TESS Delivers Five New Hot Giant Planets Orbiting Bright Stars from the Full-frame Images

The initial detection of the new planets came from data collected by the TESS mission. TESS images the sky with a 24° × 96° field of view and observes the same stars for about a month before moving on to observe a different region. During its primary mission, TESS saved and downloaded images of a smaller number of preselected stars every two minutes, while downloading coadded images of its entire field of view every 30 minutes. None of the planets described in this paper orbit stars that were preselected for two-minute cadence observations, so we use data from the 30 minute cadence FFIs.

After the data were transferred from the orbiting spacecraft back to Earth, the FFIs were calibrated using the TICA software (M. Fausnaugh et al. 2021, in preparation), and light curves for a set of stars complete down to TESS-band magnitude = 13.5 were extracted with the MIT Quick Look Pipeline (QLP; Huang et al. 2020b). The QLP extracts light curves from the FFIs using a difference image analysis technique. After removing the effects of scattered earthshine and moonshine from the images, the QLP subtracts a high-quality reference image from each individual science frame and measures difference fluxes within sets of photometric apertures surrounding each star in the image. These difference fluxes are then converted to absolute brightness measurements by adding back the median flux expected from each star based on its TESS-band magnitude. The QLP light curves have been used to discover dozens of planets (e.g., Huang et al. 2018; Rodriguez et al. 2019; Huang et al. 2020a) and a few thousand planet candidates (Guerrero et al. 2021). Additional information and a description of the QLP procedures are given by Huang et al. (2020b). The QLP light curves are shown in Figure 1. All five of these light curves were flattened using Keplerspline, ⁷² a spline fitting routine to divide out the best-fit stellar variability (Vanderburg & Johnson 2014). The spacing of the spline break points for each system was determined by minimizing the Bayesian information criterion following the methodology from Shallue & Vanderburg (2018). After removing the stellar variability, we keep all data from one full transit duration before the transit until one full transit duration after the transit, and we discard the remaining baseline data (which contains very little useful information but is computationally expensive to model). We use these light-curve segments for the global fitting of each system (see Section 3).

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Because the QLP uses aperture photometry on difference frames using a median-combined reference image, it does not always measure absolute transit depths, only difference fluxes. Transit depths measured by QLP, especially in crowded fields, might be dependent on the accuracy of the TESS-band magnitudes from the TESS Input Catalog (Stassun et al. 2018) to correct for contamination due to blending of nearby stars within the aperture. To check that the transit depths measured by QLP for these targets are reasonably accurate, we performed a spot check for TOI-1601 with light curves extracted using a more traditional simple aperture photometry method (Vanderburg et al. 2019). We did not deblend the photometry in this test because TOI-1601 is in a relatively sparse field, as shown from our high-resolution imaging (see Section 2.6.2). We ran an independent EXOFASTv2 fit for TOI-1601 b (swapping this light curve for the QLP one) following the strategy discussed in Section 3, and the results were consistent to within <1σ uncertainties. Additionally, for each system, we used the follow-up ground-based photometry within the global analysis to also constrain the depth, providing independent constraints that can be used to confirm the QLP depths (since the TFOP photometry is at a higher angular resolution than TESS). Within our global fit, we checked on any unknown contamination by fitting for a dilution term on the TESS bandpass to account for any difference compared to the SG1 photometry. In all cases other than TOI-1478, the fitted dilution was consistent with zero and well within our Gaussian 10% prior around zero, showing clear consistency between TESS and the TFOP seeing-limited photometry. TOI-1478 showed a significant Required dilution on the order of 12%. To properly account for this, we removed the TESS dilution prior (see Section 3 for details), allowing it to be a free parameter, to properly correct for this within the fit.

We searched the nonflattened QLP light curves for rotation-based modulations using the VARTOOLS Lomb–Scargle function (Hartman & Bakos 2016). Specifically, we searched from 0.1 to 30 days and detect a clear, strong periodicity at 5.296 days for TOI-1333, significantly different from the orbital period of its planetary companion (P_b = 4.72 days). This same periodicity is observed in our ground-based photometry, ruling out any systematics in the TESS observations. We see some tentative evidence of a periodicity at 10–11 days for TOI-628, but it was only observed in one TESS sector.

The WASP transit search consisted of two wide-field arrays of eight cameras, with SuperWASP on La Palma covering the northern sky and WASP-South in South Africa covering the south (Pollacco et al. 2006). Each camera used a 200 mm, f/1.8 lens with a broadband filter spanning 400–700 nm, backed by 2048 × 2048 CCDs giving a plate scale of 137 pixel⁻¹. Observations then rastered available fields with a typical 15 minute cadence.

We searched the WASP data for any rotational modulations using the methods from Maxted et al. (2011). TOI-640 was observed for spans of 150 nights in each of four years. The data from 2008, 2009, and 2010 show no significant modulation. The data from 2007, however, show significant power at a period of 62 ± 5 days, with an amplitude of 3 mmag and an estimated false-alarm probability below 1%. Since this is seen in only one season, and given that the data span only 2.5 cycles, we do not regard this detection as fully reliable. For TOI-1333, the WASP data span 130 days in 2007 and show a clear modulation with a period of 15.9 ± 0.3 days, an amplitude of 19 mmag, and a false-alarm probability below 1%. A similar periodicity is also seen in the TESS data and in the Kilodegree Extremely Little Telescope (KELT) data (see below) but at one-third of this period at 5.3 days. No significant periodicity was detected for TOI-1478 or TOI-1601.

Given knowledge of the TESS detections, transits of three of the systems described here can be found readily in the WASP data. TOI-640 was observed between 2006 and 2012, accumulating 23,000 data points. The WASP search algorithm (Collier Cameron et al. 2007) finds the transit with a period of 5.003773 ± 0.000041 and a midtransit epoch (T_C ) of 2454822.00318 ± 0.00411 HJD_TDB. This detection had been overlooked by WASP vetters owing to the near-integer day period (5.00 days), since the dominant red noise in the WASP data is at multiples of a day. TOI-1478 was observed between 2009 and 2012, accumulating 9000 data points, less than usual for WASP since the field is near the crowded Galactic plane. It had not been flagged as a WASP candidate, but the search algorithm finds the transit with a period of 10.18051 ± 0.00017 days and a T_C of 2455696.36710 ± 0.00492 HJD_TDB. TOI-1601 was observed over 2006 and 2007, accumulating 10,400 data points. The search algorithm finds the transit and gets a period of 5.33197 ± 0.00010 and a T_C of 2454186.65253 ± 0.01283 HJD_TDB. We use these T_C values as priors for the EXOFASTv2 global fits of TOI-640 b, TOI-1478 b, and TOI-1601 b. We see an ∼40% reduction in uncertainty on the period of the planet when including the WASP T_C prior.

To complement the TESS photometry, we analyzed observations of these five TOIs from the KELT survey ⁷³ (Pepper et al. 2007, 2012, 2018). For a full description of the KELT observing strategy and reduction process, see Siverd et al. (2012) and Kuhn et al. (2016). KELT has two fully robotic telescopes, each of which uses a Mamiya 645 80 mm f/1.9 lens with 42 mm aperture and Apogee 4 k × 4 k CCD on a Paramount ME mount. This setup provides a 26° × 26° field of view with a 23'' pixel scale. The two telescopes are located at Winer Observatory in Sonoita, AZ and at the South African Astronomical Observatory (SAAO) in Sutherland, South Africa. KELT covers ∼85% of the entire sky, and the observing strategy results in a 20–30 minute cadence. Some of the KELT light curves are publicly available through the NASA Exoplanet Archive. KELT observations were available for TOI-628, TOI-1333, TOI-1478, and TOI-1601. KELT-South observed TOI-628 2828 times and TOI-1478 4632 times from 2010 to 2015. KELT-North observed TOI-1333 from 2012 to 2014 and TOI-1601 from 2006 to 2014, acquiring 2580 and 8520 observations, respectively. Since KELT has been observing since 2006 in some cases, the observations significantly extend the baseline of the photometry and can provide a strong constraint on the ephemeris of each system. Following the strategy described in Siverd et al. (2012) and Kuhn et al. (2016), we also search the KELT light curves for transits of each planet. Unfortunately, no significant signs of the known planetary transits were found, likely due to the poor duty cycle for longer orbital periods.

Following the approach of Stassun et al. (1999) and Oelkers et al. (2018), we executed a search for periodic signals most likely to come from the rotation period of the star. For these stars, we postprocessed the light-curve data using the Trend-Filtering Algorithm (Kovács et al. 2005) to remove common systematics. We then searched for candidate rotation signals using a modified version of the Lomb–Scargle period-finder algorithm (Lomb 1976; Scargle 1982). We searched for periods between a minimum period of 0.5 days and a maximum period of 50 days using 2000 frequency steps. ⁷⁴ We masked periods between 0.5 and 0.505 days and 0.97–1.04 days to avoid the most common detector aliases associated with KELT's observational cadence and its interaction with the periods for the solar and sidereal day. For each star, we selected the highest statistically significant peak of the power spectrum (hereafter γ) as the candidate period.

We then executed a bootstrap analysis, using 1000 Monte Carlo iterations, where the dates of the observations were not changed but the magnitude values of the light curve were randomized, following the work of Henderson & Stassun (2012). We recalculated the Lomb–Scargle power spectrum for each iteration and recorded the maximum peak power (hereafter ${\gamma }_{\mathrm{sim}}$) of all iterations. If the highest power spectrum peak was larger than the maximum simulated peak ($\gamma \gt {\gamma }_{\mathrm{sim}}$) after 1000 iterations, we considered the periodic signal to be a candidate rotation period.

We find TOI-1333 to have a strongly significant (γ > 50) candidate rotation period at 5.3 days, which is consistent with TESS (see Section 2.1), and TOI-1601 and TOI-1478 to have weakly significant (γ > 10) candidate rotation periods of 9.3 and 16.6 days, respectively. However, we do not see these periodicities in the TESS photometry, and they are likely aliases of the KELT observing strategy. KELT did not obtain observations of TOI-640.

Table 1. Literature and Measured Properties

Other Identifiers
		TOI-628	TOI-640	TOI-1333	TOI-1478	TOI-1601
		TIC 281408474	TIC 147977348	TIC 395171208	TIC 409794137	TIC 139375960
		HD 288842	⋯	BD+47 3521A	⋯	⋯
	TYCHO-2	TYC 0146-01523-1	TYC 7099-00846-1	TYC 3595-01186-1	TYC 5440-01407-1	TYC 2836-00689-1
	2MASS	J06370314+0146031	J06385630-3638462	J21400351+4824243	J08254410-1333356	J02332674+4100483
	TESS Sector	6	6,7	15,16	7,8	18
Parameter	Description	Value	Value	Value	Value	Value	Source
αJ2000 a	R.A. (R.A.)	06:37:03.13607	06:38:56.30742	21:40:03.50398	08:25:44.10708	02:33:26.74683	1
δJ2000 a	Decl. (decl.)	01:46:03.19552	−36:38:46.14425	48:24:24.52541	−13:33:35.42756	+41:00:48.36893	1
BT	Tycho BT mag.	10.782 ± 0.051	11.178 ± 0.05	9.933 ± 0.024	11.618 ± 0.082	11.521 ± 0.067	2
VT	Tycho VT mag.	10.176 ± 0.041	10.574 ± 0.043	9.487 ± 0.021	10.805 ± 0.067	10.710 ± 0.051	2
G	Gaia G mag.	10.0579 ± 0.02	10.4006 ± 0.02	9.35 ± 0.02	10.66 ± 0.02	10.53 ± 0.02	1
BP	Gaia BP mag.	10.38 ± 0.02	10.68 ± 0.02	9.59 ± 0.02	11.03 ± 0.02	10.86 ± 0.02	1
RP	Gaia RP mag.	9.61 ± 0.02	9.99 ± 0.02	8.99 ± 0.02	10.16 ± 0.02	10.06 ± 0.02	1
T	TESS mag.	9.6565 ± 0.0066	10.0367 ± 0.006	9.03527 ± 0.0061	10.2042 ± 0.006	10.1035 ± 0.0065	3
J	2MASS J mag.	9.170 ± 0.041	9.519 ± 0.024	8.485 ± 0.027	9.590 ± 0.023	9.505 ± 0.022	4
H	2MASS H mag.	8.895 ± 0.057	9.327 ± 0.026	8.397 ± 0.043	9.255 ± 0.026	9.266 ± 0.021	4
KS	2MASS KS mag.	8.811 ± 0.02	9.243 ± 0.023	8.272 ± 0.024	9.201 ± 0.021	9.19 ± 0.02	4
WISE1	WISE1 mag.	8.76 ± 0.03	9.213 ± 0.03	7.706 ± 0.013	9.15 ± 0.03	9.16 ± 0.03	5
WISE2	WISE2 mag.	8.79 ± 0.03	9.240 ± 0.03	7.594 ± 0.012	9.19 ± 0.03	9.21 ± 0.03	5
WISE3	WISE3 mag.	8.59 ± 0.03	9.239 ± 0.03	8.035 ± 0.019	9.18 ± 0.03	9.18 ± 0.034	5
WISE4	WISE4 mag.	8.23 ± 0.19	⋯	8.043 ± 0.163	⋯	8.80 ± 0.33	5
μα	Gaia DR2 proper motion	−1.437 ± 0.117	−3.872 ± 0.040	−9.810 ± 0.050	−8.277 ± 0.058	21.708 ± 0.095	1
	in R.A. (mas yr−1)
μδ	Gaia DR2 proper motion	−1.082 ± 0.087	4.927 ± 0.045	−10.501 ± 0.046	67.943 ± 0.046	−0.874 ± 0.090	1
	in decl. (mas yr−1)
$v\sin {i}_{\star }$	Rotational velocity (km s−1)	6.9 ± 0.5	6.1 ± 0.5	14.2 ± 0.5	4.3 ± 0.5	6.4 ± 0.5	Sections 2.5.2, 2.5.2 and 2.5.3
vmac	Macroturbulent broadening (km s−1)	5.4 ± 0.7	6.32 ± 1.37	7.4 ± 1.8	4.9 ± 0.5	6.3 ± 0.6	Sections 2.5.2, 2.5.2 and 2.5.3
π b	Gaia parallax (mas)	5.601 ± 0.103	2.925 ± 0.033	4.989 ± 0.038	6.542 ± 0.047	2.974 ± 0.080	1
PRot	Rotation period (days)			5.3 ± 0.159			Sections 2.1, 2.2, and 2.3

Notes. The uncertainties of the photometry have a systematic error floor applied.

^a R.A. and decl. are in epoch J2000. The coordinates come from Vizier, where the Gaia R.A. and decl. have been precessed and corrected to J2000 from epoch J2015.5. ^b Values have been corrected for the −0.30 μas offset as reported by Lindegren et al. (2018).

References are (1) Gaia Collaboration et al. (2018), (2) Høg et al. (2000), (3) Stassun et al. (2018), (4) Cutri et al. (2003), (5) Zacharias et al. (2017).

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To refine the ephemerides and transit parameters for each system while ruling out false-positive scenarios, we obtained photometric follow-up observations on all five systems from the TESS Follow-up Observing Program Working Group ⁷⁵ subgroup 1 (SG1) for seeing-limited photometry. Specifically, the follow-up comes from the Las Cumbres Observatory (LCO) telescope network (Brown et al. 2013), Whitin Observatory at Wellesley College, KeplerCam on the 1.2 m telescope at Fred Lawrence Whipple Observatory (FLWO), Brierfield Observatory, PEST Observatory, C. R. Chambliss Astronomical Observatory (CRCAO) at Kutztown University, Adams Observatory at Austin College, and Suto Observatory. To schedule the photometric transit follow-up observations, we used the TAPIR software package (Jensen 2013). The data reduction and aperture photometry extraction was performed using AstroImageJ (Collins et al. 2017) for all follow-up data other than the PEST observations, which were done using a custom software package PEST Pipeline. ⁷⁶ The TFOP follow-up photometry for these five systems is shown in Figure 2, and a list of each telescope's information and details on each follow-up transit can be seen in Table 2. The follow-up transits presented in Figure 2 are available as machine-readable tables with this paper.

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Table 2. Photometric Follow-up Observations of These Systems Used in the Global Fits and the Detrending Parameters

Target	Observatory	Date (UT)	Size (m)	Filter	FOV	Pixel Scale	Exp (s)	Additive Detrending
TOI-628 b	FLWO/KeplerCam	2019 Dec 6	1.2	${z}^{{\prime} }$	231 × 231	0672	9	None
TOI-628 b	LCO TFN	2019 Dec 16	0.4	${z}^{{\prime} }$	19' × 29'	057	18	air mass
TOI-628 b	Whitin	2020 Feb 8	0.7	${r}^{{\prime} }$	24' × 24'	067	10	air mass
TOI-640 b	Brierfield	2019 Dec 27	0.36	I	494 × 494	147	90	X(FITS), Y(FITS)
TOI-640 b	PEST	2020 Mar 1	0.3048	R	31' × 21'	12	60	none
TOI-640 b	LCO SSO	2020 Aug 23	1.0	${z}^{{\prime} }$	27' × 27'	039	60	Y(FITS)
TOI-640 b	LCO SSO	2020 Nov 6	1.0	${z}^{{\prime} }$	27' × 27'	039	60	air mass
TOI-1333 b	CRCAO	2020 Jul 29	0.6096	I	268 × 268	039	45	air mass
TOI-1333 b	LCO McDonald	2020 Jul 29	0.4	${z}^{{\prime} }$	19' × 29'	057	30	total counts
TOI-1333 b	LCO McDonald	2020 Aug 12	0.4	${z}^{{\prime} }$	19' × 29'	057	30	Y(FITS)
TOI-1333 b	CRCAO	2020 Sep 19	0.6096	${z}^{{\prime} }$	268 × 268	039	80	air mass
TOI-1478 b	FLWO/KeplerCam	2019 Dec 14	1.2	${i}^{{\prime} }$	231 × 231	0672	7	none
TOI-1478 b	PEST	2020 Jan 3	0.3048	R	31' × 21'	12	30	air mass
TOI-1601 b	GMU	2020 Aug 30	0.8	R	23' × 23'	034	30	air mass, sky/pixels
TOI-1601 b	GMU	2020 Sep 15	0.8	R	23' × 23'	034	30	air mass, sky/pixels, X(FITS)
TOI-1601 b	CRCAO	2020 Oct 1	0.6096	${z}^{{\prime} }$	268 × 268	039	90	air mass
TOI-1601 b	Adams	2020 Oct 17	0.61	I	26' × 26'	038	60	air mass, total counts
TOI-1601 b	LCO McDonald	2020 Oct 17	1.0	${z}^{{\prime} }$	27' × 27'	039	60	air mass, sky/pixels

Note. All of the follow-up photometry presented in this paper is available as the Data behind Figure 2 in machine-readable form in the online journal. See Section D in the Appendix of Collins et al. (2017) for a description of each detrending parameter.

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To rule out false-positive scenarios and measure the mass and orbital eccentricity of each system, we obtained time-series spectroscopy coordinated through the TFOP WGs. A sample of one radial velocity (RV) point per target per instrument is shown in Table 3, with the full table available in machine-readable form in the online journal. The RVs and best-fit models from our EXOFASTv2 analysis are shown in Figure 3 (see Section 3). Following the methodology in Zhou et al. (2018), we measure the $v\sin {I}_{* }$ and macroturbulent broadening for all five systems from the Tillinghast Reflector Echelle Spectrograph except TOI-640, where the CHIRON observations were used (see Table 1).

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2.5.1. TCES Spectroscopy

2.5.2. TRES Spectroscopy

2.5.3. CHIRON Spectroscopy

We obtained a series of spectroscopic observations with the 1.5 m SMARTS/CHIRON facility (see Table 3; Tokovinin et al. 2013) for TOI-640 and TOI-1478 to measure the host star parameters and constrain their masses and eccentricities. The 1.5 m SMARTS facility is located at Cerro Tololo Inter-American Observatory (CTIO), Chile. CHIRON is a high-resolution echelle spectrograph fed via an image slicer through a single multimode fiber, with a spectral resolving power of R ∼ 80,000 over the wavelength region from 410 to 870 nm. For the case of TOI-1478, we treat the pre- and postshutdown RVs as separate instruments within the fit (see Section 3).

To obtain the stellar atmospheric parameters, we matched the CHIRON spectra against an interpolated library of ∼10,000 observed spectra classified by SPC (Buchhave et al. 2012). The metallicity from this analysis was used as a prior for the global fit of TOI-640 (see Table 4). RVs were derived via the least-squares deconvolution (Donati et al. 1997; Zhou et al. 2020) of the spectra against nonrotating synthetic templates matching the spectral parameters of each host star, generated using the ATLAS9 model atmospheres (Kurucz 1992). The RVs were then measured by fitting a least-squares deconvolution line profile with a rotational broadening kernel as prescribed by Gray (2005). The velocities for each system are presented in Table 3.

Table 4. Median Values and 68% Confidence Intervals for the Global Models

Priors:		TOI-628 b	TOI-640 b	TOI-1333 b a	TOI-1478 b b	TOI-1601 b
Gaussian	c Gaia parallax (mas)	5.601 ± 0.103	2.925 ± 0.033	⋯	6.542 ± 0.047	2.974 ± 0.080
Gaussian	[Fe/H] Metallicity (dex)	0.24 ± 0.08	0.02 ± 0.1	0.11 ± 0.08	0.07 ± 0.08	0.31 ± 0.08
Upper Limit	AV V-band extinction (mag)	2.977	0.292	⋯	0.120	0.14694
Gaussian	R⋆ Stellar radius ( R⊙)	⋯	⋯	1.963 ± 0.064	⋯	⋯	⋯
Gaussian	Teff Stellar effective temperature (K)	⋯	⋯	6250 ± 100	⋯	⋯	⋯
Gaussian	TC d Time of conjunction (HJDTDB)	⋯	2454822.00318 ± 0.00411	⋯	2455696.36710 ± 0.00492	2454186.65253 ± 0.01283
Gaussian e	DT Dilution in TESS	0.00000 ± 0.00344	0.00000 ± 0.00360	0.00000 ± 0.03817	⋯	0.0 ± 0.00196
Gaussian f	DI Dilution in I	⋯	⋯	0.3609 ± 0.0180	⋯	⋯
Gaussian f	DR Dilution in R	⋯	⋯	0.3499 ± 0.0175	⋯	⋯
Gaussian f	${D}_{{z}^{{\prime} }}$ Dilution in ${z}^{{\prime} }$	⋯	⋯	0.0664 ± 0.0033	⋯	⋯
Parameter	Units	Values
Stellar Parameters:
Probability		100%	100%	100%	100%	68.4%	31.6%
M*	Mass ( M⊙)	${1.311}_{-0.075}^{+0.066}$	${1.536}_{-0.076}^{+0.069}$	${1.464}_{-0.079}^{+0.076}$	${0.947}_{-0.041}^{+0.059}$	${1.517}_{-0.049}^{+0.053}$	${1.340}_{-0.045}^{+0.042}$
R*	Radius ( R⊙)	${1.345}_{-0.040}^{+0.046}$	${2.082}_{-0.058}^{+0.064}$	${1.925}_{-0.063}^{+0.064}$	${1.048}_{-0.029}^{+0.030}$	${2.186}_{-0.063}^{+0.074}$	${2.185}_{-0.080}^{+0.086}$
L*	Luminosity ( L⊙)	${2.48}_{-0.28}^{+0.41}$	${6.83}_{-0.54}^{+0.41}$	${5.17}_{-0.45}^{+0.49}$	${0.971}_{-0.035}^{+0.036}$	${5.40}_{-0.33}^{+0.35}$	${5.25}_{-0.33}^{+0.35}$
FBol	Bolometric flux × 10−9 (cgs)	${2.52}_{-0.27}^{+0.39}$	${1.87}_{-0.14}^{+0.10}$	⋯	1.32 ± 0.45	${1.505}_{-0.61}^{+0.52}$	${1.485}_{-0.61}^{+0.59}$
ρ*	Density (cgs)	${0.762}_{-0.078}^{+0.067}$	${0.240}_{-0.025}^{+0.024}$	${0.289}_{-0.028}^{+0.031}$	${1.16}_{-0.11}^{+0.14}$	${0.205}_{-0.018}^{+0.016}$	${0.181}_{-0.019}^{+0.020}$
$\mathrm{log}g$	Surface gravity (cgs)	${4.300}_{-0.036}^{+0.026}$	${3.987}_{-0.036}^{+0.030}$	${4.034}_{-0.033}^{+0.032}$	${4.374}_{-0.032}^{+0.039}$	${3.940}_{-0.025}^{+0.022}$	${3.885}_{-0.031}^{+0.029}$
Teff	Effective temperature (K)	${6250}_{-190}^{+220}$	${6460}_{-150}^{+130}$	6274 ± 97	${5597}_{-82}^{+83}$	${5948}_{-89}^{+87}$	${5910}_{-99}^{+96}$
[Fe/H]	Metallicity (dex)	${0.258}_{-0.080}^{+0.078}$	${0.072}_{-0.076}^{+0.085}$	${0.119}_{-0.077}^{+0.078}$	${0.078}_{-0.066}^{+0.072}$	${0.329}_{-0.075}^{+0.073}$	0.299 ± 0.076
[Fe/H]0 g	Initial metallicity	${0.271}_{-0.068}^{+0.070}$	${0.174}_{-0.080}^{+0.088}$	${0.212}_{-0.084}^{+0.083}$	${0.110}_{-0.064}^{+0.069}$	0.347 ± 0.069	${0.296}_{-0.069}^{+0.070}$
Age	Age (Gyr)	${1.28}_{-0.91}^{+1.6}$	${1.99}_{-0.40}^{+0.55}$	${2.33}_{-0.56}^{+0.71}$	${9.1}_{-3.9}^{+3.1}$	${2.64}_{-0.39}^{+0.38}$	${4.27}_{-0.42}^{+0.53}$
EEP h	Equal evolutionary phase	${331}_{-37}^{+31}$	${380}_{-17}^{+19}$	${381}_{-21}^{+20}$	${400}_{-37}^{+16}$	${403.1}_{-11}^{+7.9}$	${452.9}_{-5.2}^{+4.3}$
AV	V-band extinction (mag)	${0.22}_{-0.14}^{+0.18}$	${0.217}_{-0.095}^{+0.055}$	⋯	${0.062}_{-0.041}^{+0.039}$	${0.103}_{-0.053}^{+0.032}$	${0.086}_{-0.053}^{+0.043}$
σSED	SED photometry error scaling	${3.27}_{-0.73}^{+1.2}$	${0.84}_{-0.22}^{+0.35}$	⋯	${0.70}_{-0.17}^{+0.29}$	${1.17}_{-0.27}^{+0.42}$	${1.20}_{-0.27}^{+0.44}$
ϖ	Parallax (mas)	5.64 ± 0.10	2.925 ± 0.033	⋯	6.536 ± 0.047	${2.948}_{-0.075}^{+0.074}$	${2.973}_{-0.076}^{+0.077}$
d	Distance (pc)	${177.4}_{-3.1}^{+3.2}$	${341.8}_{-3.8}^{+3.9}$	⋯	153.0 ± 1.1	${339.2}_{-8.3}^{+8.8}$	${336.4}_{-8.5}^{+8.9}$
Planetary Parameters:
P	Period (days)	${3.4095675}_{-0.0000069}^{+0.0000070}$	5.0037775 ± 0.0000048	4.720219 ± 0.000011	10.180249 ± 0.000015	5.331751 ± 0.000011	5.331751 ± 0.000011
RP	Radius ( RJ)	${1.060}_{-0.034}^{+0.041}$	${1.771}_{-0.056}^{+0.060}$	${1.396}_{-0.054}^{+0.056}$	${1.060}_{-0.039}^{+0.040}$	${1.239}_{-0.039}^{+0.046}$	${1.241}_{-0.049}^{+0.052}$
MP	Mass ( MJ)	${6.33}_{-0.31}^{+0.29}$	0.88 ± 0.16	2.37 ± 0.24	${0.851}_{-0.047}^{+0.052}$	0.99 ± 0.11	${0.912}_{-0.10}^{+0.095}$
T0 i	Optimal conjunction time (BJDTDB)	2458629.47972 ± 0.00039	${2458459.73877}_{-0.00083}^{+0.00071}$	2458913.37033 ± 0.00045	${2458607.90338}_{-0.00049}^{+0.00052}$	${2458990.55302}_{-0.00079}^{+0.00081}$	${2458990.55306}_{-0.00082}^{+0.00081}$
a	Semimajor axis (au)	${0.04860}_{-0.00094}^{+0.00080}$	${0.06608}_{-0.0011}^{+0.00098}$	${0.0626}_{-0.0012}^{+0.0011}$	${0.0903}_{-0.0013}^{+0.0018}$	${0.06864}_{-0.00075}^{+0.00079}$	${0.06586}_{-0.00075}^{+0.00069}$
i	Inclination (degrees)	${88.41}_{-0.93}^{+1.0}$	${82.54}_{-0.59}^{+0.42}$	${85.70}_{-0.65}^{+1.3}$	${88.51}_{-0.22}^{+0.29}$	${88.84}_{-1.1}^{+0.81}$	${88.4}_{-1.3}^{+1.1}$
e	Eccentricity	${0.072}_{-0.023}^{+0.021}$	${0.050}_{-0.035}^{+0.054}$	${0.073}_{-0.052}^{+0.092}$	${0.024}_{-0.017}^{+0.032}$	${0.036}_{-0.026}^{+0.044}$	${0.057}_{-0.039}^{+0.050}$
τcirc	Tidal circularization timescale (Gyr)	${3.32}_{-0.61}^{+0.53}$	${0.206}_{-0.057}^{+0.060}$	${1.29}_{-0.33}^{+0.37}$	${42.5}_{-8.1}^{+11}$	1.85 ± 0.38	${1.52}_{-0.38}^{+0.42}$
ω*	Argument of periastron (degrees)	$-{74}_{-15}^{+13}$	${159}_{-99}^{+86}$	${105}_{-40}^{+64}$	$-{110}_{-130}^{+120}$	$-{180}_{-100}^{+110}$	${120}_{-70}^{+57}$
Teq	Equilibrium temperature (K)	${1586}_{-40}^{+52}$	${1749}_{-30}^{+26}$	${1679}_{-34}^{+35}$	918 ± 11	${1619}_{-23}^{+24}$	${1642}_{-24}^{+25}$
K	RV semiamplitude (m s−1)	${713}_{-22}^{+20}$	78 ± 14	${223}_{-21}^{+22}$	${82.5}_{-3.8}^{+4.0}$	${87.3}_{-9.9}^{+9.2}$	${87.6}_{-9.6}^{+8.9}$
RP /R*	Radius of planet in stellar radii	${0.08108}_{-0.00071}^{+0.00075}$	${0.08738}_{-0.00086}^{+0.00091}$	${0.0745}_{-0.0015}^{+0.0014}$	0.1040 ± 0.0015	${0.05827}_{-0.00070}^{+0.00071}$	${0.05834}_{-0.00072}^{+0.00074}$
a/R*	Semimajor axis in stellar radii	${7.78}_{-0.27}^{+0.22}$	${6.82}_{-0.24}^{+0.22}$	${6.98}_{-0.23}^{+0.24}$	${18.54}_{-0.60}^{+0.70}$	${6.76}_{-0.20}^{+0.17}$	6.48 ± 0.23
Depth	Flux decrement at midtransit	0.00657 ± 0.00012	${0.00764}_{-0.00015}^{+0.00016}$	0.00555 ± 0.00021	0.01083 ± 0.00032	${0.003395}_{-0.000081}^{+0.000083}$	${0.003403}_{-0.000083}^{+0.000087}$
τ	Ingress/egress transit duration (days)	${0.01247}_{-0.00061}^{+0.0012}$	${0.0454}_{-0.0026}^{+0.0028}$	${0.0177}_{-0.0033}^{+0.0027}$	0.0208 ± − 0.0022	${0.01483}_{-0.00034}^{+0.00084}$	${0.01503}_{-0.00049}^{+0.0013}$
T14	Total transit duration (days)	${0.1576}_{-0.0013}^{+0.0015}$	0.1502 ± 0.0017	${0.1934}_{-0.0029}^{+0.0025}$	0.1736 ± 0.0023	0.2627 ± 0.0020	${0.2631}_{-0.0021}^{+0.0022}$
b	Transit impact parameter	${0.23}_{-0.15}^{+0.13}$	${0.8763}_{-0.0067}^{+0.0063}$	${0.504}_{-0.19}^{+0.085}$	${0.481}_{-0.076}^{+0.050}$	${0.136}_{-0.095}^{+0.13}$	${0.18}_{-0.12}^{+0.14}$
TS,14	Total eclipse duration (days)	${0.1387}_{-0.0055}^{+0.0063}$	${0.1481}_{-0.019}^{+0.0070}$	${0.208}_{-0.013}^{+0.041}$	${0.1736}_{-0.0066}^{+0.0075}$	${0.263}_{-0.013}^{+0.014}$	${0.279}_{-0.017}^{+0.024}$
ρP	Density (cgs)	${6.58}_{-0.75}^{+0.70}$	${0.195}_{-0.040}^{+0.042}$	${1.08}_{-0.15}^{+0.18}$	${0.88}_{-0.11}^{+0.13}$	${0.640}_{-0.093}^{+0.097}$	${0.589}_{-0.091}^{+0.098}$
$\mathrm{log}{g}_{P}$	Surface gravity	${4.145}_{-0.038}^{+0.031}$	${2.841}_{-0.095}^{+0.078}$	${3.479}_{-0.056}^{0.054}$	${3.273}_{-0.043}^{+0.045}$	${3.201}_{-0.059}^{+0.052}$	${3.165}_{-0.061}^{+0.055}$
TS	Time of eclipse (BJDTDB)	${2458467.566}_{-0.038}^{+0.031}$	${2454824.46}_{-0.20}^{+0.12}$	${2458717.445}_{-0.13}^{+0.097}$	${2455701.431}_{-0.12}^{+0.092}$	${2454189.289}_{-0.17}^{+0.095}$	${2454189.27}_{-0.19}^{+0.12}$
$e\cos {\omega }_{* }$		${0.019}_{-0.018}^{+0.014}$	$-{0.012}_{-0.062}^{+0.038}$	$-{0.012}_{-0.042}^{+0.032}$	$-{0.002}_{-0.018}^{+0.014}$	$-{0.007}_{-0.049}^{+0.028}$	$-{0.013}_{-0.057}^{+0.035}$
$e\sin {\omega }_{* }$		$-{0.068}_{-0.022}^{+0.024}$	${0.007}_{-0.029}^{+0.042}$	${0.053}_{-0.056}^{+0.10}$	${0.000}_{-0.029}^{+0.030}$	${0.001}_{-0.027}^{+0.028}$	${0.031}_{-0.033}^{+0.044}$
d/R*	Separation at midtransit	${8.29}_{-0.40}^{+0.36}$	${6.76}_{-0.51}^{+0.38}$	${6.59}_{-0.77}^{+0.54}$	${18.58}_{-0.88}^{+0.97}$	${6.74}_{-0.36}^{+0.32}$	${6.27}_{-0.47}^{+0.41}$

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

^a The SED was not included within the global fit for TOI-1333. ^b No TESS dilution prior was used for TOI-1478 b because initial fits showed a fitted dilution past the 10% prior we used in the other systems. We fit for a dilution term within the fit for the TESS bandpass but with no prior. ^c The tidal quality factor (Q_S ) is assumed to be 10⁶. ^d T_C prior comes from analysis of the WASP photometry (see Section 2.2). We note that this time is in HJD_TDB while all data files and results here are BJD_TDB. The difference between these two time systems is on the order of seconds while the precision on T_C used as a prior is on order of minutes, and therefore has no influence on the results. ^e We assume the TESS correction for blending is much better than 10%. We use a prior of 10% of the determined blending from TICv8 (Stassun et al. 2018). ^f Dilution prior for TOI-1333 comes from our three-component SED analysis (see Section 2.6.4). ^g The initial metallicity is the metallicity of the star when it was formed. ^h The equal evolutionary point (EEP) corresponds to static points in a star's evolutionary history when using the MIST isochrones and can be a proxy for age. See Section 2 in Dotter (2016) for a more detailed description of EEP. ⁱ Optimal time of conjunction minimizes the covariance between T_C and period. This is the transit midpoint.

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2.5.4. FEROS Spectroscopy

2.5.5. CORALIE Spectroscopy

2.5.6. MINERVA-Australis Spectroscopy

As part of our standard process for validating transiting exoplanets to assess possible contamination of bound or unbound companions on the derived planetary radii (Ciardi et al. 2015), we obtained high-spatial-resolution imaging observations of all five systems.

2.6.1. Speckle Imaging

2.6.2. Adaptive Optics Imaging

We observed TOI-628 on UT 2019 November 11 using the ShARCS adaptive optics system on the 3 m Shane Telescope at Lick Observatory. ShARCS has a field of view of 20'' × 20'' and a pixel scale of 0033 pixel⁻¹. We conducted our observations using a square four-point dither pattern with a separation of 4'' between each dither position. Our observations were taken in natural guide-star mode with high winds. We obtained one sequence of observations in the Ks band and a second sequence in the J band for a total integration time of 510 s in the Ks band and 225 s in the J band. See Savel et al. (2020) for a detailed description of the observing strategy. Neither set of observations revealed any companions for TOI-628.

We observed TOI-1333 (Br–γ and H − cont) and TOI-1478 with infrared high-resolution adaptive optics (AO) imaging at Palomar Observatory. The Palomar Observatory observations were made with the PHARO instrument (Hayward et al. 2001) behind the natural guide-star AO system P3 K (Dekany et al. 2013). The observations were made on 2019 November 10 UT in a standard five-point quincunx dither pattern with steps of 5''. Each dither position was observed three times, offset in position from each other by 05 for a total of 15 frames. The camera was in the narrow-angle mode with a full field of view of ∼25'' and a pixel scale of approximately 0025 per pixel. Observations were made in the narrow-band Br–γ filter (λ_o = 2.1686; Δλ = 0.0326 μm) for TOI-1333 and TOI-1478, and in the H − cont filter (λ_o = 1.668; Δλ = 0.018 μm) for TOI-1333. The observations get down to ΔMag = 6.54 (Br–γ) and 7.52 (H − cont) for TOI-1333 and ΔMag = 6.8 (Br–γ) for TOI-1478 (all at ∼05).

TOI-1333 was also observed using NIRI on Gemini-North (Hodapp et al. 2003) on UT 2019 November 14 in the Br–γ filter. NIRI has a 22'' × 22'' field of view with a 0022 pixel scale. Our sequence consisted of nine images, each with exposure time 4.4 s, and we dithered the telescope between each exposure. A sky background was constructed from the dithered frames and subtracted from each science image. We also performed bad pixel removal and flat-fielding, and then aligned and coadded frames. NIRI got down to ΔMag = 6.7 at 0472.

We also observed TOI-1601 using the Near Infrared Camera 2 (NIRC2) AO setup on the W. M. Keck Observatory in the Br–γ filter and in the J − cont filter on UT 2020 September 9. The NIRC2 detector has a 9.971 mas pixel⁻¹ using a 1024 × 1024 CCD (field of view = 10'' × 10''; Service et al. 2016). Unfortunately, the lower left quadrant of the CCD is known to have higher than typical noise levels in comparison to the others. To avoid this issue, a three-point dither pattern technique was used. The images were aligned and stacked after normal flat-field and sky background corrections. No nearby companions were seen down to Δmag = 6.680 (J − cont) and 6.402 (Br–γ) for TOI-1601 at 05.

While the observing strategy differed, all of the AO data were processed and analyzed with a custom set of IDL tools. The science frames were flat-fielded and sky-subtracted. The flat fields were generated from a median combination of the dark-subtracted flats taken on sky. The flats were normalized such that the median value of the flats is unity. The sky frames were generated from the median average of the 15 dithered science frames; each science image was then sky-subtracted and flat-fielded. The reduced science frames were combined into a single combined image using an intrapixel interpolation that conserves flux, shifts the individual dithered frames by the appropriate fractional pixels, and median-coadds the frames (see Figure 4). The final resolution of the combined dither was determined from the FWHM of the point-spread function; the resolutions of the Br–γ and H − cont images are 0092 and 0075, respectively (Figure 4).

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The sensitivities of the final combined AO images were determined by injecting simulated sources azimuthally around the primary target every 20° at separations of integer multiples of the central source's FWHM (Furlan et al. 2017; M. Lund et al. 2021, in preparation). The brightness of each injected source was scaled until standard aperture photometry detected it with 5σ significance. The resulting brightness of the injected sources relative to the target set the contrast limits at that injection location. The final 5σ limit at each separation was determined from the average of all of the determined limits at that separation, and the uncertainty on the limit was set by the rms dispersion of the azimuthal slices at a given radial distance. The sensitivity curves for TOI-1333 are shown in Figure 4 along with an inset image zoomed in to the primary target showing no other companion stars.

2.6.3. TOI-1333 Companions

2.6.4. TOI-1333 Spectral Energy Distribution

The presence of the two stellar companions within a few arcseconds of TOI-1333 implies that the TESS and SG1 light curves of the TOI-1333 planet transit are likely to be diluted to some extent by the light from these other stars. Although the QLP corrects the TESS light curve for the blended contributions of known targets in the TESS input catalog (TIC), we need to correct the follow-up photometry from TFOP for different amounts of dilution. To quantify this flux dilution, we performed a multicomponent SED fit with Kurucz model atmospheres following the procedures described in Stassun & Torres (2016), utilizing the resolved broadband measurements from Gaia, 2MASS, and our AO observations (see Section 2.6.2).

We adopted the spectroscopic T_eff (6250 ± 100 K) from TRES for TOI-1333 and the T_eff from the TICv8 (Stassun et al. 2019) and from the Gaia DR2 catalog for the companions, with A_V being left as a free parameter but limited to the maximum line-of-sight value from the dust maps of Schlegel et al. (1998). The resulting fits are shown in Figure 5, with best-fit A_V = 0.06 ± 0.06 for the TOI-1333 planet host. Integrating the SED models over the TESS bandpass gives the total flux dilution (F₂ + F₃)/F₁ = 0.55 with values of 0.56 in the I band, 0.54 in the R band, and 0.58 in the Sloan ${z}^{{\prime} }$. We also used the SED fits to constrain the contribution from only the 2'' companion since some of our follow-up photometry only resolved the 7'' companion. The flux dilution of F₂/F₁ is 0.07 in the I band, 0.06 in the R band, and 0.07 in the Sloan ${z}^{{\prime} }$. By combining the deblended SED of the primary star TOI-1333 with the known Gaia DR2 parallax, we measure its radius to be R_⋆ = 1.963 ± 0.064 R_⊙. We use this as a prior on the global fit for TOI-1333 (see Section 3).

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For each of the TOIs analyzed here, we used their parallaxes, proper motions, and radial velocities and associated uncertainties from the Gaia DR2 catalog (Gaia Collaboration et al. 2018) to determine their location, kinematics, orbits, and associations with known stellar populations. ⁷⁸ We corrected the native DR2 parallaxes and uncertainties using the prescription given in Lindegren et al. (2018). From these we computed the prior (DR2-based) estimates of the distances to the systems. ⁷⁹ We used these to compute the heliocentric UVW space motions of the host stars, and then corrected for the Sun's motion (UVW)_⊙ with respect to the local standard of rest (LSR) as determined by Coşkunoǧlu et al. (2011). These resulting (UVW) values are shown in Table 1. We note that we adopt a right-handed coordinate system, such that a positive U is toward the Galactic center.

We used the Galactic latitudes and distances to the systems to estimate their Z height relative to the Sun, and then corrected for the Z_⊙ ≃ 30 pc offset of the Sun from the Galactic plane as determined by Bovy (2017) from the analysis of local giants. We use the UVW velocities relative to the LSR to determine the likelihood that the star belongs to a thin disk, thick disk, halo, or Hercules stream, ⁸⁰ using the categorization scheme of Bensby et al. (2014). We also report the estimates of the parameters of the Galactic orbits of the systems as determined by Mackereth & Bovy (2018) using Gaia DR2 astrometry and radial velocities. ⁸¹ We estimated the spectral type of each TOI using its T_eff as determined from the global fit and given in Table 4 and using the T_eff–spectral type relations of Pecaut & Mamajek (2013). We then compared the position and orbits of the systems to the scale height h_Z of stars of similar spectral type as determined by Bovy (2017).

Finally, we also consider whether the systems may belong to any of the known nearby (≲150 pc), young (≲Gyr) associations using the BANYAN Σ (Bayesian Analysis for Nearby Young AssociatioNs Σ) estimator (Gagné et al. 2018). Not surprisingly, none of the systems had any significant (≳1%) probability of being associated with these young associations, and the BANYAN Σ estimator assigned all five systems as belonging to the "field" with a high probability ≳99%. We now discuss the results for each of the systems individually.

TOI-628: We find a distance from the Sun of d = 178 ± 3 pc, consistent with the posterior value listed in Table 4, and Z − Z_⊙ ≃ − 23 pc. We derive velocities relative to the LSR of (U, V, W) = (−8.7 ± 0.4, 3.2 ± 0.2, 4.2 ± 0.1) km s⁻¹. According to the categorization scheme of Bensby et al. (2014), the system has a >99% probability of belonging to the thin disk. The Galactic orbit as estimated by Mackereth & Bovy (2018) has a perigalacticon of R_p = 7.67 kpc and apogalacticon of R_a = 8.19 kpc, an eccentricity of e = 0.03, and a maximum Z excursion from the Galactic plane of ${Z}_{\max }=63\,\mathrm{pc}$. This orbit is consistent with both the current location of the system and the scale height of 97 pc for stars of similar spectral type (F7V). Indeed, TOI-628 is relatively dynamically "cold" for its spectral type. In other words, it has an orbit that is fairly close to that of the local LSR.

TOI-640: We find a distance from the Sun of d = 340 ± 4 pc, consistent with the posterior value listed in Table 4, and Z − Z_⊙ ≃ − 76 pc. We derive velocities relative to the LSR of (U, V, W) = (−16.8 ± 0.2, −16.7 ± 0.4, −8.7 ± 0.2) km s⁻¹. According to the categorization scheme of Bensby et al. (2014), the system has an ∼99% probability of belonging to the thin disk. The Galactic orbit as estimated by Mackereth & Bovy (2018) has a perigalacticon of R_p = 6.28 kpc and apogalacticon of R_a = 8.16 kpc, an eccentricity of e = 0.13, and a maximum Z excursion from the Galactic plane of ${Z}_{\max }=150\,\mathrm{pc}$. This orbit is both consistent with the current location of the system and suggests that the system is nearing its maximum excursion above the plane. It is also consistent with the scale height of 85 pc for stars of similar spectral type (F5.5V).

TOI-1333: We find a distance from the Sun of d = 200 ± 2 pc and Z − Z_⊙ ≃ 19 pc. We derive velocities relative to the LSR of (U, V, W) = (23.0 ± 0.1, −1.00 ± 0.3, −6.0 ± 0.1) km s⁻¹. According to the categorization scheme of Bensby et al. (2014), the system has an ∼99% probability of belonging to the thin disk. The Galactic orbit as estimated by Mackereth & Bovy (2018) has a perigalacticon of R_p = 7.25 kpc and apogalacticon of R_a = 8.32 kpc, an eccentricity of e = 0.07, and a maximum Z excursion from the Galactic plane of ${Z}_{\max }=91\,\mathrm{pc}$. This orbit is consistent with the current location of the system. It is also consistent with the scale height of 97 pc for stars of similar spectral type (F7V).

TOI-1478: We find a distance from the Sun of d = 153 ± 1 pc, and Z − Z_⊙ ≃ 67 pc. We derive velocities relative to the LSR of (U, V, W) = (−37.0 ± 0.3, 26.4 ± 0.4, 32.5 ± 0.2) km s⁻¹. According to the categorization scheme of Bensby et al. (2014), the system has an ∼88% probability of belonging to the thin disk and an ∼12% probability of belonging to the thick disk (and negligible probabilities of belonging to the halo or Hercules stream). The Galactic orbit as estimated by Mackereth & Bovy (2018) has a perigalacticon of R_p = 7.71 kpc and apogalacticon of R_a = 10.34 kpc, an eccentricity of e = 0.14, and a maximum Z excursion from the Galactic plane of ${Z}_{\max }=650\,\mathrm{pc}$. Unfortunately, Bovy (2017) was unable to determine the scale height of stars of similar spectral type (G6V), due to incompleteness. Nevertheless, it would appear that TOI-1478's orbit has a maximum Z excursion that exceeds the expected scale height for stars of similar spectral type as estimated by extrapolating from the results of Bovy (2017) from earlier spectral types. Surprisingly, its current distance above the plane is only a small fraction of its predicted maximum excursion. In summary, the weight of evidence suggests that TOI-1478 may well be a thick disk star that we happen to be observing when it is near the Galactic plane. Detailed chemical abundance measurements (e.g., [α/Fe]) may provide corroborating evidence for or against this hypothesis.

TOI-1601: We find a distance from the Sun of d = 336 ± 9 pc, consistent with the posterior value listed in Table 4, and Z − Z_⊙ ≃ − 73 pc. We derive velocities relative to the LSR of (U, V, W) = (−8.1 ± 0.7, −14.5 ± 0.7, 20.9 ± 0.4) km s⁻¹. According to the categorization scheme of Bensby et al. (2014), the system has an ∼98% probability of belonging to the thin disk. The Galactic orbit as estimated by Mackereth & Bovy (2018) has a perigalacticon of R_p = 6.50 kpc and apogalacticon of R_a = 8.32 kpc, an eccentricity of e = 0.12, and a maximum Z excursion from the Galactic plane of ${Z}_{\max }=351\,\mathrm{pc}$. This orbit is consistent with the current location of the system. The maximum Z excursion is a factor of ∼3.3 times larger than the scale height of 103 pc for stars of similar spectral type (G0V). The probability that a star in a population with a given scale height h_z = 108 pc has a maximum excursion of ${z}_{\max }=351$ pc is nonnegligible. Thus, we expect that TOI-1601 is a thin disk star that is simply in the tail of the distribution of ${z}_{\max }$. Again, detailed abundances could corroborate or refute this conclusion.

After each EXOFASTv2 fit, we inspect the posteriors of each fitted and derived parameter, visually inspecting for any anomalies such as multimodal distributions. In all cases but TOI-1601 b, no issues were noted. For TOI-1601 b, we see a clear bimodal distribution in the mass and age of the host star (see Figure 6). We find two peaks in the mass distribution at 1.340 and 1.517 M_⊙, which correspond to the two peaks seen in the age distribution at 4.27 and 2.63 Gyr. There is no optimal way to represent the bimodal solution, so we split the mass of the host star at the minimum value of 1.415 M_⊙ and extract two solutions for both peaks identified. We adopt the high-mass solution for the discussion since it has a higher probability (66.7%) of being correct from our analysis, but we present both solutions in Table 4 for future analysis. We note that we observed no significant change in any systematic parameters, suggesting the bimodality is due to our limited precision that is not sufficient to completely separate similar solutions, due to the host star being slightly evolved.

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TOI-628 (TIC 281408474) is a V = 10.18 late-F star with a mass of M_* = ${1.311}_{-0.075}^{+0.066}$ M_⊙, radius of R_* = ${1.345}_{-0.040}^{+0.046}$ R_⊙, and an age of ${1.28}_{-0.91}^{+1.6}$ Gyr. Its planetary companion (TOI-628 b) has a radius of R_P = ${1.060}_{-0.034}^{+0.041}$ R_J and a mass of M_P = ${6.33}_{-0.31}^{+0.29}$ M_J and is on a 3.4096 day period orbit. Our global analysis measures a nonzero orbital eccentricity of e = ${0.072}_{-0.023}^{+0.021}$. Within our global fit, we derive a circularization timescale of τ_circ = ${3.32}_{-0.61}^{+0.53}$ Gyr (for this system, assuming equilibrium tides and tidal quality factors for the planet and star of Q_p 10⁶ and Q_* 10⁶; Adams & Laughlin 2006) for this system, which is longer than our estimated age from MIST of ${1.28}_{-0.91}^{+1.6}$ Gyr. Thus the small but nonzero eccentricity is likely a vestige of the initially high eccentricity that the planet obtained during some process that initiated high-eccentricity migration, a high eccentricity that was subsequently damped to the eccentricity we see today. Without a tighter constraint on the system's age, this is not conclusive. Also of interest is the high mass of TOI-628 b, which makes it one of only a few dozen known hot Jupiters with a mass >6 M_J, and the most massive hot Jupiter found from TESS to date (see Figure 7).

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The host star TOI-640 (TIC 147977348) is an F-star with a mass of ${1.526}_{-0.079}^{+0.072}$ M_⊙ and a radius of ${2.082}_{-0.058}^{+0.064}$ R_⊙. The host star appears to be just transitioning off the main sequence onto the subgiant branch, as suggested by our measured $\mathrm{log}g$ = ${3.987}_{-0.036}^{+0.030}$ dex (cm s⁻²) and corresponding tight age constraint within our global fit from the MIST evolutionary tracks of ${1.99}_{-0.40}^{+0.55}$ Gyr. It hosts a planetary companion, TOI-640 b, which is a highly inflated (R_P = ${1.771}_{-0.056}^{+0.060}$ R_J), Jupiter-mass (M_P = 0.88 ± 0.16 M_J) planet with a near-integer orbital period of 5.0037775 ± 0.0000048 days. The orbit of the planet is consistent with circular, e = ${0.050}_{-0.035}^{+0.054}$. It is only the third hot Jupiter known with a highly inflated radius (R_P > 1.7) and on a period >5 days, joining KELT-12 b (Stevens et al. 2017) and Kepler-435 b (Almenara et al. 2015). Interestingly, TOI-640 b is almost a twin of KELT-12 b, in that they are highly inflated Jupiter-mass planets on ∼5 day orbits around similar subgiant host stars. All three host stars in this regime are evolved, possibly suggesting that the inflation is a result of the host star's recent evolution (Assef et al. 2009; Spiegel & Madhusudhan 2012; Hartman & Bakos 2016; Lopez & Fortney 2016). Similar to KELT-12b and Kepler-435 b, we see no evidence of any significant eccentricity.

TOI-1333 (TIC 395171208) is a bright (V = 9.49), evolved F-star with a mass of M_* = ${1.464}_{-0.079}^{+0.076}$ M_⊙ and radius of R_* = ${1.925}_{-0.063}^{+0.064}$ R_⊙. The star appears to be slightly evolved, as suggested by its $\mathrm{log}g$ of ${4.034}_{-0.033}^{+0.032}$ dex (cm s⁻²). As a result of its evolutionary stage, we estimate a relatively tight age constraint from the MIST evolutionary tracks of ${2.33}_{-0.56}^{+0.71}$ Gyr. Orbiting on a 4.720219 ± 0.000011 day period, the planetary companion TOI-1333 b has a radius of ${1.396}_{-0.054}^{+0.056}$ R_J, a mass of M_P = 2.37 ± 0.24 M_J, and an eccentricity that is consistent with circular (e = ${0.073}_{-0.052}^{+0.092}$). This is not surprising given that our derived circularization timescale, ${1.29}_{-0.33}^{+0.37}$ Gyr, is similar to the age of the system.

In the case of TOI-1333, we have measured a periodicity of ∼5.3 days from the ground-based and TESS photometry (we note that WASP identified a period 3× this). We have also measured a $v\sin {I}_{* }$ of 16.5 ± 0.5 km s⁻¹. If the periodicity identified in the photometry indeed is the average rotation period of the host star, then we can estimate the inclination of the host star's rotation axis and compare it to the derived inclination of TOI-1333 b's orbit following the methodology presented in Masuda & Winn (2020). Using the EXOFASTv2 implementation of a Markov Chain Monte Carlo, we run a simple fit of the host star's rotational velocity and its projection onto our line of sight ($v\sin {I}_{* }$) using the values from our global fit for Rstar (${1.925}_{-0.063}^{+0.064}$ R_⊙), the derived rotational period of TOI-1333 from TESS and KELT (5.3 days), and the $v\sin {I}_{* }$ from the TRES spectroscopy (14.2 ± 0.5 km s⁻¹) to calculate the inclination of TOI-1333's rotation axis (relative to our line of sight). The latitudes on the Sun that show starspots have a differential rotation on the surface of a few percent. Therefore, we place a 3% error on the rotational velocity for this analysis. We require the same Gelman–Rubin statistic (<1.01) and independent draw (>1000) for convergence as the default for EXOFASTv2. We derive the inclination of the rotation axis to be $51\buildrel{\circ}\over{.} {3}_{-3\buildrel{\circ}\over{.} 3}^{+3\buildrel{\circ}\over{.} 5}$. From our global fit, TOI-1333 b has an inclination of $85\buildrel{\circ}\over{.} {70}_{-0\buildrel{\circ}\over{.} 65}^{+1\buildrel{\circ}\over{.} 3}$, suggesting that the rotation axis of the star and the orbital plane are misaligned. TOI-1333 b is an excellent candidate to confirm this result through spin–orbit alignment (λ) measurements using the Rossiter–McLauglin or Doppler tomography techniques. The planet's orbit is also misaligned with the orbit of the wide binary companion TOI-1333 B, for which we measured an inclination of ${125}_{-10}^{+18}$ degrees from our LOFTI analysis. Interestingly, we do not detect a significant orbital eccentricity from our global fit for TOI-1333 b (though a small eccentricity is still possible), but this suggested misalignment might be a remnant left over from high-eccentricity migration. The likely bound companion at 470 au (see Section 2.6.2) could be responsible for Kozai–Lidov migration of the planet.

TOI-1478 (TIC 409794137, V = 10.81) is a Sun-like G-dwarf with radius of R_* = ${1.048}_{-0.029}^{+0.030}$ R_⊙, mass of M_* = ${0.946}_{-0.041}^{+0.059}$ M_⊙, and an age of ${9.2}_{-3.9}^{+3.1}$ Gyr. Orbiting TOI-1478 is a warm Jupiter with a period of 10.180249 ± 0.000015 days, a radius of R_P = ${1.060}_{-0.039}^{+0.040}$ R_J, and a mass of M_P = ${0.851}_{-0.047}^{+0.052}$ M_J, and it resides in a circular orbit (e = ${0.024}_{-0.017}^{+0.032}$). TOI-1478 b is the longest-period planet in our sample, and the planet and its host star (other than their orbital distances) resemble the Sun and Jupiter in mass and radius, possibly an example of an alternate outcome of our own solar system. As a result of the long orbital period, the tidal forces on TOI-1478 b are too weak to have circularized the orbit. Therefore, the lack of a significant eccentricity could suggest a more dynamically quiescent migration history.

In the case of TOI-1601 b, our global model showed a clear bimodality in the posterior distribution of the host star's mass and age (see Section 3.1). This is likely due to the host star's evolutionary status, because the star sits on the Hertzprung–Russell diagram where isochrones cross, so the evolutionary state is ambiguous given the precision of our observations. To account for this, we extract two separate solutions, one for each peak in our posteriors. The higher host star mass solution, M_* = ${1.517}_{-0.049}^{+0.053}$ M_⊙, has a higher probability of being correct at 66.7%, so we adopt this solution for the discussion, but both results are available in Table 4. TOI-1601 (TIC 139375960, V = 10.71) is an evolved subgiant ($\mathrm{log}g$ of ${3.940}_{-0.025}^{+0.022}$ dex (cm s⁻²)) with a radius of R_* = ${2.186}_{-0.063}^{+0.074}$ R_⊙. We estimate the age of the system within our fit to be ${2.64}_{-0.39}^{+0.38}$ Gyr. TOI-1601 b is a Jupiter-mass planet (0.99 ± 0.11 M_J) that shows some inflation (R_P = ${1.159}_{-0.059}^{+0.062}$ R_J) and a circular orbit (e = ${0.037}_{-0.026}^{+0.045}$), and a 5.331752 ± 0.000011 day orbit. The spectroscopic analysis of the TRES spectra of TOI-1601 shows some metal enhancement ([Fe/H] = ${0.316}_{-0.074}^{+0.072}$).

While the primary goal of NASA's TESS mission is to discover and measure the masses of small planets (Ricker et al. 2015), TESS has already provided some valuable discoveries in the field of giant planets (see, e.g., Armstrong et al. 2020; Huang et al. 2020a; Vanderburg et al. 2020). Given the minimum ∼27 day baseline for any target and the completeness in the sensitivity of space-based photometry to detect a hot-Jupiter transit, TESS provides the opportunity to obtain a near-complete sample of hot Jupiters (Zhou et al. 2019). To date, TESS has discovered 26 giant planets (M_P > 0.4 M_J), 16 of which have an orbital period >5.0 days (these numbers include the five systems presented in this paper and two additional systems from Ikwut-Ukwa et al. 2021). For comparison, 36 hot Jupiters have been discovered with orbital periods >5.0 days from ground-based transit surveys (NASA Exoplanet Archive, Akeson et al. 2013).

If giant planets predominantly migrate through dynamical interactions, we may find evidence of this evolutionary history in the eccentricity distribution of hot Jupiters, specifically those that are dynamically young (where the circularization timescale by tidal forces is longer than the age of the system). Figure 7 shows the current distribution of giant planet eccentricities as a function of orbital period out to 16 days. Those 26 systems discovered by TESS are shown colored by their host star's effective temperature. Although this is not a homogeneous sample, since a variety of different analysis methods and assumptions were made within this population, there is a wider distribution of eccentricities for those systems with an orbital period >5 days, where tidal circularization timescales are longer (Adams & Laughlin 2006). Interestingly, of the five systems presented here, only TOI-628 b has a statistically significant measured eccentricity (e = ${0.072}_{-0.023}^{+0.021}$) and is consistent with dynamically driven migration since its estimated age is less than the circularization timescale of the orbit. Although the other systems show some nonzero eccentricities from our global fits, they are not statistically significant (>3σ) and could be a result of the Lucy–Sweeney bias (Lucy & Sweeney 1971). We also note that there is one very massive hot Jupiter in our sample, TOI-628 b (M_P ${6.33}_{-0.31}^{+0.29}$ M_J), and it is the most massive hot Jupiter discovered to date by TESS (we note that TESS has discovered a few transiting brown dwarfs; Jackman et al. 2019; Carmichael et al. 2020, 2021; Šubjak et al. 2020; and WD 1856+534, which has a mass limit <13.8 M_J, Vanderburg et al. 2020). These massive Jupiters provide a great laboratory for studying the effect of high gravity on the atmosphere of a gas giant, while studying the transition point between giant planets and brown dwarfs.