A Mini-Neptune Orbiting the Metal-poor K Dwarf BD+29 2654

The occurrence rate of giant planets is strongly correlated with the host star metallicity (Gonzalez 1997; Santos et al. 2004; Fischer & Valenti 2005). This strong correlation has been regarded as supporting evidence for the core accretion theory of planet formation (Pollack et al. 1996). In a metal-rich disk, a high abundance of solid materials helps planet embryos grow quickly to the critical mass that initiates runaway gas accretion and gas-giant formation. On the other hand, the close-in, sub-Neptune planets (<1 au, 1–4R_⊕, also known as the Kepler-like planets) are much more common around solar-type stars compared to giant planets (e.g., Howard et al. 2012; Fressin et al. 2013; Petigura et al. 2013). The occurrence rate of sub-Neptune planets also has a much weaker dependence on host metallicity compared to the giant planets (e.g., Wang & Fischer 2015; Petigura et al. 2018). One might argue that the formation of gas-giant planets may be a threshold-crossing event that has to occur when the gaseous disk is still present. On the other hand, the formation of sub-Neptune planets is less demanding on the core assembly rate and can proceed in low-metallicity environments. The super-Earth planets may not accrete a substantial envelope (Rogers 2015), whereas the mini-Neptunes only acquire their envelopes toward the final vestige of the disk, when the disk starts to become optically thin (Lee & Chiang 2016; Lee et al. 2018).

So far, most planet occurrence studies (e.g., Kepler Borucki et al. 2011) have been based on surveys of stars with Sunlike metallicities [Fe/H] between −0.5 and 0.5. It is not clear how the occurrence–metallicity correlation extends to a more metal-depleted regime ([Fe/H] <−0.5). The standard minimum-mass solar nebula (Hayashi 1981) has about 30M_⊕ of solid materials within the innermost 1 au for the in situ formation of the close-in sub-Neptune planets. The total amount of solid materials would decrease to 3–9 M_⊕ for −1 < [Fe/H] < −0.5. Such a limited supply of solids may prevent the formation of multiple close-in sub-Neptune planets.

To further investigate the influence of host metallicity, we (K. Schlaufman et al. 2023, in preparation) are studying the occurrence rate of transiting sub-Neptune planets around metal-poor (−1 < [Fe/H] < −0.5) stars observed as the TESS mission (Ricker et al. 2014). Thanks to the nearly full-sky coverage of TESS, we were able to crossmatch the TESS Input Catalog (Stassun et al. 2019) with ground-based spectroscopic surveys, including the Large Sky Area Multi-Object Fiber Spectroscopic Telescope Low-Resolution Survey Data Release (DR) 6 (Cui et al. 2012), the Radial Velocity Experiment DR6 (Steinmetz et al. 2020), and the GALactic Archaeology with Hermes (GALAH) DR3 (Buder et al. 2021). We identified a sample of about 10,000 dwarf stars with −1 < [Fe/H] < −0.5. We have carried out a systematic search for transiting planets among this sample. This search led to the discovery of BD+29 2654, which was also discovered independently by the TESS team as TOI-2018 (Guerrero et al. 2021). TOI-2018 is a bright, nearby K dwarf among our transiting planet hosts that is particularly amenable to follow-up observations. We also present an additional transiting signal, TOI-2018.02, which was not reported by the TESS team (Guerrero et al. 2021) due to its lower signal-to-noise ratio (S/N). We carried out a detailed characterization of the host star and Doppler mass measurements of the planets to help the community plan follow-up observations of this system.

The paper is organized as follows. Section 2 presents a detailed characterization of the host star TOI-2018, with particular attention to its metallicity. Section 3 describes our transit detection and modeling of this system based on the light curves. In Section 4, we present the radial velocity (RV) measurements of TOI-2018 and the resultant constraints on the planetary masses. Section 5 discusses the implications of our findings.

2.1. Fundamental and Photospheric Parameters

To derive the stellar parameters, we analyzed an archival high-resolution, high-S/N spectrum of TOI-2018 taken with the High Resolution Echelle Spectrometer on the 10 m Keck Telescope (Keck/HIRES; Vogt et al. 1994) on 2012 July 26. The spectrum was taken without the iodine cell and it reached an S/N of about 200 per reduced pixel near 5500 Å after a 600 s exposure. We made use of both spectroscopy and isochrones to infer the photospheric and fundamental stellar parameters, as described in Reggiani et al. (2022). Isochrones are especially useful for determining the effective temperature T_eff of the star, because high-quality multiwavelength photometry from the UV to the red optical is available. Similarly, the availability of the Gaia DR3 parallax-based distance of TOI-2018 makes the calculation of surface gravity $\mathrm{log}g$ via isochrones more straightforward than it has traditionally been. With good constraints on both T_eff and $\mathrm{log}g$ from isochrone fitting, the equivalent widths (EWs) of iron lines can be used to determine metallicity [Fe/H] and microturbulence ξ by minimizing the dependence of individual line-based iron abundance inferences on their reduced EWs.

The inputs to our photospheric and fundamental stellar parameter inference are the EWs of Fe i and Fe ii atomic absorption lines, multiwavelength photometry, the Gaia parallax, and an extinction estimate. Using atomic absorption line data from Yana Galarza et al. (2019) for lines that are relatively insensitive to stellar activity (Meléndez et al. 2014), we measured the EWs by fitting Gaussian profiles with the splot task in IRAF to our continuum-normalized spectrum. We also confirmed our splot EWs by remeasuring the lines using iSpec (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019). We only compared the clean (unblended) lines with our splot measurements and we concluded that there were no substantial differences in the EWs measured with splot and iSpec. For the blended lines, we used the deblend task to disentangle absorption lines from adjacent spectral features. We gathered u photometry and their uncertainties from Sloan Digital Sky Survey (SDSS) DR13 (Albareti et al. 2017), G photometry and its uncertainty from Gaia DR2 (Gaia Collaboration et al. 2016, 2018; Arenou et al. 2018; Evans et al. 2018; Hambly et al. 2018; Riello et al. 2018), J, H, and Ks from the Two Micron All Sky Survey (2MASS), and W1 and W2 from the Wide-field Infrared Survey Explorer (WISE). We use the Gaia DR3 parallax and its uncertainty (Fabricius et al. 2021; Lindegren et al. 2021a, 2021b; Torra et al. 2021; Gaia Collaboration et al. 2023), as well as an extinction A_V inference based on three-dimensional (3D) maps of extinction in the solar neighborhood from the STructuring by Inversion the Local Interstellar Medium program (Lallement et al. 2014, 2018; Capitanio et al. 2017). We assume Asplund et al. (2021) solar abundances. To derive the stellar parameters, we use the isochrones package by Morton (2015) to fit the MESA Isochrones and Stellar Tracks (MIST; e.g., Paxton et al. 2011, 2013, 2015; Choi et al. 2016) to the photospheric parameters as well as the multiwavelength photometry, parallax, and extinction using the nested sampling code MultiNest (Feroz et al. 2009, 2013). We present the stellar parameters in Table 1. We would like to remind readers that the stellar parameters derived from isochrone models are often subject to substantial systematic uncertainties between different isochrone models (e.g., 4% in stellar radius; Tayar et al. 2022). These are not explicitly included in the reported values here. As an additional check, we inferred T_eff of TOI-2018 using the colte code ⁴⁵ (Casagrande et al. 2021), which estimates T_eff using a combination of color–T_eff relations obtained by implementing the InfraRed Flux Method for Gaia and 2MASS photometry. As required by colte, we used Gaia DR3 G, G_BP, and G_RP plus 2MASS J, H, and K_s photometry as input. We find a colte-based T_eff = 4160 ± 81 K, consistent with our isochrone-inferred effective temperature. We could not measure the rotational broadening vsini of the host star, given the resolution of our HIRES spectrum. The vsini is likely smaller than 2 km s⁻¹ (this is consistent with the 23.5 days rotation period we determine in Section 3).

Table 1. Adopted Stellar Parameters

Property	Value	Unit
SDSS DR13 u	13.385 ± 0.0264	AB mag
Gaia DR2 G	9.720 ± 0.002	Vega mag
2MASS J	7.844 ± 0.021	Vega mag
2MASS H	7.255 ± 0.020	Vega mag
2MASS K	7.104 ± 0.017	Vega mag
WISE W1	6.984 ± 0.062	Vega mag
WISE W2	7.071 ± 0.020	Vega mag
Gaia DR3 parallax	35.666 ± 0.014	mas
Spectroscopically Inferred Parameters
[Fe/H]	−0.58 ± 0.18
vsini	<2	km s−1
SHK	0.92 ± 0.03
log${R}_{\mathrm{HK}}^{{\prime} }$	−4.75 ± 0.04
Isochrone-inferred Parameters
Effective temperature Teff	${4174}_{-42}^{+34}$	K
Surface gravity $\mathrm{log}g$	${4.62}_{-0.03}^{+0.02}$	cm s−2
Stellar mass M*	0.57 ± 0.02	M⊙
Stellar radius R*	0.62 ± 0.01	R⊙
Luminosity L*	0.10 ± 0.01	L⊙
Distance	28.038 ± 0.011	pc

Note. Substantial systematic uncertainties may exist between different isochronal models (Tayar et al. 2022).

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2.2. Chemical Abundances

To infer the elemental abundances, we first measured the EWs of the atomic absorption lines of Na i, Mg i, Al i, Si i, K i, Ca i, Sc ii, Ti i, Ti ii, V i, Cr i, Fe i, Fe ii, Ni i, Co i, Y ii, and Ba ii in our continuum-normalized spectrum by fitting Gaussian profiles with iSpec. We avoid blended lines and only kept lines with EWs smaller than 170 mÅ. We assume Asplund et al. (2021) solar abundances and local thermodynamic equilibrium (LTE) and we used the 1D plane-parallel solar composition MARCS model atmospheres (Gustafsson et al. 2008) and the 2019 version of MOOG (Sneden 1973; Sneden et al. 2012) to infer elemental abundances based on each EW measurement. We report our adopted atomic data, EW measurements, and individual line-based abundance inferences in Table 2. We report our abundance inferences in three common systems: A(X), [X/H], and [X/Fe]. The abundance A(X) is defined as $A({\rm{X}})=\mathrm{log}{N}_{{\rm{X}}}/{N}_{{\rm{H}}}+12$, the abundance ratio [X/H] is defined as [X/H] = A(X) − A(X)_⊙, and the abundance ratio [X/Fe] is defined as [X/Fe] = [X/H] − [Fe/H]. We define the uncertainty in the abundance ratio σ_[X/H] as the standard deviation of the individual line-based abundance inferences ${\sigma }_{[{\rm{X}}/{\rm{H}}]}^{\prime}$ divided by $\sqrt{{n}_{{\rm{X}}}}$, where n is the number of lines used. We define the uncertainty σ_[X/Fe] as the square root of the sum of the squares of σ_[X/H] and σ_[Fe/H]. The results are reported in Table 3.

Table 2. Atomic Data, EWs, and Line Abundances

Wavelength	Species	Excitation Potential	log(gf)	EW	${\mathrm{log}}_{\epsilon }({\rm{X}})$
(Å)		(eV)		(mÅ)
4751.822	NaI i	2.104	−2.078	41.30	5.824
6154.225	NaI i	2.102	−1.547	82.90	5.721
6160.747	NaI i	2.104	−1.246	95.30	5.528
4730.029	MgI i	4.346	−2.347	110.30	7.475
5711.088	MgI i	4.346	−1.724	116.30	7.004
6318.717	MgI i	5.108	−2.103	37.60	7.498
4512.268	CaI i	2.526	−1.900	63.50	5.617
5260.387	CaI i	2.521	−1.719	71.70	5.650
5512.980	CaI i	2.933	−0.464	167.10	5.462
5867.562	CaI i	2.933	−1.570	64.40	5.771
6166.439	CaI i	2.521	−1.142	126.30	5.352

Note. Full version online. This table is published in its entirety in machine-readable format. A portion is shown here for guidance regarding its form and content.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 3. Elemental Abundances

Species	A(X)	[X/H]	σ[X/H]	[X/Fe]	σ[X/Fe]	n
LTE Abundances
Na i	5.691	−0.529	0.123	0.051	0.089	3
Mg i	7.326	−0.224	0.228	0.356	0.169	3
Al i	5.796	−0.634	0.031	−0.054	0.032	2
Si i	7.230	−0.280	0.246	0.300	0.260	2
Ca i	5.570	−0.730	0.147	−0.150	0.077	5
Sc i	2.622	−0.518	0.207	0.062	0.151	3
Ti ii	4.624	−0.346	0.194	0.234	0.099	7
V i	3.543	−0.357	0.281	0.223	0.120	7
Cr ii	4.951	−0.669	0.000	−0.089	0.120	1
Fe i	6.880	−0.580	0.171	⋯	⋯	70
Fe ii	6.963	−0.497	0.082	⋯	⋯	4
Co i	4.724	−0.216	0.185	0.364	0.087	6
Ni i	5.947	−0.253	0.307	0.327	t 0.105	13
Cu i	4.035	−0.144	0.062	0.436	0.059	4
Y ii	1.260	−0.950	0.000	−0.370	0.033	1
Ba ii	1.519	−0.751	0.001	−0.171	0.025	2

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2.3. Age, Spectral Energy Distribution, and Thick-disk membership

To check on the system age, we measured a stellar rotation period of 23.5 ± 1.0 days in the WASP light curve of TOI-2018 using the Lomb–Scargle periodogram (Lomb 1976; Scargle 1982); the autocorrelation function (McQuillan et al. 2014) gives a consistent result. The rotation period translates to a gyrochronological age of 1.6 ± 0.1 Gyr according to the scaling relation of Mamajek & Hillenbrand (2008). If we use the more up-to-date empirical relations of Bouma et al. (2023), TOI-2018's rotation period indicates an age of 2.4 ± 0.2 Gyr. We also analyzed the chromospheric activity as seen in the Ca ii H and K lines of our HIRES spectrum. We found the activity indicator S_HK = 0.92 ± 0.03 and log${R}_{\mathrm{HK}}^{{\prime} }$= −4.75 ± 0.04 using the method of Isaacson & Fischer (2010). The activity level of TOI-2018 is at about the fiftieth percentile (see Figure 1) of stars with similar B–V color (within 0.1 in B–V) as observed by the California Planet Search (Howard et al. 2010). In addition, we looked for Lithium absorption in our HIRES spectrum of TOI-2018. We could not detect a Lithium feature that is statistically significant above the nearby continuum. We note that both the strength of Lithium absorption and log${R}_{\mathrm{HK}}^{{\prime} }$ are likely correlated with the host star metallicity [Fe/H]. The existing samples are dominated by solar metallicity stars. If TOI-2018 is indeed a thick-disk star, as we will discuss shortly, one might expect it to be old (>8–9 Gyr). A previous work by Martig et al. (2015), however, reported a curious sample of young, α-enhanced stars in the solar neighborhood. Given the quality and discrepancy of the various age indicators, we are unable to provide a precise age constraint on TOI-2018, as is often the case for late-type stars.

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We further examined the kinematics of TOI-2018. The proper motion of TOI-2018 does not fit any known comoving associations reported in Banyan-Σ (Gagné et al. 2018) and in Bouma et al. (2022). We also computed the Galactic UVW velocity of TOI-2018 (U,V,W = −59.6, 11.4, −8.9 km s⁻¹). Using the framework of Bensby et al. (2014), TOI-2018 has a 3.1% chance of being in the thick disk based on its kinematics alone.

We also investigated the α-element enhancement of TOI-2018. Using Mg, Si, and Ti abundances as a proxy for the α elements (we excluded Ca due to its association with stellar activity), we obtained [α/Fe] = 0.29±0.12. In Figure 2, we plot [α/Fe] against [Fe/H] for TOI-2018 and a crossmatch between the GALAH survey (e.g., Buder et al. 2021) and the TESS Input Catalog (Stassun et al. 2019) as presented in Carrillo et al. (2020). The α-element enhancement of TOI-2018 does favor a thick-disk membership. However, this claim needs to be further confirmed with more precise [α/Fe] and kinematic constraints.

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We fitted the spectral energy distribution (SED) of TOI-2018 following the method of Stassun & Torres (2016). We fitted Kurucz stellar atmosphere models (Kurucz 1979) to various photometric bands. Our fit yielded a reduced χ² of 1.1. We obtained a stellar mass and radius of 0.59 ± 0.04M_⊙ and 0.62 ± 0.02R_⊙, which are consistent with our isochronal analysis. We did not find any evidence for an infrared excess that may be attributable to a debris disk (Figure 3).

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2.4. High-resolution Imaging

As part of our standard process for validating transiting exoplanets, and to assess the contamination of bound or unbound companions on the derived planetary radii (Ciardi et al. 2015), we observed TOI-2018 with high-resolution imaging. The star was observed with Palomar/PHARO (Hayward et al. 2001), Lick/ShARCS (Kupke et al. 2012; Gavel et al. 2014; McGurk et al. 2014), Gemini-N/Alopeke (Howell et al. 2011), Caucasian Observatory of Sternberg Astronomical Institute/Speckle Polarimeter (Safonov et al. 2017), and Carlo Alto/AstraLux (Hormuth et al. 2008), thanks to the efforts of the TESS Follow-up Observing Program Working Group.

We present the Palomar/PHARO result here as an example. All other high-resolution imaging results did not detect any nearby stellar companions, and they are available on the ExoFOP website. ⁴⁶ The Palomar observations were made with the PHARO instrument (Hayward et al. 2001) behind the natural guide star adaptive optics (AO) system P3K (Dekany et al. 2013) on 2021 June 19 UT in a standard five-point quincunx dither pattern with steps of 5'' in the narrowband Br − γ filter (λ_o = 2.1686; Δλ = 0.0326 μm). Each dither position was observed three times, offset in position from each other by 05, for a total of 15 frames; with an integration time of 1.4 s per frame, the total on-source time was 14 s. PHARO has a pixel scale of 0025 per pixel for a total field of view of ∼25''. The science frames were flat-fielded and sky-subtracted. The reduced science frames were combined into a single combined image with a final resolution of 0091 FWHM.

To within the limits of the AO observations, no stellar companions were detected. The sensitivities of the final combined AO image were determined by injecting simulated sources azimuthally around the primary target every 20° at separations of integer multiples of the central source's FWHM (Furlan et al. 2017; Lund & Ciardi 2020). The brightness of each injected source was scaled until standard aperture photometry detected it with 5σ significance. The resulting brightness of the injected sources relative to TOI-2018 set the contrast limits at that injection location. The final 5σ limit at each separation was determined from the average of all of the determined limits at that separation. The uncertainty on the limit was set by the rms dispersion of the azimuthal slices at a given radial distance (Figure 4).

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In addition to the high-resolution imaging, we also utilized Gaia to identify any wide stellar companions that may be bound members of the system. Typically, these stars are already in the TESS Input Catalog and their flux dilution to the transit has already been accounted for in the transit fits and associated derived parameters. Based upon similar parallaxes and proper motions (e.g., Mugrauer & Michel 2020, 2021; Mugrauer et al. 2022), there are no additional widely separated companions identified by Gaia. Additionally, the Gaia DR3 astrometry provides additional information on the possibility of inner companions that may have gone undetected by either Gaia or high-resolution imaging. The Gaia Renormalized Unit Weight Error (RUWE) is a metric similar to a reduced chi-square, where values that are ≲1.4 indicate that the Gaia astrometric solution is consistent with the star being single. In contrast, RUWE values ≳1.4 may indicate an astrometric excess noise, possibly caused by the presence of an unseen companion (e.g., Ziegler et al. 2020). TOI-2018 has a Gaia DR3 RUWE value of 1.23, indicating that the astrometric fits are consistent with the single-star model.

3.1. TESS Observations

TOI-2018 (TIC 357501308) was observed by the TESS mission (Ricker et al. 2014) in Sectors 24 and 51. We started with the 2 minutes cadence light curve produced by the TESS Science Processing Operations Center (SPOC, located at the NASA Ames Research Center; Jenkins et al. 2016). The data were downloaded from the Mikulski Archive for Space Telescopes website ⁴⁷ and are available at doi:10.17909/t9-nmc8-f686. Our subsequent analysis was based on the Presearch Data Conditioning Simple Aperture Photometry (Smith et al. 2012; Stumpe et al. 2012, 2014) version of the light curves, although the Simple Aperture Photometry (Twicken et al. 2010; Morris et al. 2020) version was used to measure the stellar rotation period, since it better preserves any long-term stellar variability. We excluded anomalous data points that have nonzero Quality flags. We note that the SPOC pipeline found a difference imaging centroid offset that is only 0945 ± 255; this is again consistent with the lack of a nearby stellar companion for TOI-2018.

We removed any stellar activity or instrumental effects by fitting the light curve with a cubic spline in time of a width of 0.75 days. We searched for planetary transit signals in the detrended light curve using the Box Least Square algorithm (Kovács et al. 2002). Our pipeline was previously used for the detection of other K2 and TESS planets (Dai et al. 2017, 2021). We detected a 7.4 days planet with a signal detection efficiency (as defined by Kovács et al. 2002) of 11.7. The same candidate was reported by the TESS team (Guerrero et al. 2021) as TOI-2018.01. We also detected a second planet candidate at 11.3 days with a signal detection efficiency of 5.8, which is below the SPOC signal detection limit (S/N = 7.1). Given the low S/N of the detection, TOI-2018.02 does not meet the usual threshold for qualifying as a planet candidate. However, the orbital periods of the two planets are close to a 3:2 mean motion resonance with a small deviation of (P_out/P_in)/(3/2) − 1 ≈ 1%, which may boost the case for a real planet for TOI-2018.02. We did not find any other significant transit signal in the TESS light curve. Figure 5 shows the detrended light curve and the transits of the two candidate planets.

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We used the Python package Batman (Kreidberg 2015) to model the transit light curves of the two planets simultaneously. One of the global parameters is the mean stellar density of the host ρ = 2.39 ± 0.09ρ_⊙, as derived in Section 2. We imposed a Gaussian prior on the mean stellar density to help break the degeneracy in semimajor axis and impact parameter. Two other global parameters are the quadratic limb-darkening coefficients using the reparameterization of q₁ and q₂ suggested by Kipping (2013). We adopted a Gaussian prior using the theoretical values from EXOFAST (Eastman et al. 2013) and a standard deviation of 0.3. Both planets were assumed to have circular orbits, hence the other transit parameters are the orbital period P_orb, the time of conjunction T_c, the planet-to-star radius ratio R_p/R_⋆, the scaled orbital distance a/R_⋆, and the transit impact parameter b.

We started by assuming that both planet candidates have linear ephemerides (i.e., no transit timing variations). We fitted all transits of each planet with a constant period model. The best-fit model was determined with the Levenberg-Marquardt method implemented in the Python package lmfit (Newville et al. 2014). This best-fit model was used as a template transit to fit the mid-transit times of each individual transit. During the fits of individual transits, we varied only the mid-transit time and three parameters of a quadratic function of time that describes any residual long-term variations. A total of six and three transits were observed for the two planet candidates. We were not able to detect a statistically significant transit timing variation trend for either planet. We note that the transits of TOI-2018.02 in Sector 51 were either located in data gaps or near the end of the TESS observation (Figure 5). TOI-2018.02 could not be recovered using Sector 51 data alone. Our ephemeris of TOI-2018.02 is based on a joint fit using all sectors from TESS; the result has substantial uncertainty (Table 4), due to the ambiguity of the transit time in Sector 51. TESS will observe this system again in Sectors 77 and 78; those data will be instrumental in confirming TOI-2018.02 and for detecting transit timing variations. We carried out a Monte Carlo Markov Chain (MCMC) analysis using the emcee package (Foreman-Mackey et al. 2013). We initialized 128 walkers near the best-fit model from lmfit. We ran the MCMC for 50,000 links, which is more than two orders of magnitude longer than the typical autocorrelation function (≲300 links). The resultant posterior distribution is summarized in Table 4. Figure 6 shows the phase-folded and binned light curves for each planet candidate as well as the best-fit transit model.

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Table 4. Model Parameters of TOI-2018

Parameter	Symbol	TOI-2018 b	TOI-2018.02
From Transit Modeling
Mean Stellar Density (ρ⊙)	ρ⋆	2.29 ± 0.22	-
Limb-darkening Coefficient	q1	0.36 ± 0.22	-
Limb-darkening Coefficient	q2	0.33 ± 0.23	-
Orbital Period (days)	Porb	7.435583 ± 0.000022	11.244 ± 0.025
Time of Conjunction (BJD-2457000)	tc	1958.2580 ± 0.0013	1964.110 ± 0.020
Planet/Star Radius Ratio	Rp /R⋆	0.0335 ± 0.0010	0.0228 ± 0.0020
Impact Parameter	b	0.546 ± 0.070	0.16 ± 0.11
Scaled Semimajor Axis	a/R⋆	21.12 ± 0.69	27.82 ± 0.90
Transit Duration (hours)	T14	2.360 ± 0.090	3.09 ± 0.12
Orbital Inclination (deg)	i	88.52 ± 0.22	89.66 ± 0.31
Orbital Eccentricity	e	0 (fixed)	0 (fixed)
From RV Modeling
Semi-amplitude (m s−1)	K	4.4 ± 1.0	<1.5
GP Amplitude (m s−1)	h	5.0 ± 1.1	⋯
GP Correlation Timescale (days)	τ	${14.9}_{-9.4}^{+12.9}$	⋯
GP Periodicity (days)	T	22.5 ± 2.1	⋯
GP Weighting	Γ	1.5 ± 0.3	⋯
RV Offset (m s−1)	γ	7.5 ± 3.8	⋯
RV Jitter (m s−1)	σjit	${0.38}_{-0.24}^{+0.50}$	⋯
RV Drift (m s−1 day−1)	$\dot{\gamma }$	−0.0017±0.0008	⋯
Derived Parameters
Planetary Radius (R⊕)	Rp	2.268 ± 0.069	1.54 ± 0.14
Planetary Mass (M⊕)	Mp	9.2 ± 2.1	<3.6

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3.2. MuSCAT2 Observations

3.3. WASP Observations

We acquired a total of 38 high-resolution spectra of TOI-2018 on Keck/HIRES (Vogt et al. 1994) from UT 2011 June 18 to 2021 August 30. These spectra were obtained with the iodine cell in the path of light. The iodine cell served as the reference for our wavelength solution and the line spread function. The exposure time is typically 300–600 s, after which we obtained a median S/N of 140 per reduced pixel near 5500 Å. We extracted the RV using our forward-modeling Doppler code described in Howard et al. (2010). The estimated RV uncertainty is about 1.2 m s⁻¹. The extracted RVs and stellar activity indices are shown in Table 5.

We assumed that the planets are on circular orbits. We also experimented with nonzero eccentricities. However, the data at hand are not sufficiently constraining. The posterior samples prefer circular models with ΔBIC > 10. We simplified our analysis by focusing on circular orbits only. With circular orbits, the RV signals are hence described by the orbital period P_orb, the time of inferior conjunction T_c , and the RV semi-amplitude K. We also included an RV offset γ, a linear RV trend $\dot{\gamma }$, and a jitter term σ_jit to account for any residual astrophysical or instrumental RV uncertainties. We imposed Gaussian priors on P_orb and T_c using the posterior distribution obtained from transit analysis. We imposed log-uniform priors on the RV semi-amplitude K and the jitter σ_jit. We imposed uniform priors on the RV offset γ and linear trend $\dot{\gamma }$. To model the influence of stellar activity contamination in the RV data set, we employed a Gaussian Process (GP) model (e.g., Haywood et al. 2014; Grunblatt et al. 2015; Dai et al. 2017) with a quasiperiodic kernel:

$$\begin{eqnarray}\begin{array}{rcl}{C}_{i,j} & = & {h}^{2}\exp \left[-\displaystyle \frac{{({t}_{i}-{t}_{j})}^{2}}{2{\tau }^{2}}-{\rm{\Gamma }}{\sin }^{2}\displaystyle \frac{\pi ({t}_{i}-{t}_{j})}{T}\right]\\ & & +\,\left[{\sigma }_{i}^{2}+{\sigma }_{\mathrm{jit}}^{2}\right]{\delta }_{i,j},\end{array}\end{eqnarray} \tag{ 1 }$$

where t_i is the time of individual RV measurements; C_i,j is the covariance matrix; δ_i,j is the Kronecker delta function; h is the amplitude of the covariance; τ is the correlation timescale; Γ quantifies the relative significance between the squared exponential and periodic parts of the kernel; T is the period of the covariance; σ_i is the internal RV uncertainty; and σ_jit is the jitter term.

The corresponding likelihood function is

$$\begin{eqnarray}&&\mathrm{log}{ \mathcal L }=-\displaystyle \frac{N}{2}\mathrm{log}2\pi -\displaystyle \frac{1}{2}\mathrm{log}| {\boldsymbol{C}}| -\displaystyle \frac{1}{2}{{\boldsymbol{r}}}^{{\rm{T}}}{{\boldsymbol{C}}}^{-1}{\boldsymbol{r}},\end{eqnarray} \tag{ 2 }$$

where N is the total number of RV measurements and r is the residual after subtracting the Keplerian planetary signals from the observed RV variation.

We first trained the GP model on the out-of-transit light curves. The underlying assumption is that the stellar surface magnetic activity drives both the out-of-transit flux variation in the light curve as well as a spurious quasi-sinusoidal contamination in RV measurement. Since the out-of-transit light curves are measured to higher precision and better sampled, we conditioned all the GP hyperparameters on the light curves first, before using those hyperparameters in the RV analysis.

We experimented with including increasingly more complexity to our RV models. We increased the number of planets included, and if a GP model for stellar activity was warranted by the RV data set, and if a linear RV trend $\dot{\gamma }$ was required, we selected the best model by examining the Bayesian Information Criterion (BIC) after model optimization with the Levenberg-Marquardt method lmfit (Newville et al. 2014). The model favored by the current data set contains only planet b, a long-term RV drift ($\dot{\gamma }$), and a GP model for the stellar activity. We sampled the posterior distribution of this model using a similar sampling procedure as described in Section 3, using emcee. We performed two separate samplings. The posterior distribution of the various hyperparameters from an MCMC analysis of the WASP light curve was used as a prior for a subsequent RV analysis. The underlying assumption is that the light curve is dominated by quasiperiodic flux variations due to the host's stellar activity. We summarize the posterior distribution of the RV analysis in Table 4. The RV variation of planet b is securely detected with more than 4σ significance (Figure 7). We note that the RV alone was able to independently discover planet b; the ephemeris of the planet from the transit analysis was crucial for recovering the RV signal. A linear RV drift $\dot{\gamma }$ is marginally detected at −0.0017 ± 0.0008 m s⁻¹ day⁻¹ over the 10 yr baseline of our HIRES observation. Unfortunately, the orbital period of TOI-2018.02 is close to the first harmonic of the rotation period (11.3 days versus 23.5/2 days; Figure 8). We were only able to place an upper limit on the mass of TOI-2018.02 (<3.6M_⊕ or K < 1.5 m s⁻¹ at a 95% confidence level). Given the RV nondetection and the fact that only three transits were observed by TESS, we report TOI-2018.02 only as a possible planet candidate.

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In Figure 9, we plot the measured masses and radii of the TOI-2018 planets and other confirmed exoplanets from the NASA Exoplanet Archive. ⁴⁹ We also show various theoretical mass–radius relationships from Zeng et al. (2016), including 100%–Fe, 100%–MgSiO₃, and 100%–H₂O. In addition, we used the model by Chen & Rogers (2016) to generate the mass–radius relationships of planets with an Earthlike core and an H/He envelope of 0.5% and 1% in mass, taking into account the age and insolation of the planet as well. TOI-2018 b lies between 0.5% and 1% of H/He. However, TOI-2018 b is also consistent with an ice–rock mixture (H₂O–MgSiO₃). If we adopt a simple two-layer model (Zeng et al. 2016), TOI-2018 b is consistent with a 50%H₂O–50%MgSiO₃ composition, with a large uncertainty of about 50% ± 30% in the water mass fraction. We also show the updated mass–radius curves for water worlds when supercritical water is included in the equation of state (Aguichine et al. 2021). TOI-2018 b is consistent with having a 20%-by-mass water/steam layer on top of an Earthlike core when the supercritical state is accounted for. With only mass and radius measurements, one cannot distinguish between an H/He-enveloped TOI-2018 b and a water-world TOI-2018 b. This ambiguity in composition is common to many exoplanets, which is why it has been difficult to resolve the ongoing debate over whether the observed bimodal radius distribution for sub-Neptune planets (Fulton et al. 2017) is due to the atmospheric erosion of H/He envelopes (e.g., Lopez & Fortney 2014; Owen & Wu 2017; Ginzburg et al. 2018) or the core growth model that gives rise to water worlds (e.g., Zeng et al. 2019; Luque & Pallé 2022; Piaulet et al. 2023). As noted by Luque & Pallé (2022), late-type stars may be well suited to settling this debate. Water worlds are expected to form beyond the snowline in the disk before migrating to the close-in orbits we see them in today. For late-type stars, the snowlines are generally much closer to the host star (Kennedy & Kenyon 2009). Moreover, Type I migration proceeds faster for planets with a higher planet-to-star mass ratio (see Kley & Nelson 2012, and references therein). The short migration scale and faster Type I migration rate both favor the migration of water worlds toward the late-type star. Disk migration might have deposited a sample of close-in water worlds (typically 50%H₂O–50%MgSiO₃) around late-type host stars, as reported by Luque & Pallé (2022). The composition of TOI-2018 b is consistent with a water-world interpretation. If future follow-up observations could confirm TOI-2018.02 and its near-resonant (1% wide of 3:2) configuration with TOI-2018 b, it would further support the hypothesis that the planets underwent inward migration. This is because Type I migration is a primary channel for capturing planets into mean motion resonances (e.g., Kley & Nelson 2012; Batygin 2015; Macdonald & Dawson 2018). Brewer et al. (2018) reported evidence that the fraction of compact, multiplanet systems is enhanced around low-metallicity host stars. If TOI-2018.02 can be confirmed by future observations, TOI-2018 presents another example of such an orbital architecture around a low-metallicity star.

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With a mass of 9.2 ± 2.1M_⊕, TOI-2018 b is close to the threshold for runaway accretion and hence giant planet formation (Rafikov 2006; Lee & Chiang 2015; Lee 2019). Moreover, the low-metallicity (hence low-opacity) envelope of the planet should have cooled more easily and facilitated further accretion (Lee & Chiang 2015). Within the validity of these models, it might seem strange that TOI-2018 b failed to undergo runaway accretion, given the large core mass. Could this somehow be related to the suppressed occurrence rate of gas-giant planets around low-metallicity host stars (Fischer & Valenti 2005)? One possible explanation is that the disk lifetime is much shorter around lower-metallicity stars, as suggested by Yasui et al. (2010). Theoretically, the efficiency of the photoevaporation (and dissipation) of protoplanetary disks is enhanced at lower metallicity (the timescale for disk photoevaporation being t_phot ∝ Z^0.52; Ercolano & Clarke 2010). See also more recent hydrodynamic simulations by Nakatani et al. (2018). It may be the case that TOI-2018 b did not have enough time to initiate runaway accretion before the disk dissipated. Another relevant work by Wilson et al. (2022) has suggested that mini-Neptunes around low-metallicity host stars tend to have higher mean densities. It may indeed be the case that mini-Neptunes around low-metallicity stars typically do not accrete thick envelopes before the disks dissipate.

One measurement that may distinguish a planet with an H/He envelope and a water world is to look for metastable Helium absorption due to the exosphere of the planet in the near-infrared (e.g., Oklopčić & Hirata 2018; Spake et al. 2018). K-type stars are ideal targets for metastable Helium observation, thanks to their balance of extreme UV to far-UV flux, which, respectively, excite and destroy the metastable He population (Oklopčić 2019; Wang & Dai 2021). A substantial metastable He population in turn leads to the absorption of the 10830 Å transition. With a J-band magnitude of 7.8 and a moderately active K-type host, TOI-2018 b is a favorable target for looking for metastable Helium absorption. The detection of ongoing Helium escape would strongly favor an H/He envelope that has survived photoevaporation.

We quantify the observability of TOI-2018 b in transmission spectroscopy using the James Webb Space Telescope (JWST; Gardner et al. 2006). We computed the Transmission Spectroscopy Metric (TSM), as suggested by Kempton et al. (2018). TOI-2018 b has a TSM of roughly 103. Although there are dozens of known exoplanets that have higher TSMs (Figure 10), TOI-2018 b does provide a rare opportunity to probe the atmospheric composition of planets formed in a low-metallicity environment. It is one of the top-ranking TSM targets, with [Fe/H] < −0.5. Given how bright the host is (J = 7.8, K = 7.1), special attention to the choice of instruments and observation modes is required to avoid saturation.

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Previous results by Brinkman et al. (2023) and Demangeon et al. (2021) may suggest that super-Earths formed around low-metallicity late-type stars (L 98-59 M dwarf, [Fe/H] = −0.46±0.26 and TOI-561 K dwarf, [Fe/H] = −0.41±0.05) have lower mean densities than super-Earths around Sunlike stars. A similar trend was also pointed out by Adibekyan et al. (2021) and Castro-González et al. (2023). The lower mean densities may be the result of an alternative planet formation pathway in the low-metallicity regime. The enhanced α-element abundance (Mg, Ca, and Si) compared to Fe naturally favors the formation of a larger mantle than an iron/nickel core. If so, one might expect planets around low-metallicity stars (particularly thick-disk stars) to have lower mean densities compared to solar-type stars. The literature contains only a handful of mass and radius measurements for planets around low-metallicity host stars ([Fe/H] < −0.4). More metal-poor systems and more precise characterizations of these planets are needed to evaluate their composition as a population.

We thank Heather Knutson, Yayaati Chachan, Kento Masuda, and Yanqin Wu for helpful discussion.

This material is based on work supported by the TESS General Investigator program under NASA grant 80NSSC20K0059.

D.H. acknowledges support from the Alfred P. Sloan Foundation, the National Aeronautics and Space Administration (80NSSC21K0652), and the Australian Research Council (FT200100871).

J.M.A.M. is supported by the National Science Foundation (NSF) Graduate Research Fellowship Program under grant No. DGE-1842400. J.M.A.M. acknowledges the LSSTC Data Science Fellowship Program, which is funded by LSSTC, NSF Cybertraining grant No. 1829740, the Brinson Foundation, and the Moore Foundation; his participation in the program has benefited this work.

This article is based on observations made with the MuSCAT2 instrument, developed by ABC, at Telescopio Carlos Sánchez, operated on the island of Tenerife by the IAC in the Spanish Observatorio del Teide. This work is partly financed by the Spanish Ministry of Economics and Competitiveness through grants PGC2018-098153-B-C31.

This work is partly supported by JSPS KAKENHI grant No. JP18H05439 and JST CREST grant No. JPMJCR1761. This article is based on observations made with the MuSCAT2 instrument, developed by ABC, at Telescopio Carlos Sánchez, operated on the island of Tenerife by the IAC in the Spanish Observatorio del Teide.

D.R.C. acknowledges partial support from NASA grant 18-2XRP18_2-0007.

A.A.B. acknowledges the support of the Ministry of Science and Higher Education of the Russian Federation under the grant 075-15-2020-780 (N13.1902.21.0039).

The data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.

The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

We acknowledge the use of public TESS data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products.

J.L.-B. acknowledges financial support from the Spanish Ministerio de Ciencia e Innovaci (MCIN/AEI/ 10.13039/501100011033) and the European Union NextGeneration EU/PRTR under the Ramon y Cajal program with code RYC2021-031640-I. Based on observations collected at the Centro Astronomico Hispano en Andalucia (CAHA) at Calar Alto, operated jointly by Junta de Andalucia and Consejo Superior de Investigaciones Cientificas (IAA-CSIC).

A.C.-G. is funded by the Spanish Ministry of Science through MCIN/AEI/10.13039/501100011033 grant PID2019-107061GB-C61.

This paper has made use of data collected by the TESS mission that are publicly available from the Mikulski Archive for Space Telescopes (MAST), operated by the Space Telescope Science Institute (STScI).

Funding for the TESS mission is provided by NASA's Science Mission Directorate.

Some of the observations in this paper made use of the High-Resolution Imaging instrument Alopeke and were obtained under Gemini LLP Proposal Number GN/S-2021A-LP-105. Alopeke was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley. Alopeke was mounted on the Gemini North telescope of the international Gemini Observatory, a program of NSF's NOIR Lab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicaçóes (Brazil), and the Korea Astronomy and Space Science Institute (Republic of Korea).

Facilities: Keck: I (HIRES) - KECK I Telescope, TESS - , MuSCAT2 - , WASP - , Palomar - , Lick - , Gemini - , Carlo ALto - , Caucasian Observatory of Sternberg Astronomical Institute - .

Software: AstroImage (Collins et al. 2017), Isoclassify (Huber et al. 2017), isochrones (Morton 2015), MIST (Choi et al. 2016), SpecMatch-Syn (Petigura 2015), Batman (Kreidberg 2015), emcee (Foreman-Mackey et al. 2013), iSpec (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019), colte (Casagrande et al. 2021).