TESS-Keck Survey. XIV. Two Giant Exoplanets from the Distant Giants Survey

Our ability to draw robust statistical conclusions from the Distant Giants Survey relies critically on the assembly of a well-defined stellar sample. We designed our target selection criteria to yield a sample of Sun-like stars hosting at least one small transiting planet found by TESS. We also required that all targets be amenable to precise RV follow up from the northern hemisphere. To impose these criteria, we began with the master target list produced by Chontos et al. (2022), which contains 2136 individual TESS Objects of Interest (TOIs) among 2045 planetary systems. We then applied the following sets of filters:

• 1.  
  Photometric and astrometric measurements. To allow for efficient observation from the Northern Hemisphere, we required that all stars have δ > 0° and V < 12.5, where δ is the decl. and V is the V-band magnitude. We excluded stars with a Gaia Renormalized Unit Weight Error (RUWE; Lindegren et al. 2018, 2021) greater than 1.3 to ensure precise fits to Gaia’s 5-parameter astrometric model. RUWE < 1.2 is a conservative limit to exclude binary systems misclassified as single sources (Bryson et al. 2020; A. Kraus et al. 2022, in preparation). All but one target in the Distant Giants sample satisfy RUWE < 1.2, implying a low probability that we included any unwanted binary systems. We chose an upper bound of 10 R_⊕ on the transiting planet radius. In the event that a star hosted multiple transiting planets, we required that at least one meet our planet size requirement. These cuts reduced the target pool from 2045 to 147 systems.
• 2.  
  Data quality. We evaluated transit quality using TESS data validation (DV) reports retrieved from the TOI Catalog in 2020 July. To ensure high-significance transits, we only included TOIs with at least one light curve produced by the TESS Science Processing Operations Center pipeline (SPOC; Jenkins et al. 2016). Furthermore, we used the Multiple Event Statistic (MES; Jenkins 2002), a proxy for the signal-to-noise ratio (S/N), to evaluate transit quality. After visual inspection of a subset of SPOC transit fits, we found that MES = 12 was a suitable lower limit for identifying compelling detections. We also excluded targets with close visual companions, which we defined as companions within 4″ and 5 V-band magnitudes. These filters further reduced the pool from 147 to 67 systems.
• 3.  
  Inactive and slowly-rotating stars. We used SpecMatch(Petigura et al. 2017) to analyze each target’s “template” spectrum (Section 2.3). SpecMatchinterpolates over a grid of synthetic stellar spectra to estimate stellar parameters such as effective temperature T_eff, projected rotational velocity $v\sin (i)$, surface gravity $\mathrm{log}g$, and metallicity [Fe/H]. For stars cooler than 4700 K, we used SpecMatch-Emp (Yee et al. 2017) to interpolate over real spectra of K and M dwarfs, which are more reliable than model spectra at low temperatures. We excluded rapidly rotating stars ($v\sin (i)\gt 5$ km s⁻¹), as well as those with T_eff above the Kraft break (∼6250 K); such stars offer limited RV precision due to Doppler broadening (Kraft 1967). We also derived stellar mass according to the methods of Fulton & Petigura (2018), and selected only main sequence stars between 0.5 and 1.5 M_⊙, consistent with our solar analog requirement.We measured each star’s chromospheric activity through its $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ index (Noyes et al. 1984; Isaacson & Fischer 2010). This value quantifies the emission in the cores of the Calcium II H and K lines relative to the total bolometric emission of the star, with higher core emission corresponding to enhanced activity and therefore greater RV variability in the epoch that the activity is measured. We required that $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }\,\lt$ −4.7. This limit, adopted from Howard et al. (2010a), restricts our sample to “inactive” and “very inactive” stars, as defined by Henry et al. (1996). We note that restricting $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ and $v\sin (i)$ introduces a bias toward older stars due to the correlations between age and both Calcium H and K line emission and rotation speed (e.g., Noyes et al. 1984; Soderblom et al. 1991). We retained these filters to ensure RV quality, and will account for the associated bias in our final results.We applied this $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ filter using available activity values in mid 2020, but because stellar activity is variable, some of our targets fluctuate above the $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }\,=\,$−4.7 limit. Furthermore, two targets, TOI-1775 and TOI-2088, did not have available activity values at the time we applied this filter. They were thus not excluded based on activity, and we retained them in the sample. Since then, we have found $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }\,=\,$−4.72 for TOI-2088 and −4.28 for TOI-1775. Knowing that TOI-1775 fails our $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ cut, we will carefully monitor its activity against any signals that develop in the RVs. Of the remaining 67 systems, 48 passed these filters. Due to time constraints, 47 of these were selected for TKS by the target prioritization algorithm detailed in Chontos et al. (2022). The filters of both Distant Giants and TKS are given in Table 1.

Table 1. Survey Criteria

		Distant Giants Survey
Parameter	TKS	Photometric	Manual	Spectroscopic
decl.	>−30°	>0°	⋯	⋯
V	<13.0	<12.5	⋯	⋯
Evolutionary state	MS or SG	MS	⋯	⋯
RUWE	<2	<1.3	⋯	⋯
RP	<22 R⊕	<10 R⊕	⋯	⋯
Transit pipeline	⋯	⋯	SPOC	⋯
Detection significance	S/N > 10	⋯	MES > 12	⋯
Close companion	ΔV > 5 or sep > 2″	⋯	ΔV > 5 or sep > 4″	⋯
M⋆	⋯	⋯	⋯	0.5 M⊙ < M⋆ < 1.5 M⊙
Teff	<6500 K	⋯	⋯	<6250 K
$v\sin i$	⋯	⋯	⋯	<5.0 km s−1
$\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$	⋯	⋯	⋯	< −4.7

Note. Filters applied to 2045 TESS systems to produce the Distant Giants sample. TKS filters are taken from Chontos et al. (2022). Although other filters were applied to produce the TKS sample, we show only those used in our survey’s target selection process. MS and SG refer to main sequence and subgiant stars, respectively.

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From the original set of 2045 TOI-hosting systems, 86 were ultimately selected for TKS and 47 were selected for Distant Giants. The final Distant Giants sample is given in Table 2, and we summarize key stellar and planetary parameters of both Distant Giants and TKS in Figure 1.

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We tailored the Distant Giants observing strategy to planets with periods ≳1 yr and masses above ∼100 M_⊕. Such planets require neither high observing cadence nor high S/N to detect; however, they do require a longer observing baseline than shorter-period planets. In order to maximize Distant Giants’s sensitivity to long-period planets within a fixed telescope award, we traded observational cadence and precision for a greater survey duration and target pool. We adopted the following observing strategy: we obtain one observation per target per month. We use the HIRES exposure meter to obtain a minimum S/N of 110 per reduced pixel on blaze at 5500 Å. The procedure we use to derive radial velocities and uncertainties from raw spectra is described in Butler et al. (1996). The ∼800 spectra we have collected for Distant Giants targets at this S/N have a median statistical uncertainty of 1.7 m s⁻¹. Adding our statistical uncertainties in quadrature with the ∼2 m s⁻¹ instrumental noise floor of HIRES (Fulton 2017), we estimate a typical RV uncertainty of 3 m s⁻¹. We are conducting monthly observations of each target until we have attained 30 observations over 3 yr; the six-month surplus compensates for weather losses and target observability seasons. This baseline will allow us to resolve the full orbits of planets with orbital periods ≲3 yr and sense partial orbits of longer-period companions. Although our sample includes a few legacy RV targets with multidecade baselines (Fischer et al. 2014; Rosenthal et al. 2021), uniform observation of the Distant Giants sample began near mid 2020. The observing baselines of our full sample over a 200 day period are shown in Figure 2.

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For targets brighter than V = 10, we also obtain observations with the Levy spectrograph on the 2.4 m Automated Planet Finder telescope (APF; Vogt et al. 2014). However, because most of our targets are too dim to benefit from APF observations, we maintain monthly cadence with Keck/HIRES for all targets. This will allow us to analyze our final time series both with and without APF RVs to avoid biasing our planet sensitivity toward brighter stars.

2.2.1. Existing Observations

2.2.2. Surplus Observations and/or Baseline

We take RV observations according to the standard procedure of the California Planet Search (CPS; Howard et al. 2010b). We use the HIRES spectrometer (Vogt et al. 1994) coupled to the Keck I Telescope to observe all Distant Giants targets. We place a cell of gaseous iodine in the light path to project a series of fiducial absorption lines onto the stellar spectrum. These references allow us to track the instrumental profile and precisely wavelength-calibrate the observed spectra. For each star, we collected a high S/N iodine-free “template” spectrum. The template, together with the instrumental point-spread function and iodine transmission function, is a component of the forward model employed by the CPS Doppler analysis pipeline (Butler et al. 1996; Howard et al. 2010b).

In the first two years of our survey, we resolved the full orbits of giant planets in two of our 47 systems: TOI-1669 and TOI-1694. Although two more systems, HD 219134 and HD 75732, host resolved companions, these planets were detected using hundreds of RVs over multidecade baselines; further analysis is needed to determine whether they would have been detectable using our observing strategy alone. Finally, seven systems show non-periodic RV trends. We discuss these trends briefly in the conclusion to this paper (Section 6) and will treat them fully in future work. The parameters of the companions in the four resolved systems are given in Table 3, and their stellar parameters are given in Table 4.

Table 4. Resolved Distant Giants Stellar Properties

TOI	CPS Name	V	B-V	M⋆ (M⊙)	Teff (K)	log g	[Fe/H]	$v\sin i$ (km s−1)
1469	219134	5.57	1.02	0.79 ± 0.03	4839.5 ± 100.0	4.48 ± 0.10	0.11 ± 0.06	0.6 ± 1.0
1669	T001669	10.22	0.76	1.00 ± 0.05	5542.3 ± 100.0	4.28 ± 0.10	0.26 ± 0.06	0.6 ± 1.0
1694	T001694	11.45	0.76	0.84 ± 0.03	5066.4 ± 100.0	4.53 ± 0.10	0.12 ± 0.06	1.2 ± 1.0
1773	75732	5.95	0.86	0.97 ± 0.05	5363.3 ± 100.0	4.31 ± 0.10	0.42 ± 0.06	0.2 ± 1.0

Note. Stellar parameters for the four stars in our survey hosting fully resolved companions. The effective temperatures, surface gravities, metallicities, and rotational velocities we list here were calculated using SpecMatch, which assigns a fixed uncertainty to each derived parameter. Stellar masses incorporate isochrone constraints, as described in Fulton & Petigura (2018).

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The SPOC conducted a transit search of Sector 19 on 2020 January 17 with an adaptive, noise-compensating matched filter (Jenkins 2002; Jenkins et al. 2010, 2020), detecting a transit crossing event (TCE) for TOI-1669. An initial limb-darkened transit model was fitted to this signal (Li et al. 2019) and a suite of diagnostic tests were conducted to evaluate whether it was planetary in nature (Twicken et al. 2018). The transit signature was also detected in a search of full-frame-image data by the Quick Look Pipeline at MIT (Huang et al. 2020a, 2020b). The TESS Science Office reviewed the vetting information and issued an alert on 2020 January 29 (Guerrero et al. 2021).The signal was repeatedly recovered as additional observations were made in sectors 20, 25, 26, 52, and 53, and the transit signature of TOI-1669.01 passed all the diagnostic tests presented in the DV reports. The source of the transit signal was localized within 4925 ± 45 of the host star.

The transit signature of TOI-1694 b was identified in a SPOC transit search of Sectors 19 on 2020 January 17. It passed all the DV diagnostic tests and was alerted by the TESS Science Office on 2020 January 29. It was redetected in a SPOC multisector transit search of Sectors 19 and 20 conducted on 2020 May 5, and the difference image centroiding test located the source of the transits to within 08 ± 30 of the host star.

We visually inspected the time series of the targets in our sample, and found that TOI-1669 exhibited RV variability beyond the noise background. TOI-1669 is a bright (V = 10.2) mid-G type solar analog exhibiting low chromospheric activity ($\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }\,=\,$ −5.2) and low rotational velocity ($v\sin i=0.3$ km s⁻¹), as required by our survey filters. Because it is not shared by any other TKS science cases, TOI-1669 was observed according to the Distant Giants observing strategy: we collected 20 HIRES spectra between 2020 July and 2022 July at monthly cadence, except during periods when the target was not observable. A subset of TOI-1669's time series is given in Table 5.

We used radvel (Fulton et al. 2018) to fit a preliminary model to this system’s time series. The model consisted of the inner transiting planet, TOI-1669.01, and the newly-identified outer planet, TOI-1669 b, as well as parameters for linear and quadratic trends and a term characterizing astrophysical and instrumental jitter. We fixed the orbital period (P) and time of conjunction (T_c ) of TOI-1669.01 to the values listed in the TESS DV reports. We fit for the three remaining orbital parameters: eccentricity (e), argument of periastron (ω), and semiamplitude (K).

For TOI-1669 b, we fit for all five orbital parameters with initial values based on visual estimates from the RV time series. We imposed wide priors on free orbital parameters to minimize the bias incurred by our estimates. We used Powell’s method (Powell 1964) to optimize our likelihood function, and derived parameter uncertainties using Markov chain Monte Carlo simulations, as implemented in Foreman-Mackey et al. (2013).

We generated a set of alternative models by excluding different combinations of (1) RV trend/curvature, (2) eccentricity of both planets, and (3) the outer planet itself. We performed a model comparison using the Akaike Information Criterion (AIC; Akaike 1974) to find which of these combinations was preferred. The consideration of only one- and two-planet models leaves open the possibility that one or more planets were missed by our analysis. However, the aim of this procedure was not to find every planet in this system, but rather to determine whether it satisfied the basic detection criterion of our survey: hosting at least one outer giant planet in the presence of a close-in small one.

We found that all viable models included both TOI-1669 b and a linear trend. We ruled out models that excluded TOI-1669.01 because this planet was independently confirmed by transit photometry. Eccentricity of either planet improved the model likelihood, but not enough to outweigh the penalty imposed by the AIC for higher model complexity. Quadratic curvature was similarly disfavored. The model preferred by the AIC consists of two planets with circular orbits, as well as a linear trend.

We also considered a variation of the AIC-preferred model, with the outer giant eccentricity allowed to vary. Although this model is formally disfavored (ΔAIC = 8.6), it represents a more realistic scenario than the forced circular case. Moreover, this eccentric model subsumes the circular one, meaning that it could naturally fit a circular orbit for TOI-1669 b if it were favored by the data. The fact that this model instead fits a moderate eccentricity to the outer planet suggests that the AIC-preferred circular fit may not be physical, but rather a result of the AIC’s penalization of models with more parameters, which is intended to prevent the overfitting of small data sets. We adopt the eccentric model and quote its fitted parameters, though we present the circular model alongside it to emphasize the uncertainty in our model selection process. In subsequent sections, we refer to the model with free outer giant eccentricity as “preferred.” We show both models together with the full and phase-folded time series in Figure 3.

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To evaluate the significance of our giant planet detection, we calculated the false alarm probability (FAP) by adapting the procedure of Howard et al. (2010b). The FAP estimates the probability that a recovered signal arose from random statistical fluctuations rather than an actual planet. We created 1000 “scrambled” versions of TOI-1669's time series by randomly drawing RV values from the original data, with replacement. For each of these data sets, we compared the preferred 2-planet model to the null hypothesis: a model with the inner planet only, with P and T_c fixed and e, ω, and K allowed to vary, and no linear trend. For a given data set, the improvement of the preferred model fit to the data over the single-planet fit to the data is quantified by the difference in χ² statistic, ${\rm{\Delta }}{\chi }^{2}={\chi }_{\mathrm{inner}}^{2}-{\chi }_{\mathrm{pref}}^{2}$, where ${\chi }_{\mathrm{inner}}^{2}$ and ${\chi }_{\mathrm{pref}}^{2}$ are the minimized χ² values of the single-planet and preferred fits to the data, respectively. A more positive Δχ² value indicates greater performance of the preferred model over the single-planet model. The FAP is simply the fraction of scrambled time series with a greater Δχ² value than the original time series. Put another way, the FAP gives the fraction of scrambled time series for which the statistical improvement granted by the preferred model over a single-planet model is greater than the improvement granted by the preferred model over a single-planet model for the actual RVs. We found that no scrambled data sets had Δχ² greater than TOI-1669's original time series, implying an FAP value of less than 0.1%. We emphasize that this technique quantifies only the probability of false detections as the result of statistical noise, not the probability that one or more planetary signatures were missed in the fitting procedure. However, as we note above, the latter is irrelevant to our search for at least one outer giant in each system.

We recovered a cold sub-Jupiter orbiting TOI-1669 with a period and minimum mass of 502 ± 16 days and $M\sin i=0.573\pm 0.074\,\,{M}_{{\rm{J}}}$. We found that e_c = 0.14 ±0.13, corresponding to a 1σ upper limit of 0.27. Our data set for this system is small, consisting of only 20 RVs, so we defer precise claims about TOI-1669 b’s eccentricity until we have collected more data. Nevertheless, our data is sufficient to indicate that this planet exists and is a distant giant by the standards of our survey.

TOI-1669 also hosts a 2.7 day candidate sub-Neptune detected by TESS. Assuming TOI-1669.01 is a planet, its fitted radius of R = 2.40 ± 0.18 R_⊕ suggests that it resides on the edge of the Radius Valley, an interval between 1.5 and 2.0 R_⊕ which exhibits a distinct reduction in planet occurrence (Fulton et al. 2017; Van Eylen et al. 2018). We derived a mass of 5.2 ± 3.1 M_⊕ for TOI-1669.01 and used it to calculate a bulk density of 2.06 ± 1.13 g/cc, corresponding to a 1σ upper bound of 3.19 g/cc. Due to the uncertainty of our mass measurement, we have not independently confirmed TOI-1669.01 as a planet. Nevertheless, TOI-1669 meets our transit quality requirements (Section 2.1), so we treat TOI-1669.01 as a transiting planet for the purposes of our survey.

Finally, TOI-1669 exhibits a linear trend in the RV residuals. The trends found by our preferred model (−0.0261 ± 0.0058 m s⁻¹ day⁻¹) and the circular model (−0.0286 ± 0.0047 m s⁻¹ day⁻¹) are each significant at >4σ, and agree with each other to within 1σ. The trend is likely physical, as evidenced by its persistence in both models, and may be caused by an additional long-period companion with a period ≳2200 days. To test this hypothesis, we examined direct imaging of TOI-1669 obtained in the I band (832 nm) with the ’Alopeke speckle imager (Scott et al. 2021) coupled to the 8 m Gemini-North telescope. The imaging reached a roughly constant contrast of Δmag ≈4 from 01 to 10 and showed no evidence of a luminous companion. This rules out stellar companions ≳250 M_J within 100 au, but leaves open the possibility that a substellar companion orbits TOI-1669 at close separation. If this is the case, extending TOI-1669's observational baseline over the next year will give us greater sensitivity to the companion’s orbit.

We also observed significant RV variation in the time series of TOI-1694. TOI-1694 is an early K dwarf with V=11.4, $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }=$ −5.0, and $v\sin i=0.4$ km s⁻¹. Like TOI-1669, TOI-1694 was observed at the low cadence prescribed by Distant Giants: we obtained 20 HIRES spectra of this target between August 2020 and September 2022. We show a subset of TOI-1694's RV time series in Table 5.

We used the procedure described in Section 3.1 to fit an RV model to TOI-1694's time series. We found that a two-planet model with an eccentric outer planet and no trend was preferred over the same model with both orbits forced to circular (ΔAIC = 8.41). We also tested the preferred model with an added linear trend, and found that the fitted value was consistent with 0 m s⁻¹ day⁻¹, which we interpret as evidence that our model selection process was not heavily influenced by our limited data set. We therefore adopt the AIC-preferred model: an inner planet with a circular orbit, an eccentric outer giant, and no linear trend. Under this model, we calculated FAP <0.1% for TOI-1694 c. For consistency with our treatment of TOI-1669, we also present a modified version of the preferred model, with the outer planet’s orbit fixed to circular. This model fits similar values to the giant planet’s mass and period, suggesting that model uncertainty does not greatly contribute to our overall uncertainty in these parameters. Figure 4 shows the preferred RV model for TOI-1694, along with the alternative circular model.

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TOI-1694 hosts an RV-resolved distant giant as well as a TESS-detected inner transiting planet. The outer companion, TOI-1694c, is a Jupiter analog ($M\sin i=1.05\pm 0.05\,\,{M}_{{\rm{J}}}$) with a period of 389.2 ± 3.9 days and a modest eccentricity of e = 0.18 ± 0.05.

The inner companion in this system, TOI-1694 b, is a hot super-Neptune with a radius of 5.44 ± 0.18 R_⊕ and a period of ∼3.8 days. This planet is recovered at high significance by our RV model and has a true mass of 26.1 ± 2.2 M_⊕. With our mass and radius measurements, we calculate a bulk density of 0.89 ± 0.12 g/cc. TOI-1694 b’s low density and large radius suggest that it comprises a rocky core surrounded by a substantial gaseous envelope (Weiss & Marcy 2014; Rogers 2015; Fulton et al. 2017). TOI-1694 b is noteworthy because it lies in the Hot Neptune Desert, which refers to the low occurrence of short-period (P ≲ 10 days) planets with masses of ∼10–100 M_⊕ (Mazeh et al. 2016).