A 2:1 Mean-Motion Resonance Super-Jovian pair revealed by TESS, FEROS, and HARPS

We report the discovery of a super-Jovian 2:1 mean-motion resonance (MMR) pair around the G-type star TIC 279401253, whose dynamical architecture is a prospective benchmark for planet formation and orbital evolution analysis. The system was discovered thanks to a single transit event recorded by the Transiting Exoplanet Survey Satellite (TESS) mission, which pointed to a Jupiter-sized companion with poorly constrained orbital parameters. We began ground-based precise radial velocity (RV) monitoring with HARPS and FEROS within the Warm gIaNts with tEss (WINE) survey to constrain the transiting body's period, mass, and eccentricity. The RV measurements revealed not one but two massive planets with periods of 76.80$_{-0.06}^{+0.06}$ days and 155.3$_{-0.7}^{+0.7}$ days, respectively. A combined analysis of transit and RV data yields an inner transiting planet with a mass of 6.14$_{-0.42}^{+0.39}$ M$_{\rm Jup}$ and a radius of 1.00$_{-0.04}^{+0.04}$ R$_{\rm Jup}$, and an outer planet with a minimum mass of 8.02$_{-0.18}^{+0.18}$ M$_{\rm Jup}$, indicating a massive giant pair. A detailed dynamical analysis of the system reveals that the planets are locked in a strong first-order, eccentricity-type 2:1 MMR, which makes TIC 279401253 one of the rare examples of truly resonant architectures supporting disk-induced planet migration. The bright host star, $V \approx$ 11.9 mag, the relatively short orbital period ($P_{\rm b}$ = 76.80$_{-0.06}^{+0.06}$ d) and pronounced eccentricity (e =0.448$_{-0.029}^{+0.028}$) make the transiting planet a valuable target for atmospheric investigation with the James Webb Space Telescope (JWST) and ground-based extremely-large telescopes.

supporting disk-induced planet migration. The bright host star, V ≈ 11.9 mag, the relatively short orbital period (P b = 76.80 +0.06 −0.06 d) and pronounced eccentricity (e =0.448 +0.028 −0.029 ) make the transiting planet a valuable target for atmospheric investigation with the James Webb Space Telescope (JWST) and ground-based extremely-large telescopes.

INTRODUCTION
The number of known exoplanets discovered by different surveys up to 2022 December is more than 5200, including around 850 multiple-planet systems 1 . The majority of these exoplanets have been detected using the transit technique, primarily thanks to the highly successful NASA Kepler space telescope (Borucki et al. 2010), and the ongoing Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) mission. However, the transit signals alone do not reveal the planetary mass and orbital eccentricity. A better picture of the distribution of the planetary radii, dynamical masses, bulk densities, and orbital geometry is fundamentally important for studying exoplanet composition, evolution, and overall formation. Therefore, validating and characterizing orbital and physical parameters of transiting planets with precise radial velocity (RV) data is fundamentally important to link observations with theory.
The TESS survey has revealed many wellcharacterized exoplanet systems for which both mass and radius have been determined observationally. Indeed, the relatively small TESS telescope is the main instrument for the discovery of transiting exoplanets around relatively bright stars, which allows them to be confirmed with ground-based precise RV measurements. A major role in the global efforts to characterize TESS exoplanets is played by the Warm gIaNts with tEss (WINE) survey, which aims for the validation of warm (with periods ranging between 10 days < P < 300 days) Jovian gas-giants by inspecting the TESS Full Frame Images (FFI) data. Prospective targets are followed by an extensive RV monitoring with the FEROS 2 and the HARPS 3 precise RV spectographs. The WINE survey has been highly successful, having detected and characterized many giant planets (see e.g. Espinoza et al. 2020;Jordán et al. 2020;Brahm et al. 2020;Schlecker et al. 2020;Trifonov et al. 2021a, among many more).
In this paper, we report the discovery of a warm massive exoplanet pair around a G-dwarf star, which has been uncovered within the WINE-TESS followup survey, based on RVs obtained with HARPS and FEROS. We present the TIC 279401253 two-planet system, which exhibits a significant single transiting event detected in TESS, consistent with a Jovian-sized planet. However, the acquired RVs of the TIC 279401253 system undoubtedly reveal a strongly interacting warm giant-mass pair of planets locked in a 2:1 mean motion resonance (MMR) commensurability. The detection and observational characterization of warm Jovian planets in 2:1 MMR is still a rare event, despite its importance for constraining planet migration.
The observational data is presented in Sect. 2. We use this data to detect and characterize the warm pair of planets that orbit around TIC 279401253. We present our estimates of the stellar parameters of TIC 279401253 in Sect. 3, along with the planetary orbital analysis performed jointly with the acquired Doppler data and TESS photometry. In Sect. 3, we also provide our results from an analysis on the dynamical architecture and longterm stability of the TIC 279401253 system. Finally, in Sect. 4, we present a brief summary and our conclusions.  the data. We did not identify bright contaminators in the FFI aperture (red continuous contour); thus we concluded that the transit signals are indeed coming from TIC 279401253 and not from neighbouring stars.
The 2-minute cadence light-curves are retrieved from the Mikulski Archive for Space Telescopes 5 . Simple aperture photometry (SAP) and systematics-corrected Pre-search Data Conditioning photometry (PDC, Smith et al. 2012;Stumpe et al. 2012) are provided by The Science Processing Operations Center (SPOC; Jenkins et al. 2016) . The PDCSAP light curves are corrected for contamination from nearby stars and instrumental systematics originating from pointing drifts, focus changes, etc., and for contamination from nearby stars.

RV Data
After the detection of the TESS transit, we initiated a Doppler follow-up campaign by obtaining precise RV data with the FEROS and HARPS spectrographs. We obtained 19 spectra of TIC 279401253 with FEROS between 2021 February and 2022 October , and 14 spectra with HARPS between 2021 September and 2022 October . With both instruments, we recorded stellar spectra in conjunction with a simultaneous ThAr lamp used for wavelength calibration. The exposure times were set to 1800 seconds, yielding an average signal-to-noise ratio per spectral resolution element of 76 for FEROS, and 34 for HARPS, respectively. The MLP power spectrum of the combined FEROS and HARPS Doppler measurements of TIC 279401253. Horizontal lines reflect the ∆lnL values, which correspond to 0.1%, 1% and 10% false alarm probabilities (from top to bottom). Two significant periods are detected: one near 79.4 days and the other near 160.6 days.The bottom panel shows the residuals of our two-planet best fit model (see Table 2), no significant peaks are observed.
The FEROS spectra were reduced, extracted, and analysed with the ceres pipeline (Brahm et al. 2017a). For the HARPS spectra, we retrieved precise RV measurements derived by the ESO-DRS pipeline. Both ceres and ESO-DRS use a spectrum cross-correlation function (CCF) method with a weighted binary mask (Pepe et al. 2002). With ceres, we measure FEROS RVs and bisector span measurements with a mean un- Note 1 -Gaia Collaboration et al. (2021).
certainty ofσ FEROS = 8.2 m s −1 . The DRS pipeline also provides the CCF's full-width half-maximum (FWHM) and the Bisector Inverse Slope span (BIS-span) measurements, which are valuable stellar activity indicators (Queloz et al. 2001). The mean RV uncertainty of ESO-DRS isσ HARPS = 2.9 m s −1 . When combined in common mean RV offset, the Doppler velocities show very large end-to-end periodic RV amplitude of ∼ 880 m s −1 , suggesting suggesting a massive substellar companion (or companions).. We did not detect any significant periodicity in the FEROS and HARPS activity data. The obtained FEROS RVs are presented in Table A1, and the precise HARPS-DRS RVs and activity index data are tabulated in A2.

Stellar parameters
TIC 279401253 is a G-type star visible in the Southern Hemisphere. The star is at a distance of about 287.1 +1.9 −1.9 pc from the Sun and has an apparent magnitude of V = 11.9 mag. The atmospheric and physical parameters were obtained using three coadded HARPS spectra and the ZASPE code (Brahm et al. 2017b). For TIC 279401253 we obtain an effective temperature of T eff = 5951±80 K, a metallicity of [Fe/H] = +0.20 ± 0.05, and a projected rotational velocity of vsini = 5.0±0.5 km sec −1 . Further, we derive stellar physical parameters using the PARSEC stellar isochrones (Bressan et al. 2012), following the recipe in Brahm et al. (2018) in conjunction with the Gaia parallaxes, and the public broadband photometry (G,G BP , G RP , J, H, K). We derive a stellar mass of M = 1.13 +0.02 −0.03 M and a stellar radius of R = 1.06 ± 0.01 R . We list the remaining atmospheric and physical parameters in Table 1.

Orbital analysis
For the transit, RV, and joint RV-transit analyses, we use the Exo-Striker exoplanet toolbox 6 (Trifonov 2019). Exo-Striker allows for the use of multiple-Keplerian or self-consistent N-body dynamical models. During the course of our analysis, though, we concluded that a single-transit event and the relatively sparse RV data led to strong degeneracies in the N-body model. Therefore, in this work, we only make use of the Keplerian model. The parameters in our transit model are: period P , eccentricity e, argument of periastron ω, inclination i, time of inferior transit conjunction t 0 , and the planetary semi-major axis a/R , and radius r/R (in relative stellar units), respectively. Additionally, we use quadratic limb darkening parameters for modeling the light curve. The parameters in our RV model are: RV semiamplitude K, orbital period P , eccentricity e, argument of periastron ω, and mean anomaly M 0 . All these parameters are valid for BJD = 2459151.0, which was deliberately chosen slightly before the epoch of the TESS mid-transit event. Additional fitting parameters in our RV modeling of TIC 279401253 were the FEROS and HARPS RV data offsets and variance (i.e., RV jitter, Baluev 2009).
For deriving the best-fit orbital parameters, we adopted a maximum likelihood estimator (MLE) scheme, which optimizes the parameters via the Nelder-Mead simplex algorithm (Nelder & Mead 1965), followed by a Levenberg-Marquardt (LM) algorithm (Press et al. 1992). These best-fit estimates and the LM covariance matrix confidence intervals serve as prior knowledge for our more detailed Bayesian posterior analysis of the orbital parameters. The latter was constructed using the dynesty sampler (Speagle 2020), which utilizes a nested sampling scheme (NS, Skilling 2004).

TESS analysis
Since the TESS light curve contains of only a singletransit event, no meaningful period estimate could be derived. However, the transit shape depends on the orbital inclination, the planet radius, r p /R , and the ratio of the semi-major axis of the planetary orbit to the stellar radius, a p /R . The latter is related to Kepler's third law, from which we could obtain a crude estimate of the orbital period (e.g. Sandford et al. 2019). Assuming a  circular orbit, we fit the TESS light curve with a Keplerian model, and we extract a mid-transit time t 0 = 2459151.054 +0.001 −0.001 BJD, an inclination i = 89.8 +0.1 −0.1 deg, a companion radius R b = 1.00 +0.03 −0.03 R Jup , and an orbital period P = 82.9 +23.1 −22.2 days. Based on these estimates, we initiated an RV follow-up within the WINE survey to confirm and characterize the planetary companion.

RV-only analysis
The precise Doppler data of TIC 279401253 exhibited strong periodicity, which could be attributed to a planetary companion. We performed a period search analysis by computing a maximum likelihood periodogram (MLP; Baluev 2008) to the combined HARPS and FEROS data set. The MLP fits a sine curve to the RV data for a given frequency grid and optimizes the semiamplitude, phase, RV offset, and RV jitter parameters of FEROS and HAPRS. The resulting ∆ ln L power spectrum is shown on Fig. 2. We detected two significant periods, one near 79.4 days and the other near 160.6 days.
A single Keplerian with a base period of 79.4 d did not lead to an adequate fit to the RV data. An MLP to the residuals confirmed the ∼ 160 d significant period. The combined RV data is consistent with two strong periodic signals in the 2:1 period ratio commensurability. We found that a two-planet Keplerian model presented an excellent RV solution with no significant periodicities left in the residuals. Our MLE bestfit suggests planetary periods of P b = 77.21±0.07 d, and P c = 154.5±0.4 d, RV semiamplitudes of K b = 340.7±12.1 m s −1 , and K c = 265.6±4.1 m s −1 , and eccentricities of e b = 0.46±0.02 d, and e c = 0.18±0.04 d, for the inner and the outer planet, respectively. We de-  rived minimum planetary masses of m b sin(i) ∼ 6.9M jup , and m c sin(i) ∼ 7.5 M jup , respectively.

RV-TESS joint analysis
We use the individual transit and RV parameters' MLE estimates to define our prior ranges. Then we run a joint MLE fit and NS global parameter posterior analysis. The single-transit event, together with the evidence of two similar Jovian-mass planets, poses the question, which planet actually transits? We tested both possibilities and could construct a consistent joint fit only when the TESS transit event is related to the inner planet, TIC 279401253 b. Therefore, our work only discusses fits with TIC 279401253 b being the transiting planet.
We performed an NS run, which allowed us to efficiently explore the parameter space of orbital elements and study the probability distribution of the posteriors. We ran 100 "live-points" per fitted parameter using the "Dynamic" NS scheme, focused on 100% posterior convergence instead of log-evidence (see, Speagle 2020, for details). The final adopted parameter priors, posteriors, and best-fit solution are listed in Table 2. The right panel of Fig. 1 shows the transit joint model counterpart to the TESS data. Fig. 3 shows the RV data together with the best-fit Doppler joint model of TIC 279401253 constrained by the single TESS transit event. The middle and right bottom panels of Fig. 3 show a phase-folded representation of the RV signals of TIC 279401253 b & c, respectively. There are no significant periods left in the residuals of this fit, as can be seen from the bottom panel of Fig. 2. The final posterior probability distributions are shown in Fig. A1. We note that our analysis is not strictly coplanar, as can be seen from table  Table 2. While we fit the inclination of the transiting planet, the inclination of the outer planet remains fixed at 90 deg (and ∆Ω = 0 deg). Therefore, our posterior distribution is consistent with a nearly coplanar edge-on system, which is a plausible outcome of the system architecture. The real mutual inclination, however, could be larger and is not possible to be revealed given the available data. Future additional transit and RV data in conjunction with photo-dynamical modeling could reveal the system architecture better. Furthermore, RV measurements during the transit events could measure the magnitude of the Rossiter-Mclaughlin effect, providing a valuable insight into the spin-orbit alignment of the planet's orbit with respect to the stellar rotation, thus offering a powerful tool to study its formation and subsequent orbital evolution. However, a more precise constraint on the transit timing would be required to make these observations feasible.
Our and e c = 0.254 +0.042 −0.036 . We measured a dynamical mass of m b = 6.14 +0.39 −0.42 M jup , and a minimum mass of m c sin(i) = 8.02 +0.18 −0.18 M jup , for the inner and outer planet, respectively.

TIC 279401253: A 2:1 MMR exoplanet system
The companion periods, eccentricities, and masses in the TIC 279401253 system point to a strongly interacting planet pair, which is likely involved in a 2:1 mean motion resonance (MMR). Therefore, we performed detailed numerical orbital evolution simulations to test this possibility and study the system's dynamical architec-ture. We use a custom version of the SyMBA symplectic N -body algorithm (Duncan et al. 1998) integrated in the Exo-Striker toolbox, which directly adopts and integrates the Jacobi orbital elements from the posterior orbital analysis. We tested the stability of the TIC 279401253 system up to 1 Myr with a small timestep of 0.2 d for 5000 randomly chosen samples from the joint transit+RV orbital parameter posteriors. For each integrated sample, we automatically monitored the evolution of the planetary semi-major axes, eccentricities, secular apsidal angle ∆ω = ω b -ω c , and first-order 2:1 MMR angles c is the mean longitude of planet b and c, respectively (see, e.g., Lee 2004).
We found that 73.4% of the examined 5000 samples are stable for 1 Myr, whereas the best-fit, for which we ran a longer simulation, is stable for 10 Myr. We found that the stable configurations exhibit common dynamical behaviour with the system locked in the 2:1 MMR. Fig. 4 shows an example of a 500 yr extent of the orbital evolution simulation started from the best-fit (i.e., maximum − ln L, see Table 2). We show the evolution of the mutual period ratio P rat. , and of the eccentricities e b and e c . The TIC 279401253 system is stable and osculates in the eccentricities and in the 2:1 period ratio. The apsidal alignment argument ∆ω librates around 0 • with semiamplitude of ∼ 65 • , whereas the characteristic 2:1 MMR angles, θ 1 and θ 2 , librate around 0 • with semiamplitudes respectively of ∼ 30 • and ∼ 55 • . Therefore, the massive planetary pair is locked in a 2:1 MMR with a short secular timescale of the order of ∼ 45 yr.
We observed a similar dynamical picture when we studied the stable posterior probability distribution. We found that 90% of the stable samples are locked in 2:1 MMR with ∆ω, θ 1 and θ 2 librating around 0 deg, with a median semiamplitudes of 62.3 deg, 31.7 deg, and 54.8 deg, respectively.

Transit predictions
As we discussed in Sect. 3.3, the 2:1 MMR system is dynamically active for a short time. Therefore, we expect strong transit timing variations (TTVs), which could be predicted for future observations. We extracted transit predictions from our dynamical analysis of the posterior distribution. We found that accurate TTV predictions are very challenging due to the strong ambiguity in eccentricity versus dynamical planetary mass space (Lithwick et al. 2012). Due to the large multimodality of the TTVs, the error in transit predictions rapidly accumulates and is close to a few tens of days in 2023 and accumulates even more in future epochs. We tried to construct a joint N-body model (e.g., Trifonov et al. 2021b) from the available data and therefore predict future transits from fitting alone. However, the singletransit event and the relatively sparse RV data manifest in strong N-body model degeneracy in the posteriors, which is consistent with the TTV prediction from our stability analysis. The TTVs super period of the TIC 279401253 pair of exoplanets is of the order of the libration frequency of the resonance angles θ 1,2 , i.e, ∼ 45 yr. Our estimate shows that the semiamplitude within this secular time scale in many cases is of the order of ten days. Thus, we could not give a meaningful prediction for the TTVs.
Nevertheless, the transiting planet is a prospective target for atmospheric investigation with the James Webb Space Telescope (JWST) and ground-based extremelylarge telescopes, given its bright host star, V ≈ 11.9 mag. the relatively short orbital period, and pronounced eccentricity. We plan to follow up this target with more RVs in an attempt to overcome the dynamical degeneracy and predict TTVs for future investigations.

SUMMARY AND CONCLUSIONS
We report the discovery of a warm pair of giant planets around the G-dwarf star TIC 279401253. The system is revealed by TESS light curve photometry and precise Doppler spectroscopy with FEROS and HARPS. Using the coadded HARPS spectra, we derived a stellar mass of M = 1.13 +0.02 −0.03 M and a stellar radius of R = 1.06 +0.01 −0.01 R , among other physical and atmospheric stellar parameters. Using these stellar mass and radius estimates, we extensively analyzed the available Figure 5. Mass-radius distribution of exoplanets, colourcoded by their estimated mean density. TIC 279401253 b is marked with a triangle, among the densest warm Jovian planets found up-to-date. Assuming that TIC 279401253 c also has a Jupiter-like radius, its position is marked with diamond-shaped sign.
data and constructed orbital posterior probability distributions. As a next step, we thoroughly analyzed the planetary system's dynamical architecture.
TIC 279401253 b is a transiting massive-Jovian planet with a measured mass of m b = 6.14 +0.39 −0.42 M jup , and radius of R b = 1.00 +0.04 −0.04 R jup . Thus, the estimated density of TIC 279401253 b is ρ b = 8.2 +1.1 −1.1 g cm −3 . Fig. 5 shows the distribution of planets with measured radius and mass, colour-coded for their density. The position of TIC 279401253 b on this plot places it among the densest planets discovered so far.
Based on the available RV data, we conclude that the outer planet, TIC 279401253 c, is similar to the inner super-Jovian planet with a minimum mass of m c = 8.02 +0.18 −0.18 M jup . The available TESS light curve from Sectors 4 and 31 do not have sufficient coverage to reveal whether TIC 279401253 c is transiting, but assuming its radius is consistent with that of TIC 279401253 b, then both planets in the system have high densities.
The warm pair of massive planets is found at the 2:1 period ratio commensurability with orbital periods of P b = 76.80 +0.06 −0.06 d for the inner planet, and P c = 155.3 +0.7 −0.7 d for the outer, respectively. We performed detailed N-body simulations of the posterior probability distributions to reveal the long-term stability and the overall dynamics of the TIC 279401253 system. We found that 73.4% of the posterior samples are stable for 1 Myr, and potentially beyond. The evolution of the apsidal alignment angle ∆ω, and the characteristic 2:1 MMR angles θ 1 and θ 2 , exhibit libration about 0 • . Thus, our numerical orbital analysis of the system unveiled that the massive pair of planets are deeply inside the first-order 2:1 MMR. The TIC 279401253 system is strikingly similar to the 2:1 MMR pair orbiting HD 82943, as reported by Tan et al. (2013). Using a self-consistent dynamical fitting to the RV data of HD 82943, Tan et al. (2013) unveiled two massive Jovian planets whose orbital geometry, physical, and dynamical characteristics are analogous to those of TIC 279401253. For instance, Tan et al. (2013) found that the HD 82943 system is very likely inclined to i = 19.5±5 deg, which makes the dynamical masses of the HD 82943 planets consistent with those of TIC 279401253 b, and c (see their Table 6). Furthermore, the orbital geometry and dynamical evolution of the two systems inside the 2:1 MMR exhibit practically the same pattern (see our Fig. 4, and, e.g., Figure 7 in Tan et al. 2013).
It is plausible to assume that both systems have undergone a common formation and orbital evolution history. Such massive planet pairs are likely assembled during convergent migration in massive primordial circumstellar disks (e.g., Lee & Peale 2002;Kley & Nelson 2012). For instance, such massive planets must have gone through a slow type II migration. Given the almost equal mass ratio and large osculating eccentricities, it suggests that the planets were locked in the 2:1 MMR with initially nonzero eccentricity (see, Lee 2004). This is intriguing since planet-disk interactions tend to damp the eccentricity. Nonetheless, Papaloizou et al. (2001) showed that planet-disk interactions could pump the eccentricity of very massive Jovians up to ≈ 0.25, which is a plausible mechanism for eccentricity excitation in the disk. Alternatively, the migration of massive planets through the disk creates wide gaps, and this leads to excitation of the eccentricities in the disk (see, e.g., Goldreich & Tremaine 1980;Goldreich & Sari 2003).
Therefore, the TIC 279401253 and HD 82943 systems and their dynamical similarities are crucial forensic evidence for planetary formation mechanisms.

APPENDIX
In this Appendix, Fig. A1 shows the posterior probability distribution of the joint Doppler and TESS photometry modeling with Exo-Striker, in Table A1 and Table A2 we list the spectroscopically derived RVs and activity index time-series from FEROS, and HARPS, respectively.