by randomly shu ffl ing the mea-surements and their uncertainties, while keeping the time-stamps fixed. The frequency resolution is defined as the inverse of the time-baseline. The baseline of our HARPS observations is about 47 days,corresponding to a frequency resolution of about 1 / = − . Fig. 7.
Generalized Lomb-Scargle periodograms of the HARPS RVsand spectral activity indicators from serval (blue) and
TERRA (red).The horizontal dashed lines mark, from bottom to top, the 5%, 1%,and 0.1% FAP levels, respectively. The vertical dashed lines mark theorbital frequencies of the two transiting planets (f b = − andf c = − ) and of the stellar signal at ∼ − . Upper panel :HARPS RVs.
Second panel : RV residuals following the subtraction ofthe signal of TOI-776 c.
Third panel : RV residuals following the sub-traction of the reflex motion of TOI-776 c and of the activity-inducedstellar signal.
Fourth panel : S-index.
Fifth panel : H α line. Sixth panel :Na D lines.
Seventh panel : di ff erential line width (dLW). Eight panel :chromatic index (CRX).
Bottom panel : Window function. The arrow inthe bottom panel indicates the peak at 0.07 d − referred in the discussionof Sect. 5.1.Article number, page 8 of 26. Luque et al.: A multi-planetary system around TOI-776 Table 3.
Model comparison of RV-only fits with juliet . The prior la-bel N represents a normal distribution. The final model used for thejoint fit is marked in boldface (see Sect. 5.2.2 for details about the se-lection of the final model).Model Prior P planet GP ln Z serval ln Z TERRA − − N b (8 . , . ) . . . − − N c (15 . , . )2pl + GP1 N b (8 . , . ) EXP a − − N c (15 . , . )2pl + GP2 N b (8 . , . ) ESS b − − N c (15 . , . ) + sinusoid N b (8 . , . ) . . . -78.9 − N c (15 . , . ) N d (35 . , . ) Notes. ( a ) Simple exponential kernel (EXP) of the form k i , j = σ , RV exp (cid:16) −| t i − t j | / T GP , RV (cid:17) . ( b ) Exponential-sine-squared kernel (ESS) of the form k i , j = σ , RV exp (cid:18) − α GP , RV ( t i − t j ) − Γ GP , RV sin (cid:20) π | t i − t j | P rot;GP , RV (cid:21)(cid:19) with a uniformprior in P rot;GP , RV ranging from 5 to 50 d. We removed the Doppler reflex motion of TOI-776 c andthe activity-induced RV signal by jointly modeling the HARPSmeasurements with a circular Keplerian orbit and a sine curve.For TOI-776 c we followed the same procedure described inthe previous paragraph. For the stellar signal we fitted for thephase, amplitude, and frequency. The latter was allowed to varywithin a wide uniform prior centered around 0.04 d − . The GLSperiodogram of the RV residuals displays a peak at 0.125 d − (FAP ≈
11 %), which is very close to the frequency of the innertransiting planet TOI-776 b (f b = − ). We note that the ac-tivity indicators show also peaks close to the orbital frequency ofTOI-776 b. Yet, those peaks are separated by 0.074 d − from thestellar signal at ∼ − . As such they are very likely aliases ofthe latter. In this section, we use juliet (Espinoza et al. 2019) to modelthe photometric and Doppler data, both separately and jointly.The algorithm is built on several publicly available tools whichmodel transits ( batman , Kreidberg 2015), RVs ( radvel , Ful-ton et al. 2018), and GPs ( george , Ambikasaran et al. 2015; celerite , Foreman-Mackey et al. 2017).
First, to constrain the properties of the transiting planets anduse them for further analyses, we modeled the
TESS , LCO, andMEarth photometry with juliet . We adopted a quadratic limbdarkening law for
TESS , since Espinoza & Jordán (2015) showedit was appropriate as well for space-based missions. The limbdarkening parameters were then parametrized with a uniformsampling prior ( q , q ), introduced by Kipping (2013). For LCOand MEarth transits, we used a more simple linear limb dark-ening law, because the lower data precision with respect to TESS prevents us from adopting a more complex law. Additionally, wefollowed the parametrization introduced in Espinoza (2018). Inparticular, for each transiting planet, rather than fitting for the planet-to-star radius ratio p = R p / R ∗ and the impact parameterof the orbit b , we sampled from the uniform priors assigned totwo parameters, r and r , which are connected to p and b withthe equations (1)-(4) in Espinoza (2018). r and r were shown inEspinoza (2018) to guarantee a full exploration of the physicallyplausible values in the ( p , b ) plane. We assumed as well circularorbits and fixed the TESS dilution factor to 1, based on our anal-ysis from Sect. 3.3. Finally, we added in quadrature a jitter term σ to the TESS , LCO, and MEarth photometric uncertainties. Thedetails of the priors and the description for each parameter arepresented in Table A.1 of the Appendix.To account for the time-correlated noise in the light curve inFig. 2, even using the PDC-corrected SAP, we modeled the
TESS photometry with the exponential GP kernel k i , j = σ , TESS exp (cid:16) −| t i − t j | / T GP , TESS (cid:17) where T GP , TESS is a characteristic timescale and σ GP , TESS is theamplitude of this GP modulation. For the LCO photometry, onthe other hand, we used a linear model to detrend the data fromairmass correlations.Our photometry-only analysis increases significantly the pre-cision of the planet parameters with respect to the
TESS
DVR.The uncertainties in the period decreases by two orders of mag-nitudes which eases up future ground- and space-based follow-up e ff orts. The radii of the planets are determined to a precisionbetter than 5%. Finally, we searched for an additional planets inthe system by modeling a three-planet fit with the same priorsas in Table A.1 for the transiting planets, and varying the periodand mid-transit time of the third hypothetical planet. Our resultsignificantly exclude the presence of any additional transits inthe light curve ( ∆ ln Z = ln Z − ln Z > Even though the results of the RVs extraction slightly changewhether we use serval or TERRA , the GLS analysis in bothcases show the evidence of a stellar signal together with theRV trends associated with the transiting planets. To adequatelydescribe the data, we considered several RV-only models andcarried out a model comparison scheme as in Luque et al.(2019). We used juliet , a code which e ffi ciently computes theBayesian log-evidence of each tested model and explores the pa-rameter space using the importance nested sampling includedin MultiNest (Feroz et al. 2009) via the PyMultiNest package(Buchner et al. 2014). As discussed in Nelson et al. (2020), thismethod outperforms other samplers in choosing robustly the bestmodel for those with 3 or less planets. We considered a modelto be moderately favored over another if the di ff erence in itsBayesian log-evidence ∆ ln Z is greater than two, while stronglyfavored if it is greater than five (Trotta 2008). If ∆ ln Z (cid:46)
2, thenthe models are indistinguishable. In this case, the model withfewer degrees of freedom would be chosen.Due to the sampling and the scarce number of RV measure-ments, if we model the eccentricity with a wide uninformativeprior we derive nonphysically high eccentricities for both plan-ets that would make the system unstable in less than a hundredorbits. The eccentricity of systems with multiple transiting plan-ets is low but not necessarily zero (Van Eylen & Albrecht 2015;Xie et al. 2016; Hadden & Lithwick 2017). Therefore, insteadof assuming circular orbits, we place a prior on the orbital ec-centricity of a Beta distribution with α = .
52 and β =
29 fol-lowing Van Eylen et al. (2019). Table 3 summarizes the resultsof our analysis on both serval - or
TERRA -extracted RVs. As
Article number, page 9 of 26 & A proofs: manuscript no. main seen in Table 3, including the two transiting planets in the modelis favored against the fiducial model (0pl). On the other hand,we tested di ff erent types of two planet models. First, we con-sidered just the two transiting planets (2pl), without accountingfor additional noise sources. Then, we accounted for the stellarnoise, modeling it in three di ff erent ways: with an exponentialGP kernel (2pl + GP1), with an exponential sine-squared GP ker-nel (2pl + GP2) and with a simple sinusoid (2pl + sinusoid). Allthe tested two-planet models are statistically indistinguishable,with their Bayesian log-evidences within ∆ ln Z < serval and TERRA -extracted RVs, thenominal best model accounts for two circular orbits and an ad-ditional sinusoidal curve, whose period is equal to the stellarperiod of rotation we estimated through the long-term ground-based photometric data. For this test we imposed a normalprior on P rot , with a wide standard deviation (10). We addition-ally tried wide, uninformative priors for the period of the sinu-soidal signal and we retrieved the same posterior distributionsand log-evidences (Fig. 6) as for the test with a gaussian prior.With the RV analysis, we estimated a stellar period of rotation P rot = . + . − . d, consistent with the rotational period estimatedfrom the ground-based long-term photometry in Section 4.2. Ad-ditionally, all models presented in Table 3 derive the same RVsemi-amplitude for TOI-776 b and TOI-776 c, well within their1 σ uncertainties. This proves the robustness of the mass deter-mination for the transiting planets, independently of the stellarnoise distribution.Leveraging the prior information on the stellar rotation fromphotometry discussed in Sect. 4.2 with the presence of a sig-nificant periodicity in the RV residuals of a two-planet model(Fig. 7b), we decided to choose the 2pl + sinusoid as our finalmodel for the joint fit. With respect to the RV extraction, we pre-ferred to use the serval extracted RVs in the final joint fit dueto their nominal highest log-evidence and lower jitter comparedto TERRA . We performed a joint fit using juliet of the
TESS , LCO, andMEarth photometry and HARPS serval extracted RVs, usingthe 2pl + sinusoid model we selected after the RV-only analysisin Sect. 5.2.2. Table A.1 and 4 shows the priors and posteriorsof all the fitted parameters, respectively. Figure C.1 shows a cor-ner plot of the orbital parameters of planets b and c. The data,residuals, and joint fit best model are shown in Figs. 3 and 8 forthe photometry and the RVs, respectively. Table 5 lists the transitand physical parameters, derived using the stellar parameters inTable 2.As a sanity check, we performed an independent joint anal-ysis of the transit photometry and Doppler measurements usingthe code pyaneti (Barragán et al. 2019), which estimates theparameters of planetary systems in a Bayesian framework, com-bined with an MCMC sampling. We imposed uniform priors forall the fitted parameters. Following Winn (2010), we sampled forthe mean stellar density ρ (cid:63) and recovered the scaled semi-majoraxis ( R p / R (cid:63) ) for each planet using Kepler’s third law. We foundthat the modeling of the transit light curves provides a mean stel-lar density of ρ (cid:63) = + − kg m − , which agrees with the den-sity of 4834 + − kg m − derived from the stellar mass and radiuspresented in Sect. 4. As for the remaining parameters, the anal-ysis provides consistent parameter estimates with those derivedwith juliet , corroborating our results.
6. Results and Discussion
The TOI-776 system consists of two transiting planets. Theinner planet, TOI-776 b, has a period of 8.25 d, a radius of1 . ± . R ⊕ , a mass of 4 . ± . M ⊕ , and a bulk densityof 3 . + . − . g cm − . The outer planet, TOI-776 c, has a period of15.66 d, a radius of 2 . ± . R ⊕ , a mass of 5 . ± . M ⊕ , and abulk density of 3 . + . − . g cm − . The RV data show only one addi-tional signal with a semi-amplitude of ∼ . − and a periodof 34 d associated with the stellar rotation, as suggested by ouranalyses of the photometry and spectral line indicators. While the occurrence rate of planets around early M dwarfs(3500 K < T e ff < Kepler and K2 samples (see e.g., Dressing & Charbonneau 2013,2015; Montet et al. 2015; Hirano et al. 2018), the number ofcurrently known planets transiting low-mass stars is still muchsmaller with respect to those discovered around solar-type stars.While none of these surveys were optimized for M dwarfs, weexpect more statistically significant results from the TESS mis-sion for these stars. Figure 9 shows the confirmed transiting plan-ets around M dwarfs as a function of the orbital period and thee ff ective temperature of the host star. However, very few of thesesystems have precise determinations of the planetary masses (i.edensities), eccentricities and orbital architectures that would berequired to link the statistical properties of this population withplanet formation and evolution models in the low stellar massregime.There are several validated transiting multi-planetary sys-tems orbiting early M dwarfs similar to TOI-776 in termsof planetary architecture. Kepler-225, Kepler-236 and Kepler-231 are two-planet transiting systems composed of super-Earthand / or mini-Neptune sized companions with similar periods andsemi-major axes, all validated by Rowe et al. (2014). However,these systems are on average 5 mag fainter than TOI-776 and theplanets do not have a mass determination nor precise stellar pa-rameters. Similarly, K2-240 (Díez Alonso et al. 2018) has twotransiting super-Earths with periods of 6 and 20.5 d, althoughthey do not have mass determination and orbit an active starthat is 2 mag fainter with a clear photometric rotational periodof 10.8 d. The two outermost planets of the four-planet systemK2-133 have periods and sizes similar to TOI-776 b and c, butthe star is at the faint-end for RV follow-up and does not exhibittransit timing variations (TTVs).If compared to systems with mass determination, TOI-776shows some similarities with Kepler-26 (Ste ff en et al. 2012),Kepler-138 (Rowe et al. 2014), TOI-1266 (Demory et al. 2020),and K2-3 (Montet et al. 2015; Crossfield et al. 2015). Kepler-26 b and c have periods of 12.3 and 17.2 d, respectively, andbulk densities compatible with those of sub-Neptunes deter-mined from TTVs. However, the system has two more planetswithout mass determination, an inner Earth-sized planet and anouter mini-Neptune sized planet. Kepler-138 is a very interestingsystem of three small planets, whose densities were estimatedthrough photodynamical modeling (Almenara et al. 2018). Themost similar to the TOI-776 planets in terms of orbital period,Kepler-138 b (10.3 d) and c (13.8 d), are very di ff erent in com-position, the former being a Mars analogue and the latter a pro-totypical rocky super-Earth. The third, outermost planet seemsto have retained a substantial volatile-rich envelope. TOI-1266is the system that resembles TOI-776 the most. The two plan-ets of the system have tentative dynamical masses determined Article number, page 10 of 26. Luque et al.: A multi-planetary system around TOI-776 R V ( m / s ) O - M ( m / s ) P = 8.2466 d P = 15.665 d P = 34.4 d
Fig. 8.
Top panel: time series of the HARPS serval
RVs and the best model discussed in Sect. 5.2.2 and the residuals from the fit below. Theblue shaded area corresponds to the 1 σ confidence interval of the model. Bottom panel: RVs phase-folded to the period (shown above each panel)of the two confirmed planets (TOI-776 b, left; TOI-776 c, center) and the additional sinusoid associated with the stellar variability. In both panelsthe error bars of the RV data have the extra jitter term added in quadrature and plotted in lighter orange for its visualization. from TTVs, although RVs are likely to become available in thefuture. The planets straddle the radius valley and, interestingly,the innermost is larger and more massive than the outer one. K2-3, the brightest of all four systems, has three small transitingplanets and only the two inner ones (with periods of 10 and24.6 d) have a mass determination using HARPS-N, HARPS,HIRES and PFS RVs (Almenara et al. 2015; Damasso et al.2018; Kosiarek et al. 2019), only an upper limit is measured forthe third (with a period of 44.5 d). The planets have a similarcomposition, compatible to that of water-worlds or water-poorplanets with gaseous envelopes, however the poor bulk densityestimations of planets c and d impede further conclusions. Theright panel of Fig. 9 shows all of the aforementioned systems,color-coded by bulk density and with the J -band magnitude oftheir host stars indicated.Therefore, we conclude that, although multi-planetary sys-tems of super-Earths and / or sub-Neptunes are common aroundearly-type M dwarfs, only TOI-776 has all of its planets wellcharacterized, bulk density uncertainties better than 30%, precisestellar parameters and a host star bright enough for atmosphericfollow-up observations with current and planned facilities. We investigated possible TTVs through a 3-body simulation, us-ing the Python Tool for Transit Variations (
PyTTV ; Korth 2020).We simulated the estimated TTVs and RVs using the stellar andplanetary parameters reported in Table 2, 4 and 5 and found anexpected TTV signal with a period of ∼
150 d and a maximumamplitude of ∼ orbits ofthe inner planet, using the tool REBOUND (Rein & Liu 2012) withthe standard IAS15 integrator (Rein & Spiegel 2015). We alsoexplored the stability using the MEGNO criteria as implementedin
REBOUND . In the cases of close encounters between the bodiesor one body ejection, the system would be flagged as unstablefor the specific set of parameters. We found that the systems is
Article number, page 11 of 26 & A proofs: manuscript no. main
P (d) T ( K ) P (d)
Kepler-225, 14.0Kepler-225, 14.0Kepler-353, 13.6Kepler-353, 13.6Kepler-026, 13.4Kepler-026, 13.4Kepler-231, 13.4Kepler-231, 13.4Kepler-296, 13.4Kepler-296, 13.4Kepler-296, 13.4Kepler-296, 13.4Kepler-296, 13.4Kepler-369, 13.2Kepler-369, 13.2Kepler-236, 13.2Kepler-236, 13.2K2-264, 13.0K2-264, 13.0Kepler-249, 12.8Kepler-249, 12.8Kepler-249, 12.8Kepler-327, 12.8Kepler-327, 12.8Kepler-327, 12.8Kepler-125, 12.5Kepler-125, 12.5Kepler-186, 12.5Kepler-186, 12.5Kepler-186, 12.5Kepler-186, 12.5Kepler-186, 12.5Kepler-303, 12.4Kepler-303, 12.4K2-083, 11.6K2-083, 11.6K2-133, 11.1K2-133, 11.1K2-133, 11.1K2-133, 11.1K2-240, 10.4K2-240, 10.4Kepler-138, 10.3Kepler-138, 10.3Kepler-138, 10.3K2-155, 10.3K2-155, 10.3K2-155, 10.3TOI-1266, 9.7TOI-1266, 9.7K2-003, 9.4K2-003, 9.4K2-003, 9.4TOI-776, 8.5 123456 D en s i t y ( g c m ) Fig. 9.
Left : Confirmed transiting planets from the TEPCat database (Southworth 2011) around M dwarfs as a function of period. Black circledpoints indicate planets with a mass determination better than 30%. Circles are color-coded by the host e ff ective temperature and their sizes areproportional to the planet radius. The red stars mark the two planets in the TOI-776 system. Right : Transiting multi-planetary systems aroundearly-type M dwarfs (3500 K < T e ff < J band. dynamically stable over the entire integration time and for thewhole parameter posterior space. Figure 10 shows the location of the TOI-776 system in a mass-radius diagram. Both planets occupy a scarcely populated region,characterized by a lack of planets around M dwarfs and with pre-cise bulk density measurements. A comparison with the theoret-ical models by Zeng et al. (2016), reported in the left panel ofFig. 10, shows that TOI-776 b and c are consistent with mix-tures of silicates and water in a 50-50 proportion. We adoptedthe three-layer models from Zeng & Sasselov (2013) and Zenget al. (2016) to infer the interior structure of the planets. How-ever, given the mass and radius input, the solution of the modelis degenerate. As a consequence, the same mass-radius pair canlead to a broad range of combinations of iron, silicate and watermass fractions. On the other hand, when we applied the latestmodels by Zeng et al. (2019), assuming a 1 mbar surface pres-sure level and an equilibrium temperature of 500 K (from Ta-ble 5), we found that an Earth-like rocky core with a 0.1% anda 0.3% molecular hydrogen atmosphere is consistent with thebulk densities of TOI-776 b and c, respectively. Nonetheless, it isclear that both of the planets in the system have an internal com-position ranging from water worlds to rocky planets that haveretained a significant atmosphere.For a better understanding of the nature of the two exoplan-ets, we performed a more detailed modeling of their interiorcompositions, using their masses, radii and surface temperatures.Our model considers a canonical four-layer structure consistingof a two-component iron and silicate core, a layer of H O and aH / He envelope. We assume that the core is Earth-like in compo-sition (a third of iron, two-thirds of silicates by mass), meaningthe core, water and H / He envelope mass fractions ( x core , x H O , x H / He ) are free parameters which sum to unity. The model solvesthe planetary structure equations of mass continuity and hydro-static equilibrium assuming spherical symmetry. Further detailregarding the internal structure model can be found in Mad-husudhan et al. (2020) and Nixon & Madhusudhan (submitted).The equation of state (EOS) prescriptions for the iron andsilicate layers are adopted from Seager et al. (2007), who useda Vinet EOS of the (cid:15) phase of Fe (Vinet et al. 1989; Ander-son et al. 2001) and a Birch-Murnaghan EOS of MgSiO per-ovskite (Birch 1952; Karki et al. 2000). Thermal e ff ects in theselayers are ignored, since they have a small e ff ect on the plane-tary radius (Howe et al. 2014). However, thermal e ff ects in theouter envelope can alter the mass-radius relation significantly(Thomas & Madhusudhan 2016). For this reason the model usesa temperature-dependent EOS for the outer H O and H / He lay-ers. For H O, we used a patchwork EOS in order to cover allpossible phases of H O that might be present in the interior,compiled from Salpeter & Zapolsky (1967); Fei et al. (1993);Wagner & Pruß (2002); Feistel & Wagner (2006); Seager et al.(2007); French et al. (2009); Klotz et al. (2017), and Journauxet al. (2020). For H / He we use the EOS in Chabrier et al. (2019),which assumes a solar helium fraction ( Y = . P rc is a free parameter in the model. For this study, we consideredvalues of P rc ranging from 1–100 bar.We explore the parameter space of possible compositions in( x core , x H O , x H / He ) space. For each composition, we consider arange of masses that agree with the observed mass of the planetto within 1 σ . For a given mass ˆ M , the model radius ˆ R is com-puted and the χ statistic is calculated: χ = ( M p − ˆ M ) σ M + ( R p − ˆ R ) σ R , (1) Article number, page 12 of 26. Luque et al.: A multi-planetary system around TOI-776
M ( ) R () Mass / M ⊕ R a d i u s / R ⊕ Core + 0.11% H/He (514 K)Core + 30% H O (514 K)Core + 0.36% H/He (415 K)Core + 58% H O (415 K) b c % H O ( K ) % M g S i O Fig. 10.
Mass-radius diagrams in Earth units. In the left panel, open circles are transiting planets around F-, G-, and K-type stars with mass andradius measurement better than 30 % from the TEPCat database of well-characterized planets (Southworth 2011), red circles are planets around Mdwarfs with mass and radius measurement, orange filled circles are planets around M dwarfs with mass determinations worse than 30 %, and thered stars are TOI-776 b and c which have masses determined with accuracies of 23 % and 34 %, respectively. In the left panel, the color lines arethe theoretical R - M models of Zeng et al. (2016) and Zeng et al. (2019). In the right panel, the solid pink and purple lines show the models fromSect. 6.3 that are consistent with the mass and radius of TOI-776 b, and the orange and green lines show compositions consistent with the massand radius of TOI-776 c, assuming an Earth-like core (1 / / H O mass fraction -8 -7 -6 -5 -4 -3 -2 H / H e m a ss f r a c t i o n cb Fig. 11. H / He vs. H O mass fractions for the best-fitting interior com-positions ( ≤ σ ) permitted by the masses and radii of TOI-776 b andc, assuming an Earth-like core, for two di ff erent pressure-temperatureprofiles with radiative-convective boundaries at 1 and 100 bar. The blueshaded region indicates possible compositions for TOI-776 b, and thered shaded region shows compositions for TOI-776 c. The darker redshaded area between the two corresponds to the range of possible com-positions that could explain both planets. For TOI-776 b, the H O massfraction is constrained to be ≤
73% and the H / He mass fraction is ≤ . / He is 1 . O planet would be consistent with this mass and radius, but we onlyshow H O mass fractions up to 90%. where ( σ M , σ R ) are the observed uncertainties on the mass andradius of each planet. The bulk densities of TOI-776 b and c (3 . + . − . g cm − and3 . + . − . g cm − , respectively) are too low for either planet to havea purely terrestrial (iron plus rock) composition. Therefore, theplanets must possess an envelope with some amount of H Oand / or H / He, in order to explain their masses and radii. The rightpanel of Fig. 10 shows limiting cases for each planet in whichthe envelope composition is either purely H O or purely H / He.The mass and radius of TOI-776 b can be explained to within1 σ ( χ ≤
1) with a pure H O envelope of 12–73% by mass ora pure H / He envelope with mass fraction 1 . × − –5 . × − .Best-fit solutions (those which minimise χ ) for pure envelopesare found at x H O = . x H / He = . × − . TOI-776 cmight have larger envelopes; within 1 σ , it is consistent with apure H O layer of ≥
18% or a pure H / He envelope with massfraction 5 . × − –1 . × − . The best-fit pure-envelope solu-tions for TOI-776 c are x H O = .
58 and x H / He = . × − .Each of the best-fit models, shown in the right panel of Fig. 10,have a radiative-convective boundary at P rc =
10 bar.It is also possible that the planets in this system have bothH O and H / He components, as well as an iron / rock core. For thethree components, we explored the full range of plausible val-ues ( x core , x H O and x H / He ) that could explain the interior com-positions of each planet. We considered two di ff erent temper-ature profiles for each planet, with P rc = / He compatibleto within 1 σ ( χ ≤
1) with the masses and radii of TOI-776 band c. We obtained upper limits on the total H O and H / He massfractions for TOI-776 b: x H O ≤
73% and x H / He ≤ . O or H / He envelopes as pre-viously discussed. For TOI-776 c, we find that x H / He ≤ . O planet would theoretically be consistent with themass and radius of TOI-776 c, but this would be unrealistic froma planet formation perspective, as some rocky material is neededfor further accretion of ice and gas (Lee & Chiang 2016). Fig-ure 11 shows as well a significant overlap between the best-
Article number, page 13 of 26 & A proofs: manuscript no. main fitting shaded regions for the two planets, meaning that the plan-ets could also share the same composition.The masses and radii of TOI-776 b and c allow for a widerange of possible solutions, from water worlds with steam atmo-spheres to mostly rocky planets with hydrogen-rich envelopes,however they are inconsistent with bare rocks without atmo-spheres. Our models assume a surface pressure of 0.1 bar, mean-ing a water-world solution for either planet yields a steam atmo-sphere. On the other hand, a higher surface pressure could resultin liquid H O at the surface. A rocky planet with an outgassedsecondary atmosphere which includes carbon compounds is un-likely: Elkins-Tanton & Seager (2008) placed an upper limit onthe mass fraction for this type of atmosphere at 5%. The lowermass limits in the case of pure H O envelopes are 8% and 18%for TOI-776 b and c respectively. On the other hand, in a carbon-rich atmosphere, the dominant species, CO , has a higher meanmolecular weight than H O, leading to a lower atmospheric scaleheight. All things considered, we can infer that a 5% carbon-richatmosphere is less than what would be needed to explain theplanet radii. However, determining whether the two planets haveH O- or H / He-rich atmospheres is impossible with the presentdata. Atmospheric observations of the planets would be requiredin order to break this degeneracy.
The occurrence rate distribution of close-in planets exhibits apaucity of planets between 1 . − . R ⊕ (Fulton et al. 2017; Fulton& Petigura 2018; Hardegree-Ullman et al. 2020) around FGKstars ( T e ff > . − . R ⊕ (Hirano et al.2018; Cloutier & Menou 2020) around mid-K to mid-M dwarfs( T e ff < ffi cienttoward low-mass stars. The measured slope for mid-K to mid-Mdwarfs suggests that gas-poor formation (Lee et al. 2014; Lee &Chiang 2016; Lopez & Rice 2018) might be the main processfrom which small planets form. However, thousands of smallplanets around low-mass stars with precise radii are needed in order to robustly state if the radius valley is the result of the ero-sion or the gas-poor formation scenarios (Cloutier et al. 2020).Although enriching the sample of exoplanet systems orbiting Mdwarfs is nowadays possible thanks to TESS and future space-based missions such as
PLATO an alternative is to obtain precisebulk density measurements of exoplanets lying in the region ofdiscrepancy between models.TOI-776 b joins TOI-1235 b (Bluhm et al. 2020; Cloutieret al. 2020) and K2-146 b (Lam et al. 2020; Hamann et al. 2019)inside the period-radius region where thermally driven mass lossmodels disagree with the predictions from gas-poor formation.However, K2-146 b belongs to this region if we refer to the pa-rameters reported in Hamann et al. (2019), because the radius es-timated by Lam et al. (2020) (see translucent points in Fig. 12) ismore than 2 σ higher, causing the planet to be placed outside theradius valley. Our previous analyses show that both TOI-776 band c are likely to have retained a significant atmosphere, withslightly di ff erent envelope mass fractions. This result, given theirperiod and radius, would be consistent with the predictions fromgas-poor formation models.On the other hand, the system’s composition may be rec-onciled with thermally driven mass loss because the inner, mostirradiated planet, has a smaller envelope mass fraction comparedto its outer companion. Unlike other known systems whose plan-ets straddle both sides of the radius gap (e.g., Dumusque et al.2014; Niraula et al. 2017; Nowak et al. 2020), TOI-776 is aninteresting case where photo-evaporation could have stopped orbecome ine ffi cient early in the planet’s history. But, it is pos-sible that the planets are currently undergoing mass loss un-der the core-powered mechanism, which erodes sub-Neptuneplanets into rocky super-Earths in Gyr timescales (Ginzburget al. 2018), contrary to the few Myr timescale when photo-evaporation is e ff ective (Sanz-Forcada et al. 2011). As reportedin Table 2, the age of TOI-776 is between 2 and 10 Gyr. However,the current data precision and limited number of known planetsin this specific regime hamper any further investigation in fa-vor of one or the other mechanism of formation. New studies onthe dependence of the radius valley with other stellar parameterssuch as the age or metallicity, together with a larger sample ofwell-characterized planets in or near the radius valley, will helpdiscerning between them in a demographic sense (Hardegree-Ullman et al. 2020; Berger et al. 2020; Gupta & Schlichting2020).However, for the first time, we can compare between planetswhich belong to this region of the parameter space where forma-tion models make opposing predictions. TOI-1235 b has a rockycomposition with a 90% confidence upper limit in the envelopemass fraction of 0.5%, thus incompatible with a gas-poor forma-tion scenario. We reach the opposite conclusion for TOI-776 band c, whose bulk densities imply the presence of a volatile enve-lope making them compatible with the predictions from gas poorformation mechanisms, given their periods and radii. Therefore,although other stellar parameters might need to be taken intoaccount, we can tentatively predict that the stellar mass belowwhich thermally-driven mass loss is no longer the main forma-tion pathway for sculpting the radius valley is probably between0.63 and 0.54 M (cid:12) , which correspond to the host stellar massesof TOI-1235 and TOI-776, respectively. More planets in this in-teresting region of the parameter space with precise bulk densitymeasurements are key to reveal the mechanisms responsible ofthe radius valley emergence around low-mass stars with respectto solar-like stars. Article number, page 14 of 26. Luque et al.: A multi-planetary system around TOI-776
S (S ) R ( R ) P (d)
CM20V18
TOI-1235 bK2-146 b
Fig. 12.
Insolation-radius ( left ) and period-radius ( right ) diagrams in Earth units. In both panels the di ff erent circles represent the same planetsas in Fig. 10 from the TEPCat database (Southworth 2011). In the left panel, we plot in blue the R - S point density of all the known confirmedtransiting planets with contours, and sub-Neptunes and super-Earths density maxima with white crosses. In the right panel, the orange contoursrepresent the density of planets around M dwarfs with mass determinations worse than 30% or without mass constraints at all (orange circles inthe left panel). The dashed line represents the location of the radius valley for F-, G-, and K-type stars from Van Eylen et al. (2018), consistentwith the predictions from photo-evaporation and core-powered mass loss models, while the solid line represents the location of the radius valleyfor mid-K and mid-M dwarfs from Cloutier & Menou (2020), consistent with gas-poor formation scenarios. Together with TOI-776 b, the othertwo systems that are within both lines are K2-146 (solid, Hamann et al. 2019; Lam et al. 2020, translucent) and TOI-1235 (Bluhm et al. 2020;Cloutier et al. 2020). We used the proposed metric by Kempton et al. (2018) to eval-uate the suitability of the TOI-776 planets for atmospheric char-acterization studies. Figure 13 shows the transmission spec-troscopy metric (TSM) for all exoplanets in the Exoplanet En-cyclopedia with a radius less than 3 R ⊕ . We used the scale fac-tors listed in Table 1 from Kempton et al. (2018) as opposedto the suggested value for temperate planets, 0.167, to computethe TSM values in Fig. 13. The estimated TSM of TOI-776 band c are 77.9 and 61.8 respectively, which places them amongthe top priority targets for atmospheric follow-ups of small plan-ets around nearby stars. This is not surprising, because TOI-776is one of the brightest M dwarfs with known transiting planets.However, most of the planets shown in Fig. 13 are well below theradius gap which makes the TOI-776 system a valuable target foratmospheric characterization in order to trace the formation andevolution of multi-planetary systems orbiting low-mass stars andbreak the degeneracy of internal composition models. In order to quantitatively assess the possibility of TOI-776 band c’s atmospheric characterization with the
James Webb SpaceTelescope ( JWST ), we investigated a suite of atmospheric sce-narios and calculated their
JWST synthetic spectra using thephoto-chemical model
ChemKM (Molaverdikhani et al. 2019a)and petitRADTRANS (Mollière et al. 2019). We based the tem-perature structure of these planets on modern Earth’s tempera- ture structure, and we increased the surface temperature for itto be consistent with the equilibrium temperature of TOI-776 band c (Kawashima & Rugheimer 2019). We followed a simi-lar approach as in Luque et al. (2019): we estimated TOI-776’s( T e ff = T e ff = ff erent metallicities, carbon-to-oxygenratios and haze opacities. For our fiducial model (top left panel ofFig. 14), we assume solar abundances. Such spectra are predom-inantly consisting of water and methane features, as expected forthis type of planets (Molaverdikhani et al. 2019b). The signifi-cance of these features are on the order of 100 ppm, well aboveconservative JWST expected noise floor (20 ppm for NIRISSand 50 ppm for MIRI, Greene et al. 2016). We calculated theNIRISS-SOSS, NIRSpec-G395M, and MIRI-LRS uncertaintieswith PandExo (Batalha et al. 2017), assuming two transits andbinned for R =
50, supporting the previous statement. In thisscenario, the contribution from haze opacity partially obscuresmolecular features below 2 µ m, but it is almost ine ff ective atlonger wavelengths (see left and right upper panels of Fig. 14).We note, however, that the radiative feedback of haze particlesmight significantly a ff ect the temperature structure and the com-position of atmosphere (Molaverdikhani et al. 2020). We did nottake this e ff ect into account in this work in order to keep thetemperature profiles consistent with the Earth’s profile. Article number, page 15 of 26 & A proofs: manuscript no. main Distance from Earth (pc)10 T r a n s m i ss i o n Sp ec t r o s c o p y M e t r i c ( T S M ) TOI 776 b
TOI 776 c
Radius (R )1.02.0 250300350400450500550 E qu ili b r i u m t e m p er a t u re ( K ) Fig. 13.
The transmission spectroscopy metric (TSM) for exoplanets from the Exoplanet Encyclopedia with a radius less than 3 R ⊕ and a massdetermination by RVs or TTVs. TOI-776 b and c are labeled and marked with thicker black borderlines. Smaller planets are expected to have enhanced metallicities(e.g. Wakeford et al. 2017). Therefore, we investigated two devi-ations from our solar abundance fiducial model: 1) an enhancedcarbon-to-oxygen ratio (C / O) two-times the solar value, and 2)an enhanced metallicity of hundred times higher than solar. C / Oenhancement alone does not a ff ect the composition and spectralfeatures substantially, as seen in Fig. 14 middle panels. On theother hand, one might expect a higher metallicity to result inmore pronounced spectral features, due to higher species abun-dances. However, the bottom panels of Fig. 14 discard this pos-sibility. On the contrary, an enhanced metallicity causes a highermean molecular weight, which in turn shrinks the spectral sig-nificance (bottom-left panel of Fig. 14), and, simultaneously, itresults in a higher haze production, which also obscures the spec-tra significantly (bottom-right panel of Fig. 14). Therefore, a flattransmission spectrum may indicate a hazy atmosphere with ahigh metallicity (Kreidberg et al. 2014) as opposed to a non-existing atmosphere (Kreidberg et al. 2019). Complementary ob-servations, such as ground-based high-resolution spectroscopyor spectroscopy of the reflected light, are required to reveal thetrue nature of these flat spectra.
7. Summary
We present the discovery and characterization of the two-planetsystem transiting the bright ( V = .
54 mag , J = .
48 mag)M1 V star TOI-776. Both planets were detected by the
TESS mission, confirmed from ground-based transit follow-up obser-vations and have their dynamical masses determined with pre-cise RV measurements using HARPS. In addition, fifteen yearsof ground-based photometric monitoring by ASAS-SN, ASAS,NSVS, Catalina, and SuperWASP help us to measure a rota-tional period between 30 to 40 d, typical of inactive early-typeM dwarfs. Our findings are summarized below: – A joint fit of all the available transit photometry from
TESS ,MEarth, and LCOGT and the precise RVs from HARPS re-veals that the TOI-776 system consists of two transiting plan-ets, namely TOI-776 b, which has a period of 8.25 d, a radiusof 1 . ± . R ⊕ , a mass of 4 . ± . M ⊕ , a bulk density of3 . + . − . g cm − , and an equilibrium temperature of 514 ±
17 K;and TOI-776 c, which has a period of 15.66 d, a radius of2 . ± . R ⊕ , a mass of 5 . ± . M ⊕ , a bulk density of3 . + . − . g cm − , and an equilibrium temperature of 415 ±
14 K.The RV data show one additional signal, with a period of34 d, associated with the star’s rotation, in agreement fromour analyses of the photometry and spectral line indicators. – The bulk densities of TOI-776 b and c allow for a wide rangeof possible interior compositions, from water worlds to rockyplanets with H / He-rich atmospheres, but they are too low foreither planet to have a purely terrestrial (iron plus rock) com-position. Thus, an atmosphere is expected for both planets. – From its location in a period-radius diagram, TOI-776 b liesin the transition region where formation and evolution mod-els make di ff erent predictions for planetary systems orbiting Article number, page 16 of 26. Luque et al.: A multi-planetary system around TOI-776 [Fe/H]=1×Solar; C/O=1×Solar
Without Haze Hazy
TOI-776bTOI-776c T r a n s i t D e p t h ( pp m ) [Fe/H]=1×Solar; C/O=2×Solar [Fe/H]=100×Solar; C/O=1×Solar Fig. 14.
Synthetic atmospheric spectra of TOI-776 b (red) and c (blue).
Top : Fiducial models with solar abundance (solid lines). Estimateduncertainties are shown for
JWST
NIRISS-SOSS, NIRSpec-G395M, and MIRI-LRS configurations, assuming two transits and binned for R = Middle : Enhanced carbon-to-oxygen ratio by a factor of two.
Bottom : Enhanced metallicity by a factor of 100. The left column represents spectrawithout haze opacity and the right column with haze opacity.
M dwarfs. For the TOI-776 system, the planets lie above theradius valley carved by gas-poor formation mechanisms, inagreement with their bulk densities being incompatible withthe absence of an atmosphere. Still, it is possible that theplanets are still undergoing slow thermally driven mass lossunder the core-powered scenario. – The TOI-776 system is an excellent target for the
JWST . Itis the only known multi-planetary system with planets insideand near the radius valley for which all planets: 1) have abulk density determination with at least 30% relative uncer-tainties, and 2) are extremely suitable for atmospheric char-acterization. Thanks to the brightness of its host star, it is aremarkable laboratory to break the degeneracy in planetaryinterior models and to test formation and evolution theoriesof small planets around low-mass stars.
Acknowledgements.
This work was supported by the KESPRINT collaboration,an international consortium devoted to the characterization and research of exo-planets discovered with space-based missions. We are very grateful to the ESOsta ff members for their precious support during the observations. We warmlythank Xavier Dumusque and François Bouchy for coordinating the shared obser-vations with HARPS and Jaime Alvarado Montes, Xavier Delfosse, GuillaumeGaisné, Melissa Hobson, and Felipe Murgas who helped collecting the data. Thispaper includes data collected by the TESS mission. Funding for the
TESS missionis provided by the NASA Explorer Program. We acknowledge the use of
TESS
Alert data, which is currently in a beta test phase, from pipelines at the
TESS
Science O ffi ce and at the TESS
Science Processing Operations Center. Resourcessupporting this work were provided by the NASA High-End Computing (HEC)Program through the NASA Advanced Supercomputing (NAS) Division at AmesResearch Center for the production of the SPOC data products. This research hasmade use of the Exoplanet Follow-up Observation Program website, which isoperated by the California Institute of Technology, under contract with the Na-tional Aeronautics and Space Administration under the Exoplanet ExplorationProgram. This work has made use of data from the European Space Agency(ESA) mission
Gaia ( ), processed bythe Gaia
Data Processing and Analysis Consortium (DPAC, . cosmos.esa.int/web/gaia/dpac/consortium ). Funding for the DPAC hasbeen provided by national institutions, in particular the institutions participatingin the Gaia
Multilateral Agreement. The MEarth Team gratefully acknowledgesfunding from the David and Lucile Packard Fellowship for Science and Engi-neering (awarded to D.C.). This material is based upon work supported by theNational Science Foundation under grants AST-0807690, AST-1109468, AST-1004488 (Alan T. Waterman Award), and AST-1616624, and upon work sup-ported by the National Aeronautics and Space Administration under Grant No.80NSSC18K0476 issued through the XRP Program. This work is made possibleby a grant from the John Templeton Foundation. The opinions expressed in thispublication are those of the authors and do not necessarily reflect the views ofthe John Templeton Foundation. This work makes use of observations from theLCOGT network. Some of the Observations in the paper made use of the High-Resolution Imaging instrument Zorro. Zorro was funded by the NASA ExoplanetExploration Program and built at the NASA Ames Research Center by Steve B.Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley. Data were reducedusing a software pipeline originally written by Elliott Horch and Mark Everett.Zorro was mounted on the Gemini South telescope, and NIRI was mounted onthe Gemini North telescope, of the international Gemini Observatory, a programof NSF’s OIR Lab, which is managed by the Association of Universities for Re-search in Astronomy (AURA) under a cooperative agreement with the NationalScience Foundation on behalf of the Gemini partnership: the National ScienceFoundation (United States), National Research Council (Canada), Agencia Na-cional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología eInnovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comuni-cações (Brazil), and Korea Astronomy and Space Science Institute (Republic ofKorea). Data collected under program GN-2019A-LP-101. Based in part on ob-servations obtained at the Southern Astrophysical Research (SOAR) telescope,which is a joint project of the Ministério da Ciência, Tecnologia e Inovações(MCTI / LNA) do Brasil, the US National Science Foundation’s NOIRLab, theUniversity of North Carolina at Chapel Hill (UNC), and Michigan State Univer-sity (MSU). This work was enabled by observations made from the Gemini Northtelescope, located within the Maunakea Science Reserve and adjacent to the sum-mit of Maunakea. We are grateful for the privilege of observing the Universefrom a place that is unique in both its astronomical quality and its cultural signif-icance. Based on observations collected at the European Organization for Astro-nomical Research in the Southern Hemisphere under ESO programme 0103.C-0449(A). R. L. has received funding from the European Union’s Horizon 2020research and innovation program under the Marie Skłodowska-Curie grant agree-ment No. 713673 and financial support through the “la Caixa” INPhINIT Fellow-ship Grant LCF / BQ / IN17 / Article number, page 17 of 26 & A proofs: manuscript no. main
Centers of Excellence from “la Caixa” Banking Foundation, Barcelona, Spain.This work is partly financed by the Spanish Ministry of Economics and Com-petitiveness through projects ESP2016-80435-C2-2-R and ESP2016-80435-C2-1-R. L. M. S. and D. G. gratefully acknowledge financial support from the CRTfoundation under Grant No. 2018.2323 “Gaseous or rocky? Unveiling the natureof small worlds". This work is supported by JSPS KAKENHI Grant NumbersJP19K14783, JP18H01265 and JP18H05439, and JST PRESTO Grant Num-ber JPMJPR1775. I. J. M. C. acknowledges support from the NSF through grantAST-1824644. J. K., Sz. Cs., M. E., A. P. H., K. W. F. L., S. G. acknowledge sup-port by DFG grants PA525 / / / / / /
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H., Huber, D., & Stello, D. 2019, ApJ, 878, 136 Article number, page 19 of 26 & A proofs: manuscript no. main Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife,Spain e-mail: [email protected] Departamento de Astrofísica, Universidad de La Laguna, 38206 LaLaguna, Tenerife, Spain Dipartimento di Fisica, Università degli Studi di Torino, via PietroGiuria 1, I-10125, Torino, Italy Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidel-berg, Germany Landessternwarte, Zentrum für Astronomie der Universität Heidel-berg, Königstuhl 12, 69117 Heidelberg, Germany Institute of Astronomy, University of Cambridge, Madingley Road,Cambridge CB3 0HA, UK Department of Astronomy, University of Tokyo, 7-3-1 Hongo,Bunkyo-ky, Tokyo 113-0033, Japan Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Taut-enburg, Germany Rheinisches Institut für Umweltforschung an der Universität zuKöln, Aachener Strasse 209, 50931 Köln, Germany Center for Planetary Systems Habitability and McDonald Observa-tory, The University of Texas at Austin, Austin, TX 78730, USA Department of Earth and Planetary Sciences, Tokyo Institute ofTechnology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan Stellar Astrophysics Centre, Department of Physics and Astronomy,Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Den-mark Sub-department of Astrophysics, Department of Physics, Universityof Oxford, Oxford, OX1 3RH, UK Cerro Tololo Inter-American Observatory / NSF’s NOIRLab, Casilla603, La Serena, Chile Deutsches Zentrum für Luft- und Raumfahrt, Institut für Planeten-forschung, 12489 Berlin, Rutherfordstrasse 2., Germany Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street,Cambridge, MA 02138, USA George Mason University, 4400 University Drive, Fairfax, VA,22030 USA Exoplanets and Stellar Astrophysics Laboratory, Mail Code 667,NASA Goddard Space Flight Center, 8800 Greenbelt Rd., Green-belt MD, 20771, USA Department of Physics and Astronomy, University of Kansas,Lawrence, KS, USA Division of Geological and Planetary Sciences, California Instituteof Technology, 1200 East California Blvd, Pasadena, CA, 91125,USA Leiden Observatory, Leiden University, 2333CA Leiden, TheNetherlands Department of Space, Earth and Environment, Chalmers Universityof Technology, Onsala Space Observatory, 439 92 Onsala, Sweden Department of Earth, Atmospheric and Planetary Sciences, Mas-sachusetts Institute of Technology, Cambridge, MA 02139, USA Department of Physics and Kavli Institute for Astrophysics andSpace Research, Massachusetts Institute of Technology, Cambridge,MA 02139, USA Space Science & Astrobiology Division, NASA Ames ResearchCenter, Mo ff ett Field, CA 94035, USA Dept. of Physics & Astronomy, Swarthmore College, SwarthmorePA 19081, USA Astronomical Institute, Czech Academy of Sciences, Friˇcova 298,25165, Ondˇrejov, Czech Republic Space Telescope Science Institute, Baltimore, MD, USA Department of Physics and Astronomy, University of Louisville,Louisville, KY 40292, USA Center for Astronomy and Astrophysics, Technical UniversityBerlin, Hardenbergstr. 36, 10623 Berlin, Germany Department of Physics and Astronomy, The University of NorthCarolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA Komaba Institute for Science, The University of Tokyo, 3-8-1Komaba, Meguro, Tokyo 153-8902, Japan JST, PRESTO, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Astronomy Department and Van Vleck Observatory, Wesleyan Uni-versity, Middletown, CT 06459, USA European Southern Observatory (ESO), Alonso de Córdova 3107,Vitacura, Casilla 19001, Santiago de Chile Department of Aeronautics and Astronautics, Massachusetts Insti-tute of Technology, 77 Massachusetts Avenue, Cambridge, MA02139, USA Perth Exoplanet Survey Telescope, Perth, Western Australia Mullard Space Science Laboratory, University College London,Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK Department of Astrophysical Sciences, Princeton University, 4 IvyLane, Princeton, NJ 08544, USA Dunlap Institute for Astronomy and Astrophysics, University ofToronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada
Table 4.
Median and the 68% credibility intervals of the posterior dis-tributions for each fitted parameter of the final joint model obtained forthe TOI-776 system using juliet . Priors and descriptions for each pa-rameter can be found in Table A.1.
Parameter TOI-776 b TOI-776 c
Stellar parameters ρ (cid:63) (kg m − ) 6024 + − Planet parametersP (d) 8 . + . − . . + . − . t (a) . + . − . . + . − . r . + . − . . + . − . r . + . − . . + . − . e (b) . + . − . ( < .
18) 0 . + . − . ( < . ω − + − − + − K (m s − ) 1 . + . − . . + . − . Photometry parameters σ TESS (ppm) 1 . + . − . q , TESS . + . − . q , TESS . + . − . σ LCO-CTIO (ppm) 1000 + − M LCO-CTIO (ppm) 890 + − θ LCO-CTIO . + . − . q , LCO-CTIO . + . − . σ LCO-SAAO (ppm) 471 + − M LCO-SAAO (ppm) − + − θ LCO-SAAO − . ± . q , LCO-SAAO . + . − . σ LCO-SSO (ppm) 885 + − M LCO-SSO (ppm) − + − θ LCO-SSO − . ± . q , LCO-SSO . + . − . σ MEarth (ppm) 1734 + − M MEarth (ppm) − + − q , MEarth . + . − . RV parameters µ HARPS (m s − ) 4 . + . − . σ HARPS (m s − ) 1 . + . − . GP hyperparameters and additional sinusoid σ GP , TESS (ppm) 0 . + . − . T GP , TESS (d) 0 . + . − . K (m s − ) 2 . + . − . t (b) . + . − . P (d) 34 . + . − . Notes. ( a ) Units are BJD - 2450000. ( b ) σ upper limit in parenthesis.Article number, page 20 of 26. Luque et al.: A multi-planetary system around TOI-776 Table 5.
Derived planetary parameters obtained for the TOI-776 sys-tem using the posterior values from Table 4 and stellar parameters fromTable 2.
Parameter (a)
TOI-776 b TOI-776 c
Derived transit parametersp = R p / R (cid:63) . + . − . . + . − . b = ( a / R (cid:63) ) cos i p . + . − . . + . − . a / R (cid:63) . + . − . . + . − . i p (deg) 89 . + . − . . + . − . t T (h) 2 . + . − . . + . − . Derived physical parametersM p ( M ⊕ ) 4 . ± . . ± . R p ( R ⊕ ) 1 . ± .
13 2 . ± . ρ p (g cm − ) 3 . + . − . . + . − . g p (m s − ) 11 . + . − . . + . − . a p (au) 0 . ± . . ± . T eq (K) (b) ±
17 415 ± S ( S ⊕ ) 11 . ± . . ± . Notes. ( a ) Error bars denote the 68% posterior credibility intervals. ( b ) Equilibrium temperatures were calculated assuming zero Bondalbedo and uniform surface temperatures across the entire planet. Article number, page 21 of 26 & A proofs: manuscript no. main
Appendix A: Joint fit priors.Appendix B: HARPS RV measurements andspectral line indicators.Appendix C: Corner plots.
Article number, page 22 of 26. Luque et al.: A multi-planetary system around TOI-776
Table A.1.
Priors used for the models presented in Sect. 5 using juliet . The prior labels of N , U , B and J represent normal, uniform, Betaand Je ff rey’s distributions. The parameterization for ( p , b ) using ( r , r ) (Espinoza 2018) and the linear ( q ) and quadratic ( q , q ) limb darkeningparameterization (Kipping 2013) are both described in Sect. 5.2.1. Parameter name Prior Units Description
Stellar parameters ρ (cid:63) N (5300 , ) kg m − Stellar density.
Planet parametersP b N (8 . , . ) d Period of planet b. P c N (15 . , . ) d Period of planet c. t , b − N (8571 . , . ) d Time of transit-center of planet b. t , c − N (8572 . , . ) d Time of transit-center of planet c. r , b U (0 ,
1) . . . Parametrization for p and b of planet b. r , b U (0 ,
1) . . . Parametrization for p and b of planet b. r , c U (0 ,
1) . . . Parametrization for p and b of planet c. r , c U (0 ,
1) . . . Parametrization for p and b of planet c. K b U (0 ,
20) m s − RV semi-amplitude of planet b. K c U (0 ,
20) m s − RV semi-amplitude of planet c. e b B (1 . ,
29) . . . Eccentricity of planet b. e c B (1 . ,
29) . . . Eccentricity of planet c. ω b U ( − , ω c U ( − , Photometry parameters σ TESS J (1 , TESS . D TESS
TESS . M TESS ff set for TESS . q , TESS U (0 ,
1) . . . Quadratic limb darkening parametrization for
TESS . q , TESS U (0 ,
1) . . . Quadratic limb darkening parametrization for
TESS . σ LCO-CTIO J (10 , ) ppm Extra jitter term for LCO-CTIO. M LCO-CTIO N (0 , . ) ppm Relative flux o ff set for LCO-CTIO. θ LCO-CTIO U ( − . , .
0) . . . Airmass regression coe ffi cients for LCO-CTIO. q , LCO-CTIO U (0 ,
1) . . . Linear limb darkening parametrization for LCO-CTIO. σ LCO-SAAO J (10 , ) ppm Extra jitter term for LCO-SAAO. M LCO-SAAO N (0 , . ) ppm Relative flux o ff set for LCO-SAAO. θ LCO-SAAO U ( − . , .
0) . . . Airmass regression coe ffi cients for LCO-SAAO. q , LCO-SAAO U (0 ,
1) . . . Linear limb darkening parametrization for LCO-SAAO. σ LCO-SSO J (10 , ) ppm Extra jitter term for LCO-SSO. M LCO-SSO N (0 , . ) ppm Relative flux o ff set for LCO-SSO. θ LCO-SSO U ( − . , .
0) . . . Airmass regression coe ffi cients for LCO-SSO. q , LCO-SSO U (0 ,
1) . . . Linear limb darkening parametrization for LCO-SSO. σ MEarth J (10 , ) ppm Extra jitter term for MEarth. M MEarth N (0 , . ) ppm Relative flux o ff set for MEarth. q , MEarth U (0 ,
1) . . . Linear limb darkening parametrization for MEarth.
RV parameters µ HARPS U ( − , − Systemic velocity for HARPS. σ HARPS J (0 . , − Extra jitter term for HARPS.
GP hyperparameters and additional sinusoid σ GP , TESS J (10 − , ) ppm Amplitude of GP component for TESS. T GP , TESS J (10 − , ) d Length scale of GP component for TESS. K U (0 ,
20) m s − RV semi-amplitude of the additional sinusoid. t − U (8575 . , .
0) d Time of transit-center the additional sinusoid. P N (35 . , . ) d Period of the additional sinusoid. Article number, page 23 of 26 & A proofs: manuscript no. main
Table B.1. serval extraction.
BJD
TBD − − ) σ RV (m s − ) CRX (m s − Np − ) σ CRX (m s − Np − ) dLW (m s − ) σ dLW (m s − )1884.75667 4.3 3.1 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − Article number, page 24 of 26. Luque et al.: A multi-planetary system around TOI-776
Table B.2.
TERRA extraction.
BJD
TBD − − ) σ RV (m s − ) H α S-index σ S − index NaD NaD − − − − − − − − − − − − − − Article number, page 25 of 26 & A proofs: manuscript no. main P b [d] = 8.25 +0.000.00 . . . . . t , b [ B J D ] +8.5714e3 t b [BJD] = 8571.42 +0.000.00 . . . . r , b r b = 0.50 +0.070.10 . . . . r , b r b = 0.03 +0.000.00 . . . e b e b = 0.06 +0.030.02 b [ d e g ] b [deg] = 67.42 +117.2973.17 K b [ m / s ] K b [m/s] = 1.89 +0.400.44 . . . . . P c [ d ] +1.566e1 P c [d] = 15.67 +0.000.00 . . . . . t , c [ B J D ] +8.572e3 t c [BJD] = 8572.60 +0.000.00 . . . . r , c r c = 0.51 +0.080.08 . . . . . r , c r c = 0.03 +0.000.00 . . . . e c e c = 0.04 +0.020.01 c [ d e g ] c [deg] = 10.88 +55.1079.04 . . . . P b [d] +8.246 . . . K c [ m / s ] .
009 0 .
012 0 .
015 0 .
018 0 . t b [BJD] +8.5714e3 .
40 0 .
48 0 .
56 0 . r b .
028 0 .
030 0 .
032 0 . r b .
08 0 .
16 0 . e b
160 80 0 80 160 b [deg] K b [m/s] . . . . . P c [d] +1.566e1 .
594 0 .
597 0 .
600 0 .
603 0 . t c [BJD] +8.572e3 . . . . r c . . . . . r c .
06 0 .
12 0 .
18 0 . e c
160 80 0 80 160 c [deg] . . . K c [m/s] K c [m/s] = 2.06 +0.680.68 Fig. C.1.
Posterior distributions of the orbital parameters of the TOI-776 system. Each panel contains ∼
220 000 samples. The top panels of thecorner plot show the probability density distributions of each orbital parameter. The vertical dashed lines indicate the 16th, 50th, and the 84thpercentiles of the samples. Contours are drawn to improve the visualization of the 2D histograms and indicate the 68.3%, 95.5%, and 99.7%confidence interval levels (i.e., 1 σ , 2 σ, and 3 σσ