The TESS-Keck Survey. VIII. Confirmation of a Transiting Giant Planet on an Eccentric 261 Day Orbit with the Automated Planet Finder Telescope^*

Gas giant planets have been found to reside in many extrasolar planetary systems. The diversity in their sizes, masses, orbits, compositions, and formation pathways has been the subject of numerous studies. However, selection biases often cloud our understanding. For instance, the sensitivity of the transit method wanes for planets on orbits beyond a few tenths of an au owing to the inverse relation between transit probability and semimajor axis. Consequently, the vast majority of known exoplanets with ≳1 au orbits have been discovered via Doppler spectroscopy (e.g., Mayor et al. 2011; Fulton et al. 2021). Planet mass can be inferred from time series radial velocity (RV) observations but, without a transit, the planet radius and thereby bulk density remains unknown.

A critical component of the bulk composition for giant planets is the total mass of elements heavier than H and He (e.g., Guillot et al. 2006; Miller & Fortney 2011; Thorngren et al. 2016; Teske et al. 2019). This property is inferred using structural evolution models along with the measured planetary mass, radius, stellar age, and incident flux (e.g., Thorngren & Fortney 2019). Numerous theoretical planet formation studies have found that the correlation between the total mass of heavy elements in giant planets—or, similarly, the metal enrichment relative to the host star—and planet mass is a useful tracer of planet formation processes (e.g., Mordasini et al. 2014; Hasegawa et al. 2018; Ginzburg & Chiang 2020; Shibata et al. 2020). Probing this giant planet mass–metallicity correlation along a third axis in orbital properties (i.e., period or separation) could prove informative. Yet previous efforts have simply not had a large enough sample size of giant planets on orbits wider than a few 0.1 au to conduct such an investigation (Miller & Fortney 2011; Thorngren et al. 2016).

Transit surveys such as the Kepler (Borucki et al. 2010; Thompson et al. 2018) and Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) missions occasionally detect giant planet candidates with orbital periods of 100–1000 days (e.g., Wang et al. 2015; Foreman-Mackey et al. 2016; Osborn et al. 2016; Uehara et al. 2016; Herman et al. 2019; Kawahara & Masuda 2019; Eisner et al. 2021). These candidates warrant close scrutiny, at least based on the ∼50% false-positive rate for giant planets with similar orbits found for the Kepler mission (Santerne et al. 2014; Dalba et al. 2020a). Following vetting, long-term RV monitoring is often required to measure the planet mass, which then enables modeling of the bulk metallicity (e.g., Beichman et al. 2016; Dubber et al. 2019; Santerne et al. 2019; Dalba et al. 2021a, 2021b). TESS planets with orbital periods on the order of 100 days or more will typically be detected as single-transit events owing to the observational strategy of the TESS mission (e.g., LaCourse & Jacobs 2018; Villanueva et al. 2019; Díaz et al. 2020; Cooke et al. 2021). In this case, the RV monitoring is also necessary to determine the orbital period.

Here we describe the discovery and investigation of a 24 hr single-transit event observed for HD 238894, hereafter referred to as TOI-2180 b. The host star, TOI-2180 (TIC 298663873), is a bright (V = 9.2), slightly evolved G5 star. The confirmation of TOI-2180 b is notable relative to the current sample of TESS exoplanets, including those identified as single transits, as it is the first to surpass an orbital period of 100 days. ⁵⁸ In Section 2, we describe the TESS observations of TOI-2180, along with the follow-up photometric, imaging, and spectroscopic data sets. In Section 3, we discuss the consistency of the transit and RV data, which are then jointly modeled to determine the TOI-2180 system properties. We find that TOI-2180 b is a 2.7 M_J giant planet on a 261 day orbit with an orbital eccentricity of 0.368. In Section 4, we describe a global effort to detect an additional transit of TOI-2180 b from the ground. Although this effort failed to detect the transit, the nondetections provided a substantial improvement in precision on the orbital period. In Section 5, we determine the bulk heavy-element mass of TOI-2180 b. In Section 6, we use the long-term acceleration of TOI-2180 to place limits on the properties of a distant massive companion. In Section 7, we place TOI-2180 b in the context of other transiting giant planets and discuss the prospects for future characterization of the system. Lastly, in Section 8, we summarize our work.

2.1. TESS Photometry

TESS observed TOI-2180 (TIC 298663873) at a 2 minute (fast) cadence for the entirety of Cycle 2 of its primary mission (Sectors 14–26) and in Sectors 40 and 41 of its extended mission. The image data were processed by the Science Processing Operations Center at NASA Ames Research Center (Jenkins et al. 2016) to extract photometry from this target. A search for transiting planets failed to find a transit signature with two or more transits. Only a single transit event was observed in Sector 19 (2019 November 28 through 2019 December 22). This Sector 19 single transit was first identified by citizen scientists with the light-curve processing software LcTools (Schmitt et al. 2019), leading to early commencement of our RV follow-up campaign. In 2020 May, the Planet Hunters TESS collaboration (Eisner et al. 2020) announced this star as a community TESS object of interest (cTOI). In 2020 August, its disposition was elevated to TOI (Guerrero et al. 2021).

We downloaded the Sector 19 2 minute cadence light curve of TOI-2180 from the Mikulski Archive for Space Telescopes using the lightkurve package (Lightkurve Collaboration et al. 2018). We used the presearch data conditioning simple aperture photometry (PDCSAP) flux for which most of the high-frequency noise was removed (Smith et al. 2012; Stumpe et al. 2012, 2014). The PDCSAP light curve exhibited low-frequency noise features that we removed using a Savitzky–Golay filter after masking the clear transit event. The raw and flattened light curves, centered on the ∼0.5% transit of TOI-2180 b, are shown in Figure 1.

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Under the assumption of a circular central transit, Winn (2010, Equation (19)) showed how the transit duration (T) and stellar bulk density (ρ_⋆) can give an estimate of the orbital period (P) following

$$\begin{eqnarray}&&T\approx 13\ \mathrm{hr}\ {\left(\displaystyle \frac{P}{1\ \mathrm{yr}}\right)}^{1/3}{\left(\displaystyle \frac{{\rho }_{\star }}{{\rho }_{\odot }}\right)}^{-1/3},\end{eqnarray} \tag{ 1 }$$

where P has units of years, and ρ_☉ is the solar bulk density. For T = 24 hr and ρ_⋆ = 0.335 g cm⁻³ from the TESS Input Catalog (TIC; Stassun et al. 2019), Equation (1) gives P ≈ 547 ± 111 days assuming reasonable uncertainty in T and ρ_⋆. Combined with the nondetection of a matching transit event in the other Cycle 2 sectors, this possible orbital period suggested that TOI-2180 b was likely to be one of only a few long-period planets predicted to be detected by TESS through single-transit events (Villanueva et al. 2019).

2.2. Speckle Imaging

We acquired a high-resolution speckle image of TOI-2180 to search for nearby neighboring stars that might indicate the false-positive nature of the TESS single-transit event. We observed TOI-2180 on 2020 June 6 using the 'Alopeke speckle instrument on the Gemini-North telescope ⁵⁹ located on Maunakea in Hawai'i. 'Alopeke acquires an image of the star in a blue (562 nm) and a red (832 nm) band simultaneously. From these images, we derived contrast curves that show the limiting magnitude difference (Δm) in each band as a function of angular separation (Howell et al. 2011). As shown in Figure 2, we achieved an ∼5 mag contrast at 01 and a nondetection of sources with Δm = 5–8.5 within 12 of TOI-2180. Given the distance to TOI-2180 (116 pc; Table 2), a 01 projected separation corresponds to ∼12 au. Although we cannot rule out a scenario whereby a luminous companion star was near conjunction with TOI-2180 at the time of our speckle observation, we assume in what follows that TOI-2180 is likely a single star. The speckle imaging nondetection suggests that any massive object in this system other than TOI-2180 b is likely to be a late M star or a substellar object.

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The conclusion of TOI-2180 being a single star is further supported by the renormalized unit weight error (RUWE) as determined by Gaia Data Release (DR) 2 (Gaia Collaboration et al. 2018). The RUWE value for TOI-2180 is 1.01, which is typical of a single star (e.g., Belokurov et al. 2020).

2.3. Spectroscopy

Immediately following the discovery of the TESS single transit of TOI-2180, we began a Doppler monitoring campaign with the Automated Planet Finder (APF) telescope at Lick Observatory (Radovan et al. 2014; Vogt et al. 2014) as part of the TESS-Keck Survey (TKS). The TKS is a collaborative effort between the University of California, the California Institute of Technology, the University of Hawai'i, and NASA aimed at providing multisite RV follow-up for many of the planetary systems discovered by TESS (e.g., Dai et al. 2020; Dalba et al. 2020b; Chontos et al. 2021; Lubin et al. 2021; Rubenzahl et al. 2021; Weiss et al. 2021). The APF uses the Levy Spectrograph, a high-resolution (R ≈ 114,000) slit-fed optical echelle spectrometer (Radovan et al. 2010) that is ideal for bright (V ≤ 9) stars such as TOI-2180 (Burt et al. 2015). The starlight passes through a heated iodine gas cell that allows for precise wavelength calibration and instrument profile tracking. The precise RV is inferred from each spectrum using a forward-modeling procedure (Butler et al. 1996; Fulton et al. 2015). Table 1 lists the RVs collected in our campaign.

Table 1. RV Measurements of TOI-2180

BJDTDB	RV (m s−1)	SHK a	Tel.
2,458,888.063868	−16.1 ± 3.9	0.1304 ± 0.0020	APF
2,458,894.911472	−29.1 ± 4.5	0.1476 ± 0.0020	APF
2,458,899.027868	−36.3 ± 3.8	0.1463 ± 0.0020	APF
2,458,906.015644	−43.6 ± 3.2	0.1093 ± 0.0020	APF
2,458,914.011097	−38.9 ± 3.3	0.1506 ± 0.0020	APF
2,458,954.765221	−59.0 ± 4.0	0.1468 ± 0.0020	APF
2,458,961.864505	−49.7 ± 4.3	0.1323 ± 0.0020	APF
2,458,964.879814	−53.3 ± 3.1	0.1298 ± 0.0020	APF
2,458,965.811833	−47.5 ± 4.2	0.1363 ± 0.0020	APF
2,458,966.879965	−65.9 ± 5.5	0.1204 ± 0.0020	APF

Note. ^a The S_HK values from APF and Keck data have different zero-points.

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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In 2020 August, Lick Observatory and the APF shut down owing to nearby wildfires. To maintain our coverage of the emerging Keplerian RV signal, we temporarily conducted observations of TOI-2180 using the High Resolution Echelle Spectrometer (HIRES; Vogt et al. 1994) on the Keck I telescope at W. M. Keck Observatory. The reduction and analysis procedure for Keck-HIRES spectra is broadly similar to that for data from the APF (e.g., Howard et al. 2010). The full version of Table 1 also contains the Keck-HIRES RVs of TOI-2180.

The time series RVs from both telescopes are shown in the top panel of Figure 3. Our 1.5 yr baseline captured two periods of a 261 day eccentric (e ≈ 0.4) Keplerian signal, as well as a long-term acceleration. In Section 3, we will discuss the consistency of the RV data with the single transit from TESS and conduct a joint modeling of the system parameters.

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Each RV measurement is accompanied by an estimate of stellar chromospheric activity approximated as the S_HK index (Isaacson & Fischer 2010). The indicators calculated for each instrument have different zero-points. The Pearson correlation coefficient between the S_HK indices and the RVs for APF and Keck are −0.10 (from 84 data points) and 0.68 (from 15 data points), respectively. Although the Keck data demonstrate a positive correlation significant to 3.3σ, the much larger APF data set shows no correlation (<1σ). Furthermore, we do not detect significant periodicity in the S_HK time series. Both of these findings suggest that the RV signals are not affected, or only minimally so, by stellar activity.

The extraction of the APF and Keck RVs relies on a high signal-to-noise ratio (S/N) template spectrum of TOI-2180 acquired with Keck-HIRES without the iodine cell (Butler et al. 1996). We also used this spectrum for a basic spectroscopic analysis of TOI-2180 with SpecMatch (Petigura 2015; Petigura et al. 2017). This analysis indicated that TOI-2180 has an effective temperature of T_eff = 5739 ± 100 K, a surface gravity of $\mathrm{log}g=4.00\pm 0.10$, and a relative iron abundance (metallicity proxy) of [Fe/H] = 0.25 ± 0.06 dex, consistent with a slightly evolved mid-G-type star. These values are in close agreement with those listed in the TIC (Stassun et al. 2019).

2.4. Ground-based Photometry

3.1. Consistency between the Transit and the RV Data

3.2. Comprehensive System Modeling

We modeled the stellar and planetary parameters for the TOI-2180 system using the EXOFASTv2 modeling suite (Eastman et al. 2013, 2019). We include the TESS single-transit photometry, all of the RVs from Keck-HIRES and APF-Levy, and archival broadband photometry of TOI-2180 from Gaia DR2 (Gaia Collaboration et al. 2018), the Two Micron All Sky Survey (Cutri et al. 2003), and the Wide-field Infrared Survey Explorer (Cutri et al. 2014). EXOFASTv2 computes spectral energy distributions (SEDs) from MIST models and the Gaia parallax measurements and fits them to the archival photometry to infer the properties of the host star. We placed normal priors on T_eff and [Fe/H] based on the SpecMatch analysis of the high-S/N template spectrum of TOI-2180 (Section 2.3). The width of the T_eff prior was inflated to 115 K (2%), and a noise floor of 2% was applied to the bolometric flux used in the SED determination to account for systematic uncertainties inherent in the MIST models (Tayar et al. 2020). We also placed a uniform prior on extinction (A_V ≤ 0.1376) using the galactic dust maps of Schlafly & Finkbeiner (2011) and a normal prior on parallax (ϖ = 8.597 ± 0.017 mas) using the Gaia DR3 measurement corrected for the zero-point offset (Gaia Collaboration et al. 2021; Lindegren et al. 2021). These priors are summarized at the top of Table 2.

Table 2. Median Values and 68% Confidence Intervals for the Stellar Parameters for TOI-2180

Parameter	Units	Values
Informative Priors
Teff	Effective temperature (K)	${ \mathcal N }(5739,115)$
[Fe/H]	Metallicity (dex)	${ \mathcal N }(0.25,0.06)$
ϖ	Parallax (mas)	${ \mathcal N }(8.597,0.017)$
AV	V-band extinction (mag)	${ \mathcal U }(0,0.1376)$
Stellar Parameters
M*	Mass (M☉)	${1.111}_{-0.046}^{+0.047}$
R*	Radius (R☉)	${1.636}_{-0.029}^{+0.033}$
L*	Luminosity (L☉)	${2.544}_{-0.093}^{+0.091}$
Fbol	Bolometric flux (cgs)	6.01 × 10−9 ${}_{-2.2\times {10}^{-10}}^{+2.1\times {10}^{-10}}$
ρ*	Density (g cm−3)	${0.359}_{-0.016}^{+0.015}$
$\mathrm{log}g$	Surface gravity (cgs)	${4.057}_{-0.016}^{+0.015}$
Teff	Effective temperature (K)	${5695}_{-60}^{+58}$
[Fe/H]	Metallicity (dex)	0.253 ± 0.057
[Fe/H]0	Initial metallicity a (dex)	${0.269}_{-0.054}^{+0.055}$
Age	Age (Gyr)	${8.1}_{-1.3}^{+1.5}$
EEP	Equal evolutionary phase b	${452.1}_{-5.0}^{+3.9}$
AV	V-band extinction (mag)	${0.077}_{-0.048}^{+0.041}$
σSED	SED photometry error scaling	${0.69}_{-0.16}^{+0.24}$
ϖ	Parallax (mas)	8.597 ± 0.017
d	Distance (pc)	116.32 ± 0.23

Notes. See Table 3 in Eastman et al. (2019) for a detailed description of all parameters and default (noninformative) priors beyond those specified here. The ${ \mathcal N }(a,b)$ denotes a normal distribution with mean a and variance b², and ${ \mathcal U }(a,b)$ denotes a uniform distribution over the interval [a, b].

^a Initial metallicity is that of the star when it formed. ^b Corresponds to static points in a star's evolutionary history. See Section 2 of Dotter (2016).

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We gauged convergence of the EXOFASTv2 fit by the number of independent draws (Ford 2006), which exceeded 1000, and the Gelman–Rubin statistic (Gelman & Rubin 1992), which was smaller than 1.01, for every fitted parameter. From the fit parameters, numerous properties of TOI-2180 b were derived. Table 3 lists all relevant planetary parameters for TOI-2180 b. The derived planetary radius and transit depth assume no oblateness (e.g., Seager & Hui 2002) and no system of rings (e.g., Barnes & Fortney 2004; Akinsanmi et al. 2018), although TOI-2180 b could plausibly have both.

Table 3. Median Values and 68% Confidence Interval of the Planet Parameters for TOI-2180 b

Parameter	Units	Values
Planetary Parameters
P	Period a (days)	${260.79}_{-0.58}^{+0.59}$
RP	Radius (RJ)	${1.010}_{-0.019}^{+0.022}$
MP	Mass (MJ)	${2.755}_{-0.081}^{+0.087}$
TC	Time of conjunction (BJDTDB)	2,458,830.7652 ± 0.0010
a	Semimajor axis (au)	0.828 ± 0.012
i	Inclination (deg)	${89.955}_{-0.044}^{+0.032}$
e	Eccentricity	0.3683 ± 0.0073
ω*	Argument of periastron (deg)	−43.8 ± 1.3
Teq	Equilibrium temperature b (K)	${348.0}_{-3.6}^{+3.3}$
τcirc	Tidal circularization timescale (Gyr)	${54,600,000}_{-4,500,000}^{+3,800,000}$
K	RV semiamplitude (m s−1)	${87.75}_{-0.99}^{+0.98}$
$\dot{\gamma }$	RV slope c (m s−1 day−1)	−0.1205 ± 0.0043
$\ddot{\gamma }$	RV quadratic term c (m s−1 day−2)	${0.000214}_{-0.000038}^{+0.000039}$
δTESS	Transit depth in TESS band	${0.004766}_{-0.000076}^{+0.000078}$
τ	Ingress/egress transit duration (days)	${0.06044}_{-0.00063}^{+0.0019}$
T14	Total transit duration (days)	${1.0040}_{-0.0031}^{+0.0032}$
b	Transit impact parameter	${0.100}_{-0.070}^{+0.095}$
ρP	Density (g cm−3)	${3.32}_{-0.16}^{+0.14}$
log gP	Surface gravity (cgs)	${3.827}_{-0.015}^{+0.012}$
〈F〉	Incident flux (109 erg s−1 cm−2)	0.00442 ± 0.00018
TP	Time of periastron (BJDTDB)	2,458,760.7 ± 1.3
TS	Time of eclipse (BJDTDB)	${{\rm{2,458,745.41}}}_{-1.0}^{+1.00}$
bS	Eclipse impact parameter	${0.060}_{-0.042}^{+0.056}$
τS	Ingress/egress eclipse duration (days)	${0.03593}_{-0.00088}^{+0.00098}$
TS,14	Total eclipse duration (days)	0.599 ± 0.013
δS,2.5μm	Blackbody eclipse depth at 2.5 μm (ppm)	${0.00237}_{-0.00032}^{+0.00034}$
δS,5.0μm	Blackbody eclipse depth at 5.0 μm (ppm)	1.54 ± 0.10
δS,7.5μm	Blackbody eclipse depth at 7.5 μm (ppm)	${11.29}_{-0.50}^{+0.49}$
TESS Parameters
u1	Linear limb-darkening coefficient	0.316 ± 0.029
u2	Quadratic limb-darkening coefficient	0.248 ± 0.044
APF-Levy Parameters
γrel	Relative RV offset c (m s−1)	$-{30.0}_{-1.3}^{+1.2}$
σJ	RV jitter (m s−1)	${4.16}_{-0.62}^{+0.67}$
Keck-HIRES Parameters
γrel	Relative RV offset c (m s−1)	$-{12.7}_{-1.5}^{+1.4}$
σJ	RV jitter (m s−1)	${4.86}_{-0.93}^{+1.3}$

Notes. See Table 3 in Eastman et al. (2019) for a detailed description of all parameters and default (noninformative) priors.

^a This orbital period is derived from the full posterior from the EXOFASTv2 fit. See Section 4 for a description of the likely orbital period values (${260.18}_{-0.30}^{+0.19}$ or ${261.76}_{-0.16}^{+0.29}$ days) after the ground-based photometric transit recovery campaign for TOI-2180. ^b Assumes a Jupiter-like Bond albedo (0.34) and perfect heat redistribution. ^c Reference epoch = 2,459,157.439110.

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The TESS data and the best-fit transit model are shown in Figure 1. All RV data and the best-fit RV model are shown in Figure 3. We included a quadratic function of time in the fit to account for the force from an additional planet or star on TOI-2180. Both coefficients in the quadratic function are greater than 5σ discrepant from zero, suggesting that there is indeed a long-term variation in the RVs. Even with more than a 500 day baseline of observations, we do not sample enough of the long-term signal to determine its cause. The lack of correlation between the RVs and the S_HK activity indicators disfavors stellar activity as the true explanation (Section 2.3). Instead, we suggest that another massive object is orbiting TOI-2180 (Section 6).

Owing to the well-sampled time series of precise RVs, the posterior for the orbital period for the single transit TOI-2180 b has a standard deviation below 1 day (0.23%) that is well characterized by a normal distribution. In the following section, we will further constrain the orbital period of TOI-2180 b based on ground-based photometry acquired near the timing of an additional transit.

With each new RV we acquired of TOI-2180, we calculated the timing of the next transit of TOI-2180 b. The second transit (i.e., the first transit to occur since the TESS single transit) occurred at some point in late August or early September of 2020. At that time, the 2σ transit window—which was almost entirely determined by the uncertainty on orbital period—was approximately 10 days wide. ⁶¹

We attempted the formidable task of observing this 24 hr long, relatively shallow (0.5%) transit by planning a global ground-based photometry campaign. In total, 15 telescopes acquired 55 data sets containing over 20,000 individual exposures of TOI-2180 spanning 11 days. These included professional observatories, amateur observatories, and two portable digital eVscope telescopes. Each data set was processed with standard differential aperture photometry using background stars as references. Basic information about each telescope is provided in Appendix, a summary of each observation is listed in Table 4, and all data are plotted in Figure 9.

None of the observations provided a conclusive detection of a TOI-2180 b transit. As has been the case for other attempts to detect transits of long-period planets (e.g., Winn et al. 2009; Dalba & Muirhead 2016; Dalba & Tamburo 2019), any single observation could only observe out-of-transit baseline and ingress or egress at best. This photometric signature can be easily mimicked by flux variations between the target and reference stars as the airmass changed. On the other hand, owing to the duration of the transit and the difficulty of absolute flux calibration at the precision of the transit depth, distinguishing a fully in-transit observation from a fully out-of-transit one is challenging. Also, the ∼0.5% transit depth was on the order of the noise floor for many of the sites. All of these factors contributed to the nondetection.

However, despite the lack of an obvious transit detection, we developed a straightforward method to refine the orbital period of TOI-2180 b by simultaneously searching all data sets for times where ingress or egress did not occur to high statistical significance. Ruling out these times rules out chunks of the orbital period posterior. Conversely, at times when we cannot determine if ingress or egress occurred—or if ingress or egress even appears to be favored by the data—we do not rule out those portions of the posterior.

We began with the relative light curves for each data set, which were the aperture flux values of TOI-2180 divided by the aperture flux of one or more reference stars. We sigma-clipped the relative light curves for 4σ outliers and normalized each to its median. So far, we had not attempted to remove flux variations due to airmass. Our first task was to remove data sets with high scatter to avoid introducing spurious results in the ephemeris refinement. Although even imprecise data contain useful information, we found that many of the high-scatter data sets contained time-correlated noise or systematic noise features. Instead of attempting to correct for these noise properties, we chose to exclude the data set entirely. For the purpose of this procedure, we fit and subtracted an airmass model,

$$\begin{eqnarray}&&F^{\prime} (t)={c}_{1}{e}^{-{c}_{2}X(t)},\end{eqnarray} \tag{ 2 }$$

where $F^{\prime}$ is the flux variation owing to a varying airmass X, both of which are functions of time t. The model had two fitted coefficients, c₁ and c₂, which can have any finite value. After this airmass correction, data sets for which the standard deviation exceeded the transit depth (0.5%) were removed (gray points in Figure 9). We list this standard deviation for each data set in Table 4.

Next, we established a fine linear grid of mid-transit (T₀) times that spanned fourth contact at the time of the very first flux measurement (BJD_TDB = 2,459,085.674949) to first contact at the time of our very last flux measurement (BJD_TDB = 2,459,096.875975). These T₀ values were used to generate transit models that were compared with the data. Each value of T₀ maps to a unique value of the orbital period.

Then, we iterated over each T₀ value and data set conducting the following procedure. A transit model was generated at that T₀ using the batman package (Kreidberg 2015). All other transit parameters were fixed at the values derived from the EXOFASTv2 model (Table 3), except for the quadratic limb-darkening coefficients, which were drawn from the lookup tables of Claret & Bloemen (2011) according to filter. We subtracted this transit model from the relative light curve that was sigma-clipped and normalized to its median. Note that the light curve in this case had not been corrected for airmass variations, which were therefore still present after the subtraction. The model-subtracted light curve was then fit to Equation (2) with a basic least-squares algorithm that minimized the χ² statistic.

Consider the logic behind this procedure. If the airmass model is a good fit to the light curve after the transit model is subtracted (i.e., low χ² value), then we failed to rule out the transit at that time. We also cannot confidently claim that we have detected the transit, since the good fit to the airmass model could be coincidental. In this case, the probability of this transit time is still described by the posterior from the RV and transit joint fit. Conversely, if the airmass model is a poor fit to the light curve after the transit model is subtracted (i.e., high χ² value), then we can be confident that the transit did not occur at that time.

Each T₀ for each data set yielded its own minimum χ² value from which we calculated the corresponding log likelihood value (i.e., the maximum of the likelihood function) and Bayesian information criterion (BIC; Schwarz 1978). We then summed the BIC values across data sets to produce a total BIC as a function of T₀ and hence orbital period.

We also repeated our entire procedure and calculated the same metrics assuming that none of the observations sampled the transit. In this "no-transit" scenario, the transit occurred either before or after the observations or fell entirely within a data gap.

In Figure 4, we show the difference in BIC values (ΔBIC) between the transit and no-transit scenarios as a function of mid-transit time. The earliest and latest values of ΔBIC approach zero, as expected. Values of T₀ with substantially negative ΔBIC primarily correspond to times when ingress and/or egress occurred during data gaps, and the relatively flat ground-based photometry mimics the basin of a transit. On the other hand, values of T₀ with substantially positive ΔBIC correspond to ingress and/or egress lining up with ground-based photometry that clearly does not contain such features. We adopted a ΔBIC threshold of 10—corresponding to "very strong" evidence against the transit model (Kass & Raftery 1995)—to determine which values of T₀ we could rule out (Figure 4, gray regions) and mapped this refinement back to the orbital period. The resulting trimmed posterior for the orbital period is shown in Figure 5.

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The ground-based transit detection campaign served to broadly divide the normal posterior for the orbital period into two smaller, non-Gaussian groups while ruling out the median and most likely values of the original distribution. Described by their median and 68% credible intervals, the two possible orbital periods are ${260.18}_{-0.30}^{+0.19}$ and ${261.76}_{-0.16}^{+0.29}$ days.

To assess the efficiency of the ground-based photometry campaign, we consider the duty cycle between exposure time and orbital period posterior time to be ruled out. Multiplying the number of exposures by their respective exposure times (Table 4) for all observations (regardless of whether they were excluded from this analysis) yields 4.4 days. The aforementioned ΔBIC threshold of 10 rules out 3.8 days worth of orbital period posterior space. Therefore, the duty cycle of the campaign was 86% (i.e., for every 1 hr of exposure time, we ruled out 52 minutes of orbital period). Ideally, a campaign like this would detect the transit, and the duty cycle would be less important. However, this metric can be recalculated for any future single-transit detection campaigns that yield nondetections or proposals to conduct such campaigns to compare strategies and assess effectiveness.

4.1. Prospects for Future Transit Detection

Object TOI-2180 b is one of a small but growing collection of valuable giant transiting exoplanets on ∼au-scale orbits with precisely measured masses and radii (e.g., Dubber et al. 2019; Dalba et al. 2021a, 2021b; Chachan et al. 2021). With these two properties, we can infer bulk heavy-element mass and metallicity relative to stellar to better understand their structure and formation history.

Following Thorngren & Fortney (2019), we generated one-dimensional spherically symmetric giant planet structure models with a rock/ice core; a convective envelope consisting of rock, ice, and H/He; and a radiative atmosphere interpolated from the Fortney et al. (2007) grid. Along with the mass, radius, and age for TOI-2180 b (drawn from the posteriors of the EXOFASTv2 fit), the models recovered the total mass of heavy elements and thereby bulk metallicity needed to explain the planet's size. We find that the bulk metallicity for TOI-2180 b is Z_p = 0.12 ± 0.03, which corresponds to 105 M_⊕ of heavy elements. We can approximate the stellar metallicity using the iron abundance following Z_⋆ = 0.142 × 10^[Fe/H], which gives Z_⋆ = 0.0254 ± 0.0033. This sets the metal enrichment (Z_p /Z_⋆) at 4.7 ± 1.3.

The metallicity enrichment of TOI-2180 b is consistent with the core accretion theory of giant planet formation (Pollack et al. 1996) with late-stage accretion of icy planetesimals, which can explain enrichment by a factor of a few to a dozen (e.g., Gautier et al. 2001; Mousis et al. 2009). An alternate theory to late-stage accretion—the mergers of planetary cores during the gas accretion phase (e.g., Ginzburg & Chiang 2020)—can explain enrichment factors between 1.5 and 10 for a 2.7 M_J planet, making it a viable formation pathway as well.

In Figure 6, we plot the mass and metal enrichment of TOI-2180 b relative to the Thorngren et al. (2016) sample of giant exoplanets. We also include two other recently published high-mass giant exoplanets on long-period orbits: Kepler-1514 b (P ≈ 218 days; Dalba et al. 2021a) and Kepler-1704 b (P ≈ 989 days; Dalba et al. 2021b). The metal enrichment of TOI-2180 b relative to its host star is consistent with other giant planets with similar mass and falls near the best-fit line for all of the Thorngren et al. (2016) sample.

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The Thorngren et al. (2016) exoplanets are plotted in Figure 6 as circles. The points are given different colors based on orbital period. The two Kepler planets are shown as triangles, and TOI-2180 b is shown as a square. Although each of these planets individually is fully consistent with the Thorngren et al. (2016) mass–metallicity correlation, there is possibly a subtle difference in the slope of the relation for the longer-period planets. For lower-mass planets, enrichment appears to be higher than average for the longer-period objects, and vice versa for the higher-mass planets, including TOI-2180 b.

We explored this possibility quantitatively by separating the planets in Figure 6 into short-period (P < 100 days) and long-period (P ≥ 100 days) groups. The median orbital periods in the two groups were 10 and 223 days. Object TOI-2180 b and the Kepler planets are also given the corresponding P > 100 day color. Although 100 days is a somewhat arbitrary separation value, it possibly separates planets that experienced different formation histories. We conducted orthogonal distance regression fits, which include uncertainties on both the explanatory and response variables, to both sets of planet masses and metal enrichments in log space. The resulting power-law fits are drawn as dashed lines in Figure 6. The 1σ uncertainty regions are also shown. The fits for the short- and long-period planets are (10.4 ± 1.6) M^{(−0.372±0.084)} and (14.6 ± 2.9) M^{(−0.81±0.14)}, respectively. The slopes in these fits are inconsistent at 2.6σ.

The mass–metallicity correlation derived for planets with orbital periods below 100 days is fully consistent with that measured by Thorngren et al. (2016). On the other hand, the small set of long-period planets that includes TOI-2180 b produces a notably steeper correlation. We refrain from placing too much emphasis on this finding owing to the small number of data points and moderate statistical significance. The addition of any number of additional long-period giant planets would be elucidating. If this trend is real, though, it suggests that the current orbital properties of giant planets trace different heavy-element accretion mechanisms, such as pebble or planetesimal (Hasegawa et al. 2018). A statistically robust analysis of the mass–metallicity correlation is warranted, but we leave such an analysis to future work.

For a solar system comparison, the Galileo Entry Probe measured volatile gases in Jupiter's atmosphere and identified enrichment of 2–6 for several heavy elements and noble gases (Wong et al. 2004). More recently, the Juno spacecraft measured the equatorial water abundance on Jupiter to be one to five times the protosolar value (Li et al. 2020). The comparison between our enrichment measurement of TOI-2180 b and these measurements at Jupiter comes with caveats. For instance, the Jupiter enrichment is derived from its equatorial oxygen abundance, while the exoplanet enrichment is a model-dependent bulk value. The direct comparison of these two qualities may be problematic. However, the main point is that these values are all of a similar order of magnitude.

We characterized the trend and curvature in TOI-2180's RV time series using the technique described in Lubin et al. (2021). Because TOI-2180 is not in the Hipparcos catalog (ESA 1997), we could not calculate its astrometric acceleration using the Hipparcos–Gaia Catalog of Accelerations (Brandt 2018). Instead, we analyzed only the RV data, which leaves a degeneracy between companion mass and semimajor axis.

We sampled 10⁸ synthetic companion models, each comprising a mass M_P , semimajor axis a, eccentricity e, inclination i, argument of periastron ω, and mean anomaly M. For each model companion, we calculated the trend ($\dot{\gamma }$) and curvature ($\ddot{\gamma }$) that such a companion would produce. We then calculated the model likelihood given the measured trend and curvature in Table 3 and marginalized over {e, i, ω, M} by binning the likelihoods in a–M_P space. Figure 7 shows the joint posterior distribution for TOI-2180's companion.

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If located within a few au, the object is likely to be planetary and more massive than ∼2 M_J. Past roughly 8 au, however, the object transitions to the substellar regime. We truncate the upper mass boundary of Figure 7 at a few tenths of a solar mass, at which point we would have expected to detect such a companion in the speckle imaging (Section 2.2). For a 13 M_J object, if we extend the RV monitoring by an additional ∼3.5 yr, we will have sampled between 25% and 100% of the full orbit by period. At that point, we should be more capable of distinguishing between planetary and nonplanetary scenarios.

With an equilibrium temperature of 348 K (assuming a Jupiter-like Bond albedo; see Table 3), TOI-2180 b qualifies as a temperate Jupiter that occupies an interesting region of parameter space. It exists within 1–3 au, where the giant planet occurrence rate increases (e.g., Fernandes et al. 2019; Wittenmyer et al. 2020; Fulton et al. 2021), but it is not so close to its star that its orbit has been tidally circularized (e.g., following a high-eccentricity migration pathway). This means that its orbital properties may contain information about previous migration. Object TOI-2180 b is warmer than Jupiter and Saturn, but it receives a weak enough irradiation to not be inflated. Planets like this are useful laboratories for models of interior and atmospheric structure and planet formation.

Object TOI-2180 b stands out among other transiting temperate Jupiters for two main reasons: its long orbital period and its host star's favorable brightness. In Figure 8, we put TOI-2180 b in context with other giant planets (M_P > 0.2 M_J) with orbital periods greater than 20 days (to exclude hot Jupiters) with a measured mass and radius that did not have a controversial flag. ⁶³ The Kepler mission has so far proven most successful at discovering planets in this region of parameter space (e.g., Wang et al. 2015; Foreman-Mackey et al. 2016; Uehara et al. 2016; Kawahara & Masuda 2019). As a result, many of the planets in Figure 8 are sufficiently faint that follow-up opportunities to further characterize their systems are very limited. TESS, however, is slowly beginning to populate the long-period giant planet parameter space with systems orbiting bright host stars that are more amenable to follow-up characterization (e.g., Eisner et al. 2020).

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As a temperate giant planet, the atmosphere of TOI-2180 b represents a stepping-stone between well-characterized hot Jupiters and the cold solar system gas giant planets. At 348 K, we might expect to find nonequilibrium carbon chemistry that relies heavily on vertical transport (Fortney et al. 2020). Moreover, an atmospheric metallicity measurement of TOI-2180 b would be an ideal comparison to the now-known stellar and bulk planetary metallicity. Perhaps the atmospheric metallicity will be lower than the bulk value, since some amount of the heavy elements is likely sequestered into a core. However, evidence from solar system observations suggests that giant planets may instead have interior regions of inward-decreasing metallicity (e.g., Wahl et al. 2017; Guillot et al. 2018; Debras & Chabrier 2019). These theories could possibly be explored with transmission spectroscopy, which is suspected to probe CH₄ and the by-products of disequilibrium chemistry and photolysis in long-period giant planets (Dalba et al. 2015; Fortney et al. 2020). However, owing to its high surface gravity and an unfavorable planet–star radius ratio, TOI-2180 b is likely not amenable to transmission spectroscopy. The atmospheric scale height of TOI-2180 b is only ∼23 km, which corresponds to a transit depth of a few parts per million (ppm) and a transmission spectroscopy metric of 7 (Kempton et al. 2018). Similarly, the near-infrared depth of the secondary eclipse is likely to be on the order of or less than 10 ppm (Table 3). Any future endeavor to identify favorable targets for temperate Jupiter atmospheric characterization should examine whether the brightness of TOI-2180 compensates for the difficulty introduced by its large stellar radius and the high surface gravity of TOI-2180 b.

Other avenues of follow-up characterization for the TOI-2180 system are more promising. Continued RV monitoring of TOI-2180 would eventually capture a sufficient fraction of the long-term acceleration to infer the properties of the outer companion. This RV trend could also be interpreted jointly with imaging and astrometric data to further constrain the outer object's orbit and inclination (e.g., Crepp et al. 2012; Wittrock et al. 2016; Kane et al. 2019; Brandt et al. 2021; Dalba et al. 2021c). Be it a star or substellar object, it could have influenced the evolution and migration of TOI-2180 b, including eccentricity excitation through Kozai–Lidov oscillations (e.g., Wu & Murray 2003; Fabrycky & Tremaine 2007; Naoz et al. 2012). However, we need not invoke secular interactions (e.g., Wu & Lithwick 2011) or planet–planet scattering (e.g., Rasio & Ford 1996) to explain the moderate eccentricity (e ≈ 0.37) of TOI-2180 b. Debras et al. (2021) argued that disk cavity migration could explain warm Jupiter eccentricity up to ∼0.4. Additional modeling of the formation and dynamical evolution of the objects in the TOI-2180 system with comparison to the bulk metallicity of TOI-2180 b would be illuminating.

The degeneracy between disk migration and secular interactions could possibly be broken with a measurement of the stellar obliquity via the Rossiter–McLaughlin (RM) effect (Rossiter 1924; McLaughlin 1924). Migration via interactions with a distant massive object would cause both orbits to be misaligned with the stellar spin. Alternatively, if it migrated in the disk, and the disk is assumed to have been aligned with the stellar equator, we would expect little obliquity. This assumption may be problematic, though, as disks can be tilted such that they yield misaligned planets under disk migration (e.g., Spalding & Batygin 2016). Nonetheless, the SpecMatch analysis of the TOI-2180 spectrum returned a low rotational velocity of $v\sin i=2.2\pm 1.0$ km s⁻¹. The largest possible amplitude of the RM effect would therefore be ∼9 m s⁻¹ (Winn 2010), which is well within the capabilities of next-generation precise RV facilities such as MAROON-X (Seifahrt et al. 2018) or the Keck Planet Finder (Gibson et al. 2016). The RM effect would also be detectable from either Keck-HIRES or APF-Levy, which have average internal RV precisions of 1.2 and 3.6 m s⁻¹, respectively. Achieving the proper timing for such an experiment given the 24 hr transit is challenging, though, and may not be feasible for several years. The scientific benefit of an RM detection for this system, and for such a long-period planets in general, further motivates the need to refine the transit ephemeris.

Lastly, we briefly consider TOI-2180 b as a host for exomoons. The TESS transit offered no evidence to suggest that an exomoon is present, but the stellar brightness, long-period planetary orbit, and (possibly) gentle migration history raise the possibility of exomoon detection in this system. Object TOI-2180 is sufficiently bright that the precision of a single-transit observation would likely reach the noise floors of NIRISS and NIRSpec (several tens of ppm; Greene et al. 2016; Batalha et al. 2017). A Ganymede-size moon would produce an ∼5 ppm transit, which would not be detectable. Alternatively, an Earth-sized moon would yield an ∼30 ppm occultation, which is more reasonable. As more transits of TOI-2180 b are observed by TESS or any other facility, we recommend that the community conduct photodynamical modeling to test for variations in transit timing and duration that might indicate the presence or lack of an exomoon (e.g., Kipping et al. 2012; Heller et al. 2014; Kipping 2021).

Single-transit events are the primary avenue to discovering exoplanets with orbital periods longer than approximately a month in TESS photometry. Here we describe the follow-up effort surrounding a 24 hr long single transit of TOI-2180 (Figure 1), a slightly evolved mid-G-type star, in Sector 19 data from TESS (Section 2.1). Citizen scientists identified the transit event shortly after the data became public, allowing a Doppler monitoring campaign with the APF telescope to begin immediately (Section 2.3). After nearly 2 yr of RV observations with the APF and Keck telescopes (Figure 3), we determined that TOI-2180 b—a 2.8 M_J giant planet on a 260.79 day eccentric (0.368) orbit—was the cause of the single-transit event (Section 3.1).

Object TOI-2180 b is a member of a rare but growing sample of valuable transiting giant exoplanets with orbital periods in the hundreds of days. We conduct a thorough comprehensive fit to the transit and RV data to infer the stellar and planetary properties of this system (Section 3.2). Our precise and regularly sampled RVs refine the ephemeris of TOI-2180 b, and we attempt to detect a second transit through 11 days of photometric observations with ground-based telescopes situated over three continents (Figure 9). Although we do not detect a transit in these data, we develop a straightforward method to combine the orbital period posterior from the fit to the single transit and RVs with the extensive collection of ground-based data sets (Section 4). This analysis substantially refines the orbital period of TOI-2180 b by eliminating a substantial fraction of the most likely posterior solutions (Figure 5), leaving the prediction that TESS will likely detect the transit of TOI-2180 b in 2022 January or February (Section 4.1).

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With a measured mass and radius for TOI-2180 b, we infer the bulk heavy-element content and metallicity relative to stellar from interior structure models (Section 5). It is likely that TOI-2180 b has over 100 M_⊕ of heavy elements in its envelope and interior and is enriched relative to its host star by a factor of 4.7 ± 1.3. We place TOI-2180 b in the context of the mass–metallicity correlation for giant planets in Figure 6. Along with a few other recently characterized exoplanets on several hundred day orbital periods, TOI-2180 b suggests at 2.6σ confidence that the relation between metal enrichment (relative to stellar) and mass for giant planets is dependent on orbital properties. We leave further analysis of this possibility to future work.

Lastly, we place the discovery of TOI-2180 b in the context of other temperate giant planets with known mass and radius (Section 7, Figure 8). It is a poor candidate for transmission spectroscopy owing to its high surface gravity and the 1.6 R_☉ radius of its host star. Still, this system is a promising target for continued RV monitoring and stellar obliquity measurement to test theories of how giant planets migrate within the occurrence rate increase near 1 au but not so close as to become hot Jupiters. Object TOI-2180 b also remains an excellent candidate for exomoon investigations, since the host star brightness (V = 9.2; J = 8.0) makes it amenable to incredibly precise space-based photometry in the future.

The authors recognize and acknowledge the cultural role and reverence that the summit of Maunakea has within the indigenous Hawaiian community. We are deeply grateful to have the opportunity to conduct observations from this mountain.

The authors would like to thank the anonymous referee for helpful comments that improved this paper. We also thank Jack Lissauer for interesting conversations about giant planets that guided some of our analysis. We thank Ken and Gloria Levy, who supported the construction of the Levy Spectrometer on the Automated Planet Finder. We thank the University of California and Google for supporting Lick Observatory and the UCO staff for their dedicated work scheduling and operating the telescopes of Lick Observatory. Some of 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 NASA. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.

This paper includes data collected by the TESS mission. Funding for the TESS mission is provided by NASA's Science Mission Directorate. We acknowledge the use of public TESS data from pipelines at the TESS Science Office and 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. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This research has made use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This paper includes data collected with the TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI). The STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. We acknowledge the use of public TESS data from pipelines at the TESS Science Office and the TESS Science Processing Operations Center. This work makes use of observations from the LCOGT network. Part of the LCOGT telescope time was granted by NOIRLab through the Mid-Scale Innovations Program (MSIP). MSIP is funded by NSF.

P.D. is supported by a National Science Foundation (NSF) Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1903811. E.A.P. acknowledges the support of the Alfred P. Sloan Foundation. L.M.W. is supported by the Beatrice Watson Parrent Fellowship and NASA ADAP grant 80NSSC19K0597. A.C. is supported by the NSF Graduate Research Fellowship, grant No. DGE 1842402. D.H. acknowledges support from the Alfred P. Sloan Foundation, the National Aeronautics and Space Administration (80NSSC21K0652), and the National Science Foundation (AST-1717000). I.J.M.C. acknowledges support from the NSF through grant AST-1824644. R.A.R. is supported by the NSF Graduate Research Fellowship, grant No. DGE 1745301. C.D.D. acknowledges the support of the Hellman Family Faculty Fund, the Alfred P. Sloan Foundation, the David & Lucile Packard Foundation, and the National Aeronautics and Space Administration via the TESS Guest Investigator Program (80NSSC18K1583). J.M.A.M. is supported by the NSF Graduate Research Fellowship, grant No. DGE-1842400. J.M.A.M. also 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. T.F. acknowledges support from the University of California President's Postdoctoral Fellowship Program. N.E. acknowledges support from the UK Science and Technology Facilities Council (STFC) under grant code ST/R505006/1. D.D. acknowledges support from TESS Guest Investigator Program grant 80NSSC19K1727 and NASA Exoplanet Research Program grant 18-2XRP18_2-0136. M.R. is supported by the National Science Foundation Graduate Research Fellowship Program under grant No. DGE-1752134.

P.D. thanks the Walmart of Yucca Valley, California, for frequent and prolonged use of its wireless internet to upload hundreds of gigabytes of data.

Facilities: Keck:I (HIRES) - , Automated Planet Finder (Levy) - , TESS - , Gemini:Gillett ('Alopeke) - , LCOGT.

Software: batman (Kreidberg 2015), EXOFASTv2 (Eastman et al. 2013; Eastman 2017; Eastman et al. 2019), lightkurve (Lightkurve Collaboration et al. 2018), RadVel (Fulton et al. 2018), SpecMatch (Petigura 2015; Petigura et al. 2017), AstroImageJ (Collins et al. 2017), LcTools (Schmitt et al. 2019).

In the following sections, we briefly describe each telescope that contributed to the ground-based observing campaign. Additional information summarizing the campaign is provided in Table 4.

A.1. Maury Lewin Astronomical Observatory

A.2. Kotizarovci Observatory

A.3. Grand-Pra Observatory

A.4. Boyce-Astro Research Observatory

A.5. LCOGT-Haleakalā Observatory

A.6. LCOGT-McDonald Observatory

A.7. Wendelstein Observatory

A.8. Saint-Pierre-du-Mont Observatory

A.9. LCOGT-Teide Observatory

A.10. Dragonfly Telephoto Array

A.11. eVscope Portable Observatories (eV-A, eV-B)

A.12. Indian Astronomical Observatory

A.13. Vainu Bappu Observatory

A.14. Acton Sky Portal