A Transiting Warm Giant Planet around the Young Active Star TOI-201

2.1.1. TESS

TOI-201 was observed by the TESS mission between 2018 July 25 and 2019 July 17, in Sectors 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, and 13, using camera 4. CCD 1 was used for Sectors 3, 4, and 5, CCD 2 for Sectors 6, 7, and 8, CCD 3 for Sectors 10, 11, and 12, and CCD 4 for Sectors 1, 2, and 13. Currently, it is also being observed as part of the extended mission; the light curves from Sectors 27 and 28, which were observed between 2020 July 5 and August 25, were also incorporated into the analysis. Camera 4 in CCD 4 was used for both these Sectors.

The 2 minute cadence data for TOI-201 were processed in the TESS Science Processing Operation Center (SPOC; Jenkins et al. 2016) pipeline. Two potential transit signals were identified in the SPOC transit search (Jenkins 2002; Jenkins et al. 2010, 2020) of the TOI-201 light curve. These were designated as TESS Objects of Interest (TOIs) by the TESS Science Office based on SPOC data validation results (Twicken et al. 2018; Li et al. 2019) indicating that both signals were consistent with transiting planets. The planetary candidates are listed in the ExoFOP-TESS archive ³² : TOI-201.01, with a period of P₀₁ = 52.978306 days, and TOI-201.02, with a period of P₀₂ = 5.849173 days. The full PDCSAP light curve (Smith et al. 2012; Stumpe et al. 2012, 2014), obtained from the MAST archive, is shown in Figure 1 (top panel). Any points that were flagged as being of low quality have been removed. Six full transits of TOI-201.01 are clearly visible, in Sectors 2, 4, 6, 10, 12, and 28. A partial transit is also visible in Sector 8, at the edge of a five day gap in the light curve (Figure 1, bottom panel). This gap is due to an instrument turn-off between TJD ³³ 1531.74 and TJD 1535.00, caused by an interruption in communications between the instrument and spacecraft. The flux is clearly overestimated for the first ∼0.5 days after the gap. This artifact appears to have been introduced in the SPOC PDC processing, as the SAP light curve shows a low flux level for this period, which is likely due to the camera temperature change of ∼20° during the instrument turn-off, as detailed in the TESS Data Release Notes for Sector 8, DR10. ³⁴ The transits of TOI-201.02 have a much shallower depth (only 0.128 ± 0.013 mmag, compared to 6.843 ± 0.058 mmag for TOI-201.01), and are hence not visually obvious in the light curve.

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2.1.2. Next Generation Transit Survey

Due to the relatively large 21'' pixel size of TESS, nearby companions can contaminate its photometry. It is therefore necessary to identify possible contaminating sources, which can create false positives or dilute the transits. Ground-based photometry plays an important role in disentangling these false positives. In this context, The Next Generation Transit Survey (NGTS; Wheatley et al. 2018) observed TOI-201 on 2019 September 19, obtaining a clear ingress signal (Figure 2). Two telescopes were used, with the custom NGTS filter (520–890 nm). A total of 2484 images were obtained with an exposure time of 10 s, for an overall cadence (exposure, read out, etc.) of 13 s. The images were reduced with a custom aperture photometry pipeline (Bryant et al. 2020), using an aperture with a radius of 7 pixels (35'').

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High-resolution imaging is a valuable tool for rejecting false-positive scenarios for TESS candidates. In this context, the Southern Astrophysical Research (SOAR) TESS survey (Ziegler et al. 2020) has observed TESS planet candidate hosts with speckle imaging using the high-resolution camera (HRCam) imager on the 4.1 m SOAR telescope at Cerro Pachón, Chile (Tokovinin 2018). TOI-201 was observed on the night of 2019 February 18, with no nearby sources detected within 3''. The contrast curve and auto-correlation function are shown in Figure 3.

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The WINE consortium carried out spectroscopic follow-up of TOI-201 with the FEROS and HARPS spectrographs. In addition to these, we also obtained data from the CORALIE and Minerva-Australis teams. Finally, TOI-201 was observed once with the Network of Robotic Echelle Spectrographs (NRES), for the purpose of stellar parameter determination.

2.3.1. FEROS

2.3.2. HARPS

2.3.3. CORALIE

2.3.4.  Minerva-Australis

2.3.5. NRES

In order to characterize the host star, we first used the co-added HARPS spectra to determine the atmospheric parameters. We employed the ZASPE code (Brahm et al. 2017b), which compares the observed spectrum to a grid of synthetic models generated from the ATLAS9 model atmospheres (Castelli & Kurucz 2003) in order to determine the effective temperature T_eff, surface gravity $\mathrm{log}g$, metallicity [Fe/H], and projected rotational velocity $v\ \sin i$.

Next, we followed the second procedure described in Brahm et al. (2019) to determine the physical parameters. To summarize, we compare the broadband photometric measurements, converted to absolute magnitudes using the Gaia DR2 (Gaia Collaboration et al. 2016, 2018) parallax, with the stellar evolutionary models of Bressan et al. (2012). We use the emcee package (Foreman-Mackey et al. 2013) to sample the posterior distributions. Through this procedure, we determine the age, mass, radius, luminosity, density, and extinction. We also obtain new values for T_eff and $\mathrm{log}g$, the last of which is more precise than the one previously determined through ZASPE. Therefore, we iterated the entire procedure, using the new $\mathrm{log}g$ as an additional input parameter for ZASPE. One iteration was sufficient for the $\mathrm{log}g$ value to converge. The stellar parameters and observational properties of TOI-201 are presented in Table 1. The quoted error bars for the stellar parameters are internal errors, computed as the ±1σ interval around the median of the posterior for each parameter; they do not take into account any systematic errors on the stellar models. The parameters we derive are consistent at 1σ with those obtained from the NRES spectrum (Section 2.3.5). We find that TOI-201 is a young F-type star.

Table 1. Stellar Parameters of TOI-201

Parameter	Value	Reference
Names	HD 39474
	TIC 350618622, TOI-201	TESS
	J05493641-5454386	2MASS
	4767547667180525696	Gaia DR2
R.A. (J2000)	05h49m364138946584	Gaia DR2
Decl. (J2000)	− 54h54m38552783926	Gaia DR2
pmR.A. (mas yr−1)	7.731 ± 0.052	Gaia DR2
pmdecl. (mas yr−1)	66.448 ± 0.058	Gaia DR2
π (mas)	8.7566 ± 0.0265	Gaia DR2
T (mag)	8.5822 ± 0.006	TESS
B (mag)	10.104 ± 0.055	APASS
V (mag)	9.715 ± 0.079	APASS
J (mag)	8.103 ± 0.029	2MASS
H (mag)	7.923 ± 0.036	2MASS
Ks (mag)	7.846 ± 0.024	2MASS
Teff (K)	6394 ± 75	this work
Spectral type	F6V	PM13
Fe/H (dex)	0.240 ± 0.036	this work
$\mathrm{log}g$ (dex)	4.318 ± 0.014	this work
$v\sin i$ (km s−1)	9.52 ± 0.278	this work
R⋆ (R⊙)	1.317 ± 0.011	this work
M⋆ (M⊙)	1.316 ± 0.027	this work
L⋆ (L⊙)	2.6 ± 0.1	this work
ρ⋆ (g cm−3)	0.81 ± 0.03	this work
Age (yr)	${0.87}_{-0.49}^{+0.46}$	this work
AV (mag)	0.11 ± 0.05	this work
$\mathrm{log}{R}_{\mathrm{hk}}^{{\prime} }$	−4.76 ± 0.04	this work

Note. TESS: TESS Input Catalog (Stassun 2019); 2MASS: Two-micron All Sky Survey (Skrutskie et al. 2006); Gaia DR2: Gaia Data Release 2 (Gaia Collaboration et al. 2016, 2018); APASS: AAVSO Photometric All-Sky Survey (Munari et al. 2014); PM13: using the tables of Pecaut & Mamajek (2013).

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In this section, we present the analysis of the FEROS and HARPS spectra, all of which were processed using the CERES pipeline. For homogeneity, we do not include the CORALIE and Minerva-Australis data in this section, as they were processed using the respective instrument pipelines. Additionally, the FEROS and HARPS data have longer temporal baselines, covering both the 2018–2019 and 2019–2020 observing seasons, whereas CORALIE and Minerva-Australis only observed TOI-201 during the 2018–2019 season.

The generalized Lomb–Scargle (GLS) periodograms of the joint FEROS and HARPS RV and activity indices time series are presented in Figure 4. The 52.9 day period of the planetary candidate TOI-201.01 is highlighted. There is a clear, highly significant peak close to this period in the RV periodogram, as well as several significant long-period peaks. We do not find significant peaks close to ∼53 days for any of the activity indices, indicating that the signal in the RVs is likely to be planetary in nature. On the other hand, there are several short- and long-term signatures in the activity indices. There is no clear rotation period in the light curve according to Canto Martins et al. (2020), but given the radius and $v\sin i$ reported in Table 1, we may expect a period of ∼7 days (assuming no misalignment); there is a peak at ∼8 days in the RVs, and hints of peaks at the same period in the log(${R}_{\mathrm{HK}}^{{\prime} }$) Na ii and He i periodograms. There are also long-period peaks at ∼300 days in both the H_α and log(${R}_{\mathrm{HK}}^{{\prime} }$) periodograms, similar to that seen in the RVs. Additionally, there are peaks at ∼40 days in the Na ii and He i periodograms, with no obvious correspondence in the RVs.

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Correlations between the bisector spans and the RVs can also indicate a stellar origin for radial velocity variations (e.g., Queloz et al. 2001a). The RV measurements are plotted against the bisector spans in Figure 5 for both FEROS and HARPS data. Spearman correlation tests indicate no significant correlation between the bisector spans and the radial velocities, nor between the bisector spans and the orbital phases of TOI-201.01, for either data set. For FEROS, we find a Spearman correlation coefficient r_s = −0.31 with p-value = 0.03 between the RVs and bisector spans, and r_s = −0.02 with p-value = 0.09 between the orbital phases and bisector spans; for HARPS, we find r_s = 0.15 with p-value = 0.38 between the RVs and bisector spans, and r_s = −0.13 with p-value = 0.44 between the orbital phases and bisector spans.

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In order to further verify that the ∼53 day signal is planetary in nature, we also computed the Phase Distance Correlation (PDC) periodogram (Zucker 2018) for the FEROS data. We find a stronger signal at the 53 day period in the PDC periodogram than in a comparison GLS periodogram, as expected for eccentric orbits, as shown in Figure 6. We also ran the recent PDC extension, the USuRPER (Binnenfeld et al. 2020), which is designed to account for fluctuations in the entire spectral shape. A prominent peak is visible in the USuRPER low-frequency region (Figure 6). This result strengthens the finding that those signals are caused by some sort of periodic variation in the spectral feature shape. Both the PDC and USuRPER periodograms are implemented in the SPARTA code library (Shahaf et al. 2020).

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We use the juliet python package (Espinoza et al. 2019) to model the joint FEROS and HARPS RVs. This tool allows us to jointly fit photometric data (using the batman package; Kreidberg 2015) and RVs (using the radvel package, Fulton et al. 2018), and also to incorporate Gaussian processes (GPs) (via the celerite package; Foreman-Mackey et al. 2017). The parameter space is explored through nested sampling, using the MultiNest algorithm (Feroz et al. 2009) in its python implementation, PyMultiNest (Buchner et al. 2014), or the dynesty package (Speagle 2020).

We tested six models for the radial velocities: a flat model with no Keplerian components; a single circular planet; a single eccentric planet; two eccentric planets; a single eccentric planet plus a quadratic trend to model long-term effects; and a single eccentric planet plus a GP to account for stellar activity. The full priors for each model are listed in Table 2, and the posteriors in Table 3. For all Keplerian components, we used the periods P₀₁, P₀₂ and epochs T0₀₁, T0₀₂ listed in ExoFOP–TESS for candidates TOI-201.01 and TOI-201.02 respectively as initial constraints. For eccentric models, we used the ($e\ \sin \omega ,e\cos \omega$) parameterization.

Table 2. Prior Parameter Distributions for the Radial Velocity Analysis

Parameter	Distribution	Models
μHARPS (km s−1)	${ \mathcal U }(-30,30)$	1, 2, 3, 4, 5, 6
μFEROS (km s−1)	${ \mathcal U }(-30,30)$	1, 2, 3, 4, 5, 6
σHARPS (km s−1)	${ \mathcal J }(0.001,100)$	1, 2, 3, 4, 5, 6
σFEROS (km s−1)	${ \mathcal J }(0.001,100)$	1, 2, 3, 4, 5, 6
P01 (days)	${ \mathcal N }(52.978306,0.1)$	2, 3, 4, 5, 6
T001 (days)	${ \mathcal N }(2458376.052124,0.1)$	2, 3, 4, 5, 6
K01 (km s−1)	${ \mathcal U }(0,1)$	2, 3, 4, 5, 6
$e\sin {\omega }_{01}$	${ \mathcal U }(-1,1)$	3, 4, 5, 6
$e\cos {\omega }_{01}$	${ \mathcal U }(-1,1)$	3, 4, 5, 6
P02 (days)	${ \mathcal N }(5.849173,0.1)$	4
T002 (days)	${ \mathcal N }(2458327.244194,0.1)$	4
K02 (km s−1)	${ \mathcal U }(0,1)$	4
$e\sin {\omega }_{02}$	${ \mathcal U }(-1,1)$	4
$e\cos {\omega }_{02}$	${ \mathcal U }(-1,1)$	4
rvslope ((km s−1) day−1)	${ \mathcal U }(-100,100)$	5
rvquad ((km s−1) day−2)	${ \mathcal U }(-100,100)$	5
σGP	${ \mathcal J }(0.01,100)$	6
ρGP	${ \mathcal J }(0.01,100)$	6

Note. ${ \mathcal U }(a,b)$ indicates a uniform distribution between a and b; ${ \mathcal N }(a,b)$ a normal distribution with mean a and standard deviation b; ${ \mathcal J }(a,b)$ a Jeffreys or log-uniform distribution between a and b.

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Table 3. Radial Velocity Analysis for the Different Models Tested

Parameter	Flat Model (1)	1 Planet Circ. (2)	1 Planet Ecc. (3)	2 Planet Ecc. (4)	1 Planet + quad (5)	1 Planet + GP (6)
μHARPS (km s−1)	${16.999}_{-0.038}^{+0.009}$	${16.92}_{-0.01}^{+0.01}$	${16.92}_{-0.01}^{+0.01}$	${17.04}_{-0.05}^{+0.04}$	${16.884}_{-0.004}^{+0.003}$	${16.91}_{-0.06}^{+0.05}$
μFEROS (km s−1)	${16.983}_{-0.002}^{+0.010}$	${16.834}_{-0.003}^{+0.004}$	${16.875}_{-0.006}^{+0.005}$	${16.89}_{-0.01}^{+0.01}$	${16.855}_{-0.004}^{+0.003}$	${16.88}_{-0.06}^{+0.05}$
σHARPS (km s−1)	${0.148}_{-0.009}^{+0.007}$	${0.157}_{-0.003}^{+0.003}$	${0.068}_{-0.008}^{+0.012}$	${0.40}_{-0.04}^{+0.05}$	${0.011}_{-0.001}^{+0.002}$	${0.012}_{0.001}^{0.001}$
σFEROS (km s−1)	${0.189}_{-0.005}^{+0.013}$	${0.294}_{-0.004}^{+0.006}$	${0.047}_{-0.006}^{+0.005}$	${0.093}_{-0.008}^{+0.010}$	${0.020}_{-0.002}^{+0.003}$	${0.013}_{0.002}^{0.002}$
P01 (days)	⋯	${52.787}_{-0.006}^{+0.006}$	${52.99}_{-0.09}^{+0.08}$	${53.03}_{-0.06}^{+0.04}$	${53.04}_{-0.09}^{+0.08}$	${53.04}_{-0.06}^{+0.05}$
T001 (days)	⋯	${2458376.130}_{-0.009}^{+0.07}$	${2458375.97}_{-0.05}^{+0.04}$	${2458376.00}_{-0.04}^{+0.05}$	${2458376.1}_{-0.1}^{+0.1}$	${2458376.11}_{-0.05}^{+0.05}$
K01 (km s−1)	⋯	${0.054}_{-0.005}^{+0.005}$	${0.027}_{-0.009}^{+0.014}$	${0.08}_{-0.04}^{+0.04}$	${0.026}_{-0.003}^{+0.003}$	${0.016}_{-0.005}^{+0.005}$
$e\sin {\omega }_{01}$	⋯	⋯	${0.44}_{-0.22}^{+0.19}$	${0.30}_{-0.33}^{+0.25}$	${0.31}_{-0.09}^{+0.09}$	${0.20}_{-0.19}^{+0.16}$
$e\cos {\omega }_{01}$	⋯	⋯	${0.21}_{-0.12}^{+0.16}$	${0.50}_{-0.36}^{+0.18}$	${0.03}_{-0.08}^{+0.09}$	$-{0.10}_{-0.20}^{+0.19}$
e01	⋯	⋯	${0.52}_{-0.20}^{+0.18}$	${0.64}_{-0.29}^{+0.18}$	${0.32}_{-0.09}^{+0.09}$	${0.30}_{-0.13}^{+0.16}$
ω01 (deg)	⋯	⋯	${61}_{-18}^{+18}$	${33}_{-17}^{+26}$	${85}_{-14}^{+16}$	${110}_{-45}^{+39}$
P02 (days)	⋯	⋯	⋯	${5.85}_{-0.05}^{+0.03}$	⋯	⋯
T002 (days)	⋯	⋯	⋯	${2458327.16}_{-0.05}^{+0.04}$	⋯	⋯
K02 (m s−1)	⋯	⋯	⋯	${0.02}_{-0.01}^{+0.02}$	⋯	⋯
$e\sin {\omega }_{02}$	⋯	⋯	⋯	$-{0.08}_{-0.19}^{+0.28}$	⋯	⋯
$\cos {\omega }_{02}$	⋯	⋯	⋯	$-{0.56}_{-0.28}^{+0.41}$	⋯	⋯
e02	⋯	⋯	⋯	${0.62}_{-0.34}^{+0.27}$	⋯	⋯
ω02	⋯	⋯	⋯	${156}_{-35}^{+18}$	⋯	⋯
rvslope ((km s−1) day−1)	⋯	⋯	⋯	⋯	${0.00009}_{-0.00005}^{+0.00005}$	⋯
rvquad ((km s−1) day−2)	⋯	⋯	⋯	⋯	${0.00000013}_{-0.00000011}^{+0.00000011}$	⋯
σGP	⋯	⋯	⋯	⋯	⋯	${0.10}_{-0.02}^{+0.04}$
ρGP	⋯	⋯	⋯	⋯	⋯	${55}_{-14}^{+20}$
$\mathrm{ln}(Z)$	32.9 ± 0.2	1.16 ± 0.02	126.7 ± 0.1	25.96 ± 0.01	173.60 ± 0.01	185.71 ± 0.02
${\rm{\Delta }}\mathrm{ln}{Z}_{1}$	⋯	≈−32	≈94	≈−7	≈141	≈153

Note. Top: posterior parameter distributions. Bottom: log-evidence and difference to the baseline no-planet model. Model 6 is the final adopted model.

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• 1.  
  no planet. This model assumes that all the RV variations are due solely to jitter. The only free parameters are the systemic RVs and jitters for the two instruments. This model effectively provides us with a baseline log-evidence $\mathrm{ln}(Z)=32.9\pm 0.2$.
• 2.  
  one-planet, circular. In this model, we add a Keplerian with Gaussian priors for the period and T0 centered on those provided by the light curve, and an eccentricity fixed to zero. We find a surprisingly low log-evidence of $\mathrm{ln}(Z)=1.16\pm 0.02$. As can be seen in Table 3, the instrumental jitter values are very similar to those of the flat model, suggesting that the RV variations may be absorbed by this jitter.
• 3.  
  one-planet, eccentric. In this model, we allow for free eccentricity and ω for the Keplerian. We find a much higher log-evidence of $\mathrm{ln}(Z)=126.7\pm 0.1$.
• 4.  
  two planets, eccentric. In addition to the Keplerian with priors centered on the parameters of TOI-201.01, we include a second Keplerian (also with free eccentricity and ω) to represent TOI-201.02. We find a decreased log-evidence with respect to model 3 of $\mathrm{ln}(Z)=25.96\,\pm 0.01$, and the eccentricity for the 53 day Keplerian is increased.
• 5.  
  one-planet, eccentric, plus quadratic trend. In this model, we test the inclusion of a quadratic trend to model long-term effects. The intercept parameter is fixed to zero, as otherwise it becomes degenerate with the instrumental offsets. We find a log-evidence of $\mathrm{ln}(Z)=173.60\pm 0.01$.
• 6.  
  one-planet, eccentric, plus GP. In this model, we incorporate a GP, to account for stellar activity. We use an (approximate) Matern kernel, as implemented in celerite. We find a log-evidence of $\mathrm{ln}(Z)=185.71\pm 0.02$.

The model with a single eccentric Keplerian and a GP is clearly favored, with a ${\rm{\Delta }}\mathrm{ln}{Z}_{\mathrm{6,3}}\approx 59$ compared to the model with only a single eccentric planet, and better accounts for other trends in the data, with ${\rm{\Delta }}\mathrm{ln}{Z}_{\mathrm{6,5}}\approx 12$ compared to the model with a single eccentric planet and a quadratic trend. Likewise, the difference from the flat model is ${\rm{\Delta }}\mathrm{ln}{Z}_{\mathrm{6,1}}\approx 153$. This allows us to confirm the candidate planet TOI-201.01, referred to as TOI-201 b hereafter. The full model and components, and the FEROS and HARPS RVs, are shown in Figure 7.

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We inspected the residuals of the RVs after subtracting model 6 to check if there were any significant periodicities remaining. In particular, we wish to verify whether there is any signal at the period of the planetary candidate TOI-201.02. Figure 8 (top panel) shows the periodogram of the residuals, with the five day period of TOI-201.02 highlighted. There is no peak at or close to this period, nor any significant signals visible. We also inspected the residuals of the RVs to model 5, to rule out the possibility that the signal could be absorbed by the GP. Figure 8 (middle panel) shows their periodogram; there are no significant signals at any period, and a peak emerges around the ∼300 day period seen in the H_α and log(${R}_{\mathrm{HK}}^{{\prime} }$) periodograms, suggesting this model is less efficient at suppressing the long-term activity-induced RV variations.

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The question arises as to whether we can expect TOI-201.02 to be detectable in RVs. We use the radius of TOI-201.02, and the revised mass–radius relations of Otegi et al. (2020), to estimate a mass of M_p ≈ 6.38 M_⊕ for TOI-201.02, which leads to an RV semi-amplitude of K ≈ 1.88 m s⁻¹. While such small amplitudes are in principle detectable with HARPS, this falls below our median RV error, and the periodogram of the residuals to model 6 for HARPS data alone (Figure 8, bottom panel) shows no significant signals. We also tested whether such a planet would be recoverable from our data by injecting a Keplerian into the randomly shuffled residuals. For the injected Keplerian, we assumed a circular orbit, and used the period and epoch from the transit data and the mass estimated from the radius. The periodogram of these RVs showed no significant signals at any period.

Although we cannot detect TOI-201.02 in the RV data, we can still use these data to estimate its maximum mass. For this, we ran a more constrained two-planet model on the FEROS and HARPS data, fixing the periods and epochs to those listed in ExoFOP–TESS. We also fixed the eccentricity of the inner planet to zero, since we can expect its orbit to be circularized by its proximity to the host star. Using the semi-amplitude of the resulting Keplerian fit, $K={1.76}_{-1.14}^{+1.84}\,{\rm{m}}\,{{\rm{s}}}^{-1}$, we estimate a maximum mass for TOI-201.02 of ${M}_{\max }\approx 37.5\,{M}_{\oplus }$ with 98% confidence.

Having shown that TOI-201 b can be detected in the RVs alone, we perform a joint modeling of the full set of RVs and transit data. We adopt a one-planet model, with $e\ \sin \omega$ and $e\ \cos \omega$ constrained using the posteriors from model 6. We also include two separate GPs: one on the joint FEROS, HARPS, CORALIE, and Minerva-Australis RVs, to account for the stellar activity, as done in model 6, and one on the TESS light curve, to account for instrumental effects such as the over-estimation of flux for the partial transit in Sector 8 (Figure 1, bottom panel). Rather than fit for the planet-to-star radius ratio and impact parameter of the orbit directly, we adopt the (r₁, r₂) parameterization of Espinoza (2018), which allows for efficient sampling with uniform priors.

We find a log-evidence of $\mathrm{ln}(Z)=1236042.914\pm 0.008$. The priors are listed in Table 4, and the posteriors in Table 5. Figure 9 shows the phase-folded data and the full model for the light curves and RVs. Using the stellar parameters obtained in Section 3.1, and the posterior distributions of the full model, we compute a mass of ${0.42}_{-0.03}^{+0.05}\,{M}_{{\rm{J}}}$ and a radius of ${1.008}_{-0.015}^{+0.012}\,{R}_{{\rm{J}}}$ for TOI-201 b. The physical parameters and derived orbital parameters are also listed in Table 5.

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Table 4. Prior Parameter Distributions for the Joint Transit and Radial Velocity Analysis

Parameter	Distribution
μHARPS (km s−1)	${ \mathcal U }(16.85,16.96)$
μFEROS (km s−1)	${ \mathcal U }(16.82,16.93)$
μCORALIE (km s−1)	${ \mathcal U }(-30,30)$
μMINERVA (km s−1)	${ \mathcal U }(-30,30)$
σHARPS (km s−1)	${ \mathcal J }(0.011,0.013)$
σFEROS (km s−1)	${ \mathcal J }(0.011,0.015)$
σCORALIE (km s−1)	${ \mathcal J }(0.001,100)$
σMINERVA (km s−1)	${ \mathcal J }(0.001,100)$
Pb (days)	${ \mathcal N }(52.978306,0.1)$
T0b (days)	${ \mathcal N }(2458376.052124,0.1)$
Kb (km s−1)	${ \mathcal U }(0.011,0.021)$
$e\sin {\omega }_{{\rm{b}}}$	${ \mathcal U }(0.01,0.36)$
$e\cos {\omega }_{{\rm{b}}}$	${ \mathcal U }(-0.30,0.09)$
σGP,RV	${ \mathcal J }(0.01,100)$
ρGP,RV	${ \mathcal J }(0.01,100)$
r1,b	${ \mathcal U }(0,1)$
r2,b	${ \mathcal U }(0,1)$
ρ	${ \mathcal J }(100.,10000.)$
q1,TESS	${ \mathcal U }(0,1)$
q2,TESS	${ \mathcal U }(0,1)$
md,TESS	1.0 (fixed)
mflux,TESS	${ \mathcal N }(0,0.1)$
σTESS	${ \mathcal J }(0.1,1000)$
σGP,TESS	${ \mathcal J }(1\times {10}^{-6},1000000)$
ρGP,TESS	${ \mathcal J }(0.001,1000)$
q1,NGTS	${ \mathcal U }(0,1)$
q2,NGTS	${ \mathcal U }(0,1)$
md,NGTS	1.0 (fixed)
mflux,NGTS	${ \mathcal N }(0,0.1)$
σNGTS	${ \mathcal J }(0.1,1000)$

Note. ${ \mathcal U }(a,b)$ indicates a uniform distribution between a and b; ${ \mathcal N }(a,b)$ a normal distribution with mean a and standard deviation b; ${ \mathcal J }(a,b)$ a Jeffreys or log-uniform distribution between a and b.

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Table 5. Parameters for Planet TOI-201 b

Parameter	Distribution
μHARPS (km s−1)	${16.92}_{-0.01}^{+0.01}$
μFEROS (km s−1)	${16.89}_{-0.01}^{+0.01}$
μCORALIE (km s−1)	${16.87}_{-0.01}^{+0.02}$
μMINERVA (km s−1)	${0.02}_{-0.01}^{+0.01}$
σHARPS (km s−1)	${0.0117}_{-0.0005}^{+0.0008}$
σFEROS (km s−1)	${0.014}_{-0.001}^{+0.001}$
σCORALIE (km s−1)	${0.019}_{-0.007}^{+0.009}$
σMINERVA (km s−1)	${0.026}_{-0.004}^{+0.004}$
Pb (days)	${52.97818}_{-0.00004}^{+0.00004}$
T0b (BJD)	${2458376.0520}_{-0.0003}^{+0.0003}$
Kb (km s−1)	${0.019}_{-0.002}^{+0.001}$
$e\sin {\omega }_{{\rm{b}}}$	${0.28}_{-0.09}^{+0.06}$
$e\cos {\omega }_{{\rm{b}}}$	${0.04}_{-0.07}^{+0.04}$
σGP	${0.025}_{-0.006}^{+0.008}$
ρGP	${70}_{-27}^{+21}$
r1,b	${0.82}_{-0.01}^{+0.01}$
r2,b	${0.0786}_{-0.0007}^{+0.0010}$
ρ	${854}_{-154}^{+288}$
q1,TESS	${0.22}_{-0.06}^{+0.06}$
q2,TESS	${0.25}_{-0.18}^{+0.33}$
md,TESS	1.0
mflux,TESS	$-{0.00002}_{-0.00002}^{+0.00002}$
σTESS	${73}_{-5}^{+5}$
σGP,TESS	${0.00030}_{-0.00001}^{+0.00001}$
ρGP,TESS	${0.64}_{-0.03}^{+0.03}$
q1,NGTS	${0.47}_{-0.19}^{+0.23}$
q2,NGTS	${0.38}_{-0.25}^{+0.32}$
md,NGTS	1.0
mflux,NGTS	${0.0001}_{-0.0002}^{+0.0002}$
σNGTS	${5}_{-4}^{+56}$
eb	${0.28}_{-0.09}^{+0.06}$
ωb [deg]	${82}_{-9}^{+14}$
a [au]	${0.30}_{-0.03}^{+0.02}$
Mb [MJ]	${0.42}_{-0.03}^{+0.05}$
Rb [RJ]	${1.008}_{-0.015}^{+0.012}$
Teq a [K]	${759}_{-26}^{+37}$

Notes. Top: posterior parameter distributions for the joint transit and RV Analysis. Bottom: derived orbital parameters and physical parameters.

^a Time-averaged equilibrium temperature, using Equation (16) of Méndez & Rivera-Valentín (2017) assuming bond albedo A = 0, heat distribution β = 0.5, and emissivity = 1.

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The Minerva-Australis RVs have larger error bars and show more dispersion from the fitted model than those of the other three RV data sets, as can be clearly seen in Figure 9((b), bottom panel). Therefore, we also tested an analogous model in which the Minerva-Australis RVs were not included. The resulting parameters are the same within uncertainties, and the uncertainties on the parameters are similar for both models. This being the case, we prefer the model including the Minerva-Australis RVs.