TESS discovery of a super-Earth orbiting the M-dwarf star TOI-1680

Over its two-year primary mission, TESS (Ricker et al., 2015) performed an all-sky survey in a series of contiguous overlapping $96\times 24\leavevmode\nobreak\ \rm deg$ sectors, each observed for 27 days. Depending on the ecliptic latitude, the overlapping regions of the sectors were observed for up to $\sim$351 days. Given its high ecliptic latitude ($\beta=+81.05$ deg), TOI-1680 (TIC 259168516) is well placed in the TESS CVZ. It was then observed by TESS in all the northern sectors (from 14 to 26) in the second year of TESS primary mission, from 18 July 2019 to 4 July 2020. It was also observed in the TESS extended mission in sectors 40-41 from 25 June to 20 August 2021. Most recently, it was observed in sectors 47–59 from 31 December 2021 to 23 December 2022. The target pixel files (TPFs) and simple aperture photometry (SAP) apertures used in each sector are shown in Fig. 1, along with the superplotted locations of nearby Gaia DR2 (Gaia Collaboration et al., 2018) sources. The astrometric and photometric properties of TOI-1680 from the literature are reported in Table 2. The time series observations were processed in the TESS Science Processing Operations Center (SPOC) pipeline, originally developed for the Kepler mission at NASA Ames Research Center (Jenkins et al., 2016, 2020a). The SPOC pipeline conducted a transit search of the combined light curve from sectors 14-16 on 26 October 2019 with an adaptive, noise-compensating matched filter (Jenkins, 2002; Jenkins et al., 2010, 2020b), producing a threshold crossing event (TCE) with 4.8 day period for which an initial limb-darkened transit model was fitted (Li et al., 2019) and a suite of diagnostic tests were conducted to help make or break the planetary nature of the signal (Twicken et al., 2018). The 5.1 ppt transit signature passed all diagnostic tests presented in the SPOC data validation reports, and the source of the transit signal was localized within $4.03\pm 4.58$ ″. The TESS Science Office (TSO) reviewed the vetting information and issued an alert for TOI-1680 b on 30 January 2020 (Guerrero et al., 2021).

For subsequent analysis, we retrieved the 2-minute presearch data conditioning light curves (PDC-SAP, Stumpe et al. 2012, 2014; Smith et al. 2012) from the Mikulski Archive for Space Telescopes (MAST). We were limited to sectors 13–26 of the primary mission and sectors 47–50 of the extended mission. We removed all the bad data points flagged as ”bad quality.” We then detrended the light curves to remove stellar variability using a biweight time-windowed slider via wotan (Hippke et al., 2019). We excluded the transit signal by applying a filter window that is three times longer than the transit duration of $71.150_{-0.936}^{+0.993}$ minutes.

The pixel scale of TESS spacecraft is 21″ per pixel (Ricker et al., 2015). A targeted star might not be alone in a single pixel. Other stars in the same pixel might be suspected to be the source of the TESS detection. Even if the transit signal is on target, the depth might appear shallower because of the contaminating nearby stars. To confirm the signal on target and validate its planetary nature, a series of precise ground-based observations were collected using five observatories as part of the TESS Follow-up Observing Program (TFOP¹¹1https://tess.mit.edu/followup). We made use of TESS Transit Finder (TTF) tool, which is a customized version of the Tapir software package (Jensen, 2013), to schedule our observations described hereafter.

With the aim of better constraining the stellar properties, we also performed spectroscopic observation detailed hereafter. The analyses are presented in Sect. 3.1.1.

As part of our standard process for validating transiting exoplanets to assess the possible contamination of bound or unbound companions on the derived planetary radii (Ciardi et al., 2015), we observed the TOI-1680 with near-infrared adaptive optics (AO) imaging at Keck and Shane Observatories. Gaia DR3 is also used to provide additional constraints on the presence of undetected stellar companions as well as wide companions.

In addition to the high resolution imaging, we have used Gaia to identify any wide stellar companions that may be bound members of the system. Typically, these stars are already in the TESS Input Catalog and their flux dilution to the transit has already been accounted for in the transit fits and associated derived parameters from the TESS PDC-SAP photometry. There are no additional widely separated companions identified by Gaia that have the same distance and proper motion as TOI-1680 (see also Mugrauer & Michel, 2020, 2021).

Additionally, the Gaia DR3 astrometry provides additional information on the possibility of inner companions that may have gone undetected by either Gaia or the high resolution imaging. The Gaia renormalised unit weight Error (RUWE) is a metric, similar to a reduced chi-square, where values that are $\lesssim 1.4$ indicate that the Gaia astrometric solution is consistent with the star being single whereas RUWE values $\gtrsim 1.4$ may indicate an astrometric excess noise, possibly caused by the presence of an unseen massive (stellar) companion (e.g., Ziegler et al., 2020). TOI-1680 has a Gaia DR3 RUWE value of 1.05 indicating that the astrometric fits are consistent with the single star model.

To statistically validate TOI-1680 b, we used TRICERATOPS⁵⁵5https://github.com/stevengiacalone/triceratops (Giacalone et al., 2021), which validates planets by simulating astrophysical false positives arising from gravitationally bound stellar companions, chance-aligned foreground or background stars, and known nearby stars that are blended with the target in the TESS data. It uses a Bayesian tool that incorporates prior knowledge of the target star, planet occurrence rates, and stellar multiplicity to calculate the false positive probability (FPP) and nearby false positive probability (NFPP). The FPP quantity represents the probability that the observed transit is due to something other than a transiting planet around the target star and the NFPP quantity represents the probability that the observed transit originates from a resolved nearby star rather than the target star. Giacalone et al. (2021) state that for a planet to be statistically validated it must have $\rm FPP<0.015$ and $\rm NFPP<0.001$.

We first applied TRICERATOPS to the TESS 2-min-cadence light curve supplied with the contrast curve obtained by the NIRC2 speckle imaging in Sect. 2.4.1. The resulting FPP and NFPP values are $0.0018\pm 0.0001$ and $0.0017\pm 0.0001$ respectively. The FPP is good enough but NFPP is above the threshold to classify a validated planet (Giacalone et al., 2021). Only three nearby stars were bright enough and close enough to the target star to cause nearby false positives: TIC 1884271108 ($\Delta T=6.4$, ${\rm sep}=6\arcsec$), TIC 259168518 ($\Delta T=1.3$, ${\rm sep}=30\arcsec$), and TIC 259168513 ($\Delta T=2.6$, ${\rm sep}=37\arcsec$). However, because the event observed by TESS was confirmed to be on-target by our ground-based observations, we were able to rule out these stars as sources of false positives and set NFPP = 0 from the outset. The FPP is then reduced to $0.0001\pm 0.0001$, which is low enough for validating the planet. Independently, we also used the light curves obtained by the Artemis 1-m and LCO-Hal 2-m telescopes as they present tighter photometric constraints than the TESS data. This was supplied with the same contrast curve mentioned above and without removing any nearby star. This yields FPP and NFPP values generally lower than 0.01 and 0.001 respectively. Therefore, we consider this TESS candidate to be a validated planet.

With an ecliptic latitude of $\beta=+81.05$ deg, TOI-1680 is located near the northern ecliptic pole in the TESS CVZ. Targets in the CVZ are highly valuable for extracting long-period rotation rates. We first visually inspected the TESS PDC-SAP light curves and found no hints of rotational modulation nor evidence of flares. We then used the Systematics-Insensitive Periodogram (TESS-SIP ⁶⁶6https://github.com/christinahedges/TESS-SIP) to build a periodogram for photometric data from all the 19 sectors. This tool creates a Lomb-Scargle periodogram, while simultaneously detrending TESS systematics using a similar method to that described in Angus et al. (2016) for detrending systematics in the NASA Kepler/K2 dataset. Since the rotational period of the star might be removed by the PDC pipeline, TESS-SIP uses the TESS target pixel file (TPF) data, and apertures assigned by the TESS Pipeline to reproduce a simple aperture photometry (SAP) light curves of the target. We applied this operation on all the 19 observing sectors. Searching for periods between 10 and 365 days, we applied TESS-SIP on the target and on all the background pixels outside of the TESS pipeline aperture in the TESS TPFs for TOI-1680. The SIP powers, presented in Fig. 6, show a marked similarity between the periodograms of the target and of the background. For comparison, the lower panel shows the ratio of the target to the background powers. We do not see any significant peaks where the target would display power that would be substantially greater than that of the the background.

We also used TESS-SIP on each sector alone. We did not find any clear stellar rotation signal nor consistency between the periodograms of any sectors. In short, there is no hint of rotational variability detected for TOI-1680 in the TESS dataset, which is consistent with the lack of detectable H$\alpha$ emission in its optical spectrum.

Although the TESS CVZ light curves would encompass typical rotation periods for mid-M-dwarfs (0.1 to 140 days; e.g., Newton et al., 2016), we searched for completeness other ground-based photometric archives. Our target TOI-1680 is not part of the MEarth sample (Berta et al., 2012). We analyzed the ASAS-SN light curves (Shappee et al., 2014; Kochanek et al., 2017) for our object that had observations in $V$ and $g$, spanning from June 2012 to June 2023. We do not find rotational modulation. We note that given the faintness of our target in bluer bands (e.g., Gaia_BP = 16.27 mag), only $\sim$65% of the ASAS-SN observations were above the observational limit of each individual observation (with a median limiting magnitude of 16.832 mag in the full light curve). Furthermore, flares cannot be robustly detected in the ASAS-SN data because of its cadence (about two to three days; Jayasinghe et al., 2018).

We jointly analyzed the light curves from TESS and ground-based instrumentation described in Sect. 2 using the EXOFASTv2 (Eastman et al., 2019) software package. We included the TESS photometric data described in Sect. 2.1 from sectors 14 to 50. We detrended the ground-based light curves for the airmass, as well as for either the background or the half width at half maximum (HWHM) of the PSF. The choice of these parameters was based on the likelihood maximization. Some light curves were detrended only for airmass, especially the partial ones. Table 1 shows the detrending parameters of each light curve. The detrending was done simultaneously with the transit fitting to ensure a good propagation of the uncertainties on the derived parameters. We fixed the eccentricity to zero assuming the orbit to be circular (see justification below). We set the NOMIST flag to disable the MIST stellar track that constrains the star and, instead, we imposed Gaussian priors on the stellar mass ($0.1800\pm 0.0044\rm\,M_{\odot}$), radius ($0.2100\pm 0.0064\rm\,R_{\odot}$) and temperature ($3224\pm 100K$) from our determinations reported in Table 3 as well as uniform priors on the period ($P=4.8026\pm 0.1P$ d) and transit epoch ($T_{c}\pm P/3$) from the values reported in $ExoFOP$. We set the NOCLARET flag to disable the Claret tables (Claret, 2017; Claret & Bloemen, 2011) that are used to fit the quadratic limb-darkening parameters $u_{1}$ and $u_{2}$ and we applied our own gaussian priors computed using the PyLDTk code (Parviainen & Aigrain, 2015) for each passband (see Table 4). TESS light curves are corrected for contamination, but we still fit for dilution of the transit signal in the TESS band due to the neighboring stars using 0$\pm$10% of the contamination ratio reported in the TIC 259168516 on ExoFOP as Gaussian prior as recommended by Eastman et al. (2019) to account for any uncertainty in the correction. We ran the EXOFASTv2 analysis until convergence when the Gelman-Rubin statistic (GR) and the number of independent chain draws (Tz) were less than 1.01 and greater than 1000, respectively.

To test the impact of the detrending on our derived parameters, we performed independent analyses of the light curves with another code. We used the PyTransit package (Parviainen, 2015) and linear models of detrending vectors (FWHM, airmass and background), as done in Wells et al. (2021) and Schanche et al. (2022). We found good agreement between the fits and therefore continued with EXOFASTv2 for the full analysis. The detrended and modeled light curves are presented in Fig. 7 and the TESS phase-folded light curve is presented in Fig. 8. The results are reported in Table 5. We also fitted for an eccentric orbit to assess the evidence for orbital eccentricity using photometric-only data. A comparision of the loglikelihood of the two fits appears to favor a circular orbit.

We were concerned that the background level was overestimated and overcorrected in the SPOC pipeline in the northern year 2 sectors (14-26). Fitting only data from sectors 14 to 50 would lead to an overestimation of the planet radius by roughly 2%. However, this bias is comparable to the error bars on the planet radius and, the inclusion of the dilution term and additional ground-based data significantly mitigates the problem.

Studies performed by Fulton et al. (2017) on the Kepler small exoplanets have identified a radius valley roughly from 1.5 to 2 $\rm\,R_{\oplus}$, separating rocky super-Earths and gaseous sub-Neptunes around Sun-like stars. A low-radius peak at $1.3\,\rm\,R_{\oplus}$ corresponds to high-density super-Earths and a high-radius peak at $2.4\rm\,R_{\oplus}$ corresponds to low-density sub-Neptunes with significant primordial H/He atmospheres. This gap is considered as possible transition region between rocky and icy ”super-Earth” and ”mini-Neptunes.” Cloutier & Menou (2020) showed that the radius valley persists for low-mass stars (i.e., $M\lesssim 0.65$ $\rm\,R_{\odot}$).

Two contrasting theories have been presented to explain the radius valley. The first is gas-poor formation model which proposes that the radius valley is a feature intrinsic to the exoplanet population from formation onward (Luque, R. et al., 2021; Lee et al., 2014; Lee & Chiang, 2016; Lee & Connors, 2021). Specifically, some planets are formed with extended H/He envelopes, whereas the population of rocky planets is formed later in a gas-poor environment after the gas is dissipated from the protoplanetary disk. The second is thermally driven atmospheric mass loss (Lopez & Fortney, 2013; Owen & Wu, 2013; Jin et al., 2014; Chen & Rogers, 2016), which proposes that the radius gap is formed through evolution after the gas accretion phase. That is, planets are formed with gaseous envelopes and some of them experience atmospheric escape through two scenarios: 1) photoevaporation (Lopez & Fortney, 2013; Owen & Wu, 2013; Jin et al., 2014; Chen & Rogers, 2016) triggered by energetic EUV and X-ray flux from the host star in the first $\sim$100 Myrs (Owen & Wu, 2013) of the system and 2) core-powered mass-loss (Ginzburg et al., 2016) triggered by the energy emergent from the cooling planetary core in a Gyr timescale (Ginzburg et al., 2018).

On the contrary, a recent study performed by Luque & Pallé (2022) further suggests that there is a density gap, but not a radius gap, separating rocky planets and water-rich worlds with no planets with intermediate composition. Using a sample of 34 exoplanets with well-characterized densities around M-dwarf stars, they identified three populations: rocky planets ($\rho=0.94\pm 0.13\leavevmode\nobreak\ \rho_{\oplus}$), water-rich planets ($\rho=0.47\pm 0.05\leavevmode\nobreak\ \rho_{\oplus}$), and gas-rich planets ($\rho=0.24\pm 0.04\leavevmode\nobreak\ \rho_{\oplus}$). These study findings favor the pebble accretion model (Venturini et al., 2020; Brügger et al., 2020) as the main mechanism for forming small planets around M dwarfs, where rocky planets are formed within the ice line while water-rich planets are formed beyond the ice line and then migrated inwards. However, as for previous studies, the sample of exoplanets used in this study is not large enough to draw firm conclusions.

Figure. 9 shows the current period–radius diagram of all known exoplanets with precise radius measurements orbiting M dwarfs. The empirical locations of the radius valley for FGK stars as predicted by thermally driven photoevaporation (dashed line) given by Van Eylen et al. (2018) and for low-mass stars as predicted by gas-poor formation (solid line) given by Cloutier & Menou (2020) are also displayed. With a radius of $1.466^{+0.063}_{-0.049}\rm\,R_{\oplus}$ and orbital period of $4.8026343\pm 0.0000030$ days, TOI-1680 b is located close to the center of the super-Earth population where the two models predict the location of small rocky planets. With a future planetary mass determination, TOI-1680 b can join the growing sample of small planets with precise bulk densities around M dwarfs.

The precise mass determination of TOI-1680 b would allow us to better constrain the detectability of a possible atmosphere and better locate the planet in the radius-density gap. High-precision radial velocity (RV) measurements will not only allow us to constrain the planetary mass, but also constrain its orbit such as its eccentricity, which may shed some light onto the dynamical history of the system. TOI-1680 b has a radius of $1.466^{+0.063}_{-0.049}\rm\,R_{\oplus}$. Thus, we expect a RV semi-amplitude of $3.78^{+1.3}_{-0.82}\,\mathrm{m\,s^{-1}}$, assuming a circular orbit and a mass of $3.18^{+1.1}_{-0.69}\,\rm\,M_{\oplus}$, as predicted from the mass–radius relation of Chen & Kipping (2017).

Not many high-precision spectrographs in the northern hemisphere are capable of detecting such a shallow signal from a faint target (V = 15.87 mag and J = 11.63 mag). Many typical planet finders, mounted on 2–4 m class telescopes such as CARMENES (Quirrenbach et al., 2020), HARPS-N (Cosentino et al., 2012), NEID (Schwab et al., 2016) or EXPRES (Jurgenson et al., 2016) have limiting magnitudes that are brighter than V=15.87. MAROON-X at the 8.1 m Gemini North telescope (Seifahrt et al., 2020) has shown to reach the necessary precision for faint M-dwarf host stars (Seifahrt et al., 2022). Despite the high declination, it would be possible to reach a S/N of about 40 in the red arm after a 15 min exposure. Assuming a stellar activity level of $\rm<1.5\,m\,s^{-1}$, this would allow for an overall precision of $0.7\,\mathrm{m\,s^{-1}}$ precision with about 70 spectra. Thus, it will be possible to measure the planet mass with state-of-the-art instrumentation at $\rm 5\,\sigma$ precision by investing about 29 h of telescope time on a 8-m-class telescope.

We assess the potential for atmospheric characterization of TOI-1680 b with JWST using the transmission spectroscopy metric (TSM, Kempton et al., 2018). The TSM quantifies the expected S/N in the transmission spectrum of a given planet with a cloud-free atmosphere. Analytically, it is expressed as:

where R_p and M_p are the planetary radius and mass in Earth units, $R_{*}$ is the stellar radius in Solar radii, $T_{eq}$ is the equilibrium temperature of the planet in K and $m_{J}$ is the apparent magnitude of the star in the J band. Also, $S$ is a scale factor whose value depends on the planetary radius range.

TOI-1680 b is a cool (T${}_{eq}<$ 500 K) super-Earth (R ¡ 1.5$\rm\,R_{\oplus}$). With J=11.6, the host star is within reach of the JWST NIRSpec/PRISM (0.6–5.3 $\mu$m) instrument (Jakobsen et al., 2022), which cannot observe stars brighter than J=10.5 without saturation. We used the TSM to assess the suitability of all cool (T${}_{eq}<$ 500 K) planets with radii smaller than $1.5\rm\,R_{\oplus}$ orbiting stars fainter than J=10.5 for atmospheric studies with this instrument. This sample of exoplanets contains 63 targets. We used the empirical mass–radius relation of Chen & Kipping (2017) to estimate the mass of planets that do not have mass measurements as is the case for TOI-1680 b. TSM values of these planets are shown in Fig. 10. We found that TOI-1680 b has a TSM=7.82 which indicate that it could be a suitable target for transmission studies with the JWST NIRSpec/PRISM instrument. Specifically, amongst 63 targets, TOI-1680 b ranks as the thirteenth most amenable target for these studies. It follows all the TRAPPIST-1 planets (Gillon et al., 2017), Kepler-42 d (Muirhead et al., 2012), K2-415 b (Hirano et al., 2023), LP 791-18 d (Peterson et al., 2023), LP 890-9 b (Delrez et al., 2022) and TOI-237 b(Waalkes et al., 2021). Moreover, the TSM is based on ten hours of JWST observing time and with an ecliptic latitude of $\beta=+81.05\deg$. TOI-1680 b is located near the JWST CVZ, and it has the advantage of being observable for about 250 days per year, which encourages its atmospheric characterization.