TOI-2084 b and TOI-4184 b: Two new sub-Neptunes around M dwarf stars

We present the discovery and validation of two TESS exoplanets orbiting nearby M dwarfs: TOI-2084b, and TOI-4184b. We characterized the host stars by combining spectra from Shane /Kast and Magellan /FIRE, spectral energy distribution analysis, and stellar evolutionary models. In addition, we used Gemini-South/Zorro & -North/Alopeke high-resolution imaging, archival science images, and statistical validation packages to support the planetary interpretation. We performed a global analysis of multi-colour photometric data from TESS and ground-based facilities in order to derive the stellar and planetary physical parameters for each system. We find that TOI-2084b and TOI-4184b are sub-Neptune-sized planets with radii of R p = 2 . 47 ± 0 . 13 R ⊕ and R p = 2 . 43 ± 0 . 21 R ⊕ , respectively. TOI-2084b completes an orbit around its host star every 6.08 days, has an equilibrium temperature of T eq = 527 ± 8 K and an irradiation of S p = 12 . 8 ± 0 . 8 S ⊕ . Its host star is a dwarf of spectral M2 . 0 ± 0 . 5 at a distance of 114 pc with an effective temperature of T e ff = 3550 ± 50 K, and has a wide, co-moving M8 companion at a projected separation of 1400 au. TOI-4184b orbits around an M5 . 0 ± 0 . 5 type dwarf star ( K mag = 11 . 87) each 4.9days, and has an equilibrium temperature of T eq = 412 ± 8 K and an irradiation of S p = 4 . 8 ± 0 . 4 S ⊕ . TOI-4184 is a metal poor star ([Fe / H] = − 0 . 27 ± 0 . 09 dex) at a distance of 69 pc with an effective temperature of T e ff = 3225 ± 75 K. Both planets are located at the edge of the sub-Jovian desert in the radius-period plane. The combination of the small size and the large infrared brightness of their host stars make these new planets promising targets for future atmospheric exploration with JWST.


Introduction
M dwarfs are the most common stars in our galaxy (Henry et al. 1994;Kirkpatrick et al. 1999), and small planets occur around M dwarfs more frequently than Sun-like stars (Nutzman & Charbonneau 2008;Kaltenegger & Traub 2009;Winters et al. 2014).M dwarfs are, therefore, attractive and exciting targets for searching for small and temperate exoplanets using the transit technique, thanks to their small sizes, low masses, and luminosities.The transit signal is much deeper than that caused by similar planets orbiting Sun-like stars, which makes such planets easier to detect and characterize.Moreover, such planetary systems are suitable targets for atmospheric characterization through transmission spectroscopy, including with JWST (Kempton et al. 2018).In addition, the radial-velocity semi-E-mail: khalid.barkaoui@uliege.beamplitudes of the stellar hosts are higher, thanks to the low stellar masses, which makes them suitable targets for planetary mass measurements.M dwarf systems will allow a better understanding of the so-called radius valley between the super-Earth-and sub-Neptune-sized planets (see, e.g., Owen & Wu (2013); Fulton & Petigura (2018); Van Eylen et al. (2018).Moreover, the discovery of additional sub-Neptune desert planets (Mazeh et al. 2016) allows us to further explore and understand the physical properties of such exoplanetary systems.
The Transiting Exoplanet Survey Satellite (TESS) mission (Ricker et al. 2015) was launched by NASA in 2018 to search for planets around bright nearby dwarfs, including M-type stars.To date, TESS has discovered more than 330 exoplanets orbiting FGKM stars, including 66 planets orbiting around M dwarfs (NASA Archive of Exoplanets).In Section 2, we present the TESS photometry, high-precision photometric follow-up observations using ground-based facilities, and high-resolution imaging from Gemini.In Section 3, we present an analysis of the host star properties derived from their Spectral Energy Distributions (SEDs) and spectra.In Section 4, we validate the planetary nature of the transit signals.In Section 5, we present our global analysis of the photometric data sets of the planetary systems, which allow us to determine the physical parameters of the star and planet.In Section 6, we present planet searches and detection limits from the TESS photometry.Finally, we discuss our results and present our conclusions in Section 7.

TESS photometry
The host star TIC 394357918 (TOI-4184) was observed by TESS, (Ricker et al. 2015) mission in Sectors 1, 28 and 39 for 27 days each on TESS CCD 3 Camera 3. The Sector 1 campaign started on UTC July 25 2018 and ended on UTC August 22 2018.The Sector 28 campaign started on UTC July 30 2020 and ended on UTC August 26 2020.The Sector 39 campaign started on UTC 2021 May 26 and ended on UTC 2021 June 26.
The star TIC 441738827 (TOI-2084) was observed by TESS in 2-minutes cadence during Sectors 16 (UTC September 11 to October 07 2019), 19-23 (UTC November 27 2019 to April 16 2020), 25-26 (UTC May 13 to July 04 2020), 48-60 (UTC January 31 2021 to January 18 2023).TOI-4184 and TOI-2084 were selected by Stassun et al. (2018) to be observed using the 2minute short-cadence mode.To perform TESS data modeling, we retrieved the Presearch Data Conditioning light curves (PDC-SAP, Stumpe et al. (2012); Smith et al. (2012); Stumpe et al. (2014) constructed by the TESS Science Processing Operations Center (SPOC; Jenkins et al. (2016)) at Ames Research Center from the Mikulski Archive for Space Telescopes.PDC-SAP light curves have been corrected for instrument systematics and crowding effects.Figure 1 shows the TESS field-of-view for each target and photometric apertures used with the location of nearby Gaia DR3 sources around each target (Gaia Collaboration et al. 2021).TESS light curves for TOI-2084 and TOI-4184 are presented in Figure 2 and Figure 3.

Ground-based photometry
We used the TESS Transit Finder tool, which is a customized version of the Tapir software package (Jensen 2013), to schedule the photometric time-series follow-up observations.These are summarized in the following, and the resulting light curves are presented in Figure 4.

SPECULOOS-South
We used one of the SPECULOOS-South (Search for habitable Planets EClipsing ULtra-cOOl Stars, Jehin et al. (2018);Delrez et al. (2018); Sebastian et al. (2021) facilities to observe one full transit of TOI-4184.01 on UTC September 25 2021 in the Sloanz filter with an exposure time of 42s.Each 1.0-m robotic telescope is equipped with a 2K×2K CCD camera with a pixel scale of 0.35 and a field of view of 12 ×12 .We performed aperture photometry in an uncontaminated target aperture of 3.9 and a PSF full-width half-maximum (FWHM) of 1.7 .Data reduction and photometric measurements were performed using the PROSE1 pipeline (Garcia et al. 2021).

SPECULOOS-North
We used SPECULOOS-North/Artemis to observe two transits of TOI-2084.01.Artemis is a 1.0-m Ritchey-Chretien telescope equipped with a thermoelectrically cooled 2K×2K Andor iKon-L BEX2-DD CCD camera with a pixel scale of 0.35 , resulting in a field-of-view of 12 × 12 (Burdanov et al. 2022).It is a twin of the SPECULOOS-South (Section 2.2.1) and SAINT-EX (Section 2.2.3) telescopes.The first transit was observed on UTC 2020 August 13, and the second was observed on UTC June 25 2021.Both transits were observed in the I + z filter with an exposure time of 33 s, and we performed aperture photometry in an uncontaminated target apertures of 2.8-3.2 and a PSF FWHM of 1.4-1.6 .Data reduction (bias, dark and flat correction) and photometric measurements were performed using the PROSE pipeline (Garcia et al. 2021).

SAINT-EX
We used the SAINT-EX telescope to observe one full transit of TOI-2084.01 on UTC July 13 2021 in the r filter with an exposure time of 141 seconds.SAINT-EX (Search And char-acterIsatioN of Transiting EXoplanets, Demory et al. (2020)) is a 1-m F/8 Ritchey-Chretien telescope located at the Sierra de San Pedro Mártir in Baja California, México.SAINT-EX is equipped with a thermoelectrically cooled 2K × 2K Andor iKon-L CCD camera.The detector gives a field-of-view of 12 ×12 with a pixel scale of 0.35 per pixel.We performed aperture photometry in an uncontaminated target aperture of 3.2 and a PSF FWHM of 1.4 .Data reduction and photometric measurements were performed using the PROSE pipeline (Garcia et al. 2021).

TRAPPIST-North
We used the 60-cm TRAPPIST-North telescope to observe one partial transit and one full transit of TOI-2084.01.TRAPPIST-North (TRAnsiting Planets and PlanetesImals Small Telescope) is a 60-cm robotic telescope installed at Oukaimeden Observatory in Morocco since 2016 (Barkaoui et al. (2019), and references therein).It is equipped with a thermoelectrically cooled 2K×2K Andor iKon-L BEX2-DD CCD camera with a pixel scale of 0.6 and a field-of-view of 20 × 20 .The first transit was observed on UTC January 30 2021 in the I + z filter with an exposure time of 60 seconds.We took 154 science images and performed aperture photometry in an uncontaminated aperture of 7.6 and a PSF FWHM of 3.1 .The second transit was observed on UTC June 25 2021 in the I + z filter with an exposure time of 65 seconds.We took 216 science images and performed aperture photometry in an uncontaminated aperture of 5.6 and a PSF FWHM of 3.7 .During that second observation of TOI-2084, the telescope underwent a meridian flip at BJD 2459391.4829.
Data reduction and photometric measurements were performed using the PROSE pipeline (Garcia et al. 2021).

TRAPPIST-South
Two full transits of TOI-4184.01were observed with the TRAPPIST-South telescope.TRAPPIST-South is a 60-cm Ritchey-Chretien telescope located at ESO-La Silla Observatory in Chile, which is the twin of TRAPPIST-North (Section 2.2.4).It is equipped with a thermoelectrically cooled 2K×2K FLI Proline CCD camera with a field of view of 22 × 22 and pixelscale of 0.65 /pixel (Jehin et al. 2011;Gillon et al. 2011).The first transit was observed on UTC August 2 2021, and the second transit was observed on UTC September 25 2021.Both transits were observed in the I + z filter with an exposure time of 150 s, and we performed aperture photometry in an uncontaminated target apertures of 3.5-6.2and a PSF FWHM of 2.4-2.7 .During the second transit of TOI-4184.01,the telescope underwent a meridian flip at BJD = 2459478.8226.Data reduction and photometric measurements were performed using the PROSE pipeline (Garcia et al. 2021).

LCOGT-2.0m MuSCAT3
We used the Las Cumbres Observatory Global Telescope (LCOGT; Brown et al. (2013)) 2.0-m Faulkes Telescope North at Haleakala Observatory in Hawaii to observe two transits of TOI-2084.01simultaneously in Sloan-g , r , i and Pan-STARRS z-short filters.The first (full) transit was observed on UTC May 19 2021, and the second (partial) transit was observed on UTC May 26 2021.We used uncontaminated 4 target apertures to extract the stellar fluxes.The telescope is equipped with the MuS-CAT3 multi-band imager (Narita et al. 2020) Silla observatory in Chile.The instrument used was the DFOSC imager, operated with a Bessell I filter for two transits and a Bessell R filter for the third.In this setup, the CCD covers a field of view of 13.7 ×13.7 with a pixel scale of 0.39 pixel −1 .The images were unbinned and windowed for the first transit, resulting in a dead time between consecutive images of 10 s; however, in an effort to improve the SNR of the target PSF, the remaining transits used 2 × 2 binning and no windowing (to obtain a greater selection of comparison stars), resulting in a dead time between consecutive images of 13 s.The exposure times were 60 s for all images and transits.Due to the target being quite faint (V = 17 th mag, I = 14 th mag) and with the presence of close nearby sources (both point and extended) the telescope was marginally defocused and autoguiding was maintained through all observations.The amount of defocus applied caused the resulting PSFs to have a diameter of ≈ 10 pixels for all nights.
We reduced the Danish 1.54-m telescope data using the DE-FOT pipeline (Southworth et al. 2009(Southworth et al. , 2014)).Aperture photometry was performed with an IDL implementation of DAOPHOT (Stetson 1987), with the addition of image motion tracking by cross-correlation with a reference image to produce a differential magnitude light curve.The light curve was produced after simultaneously fitting a first-order polynomial to the out of transit data.The aperture sizes and number of suitable comparison stars were adjusted to obtain the lowest baseline scatter; this method affects the scatter in the transit data but does not significantly impact the light curve shape.The timestamps from the fits files were converted to the BJD TDB time-scale using routines from Eastman et al. (2010).

ExTrA
The ExTrA facility (Bonfils et al. 2015), located at La Silla observatory, consists of a near-infrared (0.85-1.55 µm; NIR) multi-object spectrograph fed by three 60-cm telescopes.Five fiber positioners at the focal plane of each telescope pick up light from the target and four comparison stars.We observed one full transit of TOI-4184 b on UTC September 15 2021 with two telescopes using the 8 aperture fibers.We used the spectrograph's low resolution mode (R ∼20) and 60-second exposures.We also observed 2MASS J02542961-7941578, 2MASS J03025970-7941390, 2MASS J03025068-7918174, and 2MASS J02581731-7913567, with J-magnitudes (Skrutskie et al. 2006) and effective temperatures (Gaia Collaboration et al. 2018) similar to TOI-4184, for use as comparison stars.The resulting Ex-TrA data were analyzed using custom data reduction software.

Shane/Kast Optical Spectroscopy
We obtained an optical spectrum of TOI-2084 and its co-moving companion (see below) on UTC November 13 2021 using the Kast double spectrograph (Miller & Stone 1994) mounted on the 3-m Shane Telescope at Lick Observatory in clear conditions.Six exposures of 600 s each was obtained of both sources TOI-2084 simultaneously using the 600/7500 grism and 1 .5-wide slit, providing 6000-9000 Å wavelength coverage at an average resolution of λ/∆λ = 1900.We also observed the flux calibrator Feige 110 later that night (Hamuy et al. 1992(Hamuy et al. , 1994)).Data were reduced using the kastredux package

Magellan/FIRE Spectroscopy
We obtained a spectrum of TOI-4184 with the FIRE spectrograph (Simcoe et al. 2008) on the 6.5-m Magellan Baade Telescope on UTC September 23, 2021.We used the high-resolution echellette mode with the 0 .60 slit, providing a 0.82-2.51µm spectrum with a resolving power of R∼6000.We collected a single ABBA nod sequence (4 exposures) with integration times of 95.1 s per exposure, giving a total exposure time of 380.4 s.Af-  ter the science exposures, we collected a pair of 15-s exposures of the A0 V star HD 45039 for flux and telluric calibrations followed by a pair of 10-s arc lamp exposures and a set of 10 1-s flat-field exposures.We reduced the data using the FIREHOSE pipeline4 .The final spectrum (Figure 8) has a median SNR of 77, with peaks in the J, H, and K bands of 120-140.

High-Resolution Imaging from Gemini-8m0
TOI-2084 was observed on UTC June 24 2021 using the 'Alopeke speckle instrument on the Gemini North 8-m telescope and TOI-4184 was observed on UTC December 23 2021 using the Zorro speckle instrument on the Gemini South 8-m telescope (see Scott et al. (2021)).'Alopeke and Zorro provide simultaneous speckle imaging in two bands (562 nm and 832 nm) with output data products including a reconstructed image with robust contrast limits on companion detections (e.g., Howell et al. 2016).A total of 13/11 sets of 1000 × 0.06 sec exposures were collected for TOI-2084/TOI-4184 and subjected to Fourier analysis in our standard reduction pipeline (see Howell et al. 2011).
Figure 5 shows our final 5σ contrast curves and the 832 nm reconstructed speckle images.We find that TOI-2084 and TOI-4184 are both single stars with no companion brighter than about 4-6 magnitudes below that of the target star from the diffraction limit (20 mas) out to 1.2".At the distance of TOI-2084/TOI-4184 (d=114/69 pc), these angular limits correspond to spatial limits of 2.3 to 137 au (TOI-2084) and 1.4 to 83 au (TOI-4184).

SED analysis
To determine the basic stellar parameters, we performed an analysis of the broadband spectral energy distribution (SED) of TOI-2084 and TOI-4184 together with the Gaia EDR3 parallax (with no systematic offset applied; see, e.g., Stassun & Torres 2021), in order to determine an empirical measurement of the stellar radius, following the procedures described in Stassun & Torres (2016); Stassun et al. (2017); Stassun & Torres (2018).We pulled the JHK S magnitudes from 2MASS, the W1-W3 magnitudes from WISE, the G BP and G RP magnitudes from Gaia, and the grizy magnitudes from Pan-STARRS.Together, the available photometry spans the full stellar SED over the wavelength range 0.4-10 µm (see Figure 6).We also estimated the stellar mass according to the empirical M K based relations of Mann et al. (2019).Deduced stellar parameters of TOI-2084 and TOI-4184 are presented in Table 2.

Spectroscopic analysis
In addition to the SED analysis, we also compared the Shane/Kast optical spectrum of TOI-2084 to the SDSS M dwarf templates of Bochanski et al. (2007) and found the best match to the M2 template (Figure 7).The spectral index classification relations of Lépine et al. (2003) confirm this classification.We see no evidence of Hα emission (equivalent width limit of <1.0 Å), indicating an age greater than ∼1.2 Gyr (West et al. 2008).We also measured the ζ index from TiO and CaH features (Lépine et al. 2007;Mann et al. 2013), finding ζ = 0.893±0.005,consistent with a metallicity of [Fe/H] = −0.13±0.20 based on the calibration of Mann et al. (2013).
For TOI-4184, we also analyzed its Magellan/FIRE spectrum using the SpeX Prism Library Analysis Toolkit (SPLAT, Burgasser & Splat Development Team 2017).By comparing the spectrum to NIR spectral standards defined in Kirkpatrick et al. (2010), we find the closest match to the M5.0 standard, although the M6.0 standard provides only a marginally poorer match (Figure 8).Thus, we adopt a spectral type of M5.5±0.5 for TOI-4184.We also estimated the metallicity of TOI-4184 from the Magellan/FIRE spectrum from the equivalent widths of K-band Na i and Ca i doublets and the H2O-K2 index (Rojas-Ayala et al. 2012), and used the empirical relation between these observables and stellar metallicity (Mann et al. 2014) to estimate [Fe/H].Following Delrez et al. (2022), we calculated the uncertainty of our estimate using a Monte Carlo approach.Adding in quadrature the systematic uncertainty of the relation (0.07), we obtained our  of TOI-2084B is shown in Figure 7, and is an excellent match to the M8 dwarf template from Bochanski et al. (2007).This classification is confirmed by the spectral index classification relations of Lépine et al. (2003).We see no evidence of Hα emission from this companion, although the noise is considerable in the 6563 Å region.Similarly, we are unable to reliably measure a ζ index from these data, although the close match to the dwarf template suggests a near-solar metallicity similar to TOI-2084.There are several known planetary systems orbiting stars in low-mass multiples, including the M4+M4.5 binary TOI-1452 and TOI-1760 (Cadieux et al. 2022) and the early-M triple system LTT 1445 (Winters et al. 2019)   .01 has a period of 6.078 days and a depth of 2.760 ± 258 ppt at an S/N of 11.2, and .02 a period of 8.149 days and a depth of 3.313 ± 327 ppt at an S/N of 10.8.The report was reviewed by the TOI vetting team and the candidates were released on July 15 2020.A second DV report was issued on August 7, 2020 from the SPOC pipeline which included sectors up to 26 of 2-min cadence data.The first candidate was found to have a period of 6.07830 ± 0.00010 days, a transit depth of 2.8 ± 0.2 ppt with an S/N of 12.7, and a planetary radius of 2.6 ± 0.7 R ⊕ .Silimarly, the second candidate was found to have a period of 8.14903 ± 0.00018 days, a transit depth of 2.8 ± 0.2 ppt with an S/N of 11.8, and a planetary radius of 2.6 ± 0.6 R ⊕ .The odd/even phase-folded transits were compared and agreed to 1.45σ and 0.96σ for the .01 and .02candidates, respectively.As for TOI-4184, one nearby star is contaminating the aperture, but the event was limited to be on target for the .01candidate and likely on target for .02.In addition, the DV report a difference imaging centroid test result that locates the catalog position of the target star to within 2.

Archival imaging
We obtained archival images of TOI-2084 and TOI-4184 in order to discard the case of a background unresolved companion producing the transit signals.Whether an eclipsing binary, a planetary candidate orbiting a background star, or simply an unaccounted background star, any of these scenarios Given the pixel scale of 1-1.7 , it is impossible to rule out a background star from this diagnostic alone, though it is unlikely since we ruled out any close companion star at a minimum angular separation of 0.1 (see Section 2.4).We also compared images centered on TOI-4184 from POSS II/DSS in the blue, red and in-  1977, 1989, and 1990, respectively.Because of its high proper motion of 183.87 mas yr −1 , TOI-4184 has moved by > 8 in the 44 years spanning the observations.This allows us to confirm the lack of background contaminant in the line-of-sight brighter than a limiting magnitude of ≥ 20.

Follow-up photometric validation
Photometric follow-up using ground-based facilities has two objectives: identify the source of the transit event and assess if the transit depth is wavelength dependent.The presence of contaminating stars in the TESS aperture was noted for both TOI-4184.01and TOI-2084.01 in the TESS data validation reports.

Planet radius [R ] Sub-Neptune desert
All planets TESS M-dwarf systems TESS FGK systems TOI-4184b TOI-2084b  The closest neighboring stars are respectively TIC 650071720 at 11.5 with a ∆Tmag of 4.45, and TIC 441738830 at 12.4 with a ∆Tmag of 6.15.We reached aperture sizes of a few arcseconds using ground-based facilities, which allowed us to confirm the transit events are on the expected stars for TOI-4184.01and TOI-2084.01.In the case of TOI-2084.02,twice at the expected transit times we detected a deep eclipse on the nearby star TIC 1271317080 (∆T = 4.98) at 12.9" from the target, labeled T3 in Figure 12.Thus, we rule out TOI-2084.02 as a false positive and do not consider it further.We collected photometric data for TOI-2084.01 in various bands (I+z, zs, i', r', g'), spanning the 400-1100 nm wavelength ranges.We measured a matching transit depth within 1σ in all bands.Similarly, we obtained data for TOI-4184.01 in the I+z, zs, Ic, JJ, g' bands, covering a range between 400-1210 nm where the transits depths also agree within 1σ.The transit depths measured in different wavelengths for TOI-2084 b and TOI-4184 b are presented in Figure 16, Table 4 and Table 5.

Statistical validation
To calculate the false positive probability (FPP) for TOI-2084.01and TOI-4184.01,we used the Tool for Rating Interesting Candidate Exoplanets and Reliability Analysis of Transits Originating from Proximate Stars (TRICERATOPS ; Giacalone et al. 2021).This Bayesian tool incorporates prior knowledge of the target star, planet occurrence rates, and stellar multiplicity to calculate the probability that a given transit signal is due to a transiting planet or another astrophysical source.The criteria for statistical validation of a planetary candidate is stated as FPP 5 < 0.01 and NFPP 6 < 0.001, which is the sum of probabilities for all false positive scenarios.We ran TRICERATOPS on the TESS light curves including the contrast curve obtained with Gemini/Alopeke and Gemini/Zorro for both stars, TOI-2084 and TOI-4184.We found FPP = 0.0005 and FPP = 0.0001 for TOI-2084 b and TOI-4184 b, respectively.Because triceratops determines that no nearby stars are capable of being sources of astrophysical false positives, we find NFPP = 0 for both candidates (TOI-2084.01and TOI-4184.01).Based on these results, we consider two planets to be validated.TOI-2084.02was rejected as a nearby eclipsing binary (NEB) based on groundbased photometric follow-up (see previous Section 4.3).

Photometric data modelling
We performed a joint fit of all observed light curves by TESS and ground-based telescopes described in section 2, using the Metropolis-Hastings (Metropolis et al. 1953;Hastings 1970) algorithm implemented in the updated version of MCMC (Markov-chain Monte Carlo) code described in Gillon et al. (2012).The transit light curves are modeled using the quadratic limb-darkening model of Mandel & Agol (2002), multiplied by a baseline model in order to correct for several external effects related to systematic variations (time, airmass, background, fullwidth half-maximum, and position on the detector).The baseline model was selected based on minimizing the Bayesian information criterion (BIC) described in Schwarz (1978).Table 3 shows for each transit light curve the selected baseline model based on the BIC, and correction factor CF = β w × β r to rescale the photometric errors, where β w and β r are white and red noises, respectively (see Gillon et al. (2012) for more details).TRAPPIST-South and TRAPPIST-North telescopes are equipped with German equatorial mounts that have to rotate 180 • when the meridian flip is reached.This movement results the stellar images in different position on the detector before and after the flip.The normalization offset is included as jump parameter in our global MCMC analysis.The transit light curve observed with TRAPPIST-South on UTC September 20 2021 contains a meridian flip at BJD = 2459478.8226(see Table 1), which is accounted during the global analysis.
The jump parameters sampled by the MCMC for each system were: -T 0 : the transit timing; -W: the transit duration (duration between the contacts 1 and 4); -R 2 p /R 2 : the transit depth, where R p is the planet radius and R is the star radius; -P: the orbital period of the planet; b = a cos(i p )/R : the impact parameter in case of the circular orbit, where i p is the planetary orbital inclination and a p is the semi-major axis of the orbit; -√ e cos(ω), were ω is the argument of periastron and e is the orbital eccentricity the combination q 1 = (u 1 + u 2 ) 2 and q 2 = 0.5u 1 (u 1 + u 2 ) −1 (Kipping 2013), were u 1 and u 2 are the quadratic limbdarkening coefficients, which are calculated from Claret et al. (2012); and the stellar metallicity [Fe/H], the effective temperature (T eff ), log of the stellar density (log(ρ )), and log of the stellar mass (log(M )).
For each star, we applied a Gaussian prior distribution on the stellar parameters obtained from SED and spectroscopy (which are R , M , [Fe/H], log g and T eff ).For each system, we per-Article number, page 12 of 22 formed two MCMC analyses, the first assuming a circular orbit, and the second assuming an eccentric orbit.The results are compatible with a circular orbit based on the Bayes factor BC = exp (−∆BIC/2).The eccentric solutions give e∼0.2 +0.3 −0.2 for TOI-2084.01and e∼0.1 +0.2 −0.1 for TOI-4184.01.For each transit light curve, a preliminary analysis composed of one Markov chain of 10 5 steps was performed in order to calculate the correction factor CF. Then a global MCMC analysis of three Markov chains of 10 5 steps was performed to derive the stellar and planetary physical parameters.The convergence of each Markov chain was checked using the statistical test of Gelman & Rubin (1992).Derived parameters of TOI-2084 and TOI-4184 are presented in Tables 2, 4 and 5.

Planet searches using the TESS photometry
In this section, we searched for additional planetary candidates that might remain unnoticed by SPOC and the QLP due to their detection thresholds.To this end we used our custom pipeline SHERLOCK7 , originally presented by Pozuelos et al. (2020) and Demory et al. (2020), and used in several studies (see, e.g., Wells et al. 2021;Van Grootel et al. 2021;Schanche et al. 2022).
SHERLOCK allows the user to explore TESS data to recover known planets, alerted candidates, and search for new periodic signals, which may hint at the existence of extra transiting planets.In short, the pipeline has six modules to (1) download and prepare the light curves from the MAST using the lightkurve (Lightkurve Collaboration et al. 2018), (2) search for planetary candidates through the tls (Hippke & Heller 2019), (3) perform a semi-automatic vetting of the interesting signals, (4) compute a statistical validation using the TRICERATOPS (Giacalone et al. 2021), ( 5) model the signals to refine their ephemerides employing the allesfitter package (Günther & Daylan 2021), and (6) compute observational windows from ground-based observatories to trigger a follow-up campaign.We refer the reader to Delrez et al. (2022) and Pozuelos et al. (2023) for recent SHERLOCK applications and further details.
For TOI-4184, we searched for extra planets analyzing the three available sectors (1, 28, and 39) together, exploring orbital periods from 0.3 to 30 d.For TOI-2084.01,we conducted two independent searches: 1) corresponding to the nominal mission, that is, 8 sectors from 16 to 26, and 2) corresponding to the extended mission, that is, 13 sectors from 48 to 60 (see Figure 3).In both searches, we explored the orbital periods from 0.3 to 50.The motivation to follow this strategy is twofold.On the one hand, the high computational cost of exploring at the same time 21 sectors, while adding many sectors might hint at the presence of very long orbital periods (> 50 days), the transit probabilities rapidly decrease for such scenarios.On the other hand, this strategy allows us to compare any finding in the nominal mission with the extended mission, providing an extra vetting step for the signals' credibility.
We successfully recovered the TOIs released by SPOC, the TOI-4184.01with an orbital period of 4.90 days and TOI-2084.01with an orbital period of 6.08 days.In the subsequent runs performed by SHERLOCK , we did not find any other signal that hinted at the existence of extra transiting planets.In addition to TOI-2084.01,we also recovered a signal corresponding to TOI-2084.02,which was already classified as a false positive using ground-based observations described Section 4.3 and displayed in Figure Figure 12. Surprisingly, we did not recover the signal with the orbital period issued by TESS, 8.14 days, but its first subharmonic, which corresponds to an orbital period of 4.07 days.Then, we used the two modules implemented in SHERLOCK for vetting and statistical validation of candidates with this signal.On the one hand, using the vetting module, we found that even and odd transits yielded different transit depths; ∼2.3 and ∼1.1 ppt for even and odd transits, respectively.This indicated that our detection algorithm was confusing the secondary eclipse as the primary and yielding half of the real orbital period, which confirmed that the real orbital period is 8.14 days.On the other hand, the validation module found that its FFP is ∼0.26 and NFPP is ∼0.1.According to Giacalone et al. (2021), these values place this candidate in the false positive area in the NFPP-FPP plane.Hence, these analyses agreed with the eclipsing binary nature of this signal.

Results and discussion
We presented the validation and discovery of TOI-2084 b and TOI-4184 b by the TESS mission (see phase-folded light curves in Figure 2 and individual transits in Figure 3), which were confirmed through follow-up photometric measurements collected by SPECULOOS-South/North, SAINT-EX, TRAPPIST-South/North, MuSCAT3, LCOGT, Danish and ExTrA telescopes (see phase-folded light curves in Figure 4).The host stars are characterized by combining optical spectrum obtained by Shane/Kast and Magellan/FIRE, SED and stellar evolutionary models.Then, we performed a global analysis of space TESS and ground-based photometric data to derive the stellar and planetary physical parameters for each system.Table 2 shows the astrometry, photometry, and spectroscopy stellar properties of TOI-2084 and TOI-4184.Derived stellar and planetary physical parameters from our global analysis are shown in Table 4 and Table 5. Figure 9 shows the periodogram for the system.Both planets are well detected in TESS data.(from Shane/Kast spectrum).It has a wide (∼1400 au) M8 comoving companion, with a likely mass of 0.1 M .TOI-2084 b is a sub-Neptune-sized planet orbiting around the host primary star every 6.08 days, which has a radius of R p = 2.47 ± 0.13 R ⊕ , an equilibrium temperature of T eq = 527 ± 8 K, an incident flux of S p = 12.8 ± 0.8 times that of Earth.We find that TOI-2084 b has a predicted mass of M p = 6.74 +5.31  −2.81 M ⊕ using the Chen & Kipping (2017) relationship.
TOI-4184 is a K mag = 11.86M5.5±0.5 metal-poor star with a metallicity of [Fe/H] = −0.27± 0.09 dex (from the Magellan/FIRE spectrum), an effective temperature of T eff = 3225 ± 75 K, a surface gravity of log g = 5.01 ± 0.04 dex, a mass of M = 0.240 ± 0.012 M and a radius R = 0.242 ± 0.013 R .TOI-4184 b is a sub-Neptune-sized planet that completes its orbit around its host star in 4.9 days, has a radius of R p = 2.43 ± 0.21 R ⊕ , an irradiation of S p = 4.8 ± 0.4 Earth ir-Article number, page 13 of 22 A&A proofs: manuscript no.TOI-2084.01_and_TOI-4184.01_KBarkaoui_et_al2016) are displayed with different lines and colors."Earth-like" here means a composition of 30% Fe and 70% MgSiO 3 .The 2% H 2 line represents a composition consisting of a 98% Earth-like rocky core and a 2% H 2 envelope by mass, while the 49% H 2 O + 2% H 2 line corresponds to a composition comprising a 49% Earth-like rocky core, a 49% H 2 O layer, and a 2% H 2 envelope by mass.Earth and Venus are identified in this plot as pale blue and orange circles, respectively.radiation, and an equilibrium temperature of T eq = 412 ± 8 K.We used the Chen & Kipping (2017) relationship to predict the plausible mass of TOI-4184 b, which is M p = 6.60 +5.20  −2.75 M ⊕ .Figure 10 shows the boundaries of the sub-Neptunedesert region determined by Mazeh et al. (2016)

Characterization prospects
Super-Earths and sub-Neptunes are amongst the most abundant type of exoplanets.Yet their formation, atmospheric composition, and interior structure are not well understood, as a variety of compositions can match the average density of these planets.TOI-2084 b and TOI-4184 b are part of this mysterious population.The small size and proximity of the host stars as well as their brightness in the infrared make them amenable to be further observed by most JWST modes for studying atmospheric compositions.
Given the measured properties, we made a first exploratory guess of the planet's composition.We compared their masses and radii with the models from Zeng et al. (2016) As a first approximation of the suitability of both planets for atmospheric investigations, we calculate the transmission spectroscopic metric (TSM) from Kempton et al. (2018), which was developed based on simulations with NIRISS.We estimate the TSMs for TOI-2084 b and TOI-4184 b to be 26.7 +14.7   −10.3   and 57.7 +25.7  −20.1 , respectively.With 90 being the threshold for this category of planets, it is worth noting that this metric solely considers the predicted strength of an atmospheric detection when ranking the planets.Having TSM values below the threshold does not necessarily mean that detailed atmospheric studies are impossible or challenging with current facilities.In other words, these metrics do not serve as the sole criterion for determining the best targets for atmospheric studies.
To further evaluate the feasibility of characterizing the atmosphere of both planets, we computed synthetic transit spectra from optical to infrared wavelengths (0.5-12 µm) at low spectral resolutions for different atmospheric scenarios (cloud-free H 2and cloudy H 2 -rich, water-rich).We used petitRADTRANS (Mollière et al. 2019) to compute the model transmission spectra, using the stellar parameters from Table 2 and the planetary parameters from Tables 4 & 5. Our test H 2 -rich models assume atmospheric chemical equilibrium computed using the FastChem code (Stock et al. 2018) with isothermal profiles at the equilibrium temperature, solar abundances, collisionally induced absorption (CIA) by H 2 -H 2 and H 2 -He, and Rayleigh scattering.We include as absorbers H 2 O, CO 2 , CO, CH 4 , NH 3 , C 2 H 4 , and C 2 H 2 .For the water-rich scenarios, we assume that the planets are enveloped in a clear, isothermal water-dominated atmosphere composed of 95% H 2 O and 5% CO 2 .The model includes the H 2 O and CO 2 Rayleigh scattering cross-sections.We also compare it to a pure water planet (100% H 2 O) with H 2 O Rayleigh scattering.An example of the resulting spectra for TOI-4184b is shown in Figure 14.
As predicted by earlier studies (e.g., Greene et al. (2016); Mollière (2017); Chouqar et al. (2020)), the amplitude of the transmission spectra is highly dependent on the presence and altitude of the cloud layer, and on the average molecular weight of the atmosphere: the higher the average molecular weight of the atmosphere, the lower the scale height, and thus the lower the amplitude of the transit spectroscopy signal.The transmission spectra for the H-rich atmospheres show strong absorption features due to H 2 O, CH 4 , and NH 3 over the wavelength range 0.5-12 µm (see Figure 14).The spectroscopic modulations of the cloud-free spectra are on the order of 50-350 ppm and 100-700 ppm for TOI-2084 b and TOI-4184 b, respectively.The cloudy models present smaller absorption features due to the suppression of contributions from deeper atmospheric layers.The features are essentially muted in the cases with 10 −4 bar cloud top model for both planets (not shown here).For scenarios discussed above, the mean molecular weight varies from µ = 2 g/mol for an atmosphere dominated by molecular hydrogen to µ = 18 g/mol for atmospheres dominated by heavier molecules like H 2 O which explains the weak spectral Since 2018 NASA's TESS mission has discovered several sub-Neptune-sized exoplanets around M dwarfs (e.g., TOI-1696 b & TOI-2136 b: Beard et al. (2022) TOI-1201 b: Kossakowski et al. (2021), TOI-2081 b & TOI-4479 b: Esparza-Borges et al. (2022), TOI-122 b & TOI-237 b: Waalkes et al. (2021), TOI-269 b: Cointepas et al. (2021), TOI-2406 b: Wells et al. (2021), TOI-620 b: Reefe et al. (2022), TOI-2136 b: Gan et al. (2022), TOI-2257 b: Schanche et al. (2022) and TOI-2096 c: Pozuelos et al. (2023) ).In this paper we present the discovery and validation of two new TESS exoplanets orbiting nearby M dwarfs, TOI-2084 b and TOI-4184 b.

Fig. 1 :
Fig. 1: TESS target pixel file images of TOI-2084 observed in Sector 16 (left panel) and TOI-4184 observed in Sector 1 (right panel), made by tpfplotter (Aller et al. 2020).Red dots show the location of Gaia DR3 sources, and the red shaded region shows the photometric apertures used to extract the photometric measurements.

Fig. 3 :
Fig. 3: TESS photometric data of TOI-2084.01and TOI-4184.01.The gray points show the PDSAP fluxes obtained from the SPOC pipeline.The red and blue points correspond to the location of the transit for the candidates TOI-2084.01and TOI-4184.01,respectively.

Fig. 4 :
Fig. 4: Ground-based photometric light curves of TOI-2081.01(left) and TOI-4184.01(right).The gray points are unbinned data and the black points are data binned to 10 minutes.The coloured lines are the best-fitting transit model.The light curves are shifted along the y-axis for visibility.
. TOI-2048 and TOI-2048B have an unusually wide separation among low-mass planet hosts in binary systems, although there are examples of such systems among more massive stellar binaries (Correa-Otto & Gil-Hutton 2017).

Fig. 6 :
Fig. 6: Spectral Energy Distribution (SED) fit of TOI-2084 (right) and TOI-4184 (left).The gray curves are the best-fitting NextGen atmosphere model, coloured symbols with error-bars are the observed fluxes, and black symbols are the model fluxes.

Fig. 7 :Fig. 8 :
Fig.7: Shane/Kast red optical spectra (black lines) ofTOI-2084 (left)  and its wide stellar companion TOI-2084B (right) compared to best-fit M2 and M8 SDSS spectral templates fromBochanski et al. (2007, magenta lines).The lower panels display the difference between these spectra (black line) compared to the ±1σ measurement uncertainty (grey band).Key features are labeled, including the strong telluric O 2 band at 7600 Å (⊕).Inset boxes show close-ups of the region around the 6563 Å Hα and 6708 Å Li I lines.

Fig. 10 :
Fig. 10: Period-Radius diagram of known transiting exoplanets from NASA Archive of Exoplanets.The blue and orange data points correspond to the TESS FGK and M dwarf systems, respectively.The green and red stars show TOI-2084 b TOI-4184 b, respectively.The yellow region shows the boundaries of the sub-Neptune-desert determined by Mazeh et al. (2016).

Fig. 11 :
Fig. 11: Field images cropped on a 1'×1' region around TOI-2084 (top row of images) and TOI-4184 (bottom row).The current position of the target stars is shown with the yellow circle.Top row, from left to right: 1953 red image from POSS I/DSS, 1953 infrared image from POSS II/DSS2, 2012 z' image from PanSTARRS1, and 2021 I+z image from SPECULOOS-North.Bottom row, from left to right: 1977 blue image from POSS II/DSS2, 1989 red image from POSS II/DSS2, 1990 infrared image from POSS II/DSS2, and 2021 image z' from SPECULOOS-South.
Fig. 12: TOI-2084 light curves obtained with ground-based facilities.Left panel: light curve obtained with SPECULOOS-North in the I+z filter on UTC August 17 2020.Middle panel: TOI-2084 field-of-view with nearby stars.The wide co-moving companion TOI 2084B is directly south.Right panel: light curve obtained with LCO-McD in the Sloan-i filter on UTC August 26 2020.Red and blue data points show the target (T1) and nearby star (T3) light curves, respectively.During the expected transit of TOI-2084.02,we twice detected a deep eclipse (≈ 400 ppt) on the nearby star TIC 1271317080 (∆T = 4.98) at 12.9" from the target, labeled T3.
Figure A.1 and Figure A.2 show the parameters posterior distributions for each system.7.1.TOI-2084 b and TOI-4184 b TOI-2084 is a K mag = 11.15M2-type star with an effective temperature of T = 3553 ± 50K, a surface gravity of log g = 4.75 ± 0.05 dex, a mass of M = 0.49 ± 0.03 M and a radius R = 0.475 ± 0.016 R (derived from SED analysis including Gaia EDR3 parallax) and a metallicity of [Fe/H] = −0.13±0.20

Fig
Fig.13: Mass-radius diagram of exoplanets with mass-radius measurements better than 25% from TEPCat and for our candidates, color-coded by their equilibrium temperature.Two-layer models fromZeng et al. (2016) are displayed with different lines and colors."Earth-like" here means a composition of 30% Fe and 70% MgSiO 3 .The 2% H 2 line represents a composition consisting of a 98% Earth-like rocky core and a 2% H 2 envelope by mass, while the 49% H 2 O + 2% H 2 line corresponds to a composition comprising a 49% Earth-like rocky core, a 49% H 2 O layer, and a 2% H 2 envelope by mass.Earth and Venus are identified in this plot as pale blue and orange circles, respectively.
, shown in Figure 13.The models predict that TOI-2084 b and TOI-4184 b may have low-density volatiles, such as water, an H/He atmosphere, or a combination of both.Below, we further explore these plausible atmospheres and assess the potential for atmospheric characterization of both TOI-2084 b and TOI-4184 b planets.

Fig
Fig. A.2: Posterior probability distribution for the TOI-4184 system stellar and planetary physical parameters fitted using our MCMC code as described in Methods.The vertical lines present the median value.The vertical dashed lines present the median value for each derived parameter.
3, which included image reduction, boxcar extraction of the one-dimensional spectra, TOI-4184.01Oct 10 2021 Sloan-g , i LCO-SAAO-1.0m 400,240 3.9 2.3 Full Table 1: Table shows the observational parameters: date of observation, filter used, telescope, exposure time(s), photometric aperture size, and FWHM of the point-spread function.

Table 3 :
MCMC analysis parameters.For each transit light curve selected baseline-function (based on the BIC), deduced values of β w , β r and the coefficient correction