We present the discovery of a lowdensity planet orbiting the highmetallicity early Mdwarf TOI5688 A b. This planet was characterized as part of the search for transiting giant planets R gtrsim8 Moplus through the Searching for GEMS Giant Exoplanets around Mdwarf Stars survey. The planet was discovered with the Transiting Exoplanet Survey Satellite TESS and characterized with groundbased transits from Red Buttes Observatory RBO the Table Mountain Observatory of Pomona College and radial velocity RV measurements with the HabitableZone Planet Finder HPF on the 10 m Hobby Eberly Telescope HET and NEID on the WIYN 3.5 m telescope. From the joint fit of transit and RV data we measure a planetary mass and radius of 124pm24 Moplus 0.39pm0.07 MJ and 10.4pm0.7 Roplus 0.92pm0.06 RJ respectively. The spectroscopic and photometric analysis of the host star TOI5688 A shows that it is a metalrich FeH   0.47pm0.16 dex M2V star favoring the coreaccretion formation pathway as the likely formation scenario for this planet. Additionally Gaia astrometry suggests the presence of a wideseparation binary companion TOI5688 B which has a projected separation of sim5 1110 AU and is an M4V making TOI5688 A b part of the growing number of GEMS in wideseparation binary systems.
['Astrophysics - Earth and Planetary Astrophysics']
Searching for GEMS TOI5688 A b a lowdensity giant orbiting a highmetallicity early Mdwarf
{'No Header': 'Draft version December 9, 2024 Typeset using L A T E X twocolumn style in AASTeX631', 'Searching for GEMS: TOI-5688 A b, a low-density giant orbiting a high-metallicity early M-dwarf ∗': "Varghese Reji, 1 Shubham Kanodia, 2 Joe P. Ninan, 1 Caleb I. Ca˜nas, 3, 4 Jessica Libby-Roberts, 5, 6 Andrea S.J. Lin, 5, 6 Arvind F. Gupta, 7 Tera N. Swaby, 8 Alexander Larsen, 8 Henry A. Kobulnicky, 8 Philip I. Choi, 9 Nez Evans, 9 Sage Santomenna, 9 Isabelle Winnick, 9 Larry Yu, 9 Jaime A. Alvarado-Montes, 10, 11 Chad F Bender, 12 Lia Marta Bernab'o, 13, 14 Cullen H. Blake, 15 William D. Cochran, 14 Scott A. Diddams, 16, 17 Samuel Halverson, 18 Te Han, 19 Fred Hearty, 5, 6 Sarah E. Logsdon, 7 Suvrath Mahadevan, 5, 6 Michael W. McElwain, 4 Andrew Monson, 12 Paul Robertson, 19 Devendra K Ojha, 1 Arpita Roy, 20 Christian Schwab, 10 Gudmundur Stefansson, 21 and Jason Wright 5, 6, 22  \n- 1 Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India\n- 2 Earth and Planets Laboratory, Carnegie Science, 5241 Broad Branch Road, NW, Washington, DC 20015, USA 3 NASA Postdoctoral Fellow  \n4 NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA  \n- 5 Department of Astronomy & Astrophysics, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA, 16802, USA 6 Center for Exoplanets and Habitable Worlds, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA, 16802 7 NSF NOIRLab, 950 N. Cherry Ave., Tucson, AZ 85719, USA  \n8 Department of Physics & Astronomy, University of Wyoming, Laramie, WY 82070, USA  \n9 Pomona College, 333 N. College Way Claremont, CA 91711  \n10 School of Mathematical and Physical Sciences, Macquarie University, Balaclava Road, North Ryde, NSW 2109, Australia 11 The Macquarie University Astrophysics and Space Technologies Research Centre, Macquarie University, Balaclava Road, North Ryde, NSW 2109, Australia  \n12 Steward Observatory, University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA  \n- 13 Institute of Planetary Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin  \n14 McDonald Observatory and Center for Planetary Systems Habitability, The University of Texas at Austin, Austin, TX 78730, USA 15 Department of Physics and Astronomy, University of Pennsylvania, 209 S 33rd Street, Philadelphia, PA 19104, USA 16 Electrical, Computer & Energy Engineering, University of Colorado, 425 UCB, Boulder, CO 80309, USA 17 Department of Physics, University of Colorado, 2000 Colorado Avenue, Boulder, CO 80309, USA 18 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109 19 Department of Physics & Astronomy, The University of California, Irvine, Irvine, CA 92697, USA 20 Astrophysics & Space Institute, Schmidt Sciences, New York, NY 10011, USA  \n- 21 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands\n- 22 Penn State Extraterrestrial Intelligence Center, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA, 16802, USA  \n(Received August 30, 2024; Revised November 04, 2024; Accepted December 05, 2024)  \nSubmitted to AJ", 'ABSTRACT': "We present the discovery of a low-density planet orbiting the high-metallicity early M-dwarf TOI5688 A b. This planet was characterized as part of the search for transiting giant planets ( R ≳ 8 R ⊕ ) through the Searching for GEMS (Giant Exoplanets around M-dwarf Stars) survey. The planet was discovered with the Transiting Exoplanet Survey Satellite (TESS), and characterized with groundbased transits from Red Buttes Observatory (RBO), the Table Mountain Observatory of Pomona College, and radial velocity (RV) measurements with the Habitable-Zone Planet Finder (HPF) on the  \nCorresponding author: Varghese Reji  \nvarghesereji0007@gmail.com  \n- ∗ Based on observations obtained with the Hobby-Eberly Telescope (HET), which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Ludwig-MaximilliansUniversitaet Muenchen, and Georg-August Universitaet Goettingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly  \n10 m Hobby Eberly Telescope (HET) and NEID on the WIYN 3.5 m telescope. From the joint fit of transit and RV data, we measure a planetary mass and radius of 124 ± 24 M ⊕ (0 . 39 ± 0 . 07 M J ) and 10 . 4 ± 0 . 7 R ⊕ (0 . 92 ± 0 . 06 R J ) respectively. The spectroscopic and photometric analysis of the host star TOI-5688 A shows that it is a metal-rich ([Fe/H] = 0 . 47 ± 0 . 16 dex) M2V star, favoring the core-accretion formation pathway as the likely formation scenario for this planet. Additionally, Gaia astrometry suggests the presence of a wide-separation binary companion, TOI-5688 B, which has a projected separation of ∼ 5' (1110 AU) and is an M4V, making TOI-5688 A b part of the growing number of GEMS in wide-separation binary systems.  \nKeywords: Exoplanets, M-dwarfs, Giant planets.", '1. INTRODUCTION': "M dwarfs are the most prevalent stars in our Galaxy (Henry et al. 2006; Reyl'e et al. 2021) and tend to host more planets on average compared to FGK type stars (Mulders et al. 2015). Models of planet formation core-accretion (Pollack et al. 1996) and gravitational instability (Boss 2006) - fail to explain the in-situ formation of GEMS (Giant Exoplanets around M-dwarf Stars) because of the low mass of the host stars and their protoplanetary disks, lower surface density of dust and also longer formation timescales (Laughlin et al. 2004; Ida & Lin 2005; Rafikov 2006). Instead, recent studies try to explain the ex-situ formation of GEMS through core accretion (Kanodia et al. 2024) and gravitational instability (Boss & Kanodia 2023), followed by migration to the current location. The Searching for GEMS survey aims to discover and characterize more GEMS to constrain current planet formation models empirically.  \nDespite their rarity, the all-sky survey with the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2014) has discovered ∼ 25 GEMS (Kanodia et al. 2024) with precise mass measurements. Bryant et al. (2023) reported that the occurrence rate of giant planets (0 . 6 R J ≤ R p ≤ 2 . 0 R J ) around a sample of ∼ 90 , 000 low-mass stars ( ≤ 0 . 71 M ⊙ ) observed with TESS is only 0 . 194 ± 0 . 072%. A similar study of early M-dwarfs (0 . 45 ≤ M ⋆ ≤ 0 . 65 M ⊙ ) conducted by Gan et al. (2023) finds a consistent occurrence rate for periods 0 . 8 ≤ P ≤ 10 days and radii of 7 R ⊕ ≤ R p ≤ 2 R J to be 0 . 27 ± 0 . 09%.  \nIn this manuscript, we describe the discovery of the transiting low-density planet TOI-5688 A b, using a combination of photometry from seven sectors of TESS, ground-based photometry on the 0.6 m telescope at Red Buttes Observatory and Pomona College 1 m telescope at NASA JPL's Table Mountain Facility, and also spectra and precise radial velocities (RVs) from the Habitable-zone Planet Finder (HPF) spectrograph and NEID spectrograph. The system is cataloged by ElBadry et al. (2021) as a wide separation binary based  \non Gaia astrometry. In this manuscript, the host star is called TOI-5688 A, and the companion star of the binary system is called TOI-5688 B. Section 2 contains a description of the observations. Section 3 describes the estimation of stellar parameters of the host star and its binary companion. Section 4 explains the joint fitting of transit and RV data to obtain planetary parameters. We discuss our findings in Section 5, including a comparison with other planets hosted by M-dwarfs, their formation mechanisms, as well as wide-separation binary systems hosting GEMS. Finally, we include a summary in Section 6.", '2.1. TESS': "TESS (Ricker et al. 2014) observed TOI-5688 A (TIC 193634953, 2MASS J17474153+4742171, APASS 53641204, Gaia DR3 1363205856494897024) over seven sectors (25, 26, 40, 51, 52, 53 and 54). The planet candidate was identified in the TESS Faint Star Search (Kunimoto et al. 2022) with an orbital period of ∼ 2 . 95 days. We extracted aperture photometry flux from TESS fullframe images using eleanor (Feinstein et al. 2019), which uses TESScut (Brasseur et al. 2019) to obtain a cutout of 31 × 31 pixels from the calibrated full-frame images centered on TOI-5688 A. The light curve was generated using a 'normal' aperture in eleanor , which tests various aperture sizes, determined by the magnitude of the target star, and adopts the aperture that minimizes the combined differential photometric precision. The aperture used in eleanor is shown in Figure 3. The details of observations with TESS are given in Table 1.  \nTESS's large pixels (21'/pixel) can often lead to source confusion, with multiple stars on the same pixel causing dilution. In addition, the long exposure times (30 min and 10 min) preclude accurate determination of the transit shape. To obtain more precise estimates and confirm the stellar host, we obtained ground-based transit observations of TOI-5668 A b.  \nFigure 1. TESS eleanor light curves for sectors 25, 26, 40, 51, 52, 53 and 54. The first two sectors (25 and 26) have an exposure time of 30 minutes, and the rest have 10 minutes. The top panel in each figure shows the raw photometry data along with pink masks showing the transit regions. The mask is defined as t 0 ± 0 . 25 days with t 0 as the transit center. The masked data was fit using a GP model, which was then subtracted (lower panel) before fitting the transit model.  \n<!-- image -->  \nTable 1. Summary of space-based and ground-based transit observations of TOI-5688 A b", '2.2.1. 0.6 m Red Buttes Observatory': "We observed TOI-5688 A b with the 0.6 m f/8.43 Ritchen-Chr'etien Cassegrain at Red Buttes Observatory (RBO; Kasper et al. 2016) in Wyoming, USA on 2022 October 09 and 2023 May 15. We used the AltaF16 camera with a gain of 1.39 e -/ADU, a plate scale of 0.731'/pixel, and 2 × 2 pixel on-chip binning. The target airmass ranged from 1.06 - 2.3 on 2022 October 9, and 1.01 - 1.31 on 2023 May 15. The light curve was extracted from the frames of both data sets using a modified version of the pipeline outlined in Monson et al. (2017).We included scintillation noise in quadrature to the photometric uncertainty, as explained in Stefansson et al. (2017). The final extraction was done with an aperture radius of 3 pixels (2.19'), inner sky radius of 20 pixels (14.6'), and outer sky radius of 40 pixels (29.2'). The RBO observation details are given in Table 1 and the light curves are shown in Figure 2.", '2.2.2. 1.0 m Table Mountain Facility of Pomona College': "We also used the 1.0 m telescope of Pomona College residing at NASA JPL's Table Mountain Facility (TMF), Wrightwood, California, USA (Penprase 2004) for photometric observations of TOI-5688 A on 2023 July 19. The airmass ranged between 1.03 and 1.07, with the observations being limited by twilight. The observations were carried out under 1 × 1 binning, a gain of 0.8 e -/ADU, and a plate scale of 0.232'/pixel.  \nThe light curve from this visit was extracted using AstroImageJ (Collins et al. 2017), with an aperture radius of 15 pixels (3.39'), inner sky radius of 25 pixels (5.65'), and an outer sky radius of 30 pixels (6.78'). The average FWHM of PSF of TOI-5688 A in this data is ∼ 4 . 6'. The observation parameters are listed in Table 1, and the light curve is shown in Figure 2.", '2.2.3. uTIRSPEC at the 2.0 m Himalayan Chandra Telescope': "We used the upgraded TIFR Infra-Red Spectrograph and Imager (uTIRSPEC) in its imaging mode to obtain near-infrared photometry of the TOI-5688 system. The instrument is mounted on the 2 m Himalayan Chandra telescope, Hanle, Ladakh, India. Recently, the instrument TIRSPEC (Ninan et al. 2014) was upgraded to uTIRSPEC by replacing the HAWAII-1 PACE array with an H1RG array. The field of view in the imaging mode of uTIRSPEC is 5 × 5 arcmin 2 . During the commissioning of uTIRSPEC, on 2024 May 24, we observed the TOI-5688 region. Multiple frames of 10-second exposures were taken in 2MASS J, H, and K s filters at 5 dither positions for good sky subtraction. Data were  \nprocessed using the package HxRGproc (Ninan et al. 2018), after upgrading it to support frames taken with uTIRSPEC. After sky subtraction and flat correction, the images taken from multiple dither positions were shifted and combined. The function DAOStarFinder and DAOPHOT algorithm (Stetson 1987), in photutils (Bradley et al. 2024) were used to identify the sources in the frame. PSF photometry of the stars in the field was done using the function PSFPhotometry (Bradley et al. 2024) with an effective PSF (Anderson & King 2000) of an aperture with FWHM ∼ 6 pixels ( ∼ 1 . 8'). The PSFs are slightly elongated due to windy conditions, and therefore the effective PSF was derived using bright field stars and the EPSFBuilder function.The instrument magnitudes of each source in J, H, and K s bands were calculated using PSF photometry. The conversion from instrument magnitudes to apparent magnitudes (with color correction) was subsequently performed by cross-calibrating with the field stars 2MASS J, H, and K s magnitude. While the magnitudes we estimated for TOI-5688 A and B are consistent with 2MASS magnitudes, due to better spatial resolution, uTIRSPEC magnitudes are not affected by blending, specifically for TOI-5688 B. The J, H, and K s magnitudes estimated with uTIRSPEC are given in Table 3, with a J-band image of TOI-5688 A and B taken with uTIRSPEC with TESS pixel footprint is shown in Figure 3.", '2.3. Radial velocity observation with HPF and NEID': '2.3.1. HPF  \nWe obtained NIR spectra for TOI-5688 A using the Habitable-zone Planet Finder (HPF; Mahadevan et al. 2012, 2014, 2018) spectrograph to measure its RVs. The instrument is a fiber-fed (Kanodia et al. 2018) nearinfrared (8080 -12780 ˚ A) high resolution ( R ∼ 55 , 000) precision RV spectrograph with a stabilized environment (Stefansson et al. 2016), and is mounted on the 10 m Hobby-Eberly telescope (HET; Ramsey et al. 1998; Hill et al. 2021) at McDonald Observatory, Texas, USA. The telescope is a fixed-altitude range telescope with a roving pupil design, and it is fully queue-scheduled. The observations were carried out by HET resident astronomers (Shetrone et al. 2007) over 18 nights between 2022 August and 2023 July. Two 969 exposures were taken during each visit. We performed the bias correction, nonlinearity correction, cosmic ray reduction, and calculation of slope image and variance for each raw data frame separately, using the algorithms described in the package HxRGproc (Ninan et al. 2018). We use barycorrpy (Kanodia & Wright 2018) to perform the barycentric correction on the individual spectra, which is the Python implementation of the algorithms from  \nFigure 2. Phase folded transit light curves for TOI-5688 A b. Grey points represent the raw data. The model is shown in blue color for TESS and in red color for ground-based observations, along with the 1 σ confidence intervals as translucent bands. The median statistical uncertainty is also shown at x = -0 . 05.  \n<!-- image -->  \nTime since transit (days)  \nFigure 3. J band image of TOI-5688 A and B taken with uTIRSPEC. A 10 × 10 pixel footprint from TESS Sector 40 is overlaid with the uTIRSPEC image, represented by the blue grid. The TESS aperture is highlighted in red, and both TOI-5688 A and B are marked. TESS observations of TOI-5688 A are contaminated by the presence of TOI-5688 B, making ground-based observations necessary to determine the true transit depth accurately.  \n<!-- image -->  \nWright & Eastman (2014). We did not perform simultaneous NIR Laser Frequency Comb (LFC) calibrations (Metcalf et al. 2019) due to concerns about the impact of scattered calibration light on our faint target. The wavelength solution for the target exposures was driftcorrected using the LFC exposures taken throughout the night of the observations. This approach has been demonstrated to enable precise wavelength calibration and drift correction with a precision of ∼ 30 cm s -1 per observation (Stefansson et al. 2020a). This value is much smaller than our expected per-observation RV uncertainty (instrumental + photon noise) for this object ( ∼ 45 . 7 m s -1 ). After binning for one night, this uncertainty is ∼ 31 . 2 m s -1 .  \n2.3.2. NEID  \nWe also observed TOI-5688 A using NEID (Schwab et al. 2016; Halverson et al. 2016), an ultra-precise environmentally stabilized (Robertson et al. 2019) spectro-  \ngraph at the WIYN 3.5 m telescope 1 at Kitt Peak National Observatory in Arizona, USA. NEID has a fiberfed system similar to HPF (Kanodia et al. 2023), with three fibers - science, sky, and calibration. The instrument has an extended red-wavelength coverage (380-930 nm; Schwab et al. 2016). We observed the system for five nights between 2023 April 29 and 2023 May 31 using the high-resolution mode of NEID, with a resolution R ∼ 110 , 000. In our analysis, we used the spectra with an exposure time of 1800 s with a median SNR per 1D extracted pixel of 5.2 at 850 nm. The median uncertainty in RV values is 39.9 m s -1 . The NEID observations on this target were part of a pilot program to test the faintness limit of the instrument for early M-dwarfs.  \nThe NEID data were reduced using the NEID data reduction pipeline 2 (DRP), and the level-2 1D extracted spectra were retrieved from the NEID archive 3 . The RVs were calculated using Cross-Correlation Functions with line mask 4 . Since the spectra are photon-noise limited and the number of observations is low, we do not utilize the SERVAL template matching algorithm, which requires a high S/N template. The RVs obtained from HPF and NEID that are used for the analysis are shown in Table 2, with the phase folded model shown in Figure 4.', '2.4. Speckle Imaging with NESSI at WIYN': "We conducted observations of TOI-5688 A on 2022 September 16 with the NN-Explore Exoplanet Stellar Speckle Imager (NESSI; Scott et al. 2018) mounted on the WIYN 3.5 m telescope at Kitt Peak National Observatory, to identify faint background stars and nearby stellar companions. We acquired a sequence of 40 ms diffraction-limited exposures spanning 9 minutes, employing the SDSS r' and SDSS z' filters on NESSI. The speckle images were reconstructed using the methods outlined in Howell et al. (2011). We did not detect any stellar sources fainter than ∆ r ' = 4 . 0 or ∆ z ' = 4 . 0 at separations < 1 . 2', as illustrated in Figure 5.", '3.1. Wide Separation Binary and Galactic Kinematics': "The TOI-5688 system consists of a wide-separation binary, in which the stars are ∼ 1110 AU (5 . 1'; Riello  \n<!-- image -->  \nFigure 4. (a) Series of RV measurements of TOI-5688 A with HPF (green) and NEID (red). The values are given in Table 2. The best-fitting model from the joint fit of the transit and RVs is plotted in blue, including a 16%-84% confidence interval in light blue. The bottom panel shows the residuals after subtracting the model. (b) Phase-folded RV observations at the best-fit orbital period from the joint fit from Section 4. The eccentricity was not constrained in the fit, however, the results are consistent with a circular orbit (Table 4).  \n<!-- image -->  \nTable 2. RV estimates of TOI-5688 A, taken with HPF and NEID. The RV values from HPF are binned down to one day.  \net al. 2021) apart in the projected sky plane. The values of proper motion and parallax of both TOI-5688 A and B are consistent (Table 3) suggesting that they are comoving stars. The catalog from El-Badry et al. (2021) also lists this system as binary. Using the values given  \nFigure 5. NESSI Speckle Imaging in r' and z' bands in the inset 2.4' across. The curve shows the 5σ contrast curve for TOI-5688 A in both z and r bands. The contrast curves indicate no bright companions within 1 . 2' from the host star.  \n<!-- image -->  \nin the Gaia DR3 catalog, the galactic velocities U, V, and W values of TOI-5688 A are calculated with the Python package galpy 5 (Bovy 2015). These values are consistent with the system being part of the galaxy's thin disk.  \nWe used the parameter phot bp rp excess factor to determine if any Gaia B P or R P are contaminated by the companion. Using Equation 6 and Table 2 from Riello et al. (2021), we calculated the cor-  \nrected phot bp rp excess factor , accounting for this parameter's color-dependent mean trend. The corrected phot bp rp excess factor for TOI-5688 B is ≈ 0, implying that the contamination by the companion is negligible in Gaia photometry.  \nThe companion star (TOI-5688 B) does not contaminate the spectroscopic observations from HPF and NEID with the on-sky fiber sizes are 1 . 7 '' (Kanodia et al. 2018) and 0 . 9' (Kanodia et al. 2023), respectively. Our ground-based observations confirmed that the planet is orbiting the brighter and more massive primary, TOI5688 A. The stellar parameters for TOI-5688 A and B are listed in Table 3.", '3.2. Stellar parameters of TOI-5688 A': 'We estimate the stellar parameters for TOI-5688 A using HPF-SpecMatch , available broadband photometry, and Gaia astrometry. HPF-SpecMatch (Stefansson et al. 2020b) is a Python package used to determine empirical stellar parameters from HPF spectra, using the template-matching algorithm described in Yee et al. (2017). The spectral matching was performed on HPF order index 5 (8534 - 8645 ˚ A) spectra that have minimal atmospheric contamination. TOI-5688 A is determined to have T eff = 3713 ± 59 K, [Fe/H]= 0 . 47 ± 0 . 16 dex and log g ⋆ = 4 . 69 ± 0 . 04. The resolution limit of HPF ( R ∼ 55 , 000) places a constraint of v sin i < 2 km s -1 . The estimated stellar parameters are listed in Table 3.  \nEven though HPF-SpecMatch provides a nominal metallicity estimate, we note the caveat that the HPF-SpecMatch template matching method estimates the stellar parameters by χ 2 minimization of the entire order. This method is more sensitive to T eff and log g ⋆ , while not providing robust [Fe/H] estimates (essentially the χ 2 valley is not narrow) for TOI-5688 A. Therefore, while we estimate metallicity of 0 . 47 ± 0 . 16 dex, we advise caution in interpreting this beyond being a super-solar metallicity M-dwarf.  \nThe mass and radius of the star TOI-5688 A were calculated by fitting the Spectral Energy Distribution (SED) with the package EXOFASTv2 (Eastman et al. 2019). Due to the caution of blending with the companion and potential contamination in ground-based surveys because of the faintness of the target, only the Gaia (Casagrande & VandenBerg 2018) magnitudes and 2MASS magnitudes estimated from the observations with uTIRSPEC (Section 2.2.3) were used for SED fitting.', '3.3. Stellar parameters of TOI-5688 B': 'We derive T eff = 3294 +91 -71 K, mass of 0 . 31 ± 0 . 03 M ⊙ and radius of 0 . 32 ± 0 . 02 R ⊙ for TOI-5688 B by fitting the SED with the package EXOFASTv2 (Eastman  \net al. 2019). As in the case of TOI-5688 A, we only use Gaia (Casagrande & VandenBerg 2018) and uTIRSPEC magnitudes for the SED fitting due to potential contamination in the magnitudes.', '4. JOINT FITTING OF PHOTOMETRY AND RVS': 'We jointly fit the transit and RV data using the exoplanet (Foreman-Mackey et al. 2021) package, which uses the NUTS sampling (No U-Turn Sampling; Hoffman & Gelman 2011) in the Hamiltonian Monte Carlo (HMC; Betancourt 2017) method for posterior estimation with the PyMC3 package (Salvatier et al. 2016). The exoplanet package models the transits with the package starry (Luger et al. 2018), which uses a quadratic limb-darkening law (Mandel & Agol 2002) parameterized for uninformative sampling, as explained in Kipping (2013). We fit the transit in each TESS sector and ground-based observation using separate limbdarkening coefficients. The TESS photometric fit includes a separate dilution factor (Torres et al. 2010) for each sector, which is constrained based on the groundbased observations (where the stars are spatially resolved). The fitted parameters are listed in Table 4.  \nTo correct for the stellar and instrumental variability in the light curve, we mask out the transit signals and then fit a Gaussian Process (GP) model separately for each TESS sector. This model is then subtracted out (Figure 1). We use the RotationTerm kernel (ForemanMackey et al. 2017), which is implemented in celerite2 (Foreman-Mackey 2018) as the sum of two simple harmonic oscillators. The standard deviation of the process ( σ ), the primary period of variability, the quality factor of the secondary oscillation ( Q 0 ), the difference between the quality factors of primary and secondary modes ( dQ ), and the fractional amplitude of the secondary mode compared to the primary mode ( f ) are the hyperparameters of this model. The RV data were not used in this GP model fit of the TESS light curves. The exoplanet package oversamples the time series during the model evaluation, to account for the long-cadence photometry of TESS.  \nWe model the RVs with the standard Keplerian model with free eccentricity and omega that were sampled using a prior distribution Unit Circle . We include an instrument RV offset and a linear trend for the entire RV time series. We also include a simple white-noise jitter term in quadrature to measure the stellar RV and photometry jitter from each dataset.  \nWe use scipy.optimize (Virtanen et al. 2020) to get maximum a posteriori estimates as the initial condition  \nTable 3. Summary of stellar parameters for TOI-5688 A and B.  \nReferences: Stassun (Stassun et al. 2018), Gaia DR3 (Gaia Collaboration 2018; Casagrande & VandenBerg 2018), Bailer-Jones (Bailer-Jones et al. 2021; Bailer-Jones 2023), TIRSPEC (Ninan et al. 2014)  \nFigure 6. Parameter space of giant exoplanets hosted by Mdwarfs. TOI-5688 A b is marked by the green circle. Other M dwarf planets within the range of mass 95 - 850 M ⊕ are also shown in the figure, with colors representing the stellar effective temperature. The planets around FGK type stars are added in the background and represented by gray color along with the density contours for 0.3, 0.5, 0.8, 1.0, 1.2, and 1.5 g/cm 3 .  \n<!-- image -->  \nfor posterior sampling. Four chains consisting of 9000 steps (6000 tune + 3000 draw) in each chain were sampled for HMC. The convergence of sampling was checked using the Gelman-Rubin Statistic ( ˆ R ≤ 1 . 1; Ford 2006). The estimated system parameters are listed in Table 4.', '5.1. TOI-5688 A b in M dwarf planet parameter space': "Around twenty-five giant exoplanets ( ≳ 8 R ⊕ ) hosted by M-dwarfs (T eff < 4000 K) have been discovered so far. In this section, we compare the position of TOI5688 A b in the parameter space of transiting GEMS as queried from the NASA Exoplanet Archive (NEA; Akeson et al. 2013) on 2024 May 20. The planets have > 3 σ masses, and radii in the range of radius 8.0 - 15.0 R ⊕ . The host stars of the GEMS planets have an effective temperature in the range of 3300 - 4000 K. Planets around FGK-type stars are shown in the background of the plots.  \nThe mass vs. radius plot with density contours is shown in Figure 6. In addition, the positions of Saturn and Jupiter are shown. The data points are colored on the basis of the stellar effective temperature. TOI5688 A b has a mass of 124 ± 24 M ⊕ and a radius of 10 . 4 ± 0 . 7 R ⊕ , which is similar to that of Saturn with  \n1.5  \nmass 95.2 M ⊕ and radius 9.4 R ⊕ . The planets HATS-6 b (Hartman et al. 2015), TOI-519 b (Parviainen et al. 2021), Kepler-45 b (Johnson et al. 2012), TOI-5344 b (Han et al. 2023) and HATS 75 b (Jord˙an et al. 2022) are within 1 σ of the estimated mass of TOI-5688 A b. In addition, planets such as TOI-3629 b and TOI-4860 b are within the same density range as TOI-5688 A b and its neighbors. These planets have densities between 0.3 and 0.9 g/cm 3 , masses in the range of 90 - 150 M ⊕ . Since the mass and density of Saturn in the solar system  \n<!-- image -->  \nFigure 7. Plot of planet density with metallicity and equilibrium temperature of the planet. The upper plot shows the stellar metallicity-density space. The lower plot shows the equilibrium temperature-density space. The color of data points represents the radius of the planet. Both the host-star metallicity and equilibrium temperature are likely to affect the density of the planet.  \n<!-- image -->  \nTable 4. Summary of orbital and physical parameters for TOI-5688 A b.  \nare in this range 6 , we collectively refer to these planets as 'warm Saturn-like' planets.", '5.2. Density of Saturn-like planets': 'The top panel of Figure 7 shows the metallicity of the host star and the density of the planet. The color of each data point represents the radius of the planet.  \nHowever, it is crucial to note the caveats associated with the determination of M-dwarf metallicity. Given the forest of molecular lines in M-dwarf photospheres (due to their cooler temperatures) and the difficulty in continuum estimation, it is not possible to trivially use the standard metallicity estimation methods. Furthermore, Passegger et al. (2022) show the perils of comparing M-dwarf metallicities obtained from different spectroscopic methods (with different underlying assumptions). The metallicities included in Figure 7 are determined by a combination of photometric and spectroscopic methods, further complicating this. Therefore, the discussions related to the metallicity of GEMS hosts should be interpreted with caution.  \nThe bottom panel of Figure 7 shows the planetary equilibrium temperature (assuming 0 albedo) vs its bulk density. To check whether the equilibrium temperature of the planet drives the density, we calculated the Pearson correlation coefficient ( r = 0 . 41, p-value = 0.090) between the density of the planet and the equilibrium temperature in Figure 7. This lack of statistically significant correlation suggests the absence of a direct correlation between these quantities for these cooler giant planets ( < 1000 K).', '5.3. Formation Mechanism': "Saturn-like exoplanets hosted by M-dwarfs are believed to have formed by the core accretion model of the planet formation (Hayashi et al. 1985; Pollack et al. 1996, etc), though their lower masses compared to Jupiters remains a mystery. One possible explanation by Movshovitz et al. (2010) states that Saturn-like planets are formed by the slowing down of the runaway accretion from the disk as a result of the higher opacity of the disk. Recent studies of Howard, S. et al. (2023) and Helled (2023) also refer to Saturns as 'failed giant planets'. Helled (2023) suggests that the 'Saturns' took a few Myrs to form so that they had never gone through runaway accretion. For super-solar metallicity stars, high metallicity can increase the disk's opacity. This reduces the heat transfer efficiency (Boss 2002), which slows down gas accretion. This slowdown prevents planets  \nfrom becoming excessively massive before the disk dissipates (Helled 2023). Consequently, it leads to the formation of planets in the bottom right portion of the top panel in Figure 7. Simulations from Boss (2006, 2010) and most recently by Boss & Kanodia (2023) have also explored the gravitational instability pathway to form GEMS. In the following subsections, we explore the potential formation pathways of TOI-5688 A b through both core accretion and gravitational instability.", '5.3.1. Core accretion': "The formation of giant planets through core accretion is a two-step process. First, a rocky core of mass ≳ 10 M ⊕ is formed by the coagulation of planetesimals (Pollack et al. 1996), pebbles (Lambrechts & Johansen 2012) or both (Alibert et al. 2018). Second, once the core is massive enough, i.e. M core ≳ 10 M ⊕ (Mordasini et al. 2007), runaway gas accretion takes place onto the core from the protoplanetary disk, enabling the transition of a planet to a gas giant. We can separately analyze insitu and ex-situ formation scenarios.  \nIn-situ -The in-situ formation of the core with the required mass ( > 10 M ⊕ ) within the lifetime of the disk is challenging (Fedele, D. et al. 2010; Pfalzner et al. 2022; Miotello et al. 2023; Pfalzner & Dincer 2024). In-situ formation of the planet at its present-day orbital separation necessitates high disk surface density ( ≳ 7 × 10 6 g/cm 2 ; Dawson & Johnson 2018) or a large feeding zone (∆, in terms of Hill radius; > 14000). Models predict a surface density of only ∼ 10 3 g/cm 2 at r = 0 . 03 AU (Miotello et al. 2023). Secondly, ∆ has a hard upper limit set by the escape velocity of the disk (Schlichting 2014), which is given by Equation 7 of Dawson & Johnson (2018). At TOI-5688 A b's present-day location at P = 2.95 days, and assuming a core density of 4 g/cm 3 (the average density of Saturn's core; Mankovich & Fuller 2021), ∆ max is given by  \n∆ max ≃ 13 ( P 3 day ) 1 / 3 ( ρ 8 g cm -2 ) 1 / 6 ≃ 11 . 5  \nGiven the limitations in the size of the in-situ feeding zone and disk surface density, it is highly improbable for TOI-5688 A b to have formed in-situ .  \nEx-situ -The planet could have formed farther out in the disk and subsequently migrated to its present location. We estimate the location that can support core formation using Equations 6 and 7 from Dawson & Johnson (2018). For the dust surface density profile, we adopt the power law Σ dust ( r ) = Σ 0 ( r AU ) -1 exp ( -r AU ) (Williams & Cieza 2011), where r denotes the distance from the  \nstar. Σ 0 is the normalization constant, which is the value of Σ at 1 AU, and calculated using the relation  \nΣ 0 = M dust 2 πR 2 c  \nHere, R c = 1 AU. The disk mass ( M gas + M dust ) can be estimated to be ∼ 3996 M ⊕ , which is 2% of the star (Flores et al. 2023). If the gas-to-dust ratio is 100 (Flores et al. 2023), Σ 0 can be estimated as ∼ 167 g/cm 2 . We assume the size of the maximum feeding zone, i.e., ∆ = ∆ max , and substitute Equation 7 of Dawson & Johnson (2018) and the power law of dust surface density into Equation 6 of Dawson & Johnson (2018) to obtain the relation:  \nM core = 0 . 17 ( Σ 0 g cm 2 ) 3 2 ( M ⋆ M ⊙ ) 1 2 ( r AU ) 9 4 exp ( r AU ) M ⊕ (1)  \nTo form M core ≳ 10 M ⊕ , we need r ≳ 4 . 5 AU, corresponding to an orbital period ≳ 5400 days. The formation timescale of the core with 10 M ⊕ at this location can be estimated using Equation 20 of Johansen & Lambrechts (2017), which can be written as:  \nt pla = 1 . 7Myr f -1 pla ( M 10M ⊕ ) 1 / 3 ( r 5AU ) 1 . 5 [ max ( ζ, 1) ζ ] (2)  \nf pla is a parameterization of the surface density profile of the planetesimals, which is assumed to be 1 here (Bitsch, Bertram et al. 2015; Johansen & Lambrechts 2017). ζ determines the accretion regime, which is assumed to be 1 for planetesimals in circular orbit (Rafikov 2004; Johansen & Lambrechts 2017). Therefore, the timescale to form the core of 10 M ⊕ at r = 4 . 5 AU is ∼ 1 . 4 Myr.  \nSince the planet likely formed ex-situ , it would subsequently have to migrate to its present location. The estimated value of eccentricity ( ≈ 0, see Table 4), is consistent with the possibility of migration through disk interaction (Baruteau et al. 2014). The timescale for type 1 migration, which is estimated using Equation 3 of Baruteau et al. (2014) for TOI-5688 A b is ≳ 1 Myr from ∼ 4 . 5 AU, for a disk with a gas-to-dust ratio of 100.  \nAnother possibility of planetary migration is through gravitational scattering (Cloutier & Lin 2013), followed by circularization of the planetary orbit (Pont et al. 2011). However, using the equation provided by Pont et al. (2011) with a tidal dissipation factor Q = 10 6 , the circularization timescale is approximately ∼ 10 12 years. As this timescale is greater than the age of the universe, and the lack of a highly eccentric orbit suggests that this planet is unlikely to have formed via gravitational scattering.", '5.3.2. Gravitational instability': 'The formation of this planet by Gravitational Instability (GI; Kuiper 1951; Cameron 1978) is hard to predict since it is affected by various factors such as protostellar disk mass, cooling prescription, etc. Although GI has been explored for the formation of GEMS (Boss 2006; Boss & Kanodia 2023), TOI-5688 A b is at the lower end of the planet masses or mass ratios (planet-to-star mass ratio) typically seen as a result of GI (Rice et al. 2003; Boss 2006; Boley 2009, etc.). Studies by Boss (2006); Kratter & Lodato (2016) and others have shown the propensity of GI to form objects that are typically ≳ 1 M J . Also, the simulations by Cai et al. (2005) show that the strength of GI decreases as metallicity increases. On the other hand, magneto-hydrodynamic simulations by Deng et al. (2021) show that disk fragmentation in the presence of magnetic fields in the disk could lead to the formation of intermediate-mass planets. Therefore, given a sufficiently massive protostellar disk (Boss & Kanodia 2023), while GI is possible, it is unnecessary to invoke GI as the necessary means of formation for this object.', '5.4. Wide Separation Companion': "TOI-5688 A is a member of a wide-separation binary system (Section 3.1). El-Badry et al. (2021) have cataloged wide separation binary systems from Gaia DR3 with either the main sequence or white dwarf companion based on the location of the companion in the Gaia color-absolute magnitude diagram. It is estimated that ∼ 40% of M-dwarfs in the solar neighborhood have at least one companion within ∼ 1000 AU (Fischer & Marcy 1992; Lada 2006; Raghavan et al. 2010). So far 10 (out of 25 transiting GEMS) are part of a binary system: HATS-74 (Jord˙an et al. 2022), TOI-3984 (Ca˜nas et al. 2023), TOI-5293 (Ca˜nas et al. 2023), TOI-3714 (Ca˜nas et al. 2022), K2-419 (Kanodia et al. 2024), TOI-5634 (Kanodia et al. 2024), TOI-6034 (Kanodia et al. 2024), TOI-762 A (Hartman et al. 2024), TOI-6383 (Bernab'o et al. 2024) and TOI-5688 (this work).  \nMulti-star systems are common in our galaxy, yet the influence of the companion star on the planetary system is still unclear. Studies have been conducted on the giant planet population that is orbiting FGK-type stars to test the significance of multi-body interactions on the planetary system (eg: Wang et al. 2014; Knutson et al. 2014; Ngo et al. 2015; Evans, D. F. et al. 2018). Relative to field stars, giant planets with a period < 10 days have been reported to have a high-wide binary fraction. Fontanive et al. (2019) reports that 79 +13 . 2 -14 . 7 % of systems with a massive substellar object have a wide separation companion between 50 - 2000 AU. However, Moe  \n& Kratter (2021) revisited this assertion and concluded that the wide separation companions of hosts of giant planets in 50 - 2000 AU do not significantly enhance the formation mechanism. Instead, the higher fraction of wide binaries among hot Jupiters is due to the inhibited formation of hot Jupiters in close binary systems.", '6. SUMMARY': 'In this paper, we present the discovery and characterization of a short-period Saturn-like exoplanet that is hosted by an M2V dwarf with T eff = 3713 ± 59 K. The planet has a mass 124 . 0 +23 . 3 -24 . 4 M ⊕ and radius of 10 . 4 +0 . 6 -0 . 7 R ⊕ . The density of this planet is 0 . 61 +0 . 20 -0 . 15 g/cm 3 , which makes it similar to Saturn. The host is a member of a wide-separation binary system, with the companion being a main sequence star with an effective temperature of 3231 +65 -62 K. We utilize seven TESS sectors of photometry as well as ground-based transit follow-up with the 0.6 m RBO and 1.0 m TMF, as well as photometry from uTIRSPEC, speckle imaging from NESSI, and radial-velocity observations from HPF and NEID. The planetary and orbital parameters were estimated by Bayesian analysis with Hamiltonian Monte Carlo. The estimated stellar and planetary parameters support the core-accretion formation model for such Saturn-like exoplanets.', 'ACKNOWLEDGEMENTS': "These findings stem from observations conducted using the Habitable-zone Planet Finder Spectrograph on the Hobby-Eberly Telescope (HET). We gratefully acknowledge support from various sources, including NSF grants AST-1006676, AST-1126413, AST1310885, AST-1310875, AST-1910954, AST-1907622, AST-1909506, ATI 2009889, ATI-2009982, AST2108512, AST-1907622, AST-2108801, AST-2108493 and the NASA Astrobiology Institute (NNA09DA76A), in our efforts to achieve precision radial velocities in the near-infrared (NIR). The HPF team is also appreciative of funding provided by the Heising - Simons Foundation through grant 2017-0494. Furthermore, we acknowledge the collaborative efforts of the University of Texas at Austin, the Pennsylvania State University, Ludwig-Maximilian-Universitat Munchen, and GeorgAugust Universitat Gottingen in the Hobby-Eberly Telescope project. The HET is named in recognition of its principal benefactors, William P. Hobby and Robert E. Eberly. The HET collaboration extends its appreciation to the Texas Advanced Computing Center for its support and resources. We express gratitude to the Resident Astronomers and Telescope Operators at the HET for their adept execution of observations with HPF. Additionally, we acknowledge that  \nthe HET is situated on Indigenous land. Furthermore, we wish to recognize and pay our respects to the Carrizo & Comecrudo, Coahuiltecan, Caddo, Tonkawa, Comanche, Lipan Apache, Alabama-Coushatta, Kickapoo, Tigua Pueblo, and all the American Indian and Indigenous Peoples and communities who have inhabited or become part of these lands and territories in Texas, here on Turtle Island. We acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing high-performance computing, visualization, and storage resources that have contributed to the results reported within this paper. The data presented in this work were acquired at the WIYN Observatory using telescope time allocated to NN-EXPLORE through a scientific partnership involving the National Aeronautics and Space Administration (NASA), the National Science Foundation (NSF), and NOIRLab. Funding support for this research was provided by a NASA WIYN PI Data Award, which is managed by the NASA Exoplanet Science Institute. The observations were conducted with NEID on the WIYN 3.5 m telescope at Kitt Peak National Observatory (KPNO), under NSF's NOIRLab, and were carried out under proposal 2023A-633546 (PI: S. Kanodia), managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the NSF. We thank the NEID Queue Observers and WIYN Observing Associates for their skillful execution of our NEID observations. This work was performed for the Jet Propulsion Laboratory, California Institute of Technology, and sponsored by the United States Government under Prime Contract 80NM0018D0004 between Caltech and NASA. The WIYN Observatory is a collaborative effort involving the University of WisconsinMadison, Indiana University, NSF's NOIRLab, Pennsylvania State University, Purdue University, University of California-Irvine, and the University of Missouri. We acknowledge the privilege of conducting astronomical research on Iolkam Du'ag (Kitt Peak), a mountain of special significance to the Tohono O'odham people. Several observations presented in this paper utilized the NN-EXPLORE Exoplanet and Stellar Speckle Imager (NESSI) under the proposal 2022B-936991. NESSI received funding from the NASA Exoplanet Exploration Program and the NASA Ames Research Center. Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley built NESSI at the Ames Research Center.  \nWe utilized data from the Gaia mission 7 of European Space Agency (ESA), processed by the Gaia Data  \nProcessing and Analysis Consortium (DPAC, 8 ). The DPAC's funding is provided by national institutions, particularly those involved in the Gaia Multilateral Agreement. Additionally, we acknowledge support from NSF grant AST-1907622 for conducting precise photometric observations from the ground. We express gratitude for the assistance provided by NSF grant AST1907622 in conducting meticulous photometric observations from the ground. This study has utilized the Exoplanet Follow-up Observation Program website, managed by the California Institute of Technology under contract with the National Aeronautics and Space Administration as part of the Exoplanet Exploration Program.  \nThis research has made use of the Exoplanet Followup Observation Program (ExoFOP; DOI: 10.26134/ExoFOP5) website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.  \nVR, JPN, and DKO acknowledge the support of the Department of Atomic Energy, Government of India, under project identification No. RTI 4002. VR and JPN were supported in part by a generous donation (from the Murty Trust) aimed at enabling advances in astrophysics through the use of machine learning. Murty Trust, an initiative of the Murty Foundation, is a notfor-profit organization dedicated to preserving and celebrating culture, science, and knowledge systems born out of India. Mrs. Sudha Murty and Mr. Rohan Murty head the Murty Trust. CIC acknowledges support from NASA Headquarters through an appointment to the NASA Postdoctoral Program at the Goddard  \nSpace Flight Center, administered by ORAU through a contract with NASA. L.M.B acknowledges the support of the European Union's Horizon Europe Framework Programme under the Marie Skglyph[suppress]lodowska-Curie Actions grant agreement No. 101086149 (EXOWORLD). VR would like to acknowledge the use of Grammarly, LanguageTool and ChatGPT for improving the English grammar and sentence structure in the manuscript.  \nWe express our gratitude to the anonymous referee for providing valuable feedback, which has enhanced the overall quality of this manuscript.  \nFacilities: HET (HPF), WIYN (NEID, NESSI), TESS, RBO, TMF, HCT (TIRSPEC), Exoplanet Archive, Gaia, MAST  \nSoftware: ArviZ (Kumar et al. 2019), AstroImageJ (Collins et al. 2017), astroquery (Ginsburg et al. 2019), astropy (Astropy Collaboration et al. 2013, 2018), barycorrpy (Kanodia & Wright 2018), celerite2 (Foreman-Mackey et al. 2017; Foreman-Mackey 2018), corner (Foreman-Mackey 2016), ChatGPT (OpenAI 2023), eleanor (Feinstein et al. 2019), Emacs (Stallman 1981) EXOFASTv2 (Eastman et al. 2019), exoplanet (Foreman-Mackey et al. 2021), galpy (Bovy 2015), HxRGproc (Ninan et al. 2018), HPF-SpecMatch (Yee et al. 2017), ipython (Perez & Granger 2007), lightkurve (Lightkurve Collaboration et al. 2018), matplotlib (Hunter 2007), numpy (Harris et al. 2020), Org mode (Schulte & Davison 2011) pandas (development team 2020), photutils (Bradley et al. 2024) pyastrotools (Kanodia 2023), pyMC3 (Salvatier et al. 2016), scipy (Virtanen et al. 2020), SERVAL (Zechmeister, M. et al. 2018), starry (Luger et al. 2018), telfit (Gullikson et al. 2014) Theano (The Theano Development Team et al. 2016)", 'REFERENCES': 'Akeson, R. 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