TOI-5205b: A Short-period Jovian Planet Transiting a Mid-M Dwarf

TOI-5205 (TIC-419411415, Gaia DR3 1842656663520849024) is a mid-M dwarf observed by TESS in Sector 15 in Camera 1 (Figure 1) from 2019 August 15 to 2019 September 11 at ∼30 minutes cadence (Figure 2(a)), and Sector 41 in Camera 1 from 2021 July 23 to 2021 August 20 at ∼10 minutes cadence (Figure 2(b)). The planet candidate was identified using the Quick Look Pipeline algorithm developed by Huang et al. (2020), under the "faint-star search" (Kunimoto et al. 2022) with a period of ∼1.63 days.

We extract the light curve from the TESS full-frame images (FFIs) using using eleanor (Feinstein et al. 2019), which uses the TESScut ²⁷ service to obtain a cut-out of 31 × 31 pixels from the calibrated FFIs centered on TOI-5205. The light curve is derived from the CORR_FLUX values, in which eleanor uses linear regression with pixel position, measured background, and time to remove signals correlated with these parameters. The default aperture is a 2 × 1 pixel rectangle, which does not include the target star. Instead, we set the aperturemode to "large" in eleanor, which uses a 3 × 3 pixel square aperture that includes the target star and obtains a combined differential photometric precision (CDPP) of ∼3850 and ∼4730 ppm for the two sectors, respectively (Figure 2). The CDPP is formally the rms of the photometric noise on transit timescales, and was originally defined for Kepler (Jenkins et al. 2010). We also try a custom aperture in eleanor of size 2 × 1 pixels, which includes only the two top-right pixels from the large aperture shown below. This gives us comparable posteriors to the photometry fit, while having a slightly degraded CDPP. For subsequent analysis, we use the "large" aperture shown in Figure 1.

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TOI-5205 is present in a crowded field with 10 stars located <30'' away, with the closest star (TIC 1951446034) located about 42 away and ∼1.7 mag fainter in the TESS bandpass (Figure 1). Based on Gaia DR3 astrometry, TIC 1951446034 is not comoving and is instead ∼30× more distant than TOI-5205 (∼2300 pc; Vallenari et al. 2022). The eleanor aperture includes many of these field stars, which present a significant source of dilution to the TESS light curve and necessitate ground-based follow-up that can resolve these background stars. We discuss this dilution further in Section 4 where we include a dilution term while fitting the TESS photometry.

2.2.1. 3.5 m ARC Telescope

We observed three transits of TOI-5205b using the Astrophysical Research Consortium (ARC) Telescope Imaging Camera (ARCTIC; Huehnerhoff et al. 2016) at the ARC 3.5 m Telescope at Apache Point Observatory (APO) on the nights of 2022 April 22, 2022 July 3, and 2022 July 16. All of these observations were conducted using quad-amplifier and fast readout mode using 4 × 4 on-chip binning mode to achieve a gain of 2 e⁻ ADU⁻¹, a plate scale of 0456 pixel⁻¹, and a readout time of 2.7 s. The relevant observation parameters are included in Table 1.

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Table 1. Summary of Ground-based Photometric Follow-up

Obs Date	Filter	Exposure	PSF	Field of View
(YYYY-MM-DD)		Time (s)	FWHM ('')	(')
RBO (0.6 m)
2022-05-10	Bessell I	240	2.6–6.0	8.94 × 8.94
TMMT (0.3 m)
2022-05-15	Bessell I	180	3.8–4.5	40.75 × 40.75
APO (3.5 m)
2022-04-22	SDSS i'	5	2.0–3.2	7.9 × 7.9
2022-07-03	SDSS g'	40	1.4–2.2	7.9 × 7.9
2022-07-16	SDSS i'	20	3.4–8.3	7.9 × 7.9

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2022 April 22: We observed an ingress of TOI-5205b (Figure 3(c)) in the Sloan Digital Sky Survey (SDSS) i' while the target was rising from an airmass of 1.41–1.16. To spatially resolve and separate out the background star (∼42 away), we moderately defocus the star instead of using the engineered diffuser available on ARCTIC (Stefansson et al. 2017). These observations were conducted toward the end of the night, with the transit being interrupted by morning twilight. To prevent saturating the detector with the bright sky, we used a short exposure time of 5 s. We processed the photometry using AstroImageJ (Collins et al. 2017) and the final reduction used a photometric aperture radius of 6 pixels (274), an inner sky radius of 15 pixels (68), and an outer sky radius of 25 pixels (114). This small innermost annulus separates TOI-5205 and the closest background star (∼42). Furthermore, to verify the transit depth we also perform point-spread function (PSF) photometry (instead of aperture photometry; following the routine described in Section 2.3), and obtain a comparable transit depth as that from the procedure followed above using aperture photometry.

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2022 July 3: To check for chromaticity (Appendix A.4.2), we also observed TOI-5205b on 2022 July 3 (Figure 3(d)) in SDSS g' while it was rising from an airmass of 2.35–1.45. Similar to the previous observation, we do not use a diffuser, and moderately defocus the star. The data was reduced using aperture photometry in AstroImageJ using the same annuli as above. We detrend this photometry with the FWHM of the target star across the night. The observation was interrupted due to increasing humidity and cloudy conditions, which forced us to stop observing shortly after transit midpoint.

2022 July 16: We obtained a full transit of TOI-5205b on 2022 July 16 (Figure 3(g)) while it was rising from an airmass of 2.69–1.01 in SDSS i'. During these observations the telescope secondary mirror had hardware issues that prevented us from using the focuser. This led to the stellar PSF changing by ∼2× during the night, which caused significant systematics in the photometry that had to be detrended out by the airmass and FWHM during the night. Due to the lack of focuser control, our PSF FWHM is much larger than on previous nights, necessitating larger aperture radii of 12, 18, and 25 pixels or 55, 82, and 114, respectively. The large science aperture includes varying levels of contamination from the closest background star across the night. We therefore do not use this data set to refine our transit depth, but only the ephemeris.

2.2.2. 0.6 m RBO

2.2.3. 0.3 m TMMT

We acquired near-infrared (NIR) imaging using the FourStar Infrared Camera on the 6.5 m Magellan Baade telescope (Persson et al. 2013) during the night of 2022 July 13. The plate scale for FourStar is 016 per pixel, while the seeing during observations was ∼09, which was useful to clearly separate the nearby background sources in a short 2.911 s exposure in the J, H, and Ks filters. Each filtered observation used a five-point dice-5 dither pattern and processed using a custom FourStar reduction package. We used the daophot suite of programs to perform PSF fitting photometry (Stetson 1987; Stetson & Harris 1988). The PSF photometry was compared to un-blended Two Micron All Sky Survey (2MASS) stars in the field to determine the photometric zero-points in each filter. The final JHK magnitudes are listed in Table 3.

To search for faint stellar companions or background sources that might have contributed to or diluted the detected transit signal, we acquired observations of TOI-5205 with the NN-EXPLORE Exoplanet Stellar Speckle Imager (NESSI; Scott et al. 2018) on the WIYN 3.5 m telescope at Kitt Peak National Observatory on 2021 May 5. A sequence of 40 ms diffraction-limited images was taken in the Sloan ${z}^{{\prime} }$ filter during the 9 minute observation, and these were then reconstructed following the procedures described by Howell et al. (2011). We detect no nearby sources with magnitudes brighter than ${\rm{\Delta }}{z}^{{\prime} }$ = 4.0 for separations >03. The contrast curve and reconstructed speckle image are shown in Figure 4.

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To confirm the spectral type and stellar parameters for TOI-5205, we also observe the target using LRS2 (Lee et al. 2010; Evans et al. 2016a) on the Hobby-Eberly Telescope (HET; Ramsey et al. 1998) at McDonald Observatory, in West Texas. LRS2 is a low-resolution (R ∼ 1900) optical integral field unit spectrograph composed of two arms that simultaneously observe two 6'' × 12'' fields of view separated by 100''. The blue arm (LRS2-B) consists of a pair of channels with spectral ranges of ∼3640–4670 and ∼4540–7000 Å, while the red arm (LRS2-R) is composed of two channels covering ∼6430–8450 and ∼8230–10560 Å. The LRS2-R data were obtained with an 1800 s exposure on 2022 June 11 (14 seeing), while the LRS2-B data were taken on 2022 August 3 (16 seeing) with the same exposure time.

The raw data were processed with Panacea, ²⁸ an automated reduction pipeline for LRS2 written by G. Zeimann et al. (2022, in preparation). The initial processing includes bias-correction, wavelength calibration from arc lamps taken within seven nights of the observation, fiber trace calculation from flat field exposures over ±7 nights, fiber normalization from twilight exposures over ±7 nights, fiber extraction, and an initial flux calibration from default response curves and measures of the mirror illumination as well as the exposure throughput from guider images. After the initial reduction, we used LRS2Multi, ²⁹ a python interface to perform advanced reduction steps and calibrations for Panacea products. Using LRS2Multi, we identified the target star, defined a 35 aperture, and used fibers beyond that aperture to build our sky model for each exposure. We subtracted the initial sky, and then constructed a principle component basis of 25 components with the residuals to further subtract sky residuals that occur from variable spectral PSFs for each fiber. This is especially important for the LRS2-R channels. We extracted the target spectrum from the sky-subtracted frames and normalized the LRS2-B to the LRS2-R spectrum using a 100 Å window in the overlap between the two spectrographs. Noting that the default response may not be accurate enough for spectrophotometry, we reduced and calibrated standard stars from 2021 June through 2022 August and measured the average flux calibration correction. The response correction was smoothed by a median filter with a 250 pixel kernel and was applied to our extracted spectrum. The correction was relatively small and smoothly declining with a ∼10% positive correction in blue and a ∼10% negative correction in red. Finally, the telluric correction was chosen from three empirical models constructed from a dozen HR telluric standard stars. We note that the relative chromatic flux calibration should be good to ∼5% for ∼3700–10200 Å based on the standard star analysis above, with the exception of regions with strong telluric absorption and where individual channels overlap. The final LRS2 spectra was used to estimate the spectral type of the star (Appendix A.1).

We started RV observations of TOI-5205 with HPF (Mahadevan et al. 2012; Ramsay et al. 2014) on 2022 April 20. HPF is a high-resolution NIR (8080−12780 Å), fiber-fed (Kanodia et al. 2018) precision RV spectrograph with a stabilized environment (Stefansson et al. 2016). HPF is located at HET, which is a fixed-altitude telescope with a roving pupil design, and is fully queue-scheduled, where all of the observations are executed by the HET resident astronomers (Shetrone et al. 2007). We correct for bias, nonlinearity, cosmic rays, and calculate the slope/flux and variance images from the raw HPF data, using the algorithms described in the package HxRGproc (Ninan et al. 2018). We do not utilize simultaneous calibration using the NIR Laser Frequency Comb for HPF (Metcalf et al. 2019) due to concerns about the impact of scattered calibration light given the faintness of our target. Instead, we obtain a wavelength solution for the target exposures by interpolating the wavelength solution from other LFC exposures on the night of the observations. This has been shown to enable precise wavelength calibration and drift correction with a precision of ∼30 cm s⁻¹ per observation (Stefansson et al. 2020), a value much smaller than our expected per-observation RV uncertainty (instrumental + photon noise) for this object of 22 m s⁻¹ (in 969 s exposures, and 15 m s⁻¹ in binned 30 minute exposures).

To derive the RVs from the extracted spectra, we use the template-matching method (e.g., Anglada-Escudé & Butler 2012). This has been implemented under the SpEctrum Radial Velocity AnaLyser pipeline (SERVAL; Zechmeister et al. 2018), which has since been modified for HPF (Stefansson et al. 2020). Under this method, we first create a master template from the target star observations, and then determine the Doppler shift for each individual observation by moving it in velocity space, comparing it with the template, and minimizing the χ² statistic. The master template is created using all of the HPF observations for TOI-5205, after masking out the telluric and sky-emission lines. The telluric regions are identified by a synthetic telluric-line mask generated from telfit (Gullikson et al. 2014), a Python wrapper to the Line-by-Line Radiative Transfer Model package (Clough et al. 2005). We use barycorrpy (Kanodia & Wright 2018) to perform the barycentric correction on the individual spectra, which is the Python implementation of the algorithms from Wright & Eastman (2014).

We obtained a total of seven visits on this target between 2022 April 20 and 2022 May 19 (Figure 5). Each visit was divided into two exposures of 969 s each, where the median signal-to-noise ratio (S/N) of each HPF exposure was 40 per pixel at 1070 nm. The individual exposures were then combined by weighted averaging, with the final binned RVs being listed in Table 2.

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M dwarfs with masses ∼0.35 M_⊙ have internal structures that transition from being partially convective (for the more massive stars) to fully convective (for the less-massive ones; Limber 1958; Baraffe & Chabrier 2018). On the more massive end, the partially convective stars have convective cores and envelopes separated by a radiative zone. As these stars fuse ³He in the convective core, the ³He abundance rises with temperature when in nonequilibrium (Figure 2; Baraffe & Chabrier 2018), and causes the convective core to increase in radius, and ultimately merge with the outer convective envelope that has a lower ³He abundance (MacDonald & Gizis 2018; Feiden et al. 2021). This merger is accompanied by a sudden drop in the ³He abundance in the core, which reduces the reaction rate, causing the core to contract and separate from the envelope (Figure 5 from Feiden et al. 2021). When the core contracts, the temperature begins to rise again, producing an increase in the abundance of ³He, and an episodic cycling over gigayear timescales. Due to these repeated mergers and contractions, the abundance of the convective envelope increases until the core-envelope merger is not accompanied by a sudden decrease in abundance (and associated nuclear reaction rate). At this point, the star attains a fully convective steady state. The timescale to attain this fully convective state for stars in this transition zone depends on the mass and metallicity of the star (Kroupa & Tout 1997; Feiden et al. 2021). Unsurprisingly, these oscillations are accompanied by slow and small variations in the radius and luminosity of the star (van Saders & Pinsonneault 2012; MacDonald & Gizis 2018). This transition zone is also accompanied by an inflection in the mass–luminosity relation ³⁰ for M dwarfs as was noted by Kroupa et al. (1990) and Delfosse et al. (2000). As an aside, this feature in the mass–luminosity relation causes a local maxima in the slope, which can reproduce the additional scatter in the T_eff–R_* relation for mid-M dwarfs in Mann et al. (2015).

Based on Gaia DR2, Jao et al. (2018) presented the discovery of the now eponymous gap near M_G ∼ 10.2 in the Gaia color–magnitude diagram (CMD; M_G versus G_BP − G_RP). This is a narrow diagonal region with an underdensity of stars, the width of which is a function of G_BP − G_RP color (Jao & Feiden 2020). While the gap is associated with a 10%–20% decrement in the number of stars, it is hardly seen redward of G_BP − G_RP ∼ 2.7. Theoretical models have been used to approximately reproduce the properties of the gap in the CMD relying on the ³He instability, and attribute this underdensity to the transition between partial and fully convective M dwarfs (Feiden et al. 2021).

While TOI-5205 does not lie in this gap based on Gaia photometry, it is one of the few known planet-hosting stars in its vicinity, i.e., near this transition zone between fully and partially convective M dwarfs (Silverstein et al. 2022). TOI-5205 has a G_BP − G_RP of ∼2.8, and M_G of ${10.09}_{-0.03}^{+0.01}$ from Gaia DR3, which would place it redward of this diagonal gap (M_G versus G_BP − G_RP space). The background companion to TOI-5205 at ∼4'' could contaminate the prism spectra used to obtain the color estimates. Creevey et al. (2022) mentioned that a CCD window of 35 × 21 is used while extracting the spectra, the orientation for which is quasi-random on the sky over different epochs. However the background companion is much hotter (T_eff ∼ 5450 K; Stassun et al. 2019) than TOI-5205 (T_eff ∼ 3400 K; Table 3), and therefore bluer.

Table 3. Summary of Stellar Parameters for TOI-5205

Parameter	Description	Value	References
Main identifiers:
TOI	TESS Object of Interest	5205	TESS mission
TIC	TESS Input Catalogue	419411415	Stassun
Gaia DR3	⋯	1842656663520849024	Gaia DR3
Equatorial Coordinates and Proper Motion:
αJ2016	R.A. (R.A.)	20:55:04.96	Gaia DR3
δJ2016	decl. (decl.)	+24:21:39.54	Gaia DR3
μα	Proper motion (R.A., mas yr−1)	41.68 ± 0.02	Gaia DR3
μδ	Proper motion (decl., mas yr−1)	52.07 ± 0.02	Gaia DR3
ϖ	Parallax (mas)	11.464 ± 0.026	Gaia DR3
d	Distance in parsecs	86.865 ± 0.05	Anders
Broadband photometry:
G	G mag	14.903 ± 0.003	Gaia DR3
g	PS1 g mag	16.877 ± 0.008	PS1
r	PS1 r mag	15.694 ± 0.008	PS1
i	PS1 i mag	14.21 ± 0.01	PS1
z	PS1 z mag	13.55 ± 0.02	PS1
y	PS1 y mag	13.207 ± 0.005	PS1
J	J mag	11.90 ± 0.02	This work
H	H mag	11.28 ± 0.02	This work
Ks	Ks mag	11.04 ± 0.02	This work
Derived photometry:
AG	Extinction in mag	0.12 ± 0.02	Anders
MG	Absolute G mag	10.09 ± 0.02	Anders
Stellar Parameters:
Teff a	Effective temperature in kelvin	3430 ± 54	This work
[Fe/H]	Metallicity	solar	This work
$\mathrm{log}(g)$ a	Surface gravity in cgs units	4.84 ± 0.03	This work
Sp Type b	Spectral Type	M4.0 ± 1.0	This work
R* c	Radius in R⊙	0.394 ± 0.011	This work
M* d	Mass in M⊙	0.392 ± 0.015	This work
L*	Luminosity in L⊙	0.0194 ± 0.0016	This work
ρ*	Density in g cm−3	9.0 ± 0.5	This work
Other Stellar Parameters:
$v\sin {i}_{* }$	Rotational velocity in km s−1	<2	This work
ΔRV	Absolute radial velocity in km s−1	−65.9 ± 0.3	This work
U, V, W	Galactic velocities in km s−1	−48.29 ± 0.12, −50.50 ± 0.27, 14.90 ± 0.07	This work
U, V, W e	Galactic velocities (LSR) in km s−1	−37.19 ± 0.86, −38.26 ± 0.74, 22.15 ± 0.61	This work

Notes. References are: Stassun (Stassun et al. 2018), Gaia DR3 (Vallenari et al. 2022), PS1 (Evans et al. 2016b), and Anders (Anders et al. 2022).

^a Using the T_eff-M_G relation from Rabus et al. (2019). ^b Spectral typing using relations based on Gaia color (Kiman et al. 2019). ^c Using R_*-M_K relation from Mann et al. (2015, 2016). ^d Using M_*-R_* relation from Schweitzer et al. (2019). ^e The barycentric UVW velocities are converted into local standard of rest (LSR) velocities using the constants from Schönrich et al. (2010).

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In this section, we present a simple mass budget argument ³² to estimate the minimum mass of the primordial protoplanetary disk in which this giant planet formed under the core-accretion paradigm, where models suggest that runaway gaseous accretion should initiate once a protoplanet has reached a solid core mass of ∼10 M_⊕ (Pollack et al. 1996). We calculate the heavy-element mass for TOI-5205b using the relations from Thorngren et al. (2016) to be ∼60 M_⊕ (or roughly 10× more metal-enriched than the host star), but also note that there is considerable scatter in their sample that can perhaps be attributed to the vagaries in planet formation and evolution. There are additional uncertainties due to the unknown heavy-element composition, and uncertainties in the equation of state used for their model. As it stands, these models predict ∼10 M_⊕ of heavy elements locked up in the central core, with the rest (60–10 ∼ 50 M_⊕) diffused in the H/He envelope.

The dust mass of the disk is typically estimated for millimeter-sized dust particles in Class II disks using flux continuum measurements at ∼850 μm, which is then used to calculate the mass assuming a blackbody with typical temperatures of 20 K. We decompose the total dust mass in the disk as a product of the disk mass ratio and gas-to-dust ratio (Figure 7). The canonical disk mass scaling (ratio of disk to stellar mass) assumed is ∼0.3% based on a study of the Taurus region by Andrews et al. (2013), along with the gas-to-dust ratio of 70–100 ranging from solar to the interstellar medium (ISM; Bohlin et al. 1978). Following these scaling relations suggests a total of 4–5 M_⊕ of dust available for planet formation for TOI-5205, which would be insufficient to form a 10 M_⊕ core to start runaway gaseous accretion even with 100% planet formation efficiency. In this section, we refer to planet formation efficiency as the fraction of the total dust mass of the disk that is used to form TOI-5205b. Therefore in subsequent sections we discuss more realistic scaling values based on recent studies.

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5.1.1. Disk Mass Scaling

5.1.2. Gas-to-dust Ratio

5.1.3. Disk Lifetimes (Increasing Efficiency of Planet Formation)

5.1.4. Disk Instability Scenario

Characterizing the atmosphere of TOI-5205b may provide clues needed to differentiate between formation mechanisms. Did it form via disk instability or core accretion, furthermore, under core accretion, did it form in situ or farther out and then migrate inward through disk or disk-free migration?

Assuming formation via core accretion, TOI-5205b is expected to have a superstellar metallicity if it underwent disk migration, or either sub- or superstellar metallicity if it underwent disk-free migration (Madhusudhan et al. 2014). If TOI-5205b is metal-enriched, and therefore likely formed via core accretion, the second question surrounds whether TOI-5205b formed in situ or farther out before migrating inward. Multiple studies suggest that C/O ratios could provide some indication as to whether a planet formed inside or beyond various disk snowlines (e.g., Öberg et al. 2011; Madhusudhan et al. 2014). As molecules "freeze-out," they remove those elements from the overall gas composition. When water freezes, for example, it removes some of the overall oxygen from the gas increasing the C/O ratio beyond the water-ice line (Öberg et al. 2011). Similarly, Knierim et al. (2022) showed that the ratio of refractory and volatile elements can depend on the migration history of the planet. While Dash et al. (2022) emphasized there are degeneracies and assumptions that must be considered, such as post-formation bombardment, or sublimation of the core, C/O ratios may provide the first insights into where TOI-5205b originally formed.

Under the disk instability hypothesis, TOI-5205b would have formed from a collapse of a massive region of the protoplanetary disk prior to migrating inward. Therefore, from a first approximation, it is assumed that its atmosphere should reflect that of the protoplanetary disk and its host star—i.e., should have the same metallicity and abundances as TOI-5205 (e.g., Helled & Bodenheimer 2010; Helled & Lunine 2014). However, recent works demonstrate that this initial picture may become complicated both by location of the initial collapse (Madhusudhan et al. 2014) or size of particles/objects accreted during this process (Helled et al. 2014). Hobbs et al. (2022) suggested that comparing abundances of various molecules, notably methane, carbon monoxide/dioxide, and hydrogen cyanide, may be a useful method for distinguishing the two formation pathways. Even with these complications, discovering a solar or near-solar metallicity atmosphere (heavy-element abundance of ∼1%) for TOI-5205b would hint at the potential for gravitational instability. In this scenario, the heavy-element mass estimated using the Thorngren et al. (2016) sample would be incorrect for TOI-5205b.

TOI-5205b is a compelling target scientifically, and with its 7% transit depth, it is also an object easily accessible with James Webb Space Telescope (JWST) observations. Even though it is a relatively cool (740 K) Jovian world, it still possesses a large transmission spectroscopy metric (TSM) of ∼100 placing it in the second quartile of their giant planet sample (assuming a scale factor of 1.15) from Kempton et al. (2018). TOI-5205b also has one of the largest emission spectroscopy metrics (ESM) of any planet at ∼150, in part due to its R_p /R_s and also its bright mid-M dwarf host (Figure 8).

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We calculate model transmission and thermal emission spectra assuming 1×, 10×, and 100× solar metallicity. We then simulate JWST NIRSpec PRISM data using PandExo (Batalha et al. 2017) corresponding to the 1× solar cases, assuming two transits/secondary eclipses, respectively. The transmission spectra are calculated using Exo-Transmit (Kempton et al. 2017). We predict that NIRSpec should significantly distinguish between each of the model transmission spectra, as a result of the smaller spectral feature amplitudes for the 100× solar metallicity model and the onset of a CO₂ feature in the 4–5 μm range between the 1× and 10× solar metallicity models. The model thermal emission spectra are generated using the self-consistent atmospheric model GENESIS (Gandhi & Madhusudhan 2017, 2019; Piette & Madhusudhan 2020; Piette et al. 2020). GENESIS calculates full line-by-line radiative transfer under the assumptions of radiative-convective equilibrium, hydrostatic equilibrium, and thermochemical equilibrium. Here, chemical equilibrium abundances are calculated using the analytic prescription of Heng & Tsai (2016). We include opacity due to H₂O, CH₄, NH₃, HCN, CO, CO₂, C₂H₂, and collision-induced absorption (CIA) due to H₂–H₂ and H₂–He. The absorption cross sections for these species are calculated using the methods described in Gandhi & Madhusudhan (2017), using data from ExoMol, HITEMP, and HITRAN (H₂O, CO, and CO₂: Rothman et al. 2010; CH₄: Yurchenko et al. 2013; Yurchenko & Tennyson 2014; NH₃: Yurchenko et al. 2011; HCN: Harris et al. 2006; Barber et al. 2014; C₂H₂: Rothman et al. 2013; CIA: Richard et al. 2012). As shown in Figure 8, the 1×, 10×, and 100× solar metallicity models are easily distinguishable in the ∼4–5 μm range due to the onset of an increasingly deep CO₂ feature as metallicity increases. Atmospheric characterization of TOI-5205b with both transmission and thermal emission spectroscopy is therefore a promising avenue to characterize its atmospheric metallicity and C/O ratio, and to place constraints on its formation and evolution.

• 1.  
  Template Matching (pyHammer): We classify the spectral subtype for TOI-5205 with the LRS2 spectra using pyHammer (Roulston et al. 2020), which is based on The Hammer (Covey et al. 2007), and uses an empirical template averaged across many observations. The empirical template is derived from the MaNGA Stellar Library (MaStar), which consists of well-calibrated optical spectra from SDSS IV (Yan et al. 2019). The relative calibration for this template is accurate to <5%, spanning stellar spectral types and metallicity. After applying the response and telluric correction, the combined LRS2 spectra (blue + red) matches a metal-rich M5 spectra the best (based on spectral indices; Roulston et al. 2020), and also gives the lowest residuals when comparing the entire spectra (Figure 9).
• 2.  
  Spectral ratios: We also use the spectral ratios defined by Kirkpatrick et al. (1991) surrounding CaH, Ti i, Na i, and Ca ii, to obtain a spectral type of M3–M4.5 based on the LRS2 spectra.
• 3.  
  Photometry relations: We also use relations from Kiman et al. (2019) to obtain a spectral type using the absolute G magnitude, which suggests an ∼M3.5 spectral type. Using the G − J relation from Figure 13 in Cifuentes et al. (2020) corroborates the M4 spectral type estimate for the given G − J color of ∼3.

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Considering the results from the template-matching (M5) and color relations, we adopt a spectral classification of M4.0 to which we ascribe an error of 1.0 subtype.

We obtain M_G of ${10.09}_{-0.03}^{+0.01}$ from Anders et al. (2022), which takes into account extinction using estimates from multiple photometric surveys. Using Equation (11) from Rabus et al. (2019), we estimate a T_eff from M_G of 3430 K with an error of 54 K, where we propagate the error in M_G to T_eff and combining in quadrature with the scatter in the polynomial fit. We do note that our T_eff estimate is on the hotter end of that expected for an M4 spectral type; however, this is not too surprising given the uncertainty of 1 spectral type, and the considerable scatter in theoretical models for mid-type M dwarfs.

We use the empirically calibrated polynomial relations derived by Mann et al. (2015) to estimate the stellar radius. Given the large scatter in the T_eff versus stellar radius relation (Figure 9 from Mann et al. 2015), we use the absolute K_s magnitude–stellar radius relation instead, and adopt an error of ∼3% on the stellar radius based on their cross-validation results. The full transit obtained for TOI-5205b from the 3.5 m APO telescope on 2022 July 16 is used to obtain a density constraint on the star of 8.8 ± 0.4 g cm⁻³, which is also consistent with the ∼0.39 R_⊙ obtained above. We also use M_G along with the bolometric calculator ³⁵ for the given T_eff (Creevey et al. 2022), to obtain the bolometric magnitude, luminosity, and subsequently a stellar radius of ∼0.37 ± 0.02 R_⊙, which is consistent with our radius estimate using the relations from Mann et al. (2015).

Finally, we use the Stefan–Boltzmann law to obtain a stellar luminosity, and the empirically calibrated M–R relationship for main-sequence M dwarfs (Equation (6); Schweitzer et al. 2019) to obtain a stellar mass (Table 3). We also verify the stellar mass using photometric relations from Henry & McCarthy (1993), Delfosse et al. (2000), Benedict et al. (2016), and Mann et al. (2019) and consistently obtain similar results to ∼1σ–2σ. Mass–luminosity relations in the optical (M_V ) from Henry & McCarthy (1993) and Benedict et al. (2016) give discrepant results with the M_K mag relations due to the effect of the TiO and VO molecules, especially below 0.4 M_⊙ as discussed by Baraffe et al. (1998).

Photometric relations from Bonfils et al. (2005), Schlaufman & Laughlin (2010), and Neves et al. (2012) give metallicities of 0.02, 0.19, and 0.09 dex, respectively, along with a typical uncertainty of 0.2 dex. Maldonado et al. (2020) noted that photometric metallicities have systematically lower values than corresponding spectroscopic techniques. However due to the sparse sampling of the SpecMatch-Emp library in T_eff–[Fe/H] plane for mid-M dwarfs (Yee et al. 2017), and the potential covariance between these two quantities, we do not have reliable metallicity estimates from SpecMatch-Emp for this mid-M dwarf. Instead, we adopt a qualitative estimate of solar metallicity for TOI-5205 (Table 3). See Passegger et al. (2022) for a detailed discussion of the complexities in metallicity determination for M dwarfs.

A.3.1. Using Hα from LRS2 Spectra

Emission in the Hα line compared to the overall stellar bolometric luminosity is a powerful stellar activity indicator for M dwarfs (West et al. 2015). To estimate $\mathrm{log}({L}_{{\rm{H}}\alpha }/{L}_{\mathrm{bol}}$) for TOI-5205, we measured the pseudo-equivalent width of the Hα line from the LRS-2 red channel spectrum. Prior to measuring pEW(Hα), we shifted the spectra to zero radial velocity, accounting for the barycentric velocity and absolute velocity of the star. We measure the pEW(Hα) using the following equation:

$$\begin{eqnarray}&&\mathrm{pEW}({\rm{H}}\alpha )={\int }_{{\lambda }_{1}}^{{\lambda }_{2}}\left(1-\displaystyle \frac{F(\lambda )}{{F}_{\mathrm{pc}}}\right)d\lambda \end{eqnarray} \tag{ A1 }$$

where we integrate over the limit from λ₁ = 6560 Å and λ₂ = 6566 Å. F_pc is the average of the median flux in the pseudo-continuum in the ranges from 6545–6559 Å, and 6567−6580 Å after removing a linear slope fit to that range seen in the pseudo-continuum surrounding the Hα line for late-M dwarfs. In doing so, we measure a pEW(Hα) = −0.81 ± 0.01 Å, where the error is the statistical uncertainty accounting for the S/N of the observed spectrum.

To estimate $\mathrm{log}({L}_{{\rm{H}}\alpha }/{L}_{\mathrm{bol}})$, we use the following equation:

$$\begin{eqnarray}&&\mathrm{log}\left(\displaystyle \frac{{L}_{{\rm{H}}\alpha }}{{L}_{\mathrm{bol}}}\right)=\mathrm{log}\chi +\mathrm{log}(-\mathrm{pEW}({\rm{H}}\alpha )),\end{eqnarray} \tag{ A2 }$$

where $\mathrm{log}\chi$ is the ratio of the flux in the continuum near Hα to the bolometric flux. We use the estimate χ following the methodology in Reiners & Basri (2008), which gives χ as a function of stellar effective temperature for M dwarfs stars. In doing so, we obtain a $\mathrm{log}(\chi )=-4.3$, and $\mathrm{log}({L}_{{\rm{H}}\alpha }/{L}_{\mathrm{bol}})=-4.4$. From the sample of $\mathrm{log}({L}_{{\rm{H}}\alpha }/{L}_{\mathrm{bol}})$ values in West et al. (2015), this value for TOI-5205 is suggestive of an M4 star that is not highly active.

A.3.2. Rotation Period Estimates

The stellar density estimated assuming a circular orbit (8.8 ± 0.4 g cm⁻³) confirms the mid-M dwarf spectral type for the host (Appendix A.2). This also rules out the background eclipsing binary scenario around distant giant stars.

The speckle imaging from NESSI is used to resolve the presence of any objects down to a separation of 03 or about 27 au (Figure 10). We then attempt to place constraints on unresolved stellar companions using HPF spectra, Gaia astrometry, archival imaging, photometry, and the RVs.

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A.4.1. Background Objects

A.4.2. Comoving Objects

We rule out the possibility of a system where TOI-5205b transits the primary, but is accompanied by a secondary stellar-mass companion orbiting the host star that is redder and fainter than TOI-5205 and would dilute the transit.

Assuming no unresolved companions, the transit depth (δ₀) for a planet with area A_p crossing a star with area A₁ and luminosity L₁(λ) is given by

$$\begin{eqnarray}&&{\delta }_{0}=\left(\displaystyle \frac{{A}_{p}{L}_{1}(\lambda )}{{A}_{1}}\right)\displaystyle \frac{1}{{L}_{1}(\lambda )}=\displaystyle \frac{{A}_{p}}{{A}_{1}}.\end{eqnarray} \tag{ A3 }$$

Instead, if there was an unresolved companion of later spectral type with luminosity L₂(λ), where L₂ < L₁:

$$\begin{eqnarray}&&\delta (\lambda )=\left(\displaystyle \frac{{A}_{p}{L}_{1}(\lambda )}{{A}_{1}}\right)\displaystyle \frac{1}{{L}_{1}(\lambda )+{L}_{2}(\lambda )}\end{eqnarray} \tag{ A4 }$$

$$\begin{eqnarray}&&\delta (\lambda )={\delta }_{0}\left(\displaystyle \frac{{L}_{1}(\lambda )}{{L}_{1}(\lambda )+{L}_{2}(\lambda )}\right)\end{eqnarray} \tag{ A5 }$$

$$\begin{eqnarray}&&\delta (\lambda )\propto \displaystyle \frac{1}{1+{L}_{2}(\lambda )/{L}_{1}(\lambda )}.\end{eqnarray} \tag{ A6 }$$

For λ₂ > λ₁,

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{2}}{{L}_{1}}\left({\lambda }_{2}\right)\gt \displaystyle \frac{{L}_{2}}{{L}_{1}}\left({\lambda }_{1}\right)\end{eqnarray} \tag{ A7 }$$

$$\begin{eqnarray}&&{\rm{i}}.{\rm{e}}.,\,\delta ({\lambda }_{2})\lt \delta ({\lambda }_{1}).\end{eqnarray} \tag{ A8 }$$

We obtained precise multifilter transit photometry from the 3.5 m ARC telescope (Figure 3) in the SDSS i' and g' filters. If there was a later spectral type unresolved companion (object 2) that was contaminating the photometry of the host star (object 1), it would result in different transit depths across different photometric bands. If we assume that we can compare the two transit depths (in g' and i') with a precision of , where is a small number, then

$$\begin{eqnarray}&&\displaystyle \frac{\delta (g^{\prime} )}{\delta (i^{\prime} )}=1+\epsilon .\end{eqnarray} \tag{ A9 }$$

Then by this method, we can rule out all objects with luminosity less than L₂(λ),

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{2}}{{L}_{1}}\left(i^{\prime} \right)/\displaystyle \frac{{L}_{2}}{{L}_{1}}\left(g^{\prime} \right)=1+\epsilon .\end{eqnarray} \tag{ A10 }$$

Using a separate dilution term for the ARCTIC transit in $g^{\prime}$, we probe for chromaticity in the transit depth between $g^{\prime}$ and $i^{\prime}$, but find the depths to be consistent to ∼10%, i.e., ∼ 0.1. We then use the SDSS transmission curves for the two filters, and compare the flux within the bandpass using BT-Settl CIFIST theoretical stellar spectra for a range of stellar masses (Allard et al. 2011, 2012). We conclude that this method would be sensitive to transit depth variations for an unresolved companion cooler than ∼3100 K or roughly 0.25 M_⊙ (Figure 10).

If there was a secondary stellar-mass object present in the system, i.e., a hierarchical system, it would be a source of dilution that would suggest a radius larger than the ∼1 R_J estimated here. Due to the electron degeneracy pressure, objects around this size can range from Jovian planets to very-low-mass stars (M7–M8; Zapolsky & Salpeter 1969; Burrows et al. 2001). Therefore, if TOI-5205b had a larger radius (due to unaccounted dilution), it would have to be a late-type M dwarf or larger, which would make it at least 100× more massive than the ∼1 M_J we measure (Table 4).

Finally, we put additional constraints on the possibility of a bound stellar companion, as follows:

• 1.  
  Constraints from HPF spectra: We follow the procedure outlined in Kanodia et al. (2020) to place limits on any spatially unresolved stellar companion to TOI-5205 using the HPF spectra to quantify the lack of flux from a secondary object. We combine the spectra from a single epoch to obtain a higher S/N template for comparison, and then model the test spectra (TOI-3757) as a linear combination of a primary M dwarf (GJ 273) and a secondary companions (GJ 9066, GJ 1072, GJ 1111, and LSPM J0510+2714). The flux ratio between the secondary and primary star, F, is calculated as:

  $$\begin{eqnarray}&&{S}_{\mathrm{obs}}=A\left((1-x){S}_{\mathrm{primary}}+(x){S}_{\mathrm{secondary}}\right)\end{eqnarray} \tag{ A11 }$$

  $$\begin{eqnarray}&&F=\displaystyle \frac{x}{1-x}\end{eqnarray} \tag{ A12 }$$

  where S_obs is the observed spectrum, S_primary is the primary spectrum, S_secondary represents the secondary spectrum, and A is the normalization constant. For a given primary and secondary template, we (i) perform a χ² minimization to shift the secondary spectrum in velocity space, (ii) add this shifted secondary spectrum to the primary, and (iii) fit for the value of x (and A) that best fits the observed spectrum. We perform this for a range of spectral types for the secondary from M4.5–M7 spanning velocity offsets of ±150 km s⁻¹. We place a conservative upper limit for a secondary companion of flux ratio < 0.2 or Δmag ≃ 1.8 for ∣Δv∣ >5 km s⁻¹, using HPF order index 5 spanning 8650–8770 Å. The lower limit coincides with HPF's spectral resolution (R ∼ 55,000 ≈5.5 km s⁻¹). At lower velocity offsets, the degeneracy between the primary and secondary spectra prevents any meaningful flux ratio constraints.
• 2.  
  Constraints from Gaia astrometry: Gaia DR3 (Vallenari et al. 2022) provides an additional astrometric constraint on the presence of unresolved bound companions using the re-normalized unit weight error (RUWE) metric. RUWE is sensitive to the change in the position of the primary target due to reflex motion caused by unresolved bound companions. For the single-star astrometric solution in use for Gaia DR3, this astrometric motion of the primary star around the center of mass would manifest as noise (Kervella et al. 2019), especially for orbital periods much shorter than the observing baseline for Gaia DR3 (∼34 months). The commonly accepted threshold in the literature for this is RUWE ≳1.4, which correlates with the presence of a bound stellar companion in recent studies of stellar binaries (Belokurov et al. 2020; Penoyre et al. 2020; Gandhi et al. 2021). For TOI-5205, Gaia DR3 reports an RUWE of ∼1.03, which is in agreement with a single-star astrometric solution.
• 3.  
  Constraints from RVs: A joint fit of the photometry and RVs is used to estimate the planetary and system properties (Section 4). We also include a linear RV trend in the orbital solution while fitting the RVs. We estimate this to be consistent with 0, with the estimated RV trend ∼${0.05}_{-5.08}^{+4.92}$ m s⁻¹ yr⁻¹. Assuming a circular orbit for a unresolved companion star, the maximum is at phase 0 (conjunction) and 180°, where the amplitude would be 2π K/P, where K is the RV semi-amplitude on the primary star due to a hypothetical secondary, and P is its orbital period. However, given our short observing period (∼30 days), we use this to only constrain companions with a maximum orbital period of ∼60 days, or a semimajor axis of 0.2 au.

Using the systemic velocity from HPF and proper motion from Gaia DR3, we calculate the UVW velocities in the barycentric frame using GALPY (Bovy 2015). ³⁶ We provide these velocities in Table 3, including those in the local standard of rest using the offsets from Schönrich et al. (2010). Using the BANYAN tool (Gagné et al. 2018), we classify TOI-5205 as a field star in the thin disk with very high probability (>99%; Bensby et al. 2014).