Trifon Trifonov

Lyu Abe

Abdelkrim Agabi

R Paul Butler

Mauro Barbieri

Jeffrey D Crane

Thomas Henning

Wenceslas Marie Sainte

Djamel Mékarnia

Sangeetha Nandakumar

Howard M Relles

Paula Sarkis

Pascal Torres

Stephen Shectman

Franc ¸ois-Xavier Schmider

Johanna Teske

Carl Ziegler

G Ricker

David W Latham

Alan M Levine

Scott Mcdermott

Juan Carlos

Torres Fellow

Typeset using L A T E X twocolumn style in AASTeX63

TOI-216 hosts a pair of warm, large exoplanets discovered by the TESS Mission. These planets were found to be in or near the 2:1 resonance, and both of them exhibit transit timing variations (TTV). Precise characterization of the planets' masses and radii, orbital properties, and resonant behavior can test theories for the origins of planets orbiting close to their stars. Previous characterization of the system using the first six sectors of TESS data suffered from a degeneracy between planet mass and orbital eccentricity. Radial velocity measurements using HARPS, FEROS, and PFS break that degeneracy, and an expanded TTV baseline from TESS and an ongoing ground-based transit observing campaign increase the precision of the mass and eccentricity measurements. We determine that TOI-216c is a warm Jupiter, TOI-216b is an eccentric warm Neptune, and that they librate in the 2:1 resonance with a moderate libration amplitude of 60 +2 -2 degrees; small but significant free eccentricity of 0.0222 +0.0005 -0.0003 for TOI-216b; and small but significant mutual inclination of 1.2-3.9 • (95% confidence interval). The libration amplitude, free eccentricity, and mutual inclination imply a disturbance of TOI-216b before or after resonance capture, perhaps by an undetected third planet.

INTRODUCTION

Warm Jupiters -defined here as giant planets with 10-100 day orbital periods -in systems with other nearby planets are an important population for the investigation of giant planets close to their stars. High eccentricity tidal migration -a strong contender for the origins of many close-in giant planets (see Dawson & Johnson 2018 for a review) is unlikely to have been at work in these systems (e.g., Mustill et al. 2015). Disk migration has been a persistently proposed explanation (e.g., Lee & Peale 2002) -particularly for systems in or near mean motion resonancebut recent studies have argued that in situ formation may be more consistent with these planets' observed properties (e.g., Huang et al. 2016;Frelikh et al. 2019;Anderson et al. 2020) and could possibly be consistent with resonant configurations (e.g., Dong & Dawson 2016;MacDonald & Dawson 2018;Choksi & Chiang 2020). Precise characterization of the orbital properties and resonant behavior of individual systems can test origins scenarios, complementary to population studies. One warm Jupiter system potentially amenable to such detailed characterization is TOI-216, which hosts a pair of warm, large exoplanets discovered by the TESS Mission (Dawson et al. 2019;Kipping et al. 2019). Their masses and orbits were characterized using transit timing variations (TTVs). However, previ-ously the TESS TTV dataset was not sufficiently precise to break the degeneracy between mass and eccentricity that arises when we can measure the near-resonant TTV signal but not the chopping TTV signal (e.g., Lithwick & Naoz 2011;Deck & Agol 2015). Different priors on mass and eccentricity led to two qualitatively different solutions for the system (Dawson et al. 2019): a Jupiter-mass planet accompanied by a Saturn-mass planet librating in orbital resonance, and a puffy sub-Saturn-mass planet and puffy Neptune-mass planet near but not in orbital resonance. The solutions also differed in the planets' free eccentricity, the eccentricity not associated with the proximity to resonance. Since any origins scenario under consideration needs to be able to account for the planets' masses, free eccentricities, and resonant behavior, detailed characterization of these properties with a more extended dataset is warranted.

Since our previous study (Dawson et al. 2019), seven more TESS transits of planet b, three more TESS transits of planet c, a ground-based transit of planet b, and five more ground-based transits of planet c have been observed, including recent ground-based transit observations that significantly extend the baseline for measuring transit timing variations beyond the observations conducted during the first year of the TESS primary mission. Furthermore, we have been conducting a groundbased radial-velocity campaign using HARPS, FEROS, and PFS. Radial-velocity measurements serve to break the mass-eccentricity degeneracy.

Here we combine TESS light curves, ground-based light curves, and ground-based radial velocities to precisely characterize TOI-216b and c. In Section 2, we describe our analysis of the TESS data and the observation and analysis of ground-based light curves. We identify a weak stellar activity periodicity in the TESS data that also shows up in the radial velocities. In Section 3, we present radial velocity measurements from HARPS, FEROS, and PFS and show that they immediately confirm the higher mass, lower eccentricity solution. We investigate additional weak periodicities in the radial-velocities and argue that they are caused by stellar activity. We jointly fit the transit timing variations and radial velocities in Section 4 and determine that the planet pair is librating in resonance, that the inner planet has a significant free eccentricity, and that planets have a small but significant mutual inclination. We present our conclusions -including implications for the system's origins -in Section 5.

LIGHT CURVE ANALYSIS

This paper is based on data from TESS Sectors 1-13 (2018 July 25 -2019 July 17) and Sectors 27-30 (2020 July 4 -2020 October 21), during which TOI-216 was observed with CCD 1 on Camera 4, and from ground-based observatories. We use the publicly available 2-min cadence TESS data, which is processed with the Science Processing Operations Center pipeline [START_REF] Jenkins | Proc. SPIE[END_REF]. We download the publicly available data from the Mikulski Archive for Space Telescopes (MAST). The pipeline, a descendant of the Kepler mission pipeline based at the NASA Ames Research Center (Jenkins et al. 2002(Jenkins et al. , 2010)), analyzes target pixel postage stamps that are obtained for pre-selected target stars.

We use the resources of the TESS Follow-up Observing Program (TFOP) Working Group (WG) Sub Group 1 (SG1)1 to collect seeing-limited time-series photometric follow-up of TOI-216. All photometric time series are publicly available on the Exoplanet Followup Observing Program for TESS (ExoFOP-TESS) website2 . Light curves observed on or before February 24, 2019 are described in Dawson et al. (2019). Our new time-series follow-up observations are listed in Table 1. We used the TESS Transit Finder, which is a customized version of the Tapir software package [START_REF] Jensen | Tapir: A web interface for transit/eclipse observability[END_REF], to schedule our transit observations. Un-less otherwise noted, the photometric data were extracted using the AstroImageJ (AIJ) software package (Collins et al. 2017). The facilities used to collect the new TOI-216 observations published here are Las Cumbres Observatory Global Telescope (LCOGT) network (Brown et al. 2013), Hazelwood Observatory (Churchill, Vic, Australia), El Sauce Observatory (Coquimbo Province, Chile), and the Antarctic Search for Transiting ExoPlanets (ASTEP) observatory (Concordia Station, Antarctica). All LCOGT 1 m telescopes are equipped with the Sinistro camera, with a 4k×4k pixel Fairchild back illuminated CCD and a 26 ′ ×26 ′ FOV. The LCOGT images were calibrated using the standard LCOGT BANZAI pipeline [START_REF] Mccully | Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series[END_REF]. Hazelwood is a private observatory with an f/8 Planewave Instruments CDK12 0.32 m telescope and an SBIG STT3200 2.2k×1.5k CCD, giving a 20 ′ × 13 ′ field of view. El Sauce is a private observatory which hosts a number of telescopes; the observations reported here were carried out with a Planewave Instruments CDK14 0.36 m telescope and an SBIG STT-1603-3 1536k×1024k CCD, giving a 19 ′ × 13 ′ field of view. ASTEP is a 0.4 m telescope with an FLI Proline 16801E 4k×4k CCD, giving a 63 ′ × 63 ′ field of view. The ASTEP photometric data were extracted using a custom IDL-based pipeline.

We fit the transit light curves (Fig. 1) using the TAP software package (Gazak et al. 2012), which implements Markov Chain Monte Carlo using the Mandel & Agol (2002) transit model and the Carter & Winn (2009) wavelet likelihood function, with the modifications described in Dawson et al. (2014). The results are summarized in Table 2. For TESS light curves, we use the presearch data conditioned (PDC) flux, which is corrected for systematic (e.g., instrumental) trends using cotrending basis vectors (Smith et al. 2012;Stumpe et al. 2014). For all light curves, we use Carter & Winn (2009) wavelet likelihood function (which, for the red noise component, assumes noise with an amplitude that scales as frequency -1 ) with free parameters for the amplitude of the red σ r and white noise σ r and a linear trend fit simultaneously to each transit light curve segment with other transit parameters. For the ground-based observations, we fit a linear trend to airmass instead of time. We assign each instrument and filter (TESS , Hazelwood g' and Rc, LCOGT i' and I, El Sauce Rc, and ASTEP Rc) its own set of limb darkening parameters because of the different wavebands. We use one set of noise parameters for all the TESS light curves and an additional set for each ground-based light curve. We adopt uniform priors on the planet-to-star radius ratio (R p /R ⋆ ), the impact parameter b (which can be either negative or positive; we report |b|), the mid transit time, the limb darkening coefficients q 1 and q 2 (Kipping 2013a), and the slope and intercept of each transit segment's linear trend. For the grazing transits of the inner planet, we impose a uniform prior on R p /R ⋆ from 0 to 0.17, with the upper limit corresponding to a planet radius of 0.13 solar radii (see Dawson et al. 2019 for details and justification). Despite a well-constrained transit depth (Table 2), the inner planet's radius ratio is highly uncertain due to degeneracy between the radius ratio and impact parameter (see Fig. 3 of Dawson et al. 2019). We also impose a uniform prior on the log of the light curve stellar density ρ circ . We use ρ circ , the stellar density derived from the light curve assuming a circular orbit, to compute the Mandel & Agol (2002) model normalized separation of centers z = d/R ⋆ , assuming M p << M ⋆ and a circular orbit:

z = (ρ circ /ρ ⊙ ) 1/3 (P/P ⊕ ) 2/3 (a ⊕ /R ⊙ ) ( 1
)
where P is the orbital period, the subscript ⊕ denotes the Earth, and the subscript ⊙ denotes the Sun. We will later combine the posteriors ρ circ from the light curve and ρ ⋆ (from Dawson et al. 2019's isochrone fit) to constrain the orbital eccentricity (Section 4.2). We perform an additional set of fits where we allow for a dilution factor for the TESS light curves and find the results to be indistinguishable. We measure a dilution factor of 1.000 +0.012 -0.11 . We also perform two additional fits to look for transit duration variations, following Dawson (2020). In the first fit, we allow the impact parameter to vary with the prior recommended by Dawson (2020). We find tentative evidence for the variation in the transit impact parameter for the inner planet, with an impact parameter change scale of 0.007 +0.004 -0.003 . In the second fit, we allow ρ circ (Eqn. 1) and b to vary for each transit with a prior that corresponds to a uniform prior in transit duration (Dawson 2020). Again the inner planet exhibits tentative evidence for variation in its transit durations. We fit a line to the transit durations as a function of mid-transit time and determine a three-sigma confidence interval on the slope of -0.4 -4 seconds/day for the inner planet and -1 -0.4 seconds/day for the outer planet.

For comparison and to ensure that the results are not sensitive to the correlated noise treatment, we also fit the light curves using the exoplanet package (Foreman-Mackey et al. 2019), which uses Gaussian process regression. Each set of TESS light curves along with eight ground-based light curves is modeled with a light curve transit model built from starry (Luger et al. 2019) plus a Matern-3/2 Gaussian process kernel with a white noise term. Seven sets of limb-darkening parameters (Kipping 2013b) are used for observations conducted in seven different filters. We use a log-uniform prior on stellar densities (ρ circ ), log-normal prior on transit depths, uniform prior on the impact parameters, and uniform prior on mid-transit times. We infer posteriors for each parameter using this approach that are consistent within 1 sigma to our nominal fit above. We examine the light curve for evidence of stellar rotation. We do not see any significant periodicities in the SPOC 2 minute cadence data. To investigate further, we create a systematics-corrected long cadence light curve using eleanor (Feinstein et al. 2019) with a 15 x 15 target pixel file, background size of 100, and custom square aperture of 3x3 pixels centered on TOI-216. We follow eleanor's recommendation for background subtraction: the 1D postcard background for sectors 1, 2, 4, 6, 7, 8, 11 and13; the 1D target pixel file background for sectors 3 and 5; and the 2D target pixel file background for sectors 9 and 12. Then we mask out the transits and compute a discrete autocorrelation function (DCF; Eqn. 2 of Edelson & Krolik 1988), plotted in Fig. 2.

The peak at 6.5 day and valley at approximately half that value are consistent with a 6.5 day periodicity. This periodicity could represent the rotation period or a shorter harmonic. A rotation period of ∼ 10 -40 days would be most typical for a 0.78 M ⊙ star on the main sequence (e.g., McQuillan et al. 2014), so the periodicity could plausibly be an integer fraction of the rotation period (e.g., one half, one third). The stellar radius of 0.747 +0.015 -0.014 R ⊙ (Dawson et al. 2019) and v sin i = 0.84 ± 0.70 km/s from the FEROS spectra correspond to a rotation period of 45 +225

-20 days assuming an edge-on orientation. A rotation period of 26 days would be compatible with the v sin i measurement, or a shorter rotation period would indicate a spin-orbit misalignment. A periodicity of 13 days or 26 days is challenging to detect in the TESS light curve (e.g., Canto Martins et al. 2020). 13 days is close to TESS 's 13.7 day orbital period and thus susceptible to corrections for systematics. Both are a significant fraction of the sector (27 days) and subject to imprecision in stitching together different segments. Given the many bumps and wiggles in the DCF, we do not consider this lightcurve detection of a stellar rotation harmonic definitive.

RADIAL VELOCITY ANALYSIS

TOI-216 was monitored with three different high resolution echelle spectrographs over a time span of 16 months with the goal of obtaining precision radial velocities to further constrain the masses and orbital parameters of the giant planets present in the TOI-216 system. These observations were performed in the context of the Warm gIaNts with tEss (WINE) collaboration, which focuses on the systematic characterization of TESS transiting giant planets with orbital periods longer than ≈10 days (e.g., Brahm et al. 2019;Jordán et al. 2020). All radial velocity measurements of TOI-216 are presented in Table 5. a As a summary statistic we report the mode and 68.3% confidence interval of the posterior distribution.

We obtained 27 spectra with the Fibre-fed, Extended Range, Échelle Spectrograph (FEROS, Kaufer et al. 1999) between November of 2018 and March of 2019. FEROS is mounted on the MPG 2.2 m telescope at the ESO La Silla Observatory, and has a resolving power of R ≈ 48 000. Observations were performed with the simultaneous calibration mode for tracing radial velocity variations produced by environmental changes in the instrument enclosure. The adopted exposure time of 1200 seconds yielded spectra with signal-to-noise ratios in the range from 40 to 75. FEROS spectra were processed from raw data with the ceres pipeline (Brahm et al. 2017), which delivers precision radial velocities and line bisector span measurements via cross-correlation with a binary mask resembling the spectral properties of a G2-type star. The radial velocity uncertainties for the FEROS observations of TOI-216 range between 7 and 15 m s -1 . We remove two outliers from the FEROS radial-velocity time series at 1503.75 and 1521.57 days. All subsequent results do not include these outliers. We have checked that no results except the inferred jitter for the FEROS dataset are sensitive to whether or not the outliers are included.

We observed TOI-216 on 15 different epochs between December of 2018 and October of 2019 with the High Accuracy Radial velocity Planet Searcher (HARPS Mayor et al. 2003) mounted on the ESO 3.6 m telescope at the ESO La Silla Observatory, in Chile. We adopted an exposure time of 1800 seconds for these observations using the high radial velocity accuracy mode (HAM, R ≈ 115 000), which produced spectra with signal-tonoise ratios of ≈40 per resolution element. As in the case of FEROS, HARPS data for TOI-216 was processed with the ceres pipeline, delivering radial velocity measurements with typical errors of ≈5 m s -1 .

TOI-216 was also monitored with the Planet Finder Spectrograph (PFS; [START_REF] Crane | Society of Photo-Optical Instrumentation Engineers[END_REF][START_REF] Crane | Society of Photo-Optical Instrumentation Engineers[END_REF][START_REF] Crane | The Carnegie Planet Finder Spectrograph: integration and commissioning[END_REF] mounted on the 6.5 m Magellan II Clay Telescope at Las Campanas Observatory (LCO), in Chile. These spectra were obtained on 18 different nights, between December of 2018 and March of 2020, using the 0.3 ′′ ×2.5 ′′ slit, which delivers a resolving power of R = 130 000. Due to its moderate faintness, TOI-216 was observed with the 3×3 binning mode to minimize read-out noise, and an exposure time of 1200 seconds was adopted to reach a radial velocity precision of ≈2 m s -1 . An iodine cell was used in these observations as a reference for the wavelength calibration. The PFS data were processed with a custom IDL pipeline (Butler et al. 1996). Three consecutive 1200 second iodine-free exposures of TOI-216 were obtained to construct a stellar spectral template for disentangling the iodine spectra from the stellar one for computing the radial velocities.

It is immediately evident that the radial velocities show good agreement with Dawson et al. (2019)'s higher mass solution, which was fit to the earlier, transit time only dataset (Fig. 3), and with Kipping et al. (2019)'s solution based on transit times from the first six sectors. The bottom panel of Fig. 3 shows the RVs phased to the outer planet's orbital period.

We compute a generalised Lomb-Scargle periodogram (Cumming et al. 1999;Zechmeister & Kürster 2009) in Fig. 4 and5. The x-axis is frequency f in cycles per day. The y-axis is the square root of the power, where we define power as

Power f = Σ i (v i,f -vi,0) 2 σ 2 i -Σ i v 2 i,0 σ 2 i 2Σ i 1 σ 2 i , (2)
where σ i is the reported uncertainty (Table 5) and v i,0 is the radial-velocity (Table 5) with the error weighted mean

Σivi/σ 2 i 1 σ 2 i
for each of the three datasets (PFS, HARPS, and FEROS) subtracted. The sinusoidal function v i,f is

v i,f = A cos[2πf (t i -t 0 )]+BA sin[2πf (t i -t 0 )]+C k (3)
where A and B are computed following Zechmeister & Kürster (2009), k is each of the three datasets, t 0 is the time of the first observed radial velocity, and

C k = - Σ i (A cos[2πf (ti-t0)]+BA sin[2πf (ti-t0)]) σ 2 i Σ i 1 σ 2 i . ( 4
)
We see a peak in the periodogram at planet c's orbital period (Fig. 4, left panel). The noise-free c model (overplotted, dashed; a Keplerian signal computed using the parameters of planet c from Table 4 sampled at the observed times in Table 5) shows that many of the other peaks seen in the three periodograms are aliases of planet c's orbital period ( i.e., they caused by the observational time sampling of the planet's signal). Planet b's signal is below the noise level (Fig. 3, bottom right panel; Figure 4, right panels). In the PFS dataset, including planet b improves the chi-squared from 403 to 328 (for 18 datapoints and five additional parameters); for the HARPS and FEROS datasets, there is no improvement in chi-squared. Given that planet b is barely detected, we cannot rule out other planets in the system with smaller orbital radial velocity amplitudes.

Systems containing an outer planet in or near a 2:1 mean motion resonance with a less massive inner planet can be mistaken for a single eccentric planet, because the first eccentricity harmonic appears at half the planet's orbital period (e.g., Anglada-Escudé et al. 2010;Kürster et al. 2015). In the case of the system TOI-216, the lack of detection of TOI-216b is not due to this phenomenon because solution we subtract off for planet c has near 0 eccentricity. However, without prior knowledge that the system contains a resonant pair, if we only had the radial-velocity datasets and the datasets were less noisy (or had more data points), we might be sensitive to planet b's signal but mistakenly interpret it as planet c's eccentricity. The residuals of the two-planet fit (and one-planet fit) show evidence of a signal that we attribute to stellar activity. We examined the periodograms of the residuals of each of three datasets; the bisectors for the HARPS and FEROS datasets; and H alpha for the FEROS dataset, computed with the ceres pipeline, following Boisse et al. (2009). Periodograms of the PFS residuals and FEROS H alpha are shown in Figure 5. There are no strong peaks in any of the residual or activity indicator periodograms. Some residuals datasets exhibit (weak) peaks near the 6.5 day periodicity (HARPS residuals and bisectors; FEROS residuals) identified in the light curve (Section 2), or a multiple of 6.5 days (PFS; FEROS bisectors and H alpha). In Fig. 6, we plot the residuals of the two-planet fit with best-fit sinusoids for 6.5, 13, and 26 day periodicities for each dataset. Comparing the three datasets, best-fit sinusoids are out of phase with each other. The similarity of the periodicities to those seen in the light curve, the appearance of the 6.5 day periodicity in the HARPS bisectors, the 6.5 and 26 day periodicities in the FEROS H alpha, and the 13 day and 6.5 day periodicities in the FEROS bisectors, and the difference in phase among datasets suggest the 4 sampled at the observed times in Table 5). 4) for PSF and H alpha for FEROS. The 6.5, 13, and 26 day periodicities (associated with the periodicity in the light curve, Fig. 2) are overplotted as dotted lines.

weak periodicities do not arise from additional planets. They are possibly caused by stellar variability.

JOINT FIT AND ORBITAL ARCHITECTURE

Here we jointly fit the transit light curves (Section 2) and radial-velocity measurements (Section 3) to precisely measure the orbital parameters and masses of both planets. In Section 4.1, we describe our analysis of the transit timing measurements. In Section 4.2, we jointly fit the transit and radial-velocity measurements.

Transit timing variation analysis

TOI-216b and c exhibit transit timing variationsplotted in Fig. 7 -due to the near-resonant effect (e.g., Agol et al. 2005;Lithwick et al. 2012). We have not yet observed a full super-period (which depends on the plan-ets' proximity to the 2:1 resonance). The amplitude depends on the perturbing planet's mass and the free eccentricity of the transiting and perturbing planets. We previously found a significant free eccentricity, with the exact value and partition between planets degenerate with planet mass (Dawson et al. 2019).

We fit the transit times using our N-body integrator TTV model (Dawson et al. 2014). Our model contains five parameters for each planet: the mass M , orbital period P , mean longitude λ, eccentricity e, and argument of periapse ω. All orbital elements are osculating orbital elements at the epoch 1325.3279 days. For each planet, we fix the impact parameter b to the value in Table 2 and set the longitude of ascending node on the sky to Ω sky = 0. We use the conventional coordinate system where the X -Y plane is the sky plane and the Z axis points toward the observer. We will explore other possibilities for b and Ω sky in Section 4.2.

We begin by fitting the transit times only. To explore the degeneracy between mass and eccentricity, we use the Levenberg-Marquardt alogrithm implemented in IDL mpfit (Markwardt 2009) to minimize the χ 2 on a grid of (M c , e b ). We first use a dataset consisting of all the ground-based data and the TESS Year 1 data. We contour the total χ 2 for thirty-four transit times and ten free parameters, i.e., twenty-four degrees of freedom in Fig. 8. Even with the additional transits since Dawson et al. (2019), the fits still suffer from a degeneracy between mass and eccentricity, though the relationship is much tighter. We integrate a random sample of 100 solutions with χ 2 < 50 and find that they all librate in the 2:1 resonance with the resonant angle involving the longitude of periapse of the inner planet. Next we add TESS Year 3 transits from the TESS Extended Mission, which became available while this manuscript was under review. This very extended baseline for the TTVs 4) phased to periodicities of 26 days (top), 13 days (middle), and 6.5 days (bottom). Best-fit sinusoids for these periodicities are overplotted as dashed lines. Comparing the three datasets, the best-fit sinusoids are out of phase with each other, indicating that these signals are unlikely to arise from additional planets. substantially reduces the degeneracy between mass and eccentricity. We also contour the total χ 2 for these fortythree transit times and ten free parameters, i.e., thirtythree degrees of freedom in Fig. 8.

A resonant or near-resonant planet's total eccentricity is the vector sum of its free and forced eccentricity. The forced eccentricity vector is dictated by the resonant dynamics, and the free eccentricity vector oscillates about the tip of the forced vector. Dissipation (e.g., eccentricity damping from the disk) tends to damp the free eccentricity, and other perturbations (e.g., from a third planet) can excite it. We estimate the eccentricity components from simulations as e free = (e max -e min )/2) and e forced = (e max + e min )/2). The transit times continue to provide evidence for a moderate free eccentricity (Fig. 9), but pinning down the outer planet's mass with a joint radial-velocity fit will allow for a tighter constraint.

Joint transit and radial velocity fit

We perform a joint N-body fit to the transit times and radial velocities, imposing two additional constraints. One constraint is the transit exclusion intervals reported in Dawson et al. (2019). The other is the light curve joint posterior of stellar density ρ circ vs. impact parameter b (Table 2; Eqn. 1) combined with the ρ ⋆ posterior from Dawson et al. (2019). Following With ground-based transits and Year 1 of TESS data (bluedashed), fits to the transit times only result in degeneracy between the inner planet's (osculating) eccentricity and the outer planet's mass. The levels are χ 2 = 42, 47, 52, 62, and 77 and the best-fit solutions occupy the innermost contour. The black contours show χ 2 for these same solutions compared to the RV measurements, with an RV offset for each instrument as the only free parameter. The levels are χ 2 =540, 560, 600, and 650 and the best-fit solutions occupy the innermost contour. The RV measurements break the degeneracy between mass and eccentricity. The addition of Year 3 TESS Extended Mission data (through sector 30; red solid) reduces the degeneracy between mass and eccentricity and shows good agreement with the RV data. The levels are χ 2 = 65, 70, 75, 85, and 100 and the best-fit solutions occupy the innermost contour.

Dawson & Johnson (2012), we convert the ρ circ vs. b to a g vs. b posterior according to g = (ρ circ /ρ ⋆ ) 1/3 . We use the g vs. b posterior to add a term to the likelihood based on e and ω using g = (1 + e sin ω)/(1 -e 2 ) 1/2 . We compute the sky-plane inclination for the dynamical model from b according to sin i sky a/R ⋆ = (1 + e sin ω)/(1 -e 2 ). Following Dawson et al. (2014), we derive posteriors for the parameters using Markov Chain Monte Carlo with the Metropolis-Hastings algorithm. Instead of including the orbital period and mean longitude at epoch 1325.3279 days as parameters in the MCMC, we optimize them at each jump (i.e., each MCMC step) using the Levenberg-Marquardt algorithm (i.e., optimizing the dynamical model). We also optimize the radial velocity . Long-term (10 6 days) behavior of solutions with χ 2 < 60 (TTV-only fits with ground-based transits and Year 1 of TESS data, gray and and black, which have discrete values because they are performed on a grid); χ 2 < 80 (TTVonly fits with addition of Year 3 TESS Extended Mission data, orange and light blue); and from the MCMC posterior for the joint RV-TTV fit (red and blue, Table 4). Row 1: e free (approximated as (emaxemin)/2); Row 2: e forced (approximated as (emax + emin)/2).

offset for each instrument at each jump. We fit for a radial velocity jitter term for each of the three instruments; even though we identified possible periodicities in Fig. 5, none are strong enough to justify to explicitly modeling (e.g., with false alarm probabilities of 0.2, 0.002, and 0.02 for the highest peak in the periodogram for PFS, FEROS, and HARPS respectively; Cumming 2004). We visually inspect each parameter for convergence. We know there is a mutual inclination perpendicular to the sky plane because the inner planet exhibits grazing transits and the outer planet does not, To also allow for a mutual inclination parallel to the sky plane, we fit for ∆Ω sky , the difference in longitude of ascending node.

Following Dawson et al. (2019), we perform two fits with different priors to assess the sensitivity to these priors. The first solution (Table 4) imposes uniform priors on eccentricities and log uniform priors on mass (i.e., priors that are uniform in log space). The second imposes uniform priors on mass and log-uniform priors on eccentricity. All other fitted parameters (orbital period, mean longitude, argument of periapse, radial velocity jitters, difference in longitude of ascending node) have uniform priors. With the dataset in Dawson et al. (2019), the results were very sensitive to the priors; with the new dataset that includes radial-velocities and an expanded TTV baseline, the results with different priors are nearly indistinguishable. In both cases, we impose the threesigma limits on change in transit duration derived in Section 2. We measure a small but significant mutual inclination of 1.2-3.9 • (95% confidence interval).

To ensure that our results are robust and that the parameter space has been thoroughly explored by the fitting algorithm (particularly the degeneracy between eccentricity and mass), we carry out a fit using a different N-body code and fitting algorithm. We use the Python Tool for Transit Variations (PyTTV; Korth (2020)) to fit the transit times (Table 2), RVs (Table 5), and the stellar parameters reported in Dawson (2020). The parameter estimation is carried out by a joint-N-body fit using Rebound with the IAS15 integrator (Rein & Liu 2012;Rein & Spiegel 2015) and Reboundx (Tamayo et al. 2020), to model all the observables without approximations. Within the simulation, carried out in barycentric coordinates, a common coordinate system was chosen where the x -y plane is the plane of sky. The x-axis points to the East, the y-axis points to the North, and the z-axis points to the observer. Ω is measured from East to North, and ω is measured from the plane of sky. For the parameter estimation with PyTTV, the gravitational forces between the planets and the influence of general relativity (GR) were considered, in case the influence of GR is significant enough to be visible in the TTVs; for this system, general relativistic precession does not significantly affect the TTVs. The parameter estimation is initialized using Rayleigh priors on eccentricities (Van Eylen et al. 2019) and uniform priors on log values for the planetary masses. The estimation of physical quantities from the TTV signal is done in two steps. First, the posterior mode is found using the Differential Evolution algorithm implemented in PyTransit (Parviainen 2015). The optimization is carried out varying the planetary masses, orbital periods, inclinations, eccentricities and arguments of periastron. The eccentricity and argument of periastron are mapped from sampling-parameters √ e cos ω and √ e sin ω. The longitudes of the ascending nodes are fixed for both planets. After the posterior mode is found, a sample from the posterior is obtained using the affineinvariant Monte Carlo Markov Chain ensemble sampler emcee (Foreman-Mackey et al. 2013). The parameters and uncertainties are consistent with those reported in Table 4.

Dynamics and origin

We randomly draw 1000 solutions from the posterior for longer integrations of 10 6 days using mercury6

∆Ω sky = Ω c,sky (deg) -1 +2 -2 i b,sky (deg) 89.84 +0.10 -0.08 2λc -λ b -̟ b (deg). 42.5 +0.4 -0.3 imut(deg) c 2.0 +1.2 -0.5
Jitter (m/s):

HARPS 8 +3 -2 FEROS 22 +5 -4 PFS 7.7 +1.7 -1.3
a As a summary statistic we report the median and 68.3% confidence interval of the posterior distribution. An example fit with high precision suitable for numerical integration is given in Table 6.

b Stellar parameters fixed to the values reported by Dawson et al. (2019): 0.77±0.03M ⊙ and 0.748±0.015R ⊙ . Uncertainties in estimated planetary masses only account for the dynamical fitting, i.e., they do not include uncertainties in the star's mass.

c 95% confidence interval is 1.2-3.9 • . The 99.7% confidence interval is 1.1-4.3 • . (Chambers et al. 1996). We compute the libration amplitudes for the 2:1 resonant angle 2λ c -λ b -̟ b , where the longitude of periapse ̟ b = ω b + Ω b . We can now definitively determine that the system is librating in resonance. The libration amplitude is well-constrained to 60 +2 -2 degrees. The very small uncertainty in the libration amplitude leads us to believe that its moderate value is real, not an artifact of imperfect characterization (e.g., Millholland et al. 2018). Fig. 10 shows a trajectory demonstrating libration about a fixed point. In our solutions, the other 2:1 resonant angle 2λ c -λ b -̟ c always circulates. However, the outer planet's eccentricity and longitude of periapse are poorly constrained, so it is possible that solutions where this angle librates are also consistent with the data. The inner planet has a forced eccentricity (Fig. 9) of 0.146 +0.003 -0.003 and a modest but significant free eccentricity of 0.0222 +0.0005 -0.0003 . The outer planet has very small forced and free eccentricities of 0.0048 +0.0028 -0.0013 and 0.00162 +0.00011 -0.00010 respectively. In our integrated solutions, we find that the timescale for the biggest variations in both planets' semi-major axes and the inner planet's eccentricity is the resonant libration timescale (approximately 5 years), and the outer planet's eccentricity varies on apsidal alignment timescale (approximately 25 years). This system falls into the regime of resonant TTVs (e.g., Nesvorný & Vokrouhlický 2016) -rather than the more commonly characterized near-resonant TTVs (e.g., Lithwick et al. 2012)-and we expect the TTVs to oscillate on the libration timescale, which has not yet been fully covered by the observational baseline (Fig. 7). We integrate a random subset of 200 solutions for 1 Myr and find that all are stable.

One possible scenario for establishing the resonance is convergent migration of planet c preceded or followed by perturbations of planet b by another body (Fig. 11). We show example simulations that apply a migration force using the user-defined force feature of mercury6 (as described in Wolff et al. 2012); the simulations are done in 3D with initial inclinations set to the present day values. Planet c migrates a short distance (0.8% of its initial semi-major axis) toward planet b and captures b into resonance. In the first example (top), planet b starts with a modestly eccentric (bottom) orbit (e = 0.0798). In the second example, planet b starts with a lower eccentricity (e = 0.02) and is captured into resonance with a tight libration amplitude. At about 80,000 years, planet b's orbit is disturbed, which we approximate as an instantaneous change in the magnitude and direction of its eccentricity vector. The first history results in large amplitude libration of the resonant angle involving ̟ c and the second in circulation; because we are not confident that only circulating resonant angles are compatible with the data, we cannot use this distinction to favor one history over the other.

These example dynamical histories are compatible with in situ formation, but are potentially compatible with long distance migration as well. In the in situ formation scenario, three or more planets form in situ, and planet c migrates a tiny distance toward b. A third planet jostles b -exciting its eccentricity and mutual inclination -before or after c's migration. In the long distance migration scenario, the disturbing third planet could have migrated earlier. As future work, orbital dynamics simulations could place limits on the properties of this possible third planet. Although we have invoked a third planet in the example scenarios, we have not ruled out the possibility that planet b itself disturbed planet c, in a process separate from migration.

Another hypothesis for the mutual inclination is that it was excited when the planets passed through the 4:2 inclination resonance during migration (Thommes & Lissauer 2003). Precession from the proto-planetary disk can separate the 4:2 inclination resonances from the 2:1 eccentricity resonance. Figure 12 shows a proof of concept simulation where the potential of the proto-planetary disk is approximated as a J 2 oblateness term for the stellar potential. A small but significant mutual inclination is excited.

We place planet b and c on a mass-radius plot of warm exoplanets in Fig. 13. TOI-216c has a typical radius for its mass; its bulk density is 0.885 +0.014 -0.13 gcm -3 . TOI-216b likely also has a typical radius for its mass, but because of its grazing transit (Section 2) and the result- ing degeneracy with impact parameter, we cannot rule out a large radius that would result in a low density for its mass compared to similar mass planets. Its poorlyconstrained bulk density is 0.17 +0.18 -0.10 gcm -3 .

5. CONCLUSION TOI-216b and c are now a very precisely characterized (with the exception of planet b's radius) pair of warm, large exoplanets. Radial velocity measurements using HARPS, FEROS, and PFS broke a degeneracy between mass and eccentricity in the TTV-only fits that was particularly severe before the TESS Extended Mission observations, and an expanded TTV baseline from TESS and an ongoing ground-based transit observing campaign increased the precision of the fits. We can now better assess the consistency of its properties with different theories for formation and evolution of giant planets orbiting close to their stars.

We now know that TOI-216c is a warm Jupiter (0.54± 0.02 Jupiter masses) with a mass and radius typical of other 10-200 day giant planets (Fig. 13). TOI-216b has a mass similar to Neptune's (18.4±0.6M ⊕ ). Its radius is not well constrained due to its grazing transits; its radius may very well be typical for its mass (Fig. 13). Given the large uncertainty in planet b's radius, no inflation mechanisms or scenarios requiring formation beyond the ice line (e.g., Lee & Chiang 2016) are required to explain either planet's radius.

Furthermore, we know now that TOI-216b and c are not just near but librating in the 2:1 resonance. The argument involving the longitude of periapse of TOI-216b librates with an amplitude of 63 +3 -3 degrees. TOI-216b has a small but significant free eccentricity 0.0222 +0.0005 -0.0003 . The mutual inclination with respect to TOI-216c is between 1.2-3.9 • (95% confidence interval). The libration amplitude, free eccentricity, and mutual inclination imply a disturbance of TOI-216b before or after resonance capture, perhaps by an undetected third planet. The orbital properties can be consistent either with in situ formation, with resonance capture through a very short distance migration, or long distance migration. Future origins scenarios must match these precisely constrained properties. Future atmospheric characterization by the James Webb Space Telescope (JWST) may help distinguish between these origin scenarios. If the planet formed outside the water snow line, we expect its C/O ratio to be significantly smaller than that of its host star; in-situ formation, on the other hand, would imply C/O ratios closer to the star (Espinoza et al. 2017). Simulations performed with PandExo (Batalha et al. 2017) show that water features in the spectra that constrain the C/O ratio may be detectable for TOI-216c with the JWST Near Infrared Imager and Slitless Spectrograph (NIRISS), even beneath a moderate cloud layer. This system will benefit from continued long-term radial-velocity and transit monitoring. Long-term radial velocity monitoring could reveal the presence of additional planets in the system, though stellar activity poses a challenge for detecting low amplitude signals.

Observations by the TESS Extended Mission are continuing and will further increase the baseline of observations. The new TESS observations may allow us to better constrain the change in impact parameter tentatively detected here for TOI-216b, allowing for tighter constraints on the mutual inclination.

Figure 1 .

 1 Figure 1. Detrended light curves, spaced with arbitrary vertical offsets, and with a model light curve overplotted. The light curves are phased based on a constant orbital period linear ephemeris to show the TTVs. TESS data are publicly available from MAST and ground-based data from the ExoFOP-TESS website.

  Figure 2. Discrete autocorrelation function (Eqn. 2 of Edelson & Krolik 1988) of eleanor long cadence TOI-216 light curve.

Figure 3 .

 3 Figure 3. Top: Radial velocity measurements of TOI-216 from HARPS (gray), FEROS (red; outliers in lighter red), and PFS (blue). Best-fit models from this work (Table 4) and from Dawson et al. (2019)'s earlier analysis of transit times only are overplotted. Row 2, left: RVs phased to planet c's orbital period with same models as row 1 for planet c only (i.e., the RV variation only due to planet c) overplotted. Row 2, right: Residuals of Table 4 model for planet c only, with b component of the model overplotted, phased to planet b's orbital period.

Figure 4 .

 4 Figure 4. Left: Periodograms of the combined RV dataset (black solid), with periodogram of noise-free planet c only model ( i.e., a Keplerian signal computed using the parameters of planet c from Table 4 sampled at the observed times in Table 5; gray dashed) overplotted. Right: Same for residuals to planet c only model, with noise-free planet b only model overplotted (i.e., a Keplerian signal computed using the parameters of planet b from Table4sampled at the observed times in Table5).

Figure 5 .

 5 Figure 5. Periodograms of residuals of the best two planet fit (Table4) for PSF and H alpha for FEROS. The 6.5, 13, and 26 day periodicities (associated with the periodicity in the light curve, Fig.2) are overplotted as dotted lines.

Figure 6 .

 6 Figure 6. Residuals to the best two planet fit (Table4) phased to periodicities of 26 days (top), 13 days (middle), and 6.5 days (bottom). Best-fit sinusoids for these periodicities are overplotted as dashed lines. Comparing the three datasets, the best-fit sinusoids are out of phase with each other, indicating that these signals are unlikely to arise from additional planets.

  Figure 7.Observed mid-transit times (diamonds) with subtracted linear ephemeris for TOI-216b (top) and TOI-216c (bottom), with the best fit model overplotted (diamonds, dotted line).

Figure 8 .

 8 Figure 8. Contours of χ 2 for the fit to transit times only.With ground-based transits and Year 1 of TESS data (bluedashed), fits to the transit times only result in degeneracy between the inner planet's (osculating) eccentricity and the outer planet's mass. The levels are χ 2 = 42, 47, 52, 62, and 77 and the best-fit solutions occupy the innermost contour. The black contours show χ 2 for these same solutions compared to the RV measurements, with an RV offset for each instrument as the only free parameter. The levels are χ 2 =540, 560, 600, and 650 and the best-fit solutions occupy the innermost contour. The RV measurements break the degeneracy between mass and eccentricity. The addition of Year 3 TESS Extended Mission data (through sector 30; red solid) reduces the degeneracy between mass and eccentricity and shows good agreement with the RV data. The levels are χ 2 = 65, 70, 75, 85, and 100 and the best-fit solutions occupy the innermost contour.

  Figure9. Long-term (10 6 days) behavior of solutions with χ 2 < 60 (TTV-only fits with ground-based transits and Year 1 of TESS data, gray and and black, which have discrete values because they are performed on a grid); χ 2 < 80 (TTVonly fits with addition of Year 3 TESS Extended Mission data, orange and light blue); and from the MCMC posterior for the joint RV-TTV fit (red and blue, Table4). Row 1: e free (approximated as (emaxemin)/2); Row 2: e forced (approximated as (emax + emin)/2).

Figure 10 .

 10 Figure 10. Example trajectory for TOI-216 solution. The trajectory does not pass through the origin, indicating libration about a fixed point. The offset from the origin is the forced eccentricity.

Figure 11 .

 11 Figure 11. Examples of resonance capture through short distance convergent migration of planet c. Rows 1-2: resonant angle; row 3: semi-major axis of planet c (top black line) and planet b (bottom black line); row 4: eccentricity of planet b (top black line) and planet b (bottom black line). Values from simulations with the present-day observed orbits (i.e., range of oscillation) are marked with a dotted red line.

Figure 12 .

 12 Figure 12. Examples of excitation of a mutual inclination during short distance convergent migration of planet c. Row 1: eccentricity resonant angle; row 2: mutual inclination; row 3: semi-major axis of planet c (top black line) and planet b (bottom black line); row 4: eccentricity of planet b (top black line) and planet b (bottom black line). Values from simulations with the present-day observed orbits (i.e., range of oscillation) are marked with a dotted red line.

Figure 13 .

 13 Figure 13. Warm (10-200 day orbital period) planets with both mass and radius measurements (exoplanet.eu; Schneider et al. 2011), including TOI-216 (orange).

Table 1 .

 1 Observation Log: TOI-216/TIC 55652896

	TOI-216	Date (UTC)	Telescope	†	Filter	ExpT Exp (sec) (N) (min) Dur.	Transit Coverage	Ap. Radius FWHM (arcsec) (arcsec)
	b	2019-10-30 LCOGT-CTIO-1.0	I	40	220	241	Full	5.8	2.4
		2020-05-23 ASTEP-0.4	∼Rc	120	376	924	Full	10.2	5.3
	c	2018-12-16 LCOGT-SAAO-1.0 2019-01-20 Hazelwood-0.3	i ′ g ′	90 240	331 101	450 449	Full Egress+70%	5.8 5.5	2.1 3.2
		2019-02-24 El Sauce-0.36	Rc	30	514	303	Egress+90%	5.9	3.4
		2019-06-07 ASTEP-0.4	∼Rc	120	549	1440	Full	12.0	5.0
		2019-11-27 Hazelwood-0.3	Rc	60	114	255	Egress+60%	5.5	3.1
		2019-12-31 LCOGT-SAAO-1.0	Ic	40	316	345	Ingress+90%	4.7	2.0
		2020-02-24 Hazelwood-0.3	Rc	120	161	380	Egress+60%	5.5	3.1
		2020-03-09 LCOGT-CTIO-1.0	I	40	146	176	Egress+30%	8.2	2.6
		2020-06-21 ASTEP-0.4	∼Rc	120	272	656	Full	11.0	5.0
				† Telescopes:
	LCOGT-CTIO-1.0: Las Cumbres Observatory -Cerro Tololo Inter-American Observatory (1.0 m)
	LCOGT-SAAO-1.0: Las Cumbres Observatory -South African Astronomical Observatory (1.0 m)
	LCOGT-SSO-1.0: Las Cumbres Observatory -Siding Spring Observatory (1.0 m)
	Hazelwood-0.3: Stockdale Private Observatory -Victoria, Australia (0.32 m)
	El Sauce-0.36: El Sauce Observatory -Coquimbo Province, Chile (0.36 m)
	ASTEP-0.4: Antarctic Search for Transiting ExoPlanets -Concordia Station, Antarctica (0.4 m)

Table 2 .

 2 Planet Parameters for TOI-216b and TOI-216c Derived from the Light Curves

	Parameter	Value a
	TOI-216b
	Planet-to-star radius ratio, Rp/R⋆	0.10 +0.03 -0.02
	Transit depth [ppm]	4750 +140 -150
	Planet radius, Rp [R ⊕ ] Light curve stellar density b , ρ circ [ρ ⊙ ]	8 +3 -2 1.1 +0.3 -0.2
	Impact parameter, |b| Mid-transit times (days c,d )	0.98 +0.05 -0.04 1325.328 +0.004 -0.004
		1342.430 +0.003 -0.003
		1359.540 +0.003 -0.003
		1376.631 +0.003 -0.003
		1393.723 +0.003 -0.003
		1427.879 +0.003 -0.003
		1444.958 +0.003 -0.003
		1462.031 +0.003 -0.003
		1479.094 +0.003 -0.003
		1496.155 +0.003 -0.003
		1513.225 +0.004 -0.004
		1547.338 +0.003 -0.003
		1564.403 +0.004 -0.004
		1598.529 +0.003 -0.003
		1615.604 +0.003 -0.003
		1632.679 +0.003 -0.003
		1649.759 +0.004 -0.004
		1666.851 +0.003 -0.003
	LCOGT	1786.698 +0.002 -0.002
	ASTEP	1993.486 +0.002 -0.002
		2045.465 +0.003 -0.003
		2062.800 +0.003 -0.003
		2080.157 +0.003 -0.003
		2097.511 +0.003 -0.003
		2132.243 +0.003 -0.003
	Best fit linear ephemeris:
	Period (days)	17.16073
	Epoch (days)	1324.5911
	TOI-216c
	Planet-to-star radius ratio, Rp/R⋆	0.1230 +0.0008 -0.0006
	Transit depth [ppm]	18310 +120 -120
	Planet radius, Rp [R ⊕ ]	10.1 +0.2 -0.2
	Light curves stellar density, ρ circ [ρ ⊙ ]	1.73 +0.04 -0.08
	Impact parameter, |b| Mid-transit times (days c,d ) 1331.2850 +0.0008 0.14 +0.08 -0.09 -0.0008
		1365.8244 +0.0008 -0.0008
		1400.3686 +0.0008 -0.0008

Table 2 continued

 2 Table 2 (continued)

	Parameter	Value a
		1434.9227 +0.0008 -0.0008
		1469.4773 +0.0008 -0.0008
	LCOGT	1469.4781 +0.0004 -0.0004
	Hazelwood	1504.036 +0.002 -0.002
	El Sauce	1538.5938 +0.0015 -0.0015
		1538.5921 +0.0008 -0.0008
		1607.7082 +0.0008 -0.0008
		1642.2612 +0.0009 -0.0009
	ASTEP	1642.2595 +0.0011 -0.0011
		1676.8085 +0.0008 -0.0008
	Hazelwood	1814.939 +0.003 -0.003
	LCOGT	1849.4526 +0.0005 -0.0005
	Hazelwood	1883.955 +0.002 -0.002
	LCOGT	1918.4506 +0.0007 -0.0007
	ASTEP	2021.8887 +0.0010 -0.0010
		2056.3520 +0.0008 -0.0008
		2090.8107 +0.0009 -0.0009
		2125.2698 +0.0008 -0.0008
	Best fit linear ephemeris:
	Period (days)	34.525528
	Epoch (days)	1331.4110

a As a summary statistic we report the median and 68.3% confidence interval of the posterior distribution. b Eqn. 1 c BJD -2457000.0 days d Mid-transit times not otherwise noted are from TESS light curves.

Table 3 .

 3 Light Curve Parameters a for the TOI-216 system

		q 1	q 2		σr	[ppm]	σw	[ppm]
	TESS	0.29 +0.08 -0.05	0.50 +0.11 -0.10
		2 min 3900	+600 -600	2475	+14 -14
		20 s 15000 +2000 -2000	5364	+26 -27
	LCOGT i'	0.55 +0.10 -0.10	0.20 +0.07 -0.07	1600 +1970 -1100	1060 +40 -40
	Hazelwood g'	0.51 +0.25 -0.15	0.6 +0.2 -0.2	4000 +3000 -3000	2450 +190 -180
	El Sauce	0.5 +0.2 -0.2	0.3 +0.2 -0.2	10 4 +4000 -4000	3130 +80 -80
	Hazelwood Rc:	0.6 +0.3 -0.4	0.11 +0.18 -0.08
	Nov. 2019				9000 +3000 -2000	2100 +200 -200
	Feb. 2020				10 4 +3000 -3000	1920 +160 -160
	LCOGT I:	0.29 +0.07 -0.09	0.49 +0.19 -0.10
	Oct. 2019				1400 +1500 -1100	2360 +110 -100
	Dec. 2019				1200 +1100 -800	1130 +40 -40
	Mar. 2020				1600 +1400 -1100	990 +50 -50
	ASTEP	0.52 +0.18 -0.13	0.4 +0.2 -0.2
	June 2019				13000 +2000 -2000	2100 +100 -100
	May 2020				3800 +1300 -1100	1270 +50 -50
	June 2020				11900 +1500 -1500	1360 +70 -70

Table 4 .

 4 Planet Parameters (Osculating Orbital Elements at Epoch 1325.3279 days) for TOI-216b and TOI-216c Derived from joint TTV/RV fit

	Parameter	Value a
	M⋆(M ⊙ ) b	0.77
	R⋆(R ⊙ ) b	0.748
	M b (M Jup )	0.059 +0.002 -0.002
	P b	17.0968 +0.0007 -0.0007
	e b	0.160 +0.003 -0.002
	̟ b (deg.)	291.8 +0.8 -1.0
	λ b (deg)	82.5 +0.2 -0.3
	Ω b,sky (deg)	0
	i b,sky (deg)	88.60 +0.03 -0.04
	Mc (M Jup )	0.56 +0.02 -0.02
	Pc	34.5516 +0.0003 -0.0003
	ec	0.0046 +0.0027 -0.0012
	̟c (deg.)	190 +30 -50
	λc (deg) 27.8 +1.7 -1.5

Table 5 .

 5 HARPS,FEROS, and PFS radial velocity measurements of TOI-216.

	BJD	RV	σRV	BIS	σBIS	Inst. Note
	-2450000	(m s -1 ) (m s -1 ) (m s -1 ) (m s -1 )
	8449.70722 36690.0	7.8	-16.0	12.0	FEROS
	8450.62181 36709.1	8.0	-12.0	12.0	FEROS
	8450.75019 36686.8	8.3	-35.0	12.0	FEROS
	8451.72708 36706.3	7.7	-21.0	12.0	FEROS
	8451.74212 36696.3	7.2	-44.0	11.0	FEROS
	8451.75750 36694.2	7.2	-25.0	11.0	FEROS
	8452.77587 36713.0	7.6	-48.0	11.0	FEROS
	8464.76381 36754.4	8.7	11.0	11.0	HARPS
	8464.81000 36744.7	10.3	19.0	13.0	HARPS
	8465.73524 36759.3	4.1	9.0	5.0	HARPS
	8465.75656 36753.4	4.6	5.0	6.0	HARPS
	8466.72641 36733.7	6.4	-5.0	8.0	HARPS
	8466.74802 36730.1	7.4	-11.0	10.0	HARPS
	8467.74159 36714.5	7.9	-35.0	12.0	FEROS
	8468.67914	10.49	1.11	. . . . . . .	. . . . . . .	PFS
	8468.74406 36727.7	7.7	0.0	12.0	FEROS
	8472.76399	1.38	1.23	. . . . . . .	. . . . . . .	PFS
	8476.74101	-23.94	1.18	. . . . . . .	. . . . . . .	PFS
	8479.63075	-33.40	1.15	. . . . . . .	. . . . . . .	PFS
	8480.71817	-33.50	1.33	. . . . . . .	. . . . . . .	PFS
	8481.63918 36681.1	5.6	3.0	7.0	HARPS
	8481.66088 36670.1	4.9	-7.0	6.0	HARPS
	8482.63750 36690.5	4.1	2.0	5.0	HARPS
	8482.65892 36684.0	4.3	-1.0	6.0	HARPS
	8483.63626 36702.2	4.3	-8.0	6.0	HARPS
	8483.65821 36704.1	4.1	11.0	5.0	HARPS
	8483.76291 36668.1	8.0	-1.0	12.0	FEROS
	8485.70826 36650.9	13.9	47.0	19.0	FEROS
	8493.72558 36735.9	9.0	-11.0	13.0	FEROS
	8497.62083 36696.5	7.8	-40.0	12.0	FEROS
	8501.68699	34.11	1.72	. . . . . . .	. . . . . . .	PFS
	8503.65356 36813.1	14.3	64.0	19.0	FEROS Outlier
	8504.65888 36684.4	9.0	-61.0	13.0	FEROS
	8507.66569	-11.68	2.42	. . . . . . .	. . . . . . .	PFS
	8510.68697	-27.18	1.88	. . . . . . .	. . . . . . .	PFS
	8521.56775 36625.2	7.6	5.0	11.0	FEROS Outlier
	8528.60948	46.62	1.76	. . . . . . .	. . . . . . .	PFS
	8529.58589	45.56	1.65	. . . . . . .	. . . . . . .	PFS
	8542.55798 36659.1	8.7	-44.0	13.0	FEROS
	8543.54347 36640.3	7.4	-6.0	11.0	FEROS
	8544.61674 36663.3	7.8	-26.0	12.0	FEROS
	8545.57452 36676.3	7.6	-3.0	11.0	FEROS
	8546.58251 36714.8	9.7	38.0	14.0	FEROS
	8547.53676 36635.1	7.9	-17.0	12.0	FEROS
	8548.58309 36652.2	7.7	23.0	12.0	FEROS

Table 5 .

 5 Continued.

	BJD	RV	σRV	BIS	σBIS	Inst. Note
	-2450000	(m s -1 ) (m s -1 ) (m s -1 ) (m s -1 )
	8550.61335 36613.1	8.2	-62.0	12.0	FEROS
	8551.62488 36637.6	11.4	-26.0	16.0	FEROS
	8554.56409 36707.0	8.9	-38.0	13.0	FEROS
	8557.56708 36713.0	9.2	-4.0	13.0	FEROS
	8708.90979	28.50	2.14	. . . . . . .	. . . . . . .	PFS
	8711.89325	12.38	2.62	. . . . . . .	. . . . . . .	PFS
	8714.92414	-16.98	2.14	. . . . . . .	. . . . . . .	PFS
	8742.88505	19.06	2.19	. . . . . . .	. . . . . . .	PFS
	8764.84159 36736.7	5.2	-1.0	7.0	HARPS
	8766.79176 36750.6	6.4	3.0	8.0	HARPS
	8767.86802	29.71	1.98	. . . . . . .	. . . . . . .	PFS
	8777.79725 36695.8	23.5	23.0	31.0	HARPS
	8914.55281	21.41	2.73	. . . . . . .	. . . . . . .	PFS
	8920.52884	-5.82	1.77	. . . . . . .	. . . . . . .	PFS
	8923.53817	-33.84	1.94	. . . . . . .	. . . . . . .	PFS

Table 6 .

 6 Example Fit with High Precision Parameters (Osculating Orbital Elements at Epoch 1325.3279 days) for TOI-216b and TOI-216c Derived from joint TTV/RV fit

	Parameter	Value
	M⋆(M ⊙ )	0.77
	M b (M Jup )	0.061381
	P b	17.096824
	e b	0.15830
	̟ b (deg.)	292.55926
	λ b (deg)	82.329609
	Ω b,sky (deg)	0
	i b,sky (deg)	88.594066
	Mc (M Jup )	0.55454
	Pc	34.551590
	ec	0.0056764
	̟c (deg.)	200.93260
	λc (deg)	27.931018
	∆Ω sky = Ω c,sky (deg) -0.20544800
	i b,sky (deg)	89.785658

https://tess.mit.edu/followup/

https://exofop.ipac.caltech.edu/tess/

ACKNOWLEDGMENTS

We thank the TESS Mission team and follow up working group for the valuable dataset. We acknowledge the use of public TESS Alert data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center. This paper includes data collected by the TESS mission, which are publicly available from the Mikulski Archive for Space Telescopes (MAST). Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. This research has made use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and

Space Administration under the Exoplanet Exploration Program. This work has made use of observations from the Las Cumbres Observatory network.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. We acknowledge support for ASTEP from the French and Italian Polar Agencies, IPEV and PNRA, and from Université Côte d'Azur under Idex UCAJEDI (ANR-15-IDEX-01). This paper includes data gathered with the 6.

Software:

mpfit (Markwardt 2009), TAP (Gazak et al. 2012), Tapir [START_REF] Jensen | Tapir: A web interface for transit/eclipse observability[END_REF], TESS pipeline [START_REF] Jenkins | Proc. SPIE[END_REF]Twicken et al. 2018;Li et al. 2019), AstroImageJ (Collins et al. 2017), exoplanet (Foreman-Mackey et al. 2019), astropy (Astropy Collaboration et al. 2013, 2018), celerite (Foreman-Mackey et al. 2017;Foreman-Mackey 2018), starry (Luger et al. 2019), pymc3 (Salvatier et al. 2016), theano (Theano Development Team 2016), ceres (Brahm et al. 2017), PyTTV, PyTransit (Parviainen 2015), emcee (Foreman-Mackey et al. 2013), eleanor (Feinstein et al. 2019)


domain: sdu spi

text:
Nicolas Crouzet
email: nicolas.crouzet@esa.int

Abdelkrim Agabi
email: agabi@unice.fr

Tristan Guillot

Lyu Abe

François-Xavier Schmider

Djamel Mékarnia

Amaury H M J Triaud

Yves Bresson

Nicolas Mauclert

Christophe Bailet

Dennis Breeveld

Sander Blommaert

Brian Shortt

Jean-Baptiste Daban

Anne-Marie Lagrange

Romain Touzé

Justin Dufour

Valentin Stee

Jocelyn Caruana

Keywords: Photometry, Times-series, Exoplanets, Transits, Antarctica, ASTEP

Dome C, Antarctica is unique in particular for long-duration astronomical observations due to the excellent weather conditions and nearly uninterrupted nights during the Southern winter period. The 40 cm telescope ASTEP has been operating successfully at the Concordia base, at Dome C, since 2010. We describe the new ASTEP+, a major upgrade of its camera box which will allow it to observe simultaneously in two colors. Approximately three times more photons will be collected for science, yielding more sensitive and accurate observations. The southern location of the telescope means that it is ideally located to follow-up exoplanetary targets in preparation for the future JWST and Ariel observations, in particular when located in the southern continuous viewing zones of these space-based telescopes.

Towards ASTEP+, a two-color photometric telescope at Dome C, Antarctica

INTRODUCTION

Dome C in Antarctica offers unique conditions on Earth for astronomical observations. The 3-month continuous night during the Antarctic winter enables uninterrupted observations. The atmospheric conditions are excellent in particular during the winter. Thanks to its location on a summit of the high Antarctic plateau at an altitude of 3233 m, 1100 km away from the coast, this site is not affected by katabatic winds. The air is extremely dry and cold, the pressure is low (the equivalent altitude is around 4000 m), so the atmospheric transmission is increased in the visible and even more in the infrared compared to other sites on Earth. [START_REF] Kenyon | A Review of Optical Sky Brightness and Extinction at Dome C, Antarctica[END_REF][START_REF] Lawrence | Infrared and Submillimeter Atmospheric Characteristics of High Antarctic Plateau Sites[END_REF] The wind speed is low (generally a few m/s), the sky is photometric 67% of the time during the observing season, which is comparable to La Silla and Mauna Kea, and scintillation is decreased. [START_REF] Crouzet | Four winters of photometry with ASTEP South at Dome C, Antarctica[END_REF][START_REF] Crouzet | ASTEP South: an Antarctic Search for Transiting ExoPlanets around the celestial south pole[END_REF][START_REF] Aristidi | An analysis of temperatures and wind speeds above Dome C, Antarctica[END_REF][START_REF] Kenyon | Atmospheric Scintillation at Dome C, Antarctica: Implications for Photometry and Astrometry[END_REF] These conditions are highly beneficial to time-series observations. Dome C is the location of the French-Italian Concordia station which is inhabited all year long since 2005. The ASTEP project (Antarctic Search for Transiting ExoPlanets, 7 PI: T. Guillot, Laboratoire Lagrange, CNRS, Nice, France) aims at detecting and characterizing transiting exoplanets from this site. A 40 cm Newton telescope was designed and built to perform high precision photometry under the extreme conditions of the Antarctic winter. [START_REF] Daban | ASTEP 400: a telescope designed for exoplanet transit detection from Dome C, Antarctica[END_REF] The ASTEP telescope is equipped with a front-illuminated 4096 × 4096 pixel CCD camera (FLI Proline KAF 16801E) for science observations and a SBIG camera for guiding; a dichroic filter sends the red wavelengths to the science channel and the blue wavelengths to the guiding channel. This telescope was installed at Concordia in 2010 and provided excellent data since then. [START_REF] Abe | The secondary eclipses of WASP-19b as seen by the ASTEP 400 telescope from Antarctica[END_REF][START_REF] Guillot | Thermalizing a telescope in Antarctica -analysis of ASTEP observations[END_REF][START_REF] Mékarnia | Transiting planet candidates with ASTEP 400 at Dome C, Antarctica[END_REF][START_REF] Chapellier | A Catalog of Eclipsing Binaries and Variable Stars Observed with ASTEP 400 from Dome C, Antarctica[END_REF][START_REF] Mékarnia | The δ Scuti pulsations of β Pictoris as observed by ASTEP from Antarctica[END_REF] Here, we present the ongoing upgrade of the system, which consists in two new cameras and a new camera box for simultaneous observations at visible and red to near-infrared wavelengths.

SCIENCE GOALS

The broad objective of ASTEP is to discover and characterize transiting exoplanets. We will conduct observations following four main axes of research.

a) Terrestrial exoplanets. One axis is the detection of transiting terrestrial exoplanets, in particular around red dwarfs. A hot topic in the exoplanet field is the detection of terrestrial exoplanets with atmospheres that can be characterised. This requires small and relatively bright host stars. M dwarfs are the most favorable targets to search for terrestrial exoplanets: their small size and low mass yield deeper planetary transits and larger radial velocity amplitudes, the habitable zone is closer to the star which increases the transit probability for planets in this region, they account for 75% of stars in the Galaxy, and the occurrence rate of small planets around them is high (at least 1.4 Earth-size planets per star [START_REF] Dressing | The Occurrence Rate of Small Planets around Small Stars[END_REF][START_REF] Morton | The Radius Distribution of Planets around Cool Stars[END_REF][START_REF] Dressing | The Occurrence of Potentially Habitable Planets Orbiting M Dwarfs Estimated from the Full Kepler Dataset and an Empirical Measurement of the Detection Sensitivity[END_REF] ). The potential for characterising their atmospheres via transit spectroscopy is also enhanced. Their emission peak is around 800-900 nm. The new setup of ASTEP will include a red-enhanced, back-illuminated camera specifically chosen to observe M dwarfs (see Section 3).

b) Long period exoplanets. Another goal is the detection of warm and cold giant exoplanets, with orbital periods typically longer than 30 days, which remain a poorly constrained population. Studying this population would put our knowledge of the physics of close-in gas giant planet and of their atmospheres into perspective.

Observations from Dome C are particularly useful for long transits, generally corresponding to long period objects, which cannot be covered fully from temperate sites. An example of such observation is given in Figure 1. We will also search for terrestrial planets with long orbital periods, potentially in the habitable zone of their stars. Again, M dwarfs are the most favorable targets to find such planets. c) Exoplanets around young stars. We will also search for transiting exoplanets around young stars (a few Myr). Observing these systems is key to understand the formation and early evolution of planets. Detecting these planets is challenging because young stars are generally active and the planets may be hidden in a circumstellar disk. The two new cameras will transform the current single color telescope into a simultaneous two-color device. The two-color photometry will allow us to distinguish stellar variability and planetary transits: stellar photometric variations are stronger in the blue than in the red whereas exoplanet transits are achromatic at the level of precision we will reach.

d) Circumbinary planets. Long thought to be impossible to form, circumbinary planets (planets orbiting both stars of a binary) were unambiguously detected by Kepler. [START_REF] Doyle | Kepler-16: A Transiting Circumbinary Planet[END_REF] So far only a dozen systems have been identified and much remains to be explored. [START_REF] Martin | Populations of Planets in Multiple Star Systems[END_REF] The properties of circumbinary planets are important to understand the processes of planet formation and of disc-driven migration. ASTEP will participate in several ways: 1 -by targeting predicted planet transit times of systems identified with TESS, 2 -by attempting to detect the transits of circumbinary planets discovered with radial-velocities, and 3 -by collecting binary eclipses of TESS or radialvelocity systems to measure eclipse-timing variations. Circumbinary planet transit durations regularly exceed a typical non-Antarctic night, and can carry large uncertainties, both of which are dealt efficiently with ASTEP.

e) Targets of opportunity. The unique location of ASTEP means that it can also be used for many purposes, including the observation of variable stars, asteroids, comets, occultations by solar system objects or participate in programs to monitor any transient events. The possibility to have a reliable, automatic observatory at Concordia is an asset for many astrophysical programs.

A significant fraction of potential targets for goals a) to d) comes from the NASA TESS mission. [START_REF] Ricker | Transiting Exoplanet Survey Satellite (TESS)[END_REF] Nearly 2400 "TESS Objects of Interest" (TOIs) have been delivered so far and intensive follow-up observations are needed. ASTEP is part of the TESS Follow-up Program (TFOP) and we observed more than 100 TOIs during the winter 2020; the new setup will make our observations much more efficient. We will continue this program to confirm the nature of the system and to maintain accurate transit ephemerides, which will be crucial for future observations with space-based facilities, in particular JWST and Ariel. For these two space telescopes, the southern observation zone with maximum visibility fully overlaps with ASTEP's visibility zone. The first focal box of ASTEP included a FLI PL16801E camera at the focal plane, allowing a 1 • × 1 • field on 16 Mpxs. The guiding was ensured thanks to a separate small SBIG ME camera imaging the center of the field.

A NEW TWO-COLORS CAMERA BOX

We decided to change the focal box to allocate two-colors photometry on two separate cameras to increase the bandwidth, get more information on the targets and improve the photometric quality.

The first camera is an iKon-L 936 from Andor (iKon936 BEX2-DD). It has a back-illuminated 2048 × 2048 pixel CCD, with deep-depletion, fringe suppression and dual anti-reflection coating, and with a quantum efficiency of 95% at 800 nm. This high quantum efficiency in the red/near-infrared is ideal to observe cool stars. The same camera is used by the 12 20-cm NGTS telescopes 20 at Paranal Observatory, and by the six 1-m SPECULOOS telescopes [START_REF] Delrez | SPECULOOS: a network of robotic telescopes to hunt for terrestrial planets around the nearest ultracool dwarfs[END_REF][START_REF] Murray | Photometry and performance of SPECULOOS-South[END_REF] at Paranal, El Teide and San Pedro Mártir Observatories, and which are focused on monitoring ultracool dwarfs. [START_REF] Sebastian | SPECULOOS -Ultracool Dwarf Transit Survey: Target List and Strategy[END_REF] This camera will be used for science observations. The second camera is a Kepler KL 400 from Finger Lake Instrumentation (FLI). It has a back-illuminated 2048 × 2048 pixel Scientific CMOS detector with a quantum efficiency of 95% at 550 nm. Its high frame rate capability (up to 48 frames per second) and very low reading noise makes it ideal for guiding and its performances are compatible with high quality science imaging. Thus this camera will be used both for guiding and science observations. A dichroic filter will split the incident flux at 690 nm sending the red/near-infrared wavelengths to the Andor camera and the visible/blue wavelengths to the FLI camera.

With the new cameras, the total flux recorded between 400 and 1100 nm corresponds to an equivalent bandwidth of 507 nm (integral of the two QE curves in Figure 2). This has to be compared with the previous ASTEP box, providing an equivalent bandwidth of 150 nm. The transmission of the telescope and the optics (see below) beeing almost unchanged, the photometric gain is about 3.4. This will considerably impact the noise level of our measurements.

OPTICAL DESIGN

ASTEP's original CCD size, focal scale, the focal ratio and the aperture diameter were defined so as to observation of a large number (thousands) of stars of magnitudes m v from 8 to 12 while avoiding too much overlap. With its new camera box, ASTEP's main goals remains to discover, monitor and characterize exoplanets. This drives the same technical requirements as previously, [START_REF] Daban | ASTEP 400: a telescope designed for exoplanet transit detection from Dome C, Antarctica[END_REF] with the addition that accurate photometry now must be possible on both cameras. Two slight modifications with the present setup are to allow for a slightly smaller field of view than the initial 1 • × 1 • (at least 0.5 • × 0.5 • ) and an in-focus PSF that can have a FWHM that is smaller than one pixel in order to seek higher angular resolution when required. To ensure a stable and accurate photometry, the optical combination of the Wynne field corrector was optimized under Zemax in order to obtain a PSFs quality as close as possible to the theoretical ones with the same regularity throughout the whole field either in focus or out-of-focus.

Figure 3 shows the optical layout. A flat entrance window of 110 mm diameter forms the transition between the cold outer atmosphere and the insulated camera box. A dichroic mirror with a cutting frequency at 690nm separates the blue wavelengths, directed towards the FLI camera, and the red wavelengths directed towards a ZERODUR® flat mirror and the Andor camera.

In order to ensure the correct PSF shapes, a field corrector is formed of a set of three lenses on each optical channel: A 108 mm convex meniscus lens (L1), a 90 mm diverging meniscus lens (L2) and a set of two 50 mm convex lenses for each channel (L3 Andor, L3 FLI). These L3 lenses can be displaced with a translation stage in order to adjust the focal length and obtain the PSF sizes corresponding to the desired scientific program. The field of view obtained on the detectors corresponds to 36' square for the blue channel and 44' square for the red one.

The resulting characteristics of the PSFs in the two channels are shown in Fig. 4, both for the in-focus and out-of-focus modes. An excellent homogeneity of the field with minimal variations as a function of position was obtained over the whole field of the blue channel camera. On the red channel, the optical design leads to a ∼ 10% variation of the PSF size accross the CCD, which meets specifications. These properties are obtained both in the in-focus and out-of-focus modes. The spot images are regular and there are no optical aberrations.

Red Channel

Blue Channel Figure 4. Point spread functions obtained for the red channel (top row) and the blue channel (lower row), when the image is in focus (left column) or slightly out of focus, with a displacement of the last lens by 1 mm relative to its in-focus position (middle and right columns). The left-hand side and middle-column diagrams show the fraction of the energy that is enclosed within a circle of a given radius, in microns. Five sets of lines (often super-imposed) correspond to the images obtained at the center and four corners of the CCDs. The spots on the right column correspond to the energy distributions on the two cameras in units of their pixel sizes. The pixel size is equal to 13.5 µm for the red channel camera, and to 11 µm for the blue channel camera.

Table 1 provides a quantitative comparison of the two channels and the characteristics of the PSFs, both in the in-focus and out-of-focus modes. The in-focus mode yields an FWHM with is smaller than 1px, but a slight (1mm) displacement of the L3 lens on either channel leads to a FWHM of order 2 to 3 pixels and 99% of the energy in a circle of diameter of about 10 to 12 pixels.

Blue channel

Red channel Field of view 0.58

MECHANICAL DESIGN AND THERMALIZATION

Mechanical design of focal box

The mechanical design was studied by Sophia Engineering (https://www.sophiaengineering.com/en/), based on the scientific and optical specifications. The opto-mechanical modules are fixed on the upper part of the carbon composite plate which is made with a 20 mm thickness honeycomb sandwich panel. The cameras electronics (power supplies, USB-RJ45 converters, etc.) and the thermalization interfaces are gathered on the other side of carbon plate.

These two parts, opto-mechanical compartment and electronics compartment Figure 5 are separately covered and thermally insulated, the necessary heat for thermalization passes through the two planned holes on the carbon plates.

The focal box upper space (opto-mechanical compartment) is divided in three zones, one for the optical modules and one zone for each camera and thus, each space can be locally thermalized. As for the manufactured material, the design imposes using Titanium alloy for all optical mounts due to its low coefficient of thermal expansion (CTE), excepted the two cameras supports which can be made of aluminium since these modules are located in positive temperature space. On the optical path Figure 6 on the left, at the input of focal box, we have the first module composed of a window and the two first lenses L1/L2 of Wynne field corrector, after that, a dichroic mirror which reflects the blue part of the signal to the FLI camera and a mirror which reflects the red part of the signal to the Andor camera. The mounts of these two optical components are put on the same base which allows them to be removed and repositioned during the alignment phases on the telescope. On each optical channel (blue and red), there is a manually rotated filter holder allowing the selection of a specific filter adapted to the type of observation. Finally, the last Wynne field corrector focusing lenses, L3 FLI and L3 Andor, are positioned on mobile modules operated by a PI-MTS65 translation stage which is fixed on each camera support. The support of alignment tools equipped Figure 6 on the right with focusing L3 Alignment lens is planned for the optical telescope M1 and M2 alignment.

Thermalisation of the focal box

The thermalization of focal box is designed to minimize temperature fluctuations and turbulence on the optical path for extreme cases of hot temperature during summer (-30°C) and extreme cases of cold during winter (-75°C). For this, we have two compartments one for opto-mechanical modules isolated by Styrodur 20mm thick separations with thermal resistance R = 0.6 K m 2 /W and one for the electronics compartment isolated by 6mm thick Depron, R=0.16 K m 2 /W. This combination allowing limited heat dissipation at most 130W for an outside temperature of -50°C. We therefore sized the thermalization heat taking into account, on one hand, this loss and, on the other hand, the heat produced by the electronics of the two sciences cameras. The set point thermalization temperature is around +10°C in camera areas, which allows electronic equipments to operate correctly and -20°C in optical zones. Heating resistances and PT100 temperature sensors, are positioned on each module (iKon camera, FLI, displacement stage, control electronics) and activated by PID (Proportional-Integral-Derivative) regulators to maintain the set-point temperature for each component. Fans provide permanent air circulation between the electronic compartment and the two cameras areas. The various temperature set-points will be determined during the test phases in the thermal chamber (-75°C).

Structure modeling and thermal dilatation

The optical and mechanical design of ASTEP 400 is described elsewhere. [START_REF] Daban | ASTEP 400: a telescope designed for exoplanet transit detection from Dome C, Antarctica[END_REF] The telescope is a 40cm diameter Newtonian type with a carbon tubes for the Serrurier structure. The mount is a commercial AP3600 from Astro-Physics modified to operate in extreme conditions (-75°C) with a load capacity of 134 kg. In this design the focal box is attached to the Serrurier structure (Figure 8). The thermomechanical study and the finite elements modelling of the ASTEP400 telescope structure yields small differential displacements and tilts of the centre of primary mirror (M1), secondary mirror (M2) and the focal box entrance relative to one of four pointing configurations of the telescope over 24 hours observations. This study was based on thermal fluctuations of 30°C and a total telescope weight of 83 kg including 23 kg for the focal box.

The mechanical design of the new optical configuration required an optimization of geometric configuration of the box and its supporting structure due to the importance of the two sensors weight, 5.9 kg (iKon-L-936 and FLI KL400) compared to the old ones 3 kg (FLI Proline and SBIG ME).

For this, a thermo-elastic study of new focal box supporting structure was carried-out in order to meet the ASTEP 400 telescope specifications, new optical design and load limit of the mount. The new focal box is attached to the main part of the Serrurier and fixed on the mount to avoid elasticity stress of the Serrurier structure bar.

The new mechanic study and the modelization by finite elements of the focal box supporting structures have been carried out to minimize the deformations in order to meet the tolerance of stability of camera box position at the level of the entry window maximum ±0.50 mm in translation and ±3' in Tip/Tilt. Models the total weight the structure and the the opto-mechanical elements, cameras, electronics (cables, connectors, etc.) and the cover hoods for the new focal box give an estimate of around 31 kg. The thermal dilatation of the structure was analysed for a 40°C thermal gradient. The results obtained by the model of the structure for the four observation orientations of the telescope over 24 hours show a very good stability. In fact, the translation on the three axes (X, Y, Z) of the center of the entrance window by the effect of gravity and thermal gradient Figure 8 and Figure 9 is at most 0.24 mm, i.e. 30% below the specifications. The structure is more efficient in Tip/Tilt with an angle of 1.3' at most, i.e. 50% below the specified limit.

MANUFACTURING, ASSEMBLY, AND OPERATIONS

The internal parts for the assembly were manufactured in the mechanical workshop of the Science Payload Validation Section SCI-FIV at ESTEC. The parts were manufactured out of Ti grade 2, using a CNC (Computer Numerical Control) milling machine with carbide cutting tools and cutting fluid. The CAD (Computer-Aided Design) models were used to generate tool paths in a CAM (Computer-Aided Manufacturing) software. The CAM software was then used to generate machine code for the machine to execute the cutting sequences (Figures 11 and12). Figure 13 shows the camera box on the optical bench at the Fizeau laboratory. The two cameras and lens holders are installed on the carbon fiber plate. Further developments and tests of the optical system are on their way.

The new ASTEP Camera box was to be installed at Concordia at the end of 2020. Because of the COVID-19 pandemic and the subsequent reduction of the scientific operations at the base, installation has been postponed to the end of 2021, with a start of scientific operations on March 2022. The telescope will be operated automatically: Targets will be chosen by the ASTEP Scientific Committee and uploaded regularly. Once uploaded on the telescope control computer in Concordia, the pointing and guiding is automatic. Alerts are issued to the Nice telescope control team if the star field is not recognized (usually due to bad weather). Due to the limitation of the internet bandwidth, the observation images can be downloaded only in case of need. However, the ASTEP computer server in Concordia is processing the images automatically using an aperture photometry pipeline [START_REF] Mékarnia | Transiting planet candidates with ASTEP 400 at Dome C, Antarctica[END_REF] and sending control data and lightcurves to the ASTEP team. The current photometric precision of ASTEP is ∼ 2 mmag for bright (R∼12 mag) stars as described in Ref. 11. With the new system, we expect a photometric gain of about 3.4, which corresponds to an improvement, by a factor of 1.85, of the source photon noise. An improvement of 2.6 can even be achieved by using the correlation between the red and blue channels.

EXPECTED PRECISION

However, effects of correlated noise are significant, particularly for bright stars, and are key limitations of the current system. We identified some guidance to minimize these effects and the new focal box provides some solutions for dealing with these effects. We expect to reach at least a value of ∼ 800 ppm for these systematics. Fig. 14 displays a typical light curve RMS vs. ASTEP R-band magnitude together together with line representing the theoretical total noise for the current situation. Fig. 14 also displays the expected photon noise, the background noise, a 800 ppm systematic noise and the total noise budget limits expected with the new system. The reduction of the noise level is significant. This result can be further improved if we can decrease the effects of the correlated noise, for example by combining the observations in the two channels.

CONCLUSION

We have described the characteristics of the new ASTEP+ camera box. When installed on the telescope based at Concordia, Antarctica, at the end of 2021, it will allow accurate photometric observations of stars with exoplanets simultaneously in the blue and red channels. This new capability will enable collecting and effectively using for science purposes three times more photons than the previous camera. Thanks to the two-color observations, it will also enable a more efficient determination of chromatic effects, important to separate bona-fide transiting planets from background eclipsing binaries.

With the forthcoming launch of JWST and, a bit further down the road, of Ariel, the possibility to have an observatory in Antarctica is crucial, in particular to monitor and prepare the observations of these missions by a first characterization of the objects to be observed and a refinement of their ephemerides, in the case of transiting exoplanets. Indeed, Concordia is ideally located to observe the southern continuous viewing zones of these two telescopes which corresponds to a circumpolar region, i.e. a region of the sky which never sets, allowing a continuous viewing by ASTEP during the southern winter. This was exemplified by the successful monitoring of β-Pictoris [START_REF] Mékarnia | The δ Scuti pulsations of β Pictoris as observed by ASTEP from Antarctica[END_REF][START_REF] Lagrange | Evidence for an additional planet in the β Pictoris system[END_REF] in 2017 and 2018 and the follow-up of TESS targets starting in 2019. [START_REF] Bouma | Cluster Difference Imaging Photometric Survey. II. TOI 837: A Young Validated Planet in IC 2602[END_REF] The exploration of exoplanets in our Galaxy will require many observing facilities for the extremely important and massive follow-up work that is needed. With its new two-wavelength approach, ASTEP+ will provide much needed photometric observations of exoplanets and exoplanetary candidates.

Figure 1 .

 1 Figure1. Lightcurve of the 29.75 day period gas-giant exoplanet candidate TOI-173.01 obtained by ASTEP at Concordia on 18th May, 2020. This object orbits a bright, F-type star (Vmag = 9.32, T eff ≈ 6680 K) and was discovered by the TESS mission. The transit lasts 8 hours and has a depth of 0.63% corresponding to a radius of 1.1 RJup for the transiting object. Dome C is an ideal location to observe such long transits and the new system will make these observations even more efficient.

Figure 2 .

 2 Figure 2. Quantum efficiency of the Andor iKon camera (red) and of the FLI KL 400 camera (blue). A dichroic filter will split the flux at 690 nm. The quantum efficiency of the FLI Proline KAF 16801E camera currently installed on the telescope is shown for comparison (black).

Figure 3 .

 3 Figure 3. Optical layout.

Figure 5 .

 5 Figure 5. Focal box design: on the left the main carbon composite plat with all opto-mechanic modules, on the right the two closed part of the final box attached to the telescope by fiber carbon structure bars.

Figure 6 .

 6 Figure 6. View of the new ASTEP400 focal box optical path and associated opto-mechanical modules.

Figure 7 .

 7 Figure 7. Thermalization zones.

Figure 8 .

 8 Figure 8. View of the ASTEP 400 telescope design. The previous design is shown on the left, the new design is shown on the right-hand side.

Figure 9 .

 9 Figure 9. Mechanical deformation of the focal box attach to the telescope structure under the gravity effect according to four telescope orientations cases: Declination of 45 towards the North, Est, South and West

Figure 11 .

 11 Figure 11. View of part in CAM software with milling features and tool paths (left) and check of the assembly of the dichroic block (right).

Figure 12 .

 12 Figure 12. Internal parts of the camera box manufactured at the mechanical workshop of the Science Payload Validation Section SCI-FIV at ESTEC.

Figure 13 .

 13 Figure 13. ASTEP+ camera box on the optical bench at the Fizeau laboratory, Université Côte d'Azur. The set includes the FLI camera (left-hand side) with its filter wheel, the set of elements to hold the lenses and mirrors (center) and the Andor camera (right-hand side) with its filter wheel.

Figure 14 .

 14 Figure 14. Typical photometric precision attained with the current ASTEP. The group of symbols (black) shows the point to point RMS of light curves for each star, of a typical field, containing more than 10 000 stars, and the theoretical photometric precision of the current instrument (blue line). The red dashed, dot-dashed, triple dot dashed and solid line represent the expected source photon noise, sky photon noise, a 800 ppm constant added to account for systematics, and the final precision (quadrature sum of the other three lines) respectively for the new system.

Table 1 .

 1 • × 0.58 • 0.72 • × 0.72 • Characteristics of the optical solution.

	Pixel size	11 µm = 1.06 arcsec 13 µm = 1.3 arcsec
	Wavelength range	400 -690 nm	690 -1000 nm
	PSF diameter	E = 50% 0.40 px	0.60 -0.70 px
	(in-focus)	E = 90% 1.8 px	2.3 -2.5 px
		E = 95% 3.5 px	4.6 px
		E = 99% 8.9 px	11.5 px
	PSF diameter	E = 50% 3.06 -3.19 px	2.40 -2.98 px
	(out-of-focus)	E = 90% 4.61 -4.86 px	4.30 -4.88 px
		E = 95% 5.83 -5.93 px	5.79 -6.28 px
		E = 99% 9.74 -9.94 px	11.6 -11.9 px

ACKNOWLEDGMENTS

The ASTEP project was funded by the Agence Nationale de la Recherche (ANR), the Institut National des Sciences de l'Univers (INSU), the Programme National de Planétologie (PNP), the Observatoire de la Côte d'Azur and the Université Côte d'Azur through Idex UCA JEDI (ANR-15-IDEX-01). The logistics at Concordia is handled by the French Institut Paul-Emile Victor (IPEV) and the Italian Programma Nazionale di Ricerche in Antartide (PNRA). This research received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement n • 803193/BEBOP), and from the Science and Technology Facilities Council (STFC; grant n • ST/S00193X/1). This work made use of the NASA's Astrophysics Data System bibliographic services.