# The TESS Grand Unified Hot Jupiter Survey. I. Ten TESS Planets

Samuel W. Yee<EMAIL_ADDRESS>Joshua N. Winn Joel D. Hartman Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA  Joseph E. Rodriguez Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA  George Zhou University of Southern Queensland, Centre for Astrophysics, West Street, Toowoomba, QLD 4350, Australia  Samuel N. Quinn Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  David W. Latham Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Allyson Bieryla Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Karen A. Collins Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Brett C. Addison University of Southern Queensland, Centre for Astrophysics, West Street, Toowoomba, QLD 4350 Australia  Isabel Angelo Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  Khalid Barkaoui Astrobiology Research Unit, Université de Liège, 19C Allée du 6 Août, 4000 Liège, Belgium  Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife, Spain  Paul Benni Acton Sky Portal (Private Observatory), Acton, MA, USA  Andrew W. Boyle Caltech/IPAC-NASA Exoplanet Science Institute, 770 S. Wilson Avenue, Pasadena, CA 91106, USA  Rafael Brahm Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibaáñez, Av. Diagonal las Torres 2640, Penñalolén, Santiago, Chile  Millennium Institute for Astrophysics, Chile  R. Paul Butler Earth and Planets Laboratory, Carnegie Institution for Science, 5241 Broad Branch Road, NW, Washington, DC 20015, USA  David R. Ciardi Caltech/IPAC, NASA Exoplanet Science Institute, 770 S. Wilson Avenue, Pasadena, CA 91106, USA  Kevin I. Collins George Mason University, 4400 University Drive, Fairfax, VA, 22030 USA  Dennis M. Conti American Association of Variable Star Observers, 49 Bay State Road, Cambridge, MA 02138, USA  Jeffrey D. Crane Earth and Planets Laboratory, Carnegie Institution for Science, 5241 Broad Branch Road, NW, Washington, DC 20015, USA  Fei Dai Division of Geological and Planetary Science, California Institute of Technology, Pasadena, CA 91125, USA  Courtney D. Dressing Department of Astronomy, University of California Berkeley, Berkeley, CA 94720, USA  Jason D. Eastman Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  Zahra Essack Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Raquel Forés-Toribio Departamento de Astronomía y Astrofísica, Universidad de Valencia, E-46100 Burjassot, Valencia, Spain  Observatorio Astronómico, Universidad de Valencia, E-46980 Paterna, Valencia, Spain  Elise Furlan Caltech/IPAC, NASA Exoplanet Science Institute, 770 S. Wilson Avenue, Pasadena, CA 91106, USA  Tianjun Gan Department of Astronomy, Tsinghua University, Beijing 100084, China  Steven Giacalone Department of Astronomy, University of California Berkeley, Berkeley, CA 94720, USA  Holden Gill Department of Astronomy, University of California Berkeley, Berkeley, CA 94720, USA  Eric Girardin Grand Pra Observatory, Switzerland  Thomas Henning Max-Planck-Institut fur Astronomie, Konigstuhl 17, 69117 Heidelberg, Germany  Christopher E. Henze  NASA Ames Research Center, Moffett Field, CA 94035, USA  Melissa J. Hobson Max-Planck-Institut fur Astronomie, Konigstuhl 17, 69117 Heidelberg, Germany  Jonathan Horner University of Southern Queensland, Centre for Astrophysics, West Street, Toowoomba, QLD 4350 Australia  Andrew W. Howard Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Steve B. Howell NASA Ames Research Center, Moffett Field, CA 94035, USA  Chelsea X. Huang University of Southern Queensland, Centre for Astrophysics, West Street, Toowoomba, QLD 4350, Australia  Howard Isaacson Department of Astronomy, University of California Berkeley, Berkeley, CA 94720, USA  University of Southern Queensland, Centre for Astrophysics, West Street, Toowoomba, QLD 4350, Australia  Jon M. Jenkins NASA Ames Research Center, Moffett Field, CA 94035, USA  Eric L. N. Jensen Department of Physics & Astronomy, Swarthmore College, Swarthmore PA 19081, USA  Andrés Jordán Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibaáñez, Av. Diagonal las Torres 2640, Penñalolén, Santiago, Chile  Millennium Institute for Astrophysics, Chile  Stephen R. Kane Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA  John F. Kielkopf Department of Physics and Astronomy, University of Louisville, Louisville, KY 40292, USA  Slawomir Lasota  Silesian University of Technology, Department of Electronics, Electrical Engineering and Microelectronics, Akademicka 16, 44-100 Gliwice, Poland  Alan M. Levine Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Jack Lubin Department of Physics & Astronomy, University of California, Irvine, Irvine, CA 92697, USA  Andrew W. Mann Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA  Bob Massey Villa ’39 Observatory, Landers, CA 92285, USA  Kim K. McLeod Department of Astronomy, Wellesley College, Wellesley, MA 02481, USA  Matthew W. Mengel University of Southern Queensland, Centre for Astrophysics, West Street, Toowoomba, QLD 4350 Australia  Jose A. Muñoz Departamento de Astronomía y Astrofísica, Universidad de Valencia, E-46100 Burjassot, Valencia, Spain  Observatorio Astronómico, Universidad de Valencia, E-46980 Paterna, Valencia, Spain  Felipe Murgas  Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain  Enric Palle Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain  Peter Plavchan George Mason University, 4400 University Drive MS 3F3, Fairfax, VA 22030, USA  Adam Popowicz Silesian University of Technology, Department of Electronics, Electrical Engineering and Microelectronics, Akademicka 16, 44-100 Gliwice, Poland  Don J. Radford Brierfield Observatory, New South Wales, Australia  George R. Ricker Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Pamela Rowden Royal Astronomical Society, Burlington House, Piccadilly, London W1J 0BQ, UK  Boris S. Safonov Sternberg Astronomical Institute, Lomonosov Moscow State University, 119992, Universitetskij prospekt 13, Moscow, Russia  Arjun B. Savel Department of Astronomy, University of Maryland, College Park, College Park, MD, USA  Richard P. Schwarz Patashnick Voorheesville Observatory, Voorheesville, NY 12186, USA  S. Seager Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Ramotholo Sefako  South African Astronomical Observatory, P.O. Box 9, Observatory, Cape Town 7935, South Africa  Avi Shporer Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Gregor Srdoc  Kotizarovci Observatory, Sarsoni 90, 51216 Viskovo, Croatia  Ivan S. Strakhov  Sternberg Astronomical Institute, Lomonosov Moscow State University, 119992, Universitetskij prospekt 13, Moscow, Russia  Johanna K. Teske  Earth and Planets Laboratory, Carnegie Institution for Science, 5241 Broad Branch Road, NW, Washington, DC 20015, USA  C.G. Tinney  Exoplanetary Science at UNSW, School of Physics, UNSW Sydney, NSW 2052, Australia  Dakotah Tyler Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  Robert A. Wittenmyer University of Southern Queensland, Centre for Astrophysics, West Street, Toowoomba, QLD 4350 Australia  Hui Zhang  Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China  Carl Ziegler Department of Physics, Engineering and Astronomy, Stephen F. Austin State University, 1936 North Street, Nacogdoches, TX 75962, USA Samuel W. Yee

###### Abstract

Hot Jupiters – short-period giant planets – were the first extrasolar planets
to be discovered, but many questions about their origin remain. NASA’s
Transiting Exoplanet Survey Satellite (TESS), an all-sky search for transiting
planets, presents an opportunity to address these questions by constructing a
uniform sample of hot Jupiters for demographic study through new detections
and unifying the work of previous ground-based transit surveys. As the first
results of an effort to build this large sample of planets, we report here the
discovery of ten new hot Jupiters (TOI-2193A b, TOI-2207 b, TOI-2236 b,
TOI-2421 b, TOI-2567 b, TOI-2570 b, TOI-3331 b, TOI-3540A b, TOI-3693 b,
TOI-4137 b). All of the planets were identified as planet candidates based on
periodic flux dips observed by TESS, and were subsequently confirmed using
ground-based time-series photometry, high angular resolution imaging, and
high-resolution spectroscopy coordinated with the TESS Follow-up Observing
Program. The ten newly discovered planets orbit relatively bright F and G
stars ($G<12.5$, $T_{\mathrm{eff}}$ between 4800 and 6200 K). The planets’
orbital periods range from 2 to 10 days, and their masses range from 0.2 to
2.2 Jupiter masses. TOI-2421 b is notable for being a Saturn-mass planet and
TOI-2567 b for being a “sub-Saturn’, with masses of $0.322\pm 0.073$ and
$0.195\pm 0.030$ Jupiter masses, respectively. We also measured a detectably
eccentric orbit ($e=0.17\pm 0.05$) for TOI-2207 b, a planet on an 8-day orbit,
while placing an upper limit of $e<0.052$ for TOI-3693 b, which has a 9-day
orbital period. The ten planets described here represent an important step
toward using TESS to create a large and statistically useful sample of hot
Jupiters.

††facilities: TESS, MAST, Gaia, Keck:I (HIRES), WIYN (NEID), Magellan:Clay
(PFS), CTIO:1.5m (CHIRON), Max Planck:2.2m (FEROS), FLWO:1.5m (TRES), LCOGT,
Gemini††software: astropy (Astropy Collaboration et al., 2013, 2018),
lightkurve (Lightkurve Collaboration et al., 2018), EXOFASTv2 (Eastman et al.,
2019), SpecMatch-Emp (Yee et al., 2017), SpecMatch-Synth (Petigura, 2015),
AstroImageJ (Collins et al., 2017), TAPIR (Jensen, 2013), numpy (Harris et
al., 2020), scipy (Virtanen et al., 2020), pandas (pandas development team,
2020; Wes McKinney, 2010), matplotlib (Hunter, 2007),

##  1 Introduction

The origin of hot Jupiters is one of the longest-standing unresolved problems
in exoplanet science. Prior to the discovery of the first hot Jupiter 51
Pegasi b (Mayor & Queloz, 1995), our understanding of planet formation was
entirely based on our knowledge of our solar system. It was thought that giant
planets could only form beyond a few astronomical units from their host stars,
where the surface density of solids within the protoplanetary disk would be
high enough to allow for the formation of a solid body massive enough to
undergo runaway gas accretion. The existence of hot Jupiters implies that
either this expectation was incorrect and giant planets can form close in to
their host stars, or that the initially wide orbits of giant planets can
sometimes shrink by a factor of 100 (see the reviews by Dawson & Johnson 2018;
Fortney et al. 2021, and references therein). In the latter scenario, the
orbital shrinkage might be due to gravitational interactions with the gaseous
protoplanetary disk, and would therefore need to occur within the first few
million years after the formation of the star (Lin & Papaloizou, 1986), or the
orbital alterations might be caused by eccentricity excitation followed by
tidal orbital circularization, which need not occur early in the system’s
history (Rasio & Ford, 1996; Fabrycky & Tremaine, 2007). Each of these
possible formation pathways would shape the population of hot Jupiters in
different ways, and hence studying the demographics of hot Jupiters and the
distributions of their orbital properties may help us understand their
relative importance.

NASA’s ongoing TESS mission (Ricker et al., 2015) was designed to detect
smaller planets — super-Earths and sub-Neptunes — but TESS is also capable of
revolutionizing our knowledge of hot Jupiter demographics. As a nearly all-sky
space-based photometric survey that dwells on a given star field for 27 days
at a time, the TESS survey should be able to identify nearly all of the hot
Jupiters that transit stars which are bright and nearby enough for detailed
follow-up observations and characterization (Zhou et al., 2019). Simulations
have predicted that the TESS planet catalog will eventually contain
$\approx$400 hot Jupiters around FGK stars brighter than $G=12.5$ (Yee et al.,
2021). Such a sample would be an order of magnitude larger than the sample of
40 hot Jupiters found during the original Kepler mission, which is the largest
statistically useful sample of such planets currently available. The process
of constructing a very large sample of hot Jupiters around bright stars is
greatly facilitated and accelerated by the fact that hundreds of these planets
have already been discovered by the ground-based transit surveys such as TrES
(Alonso et al., 2004), XO (McCullough et al., 2005), WASP (Pollacco et al.,
2006), HATNet and HATSouth (Bakos et al., 2004, 2013), KELT (Pepper et al.,
2007, 2012), and NGTS (Wheatley et al., 2018), accounting for roughly 40% of
the expected 400 planets in a $G<12.5$ magnitude-limited sample. The hard work
of these previous surveyors over many years led to the discovery of many
important and well-studied systems, but the selection functions of these
surveys are complex, different from each other, and not well documented. TESS
will provide a homogeneous dataset that encompasses essentially all of the
previously known planets and has a selection function that should be easier to
model. Hence, TESS offers the possibility of unifying all of the previous
surveys and leveraging over two decades of observational effort.

Still, even with TESS, expanding and completing a statistical sample suitable
for demographic study will require a significant follow-up effort to rule out
astrophysical false positives (generally eclipsing binaries that masquerade as
transiting planets), measure planet masses, and model the selection function.
Ground-based imaging and time-series photometric follow-up with higher angular
resolution than TESS can be used to check for nearby eclipsing binaries and
confirm that the transit signal belongs to the identified star and not a
foreground or background star. Additional transit observations help to improve
our knowledge of the planet parameters and transit ephemerides, while
observations in multiple bandpasses can also be used to check for chromatic
effects that are indicative of eclipsing binaries. High-resolution Doppler
spectroscopy provides final confirmation of the planet’s existence and
measures its mass, as well as providing a high signal-to-noise spectrum that
is useful for characterizing the host star.

Given all the different types of observations and resources that are needed,
confirming hundreds of new hot Jupiters from TESS within a reasonable amount
of time is only feasible with a large community effort.

The lead authors of this paper have begun to organize such an effort, the
Grand Unified Hot Jupiter Survey, by playing a linking role between the new
planet discoveries from various TESS follow-up groups, and the planets (and
false positives) that have already been investigated in previous planet
searches. This work is being conducted as part of the TESS Follow-Up Observing
Program (TFOP; Collins et al. 2018; ExoFOP
2019)111https://heasarc.gsfc.nasa.gov/docs/tess/followup.html,222https://exofop.ipac.caltech.edu/tess/,
which provides a platform for coordinating observations and sharing data, and
is open to any interested astronomer.

The 10 planets described in this paper are the first newly discovered planets
from this survey, and are based on data contributed by many TFOP members. The
planets are known by their TESS Object of Interest (TOI) numbers: TOI-2193A b,
TOI-2207 b, TOI-2236 b, TOI-2421 b, TOI-2567 b, TOI-2570 b, TOI-3331 b,
TOI-3540A b, TOI-3693 b, and TOI-4137 b. Section 2.1 presents time-series
photometry from TESS, and Sections 2.2 through 2.4 describe ground-based
follow-up photometry, imaging, and spectroscopic follow-up observations.
Section 3 presents a characterization of each host star, and Section 4
describes the application of EXOFASTv2 (Eastman et al., 2019) to jointly model
all of the data and determine the parameters of each system. Section 5
examines the properties of the new planets within the context of the entire
known sample of hot Jupiters, and Section 6 draws some conclusions.

##  2 Observations and Data

###  2.1 TESS Photometry

All of the new planets described here were first detected in TESS photometry.
TESS observes a $24^{\circ}\times 96^{\circ}$ region of the sky for 27 days at
a time, before rotating its field of view to a new sector. During its initial
two-year Prime Mission (Sectors 1 – 26, running from July 2018 to July 2020),
TESS obtained high-precision photometry of $\gtrsim$ 200,000 preselected stars
with a two-minute cadence, with the remainder of the field-of-view being
observed in the full-frame images (FFIs) at 30-minute cadence. With the
Extended Mission beginning in 2020 (Sectors 27 onward), two-minute cadence
data continues to be obtained for $\approx$ 20,000 targets per sector, while
the FFI cadence has been reduced to 10 minutes.

The 2-minute TESS photometry was extracted and reduced by the TESS Science
Processing Operations Center (SPOC) pipeline, as described by Jenkins et al.
(2016). Only one of the 10 planet-hosting stars presented in this paper had
been preselected for 2-minute cadence observations (TOI-2207, Sector 27).
However, several others were added to the short-cadence target list in the
Extended Mission following their identification as planet candidates in the
FFIs from the Prime Mission. The longer-cadence FFI data were calibrated with
the tica software (Fausnaugh et al., 2020), and the light-curves were
extracted with the MIT Quick-Look Pipeline (QLP; Huang et al. 2020a, b;
Kunimoto et al. 2021).

Both the SPOC pipeline and QLP search the extracted light-curves for transit-
like signals (“Threshold Crossing Events” or TCEs) which are then vetted by
the TESS Science Office (TSO). Objects with signals surviving the vetting
process are designated TESS Objects of Interest (TOIs; Guerrero et al. 2021)
and public notifications are distributed. All of the planets in this paper
were alerted as TOIs, including some from the recent search of QLP light-
curves for stars fainter than $T>10.5$ by Kunimoto et al. (2022). Table 2.1
summarizes the ten targets and the TESS sectors they were observed in.

In addition, four of the targets had previously been identified as “community
TOIs” (cTOIs) by separate investigators. TOI-2421 b was first flagged as a
planet candidate by Montalto et al. (2020), who used the DIAmante pipeline to
extract difference imaging light-curves from the first year of TESS FFIs. They
then identified transit events in the light-curves with the Box-Least Squares
algorithm (Kovács et al., 2002), and vetted the candidate events with a Random
Forest classifier. TOI-2567 b, TOI-2570 b, and TOI-4137 b were identified as
planet candidates by Olmschenk et al. (2021), who classified light-curves from
the SPOC-calibrated FFIs extracted by the eleanor pipeline (Feinstein et al.,
2019) with a convolutional neural network. These light-curves were then
subjected to the Quasi-Automated Transit Search (QATS; Kruse et al. 2019)
pipeline and vetted with the Discovery and Vetting of Exoplanets pipeline
(DAVE; Kostov et al. 2019). All four cTOIs were later promoted to TOIs
following vetting by the TESS Science Office (Mireles et al., 2021).

We identified these targets as candidate hot Jupiters ($R_{p}>8$ $R_{\oplus}$,
$P<10$ days) from the TOI catalog, with selection based on catalog photometry
and astrometry indicating that they orbit FGK stars. We then began performing
follow-up observations to determine whether the transit-like signals are truly
from transiting planets or are instead from eclipsing binaries or other “false
positives.” When analyzing each planetary system (Section 4), we used all of
the available photometry from TESS. We used the lightkurve package (Lightkurve
Collaboration et al., 2018) to download the TESS light-curves from the
Mikulski Archive for Space Telescopes (MAST). When available, we used light-
curves produced from the SPOC pipeline – this applies to all the short-cadence
data, as well as some of the long-cadence FFI data, for which the SPOC
pipeline has recently begun processing 160,000 targets per sector (Caldwell et
al., 2020). We used the Presearch Data Conditioning (PDC; Stumpe et al. 2012;
Smith et al. 2012; Stumpe et al. 2014) light-curves, which have been corrected
for instrumental effects. We additionally “flattened” the SPOC PDC light-
curves with the Keplerspline333https://github.com/avanderburg/keplersplinev2
routine (Vanderburg & Johnson, 2014; Shallue & Vanderburg, 2018), which fits a
spline to the light-curve (with transit events masked) to correct for stellar
or instrumentally induced variability (Figure 1). When SPOC light-curves were
unavailable for the long-cadence data, we used the light-curves extracted by
the QLP, which were also flattened with Keplerspline. We provide the flattened
and normalized TESS photometry in Table 2.1.

Table 1: Summary of TESS Observations

Target | Sector | Source | Cadence (s)
---|---|---|---
TOI-2193 | 13 | SPOC | 1800
$\cdots$ | 27 | SPOC | 120
TOI-2207 | 27 | SPOC | 120
TOI-2236 | 12,13 | SPOC | 1800
$\cdots$ | 27,39 | SPOC | 600
TOI-2421 | 3 | SPOC | 1800
$\cdots$ | 30 | SPOC | 600
TOI-2567 | 14–26 | SPOC | 1800
$\cdots$ | 40,41 | SPOC | 120
TOI-2570 | 19 | SPOC | 1800
$\cdots$ | 44,45 | SPOC | 120
TOI-3331 | 13 | QLP | 1800
TOI-3540 | 15 | QLP | 1800
TOI-3693 | 17,18 | SPOC | 1800
TOI-4137 | 19,26 | SPOC | 1800
Table 2: Flattened & Normalized TESS Photometry  aaPrecision is computed as
the rms of the residuals after subtracting the transit and detrending model.

Flux has been detrended and normalized such that the mean out-of-transit flux
has a baseline of 1.0.

Note. — This table is available in its entirety in machine-readable form.

Figure 1: TESS Sector 27 light-curve for TOI-2207, extracted by the SPOC
pipeline. Top panel: SPOC PDC light-curve, with red points highlighting
transit events, which are masked out when performing the spline fit. Middle
panel: Keplerspline fit to the masked light-curve. Bottom panel: Flattened
light-curve.

###  2.2 Ground-Based Photometry

Additional ground-based photometry of each of our targets was obtained as part
of TFOP’s Seeing-limited Photometry Sub-Group 1 (SG1). These multi-band
photometric observations of individual transits helped to rule out false-
positive scenarios such as nearby eclipsing binaries. We also used the ground-
based light-curves to refine the transit parameters and ephemerides.
Observations were obtained from the Brierfield Observatory; KeplerCam on the
Fred Lawrence Whipple Observatory (FLWO) 1.2m telescope; the Hazelwood
Observatory; the Acton Sky Portal; the Villa ’39 observatory; the Observatori
Astronòmic de la Universitat de València (OAUV) TURIA2 0.3m telescope; the
Grand-Pra Observatory; the Silesian University of Technology Observatories
(SUTO) OTIVAR 0.3m telescope; the MEarth-South telescope array (Nutzman &
Charbonneau, 2008; Berta et al., 2012) at the Cerro Tololo Inter-American
Observatory (CTIO); as well as the 0.4m and 1.0m telescopes of the Las Cumbres
Observatory Global Telescope (LCOGT; Brown et al. 2013) global network, using
sites at the Observatorio del Teide, CTIO, the Siding Spring Observatory
(SSO), and the South African Astronomical Observatory (SAAO). Data reduction
and aperture photometry for all follow-up observations, except for the MEarth-
South observations, was done with the AstroImageJ software (Collins et al.,
2017). The MEarth-South data were reduced according to the procedures
described in Berta et al. (2012) and Irwin et al. (2007). We summarize the
observations and facilities used for each target in Table 2.2, and present the
complete set of photometric observations in Table 2.2.

Table 3: Summary of Ground-Based Photometric Follow-Up Observations  Table 4:
TFOP SG1 Photometry

Note. — This table is available in its entirety in machine-readable form.

###  2.3 High-Resolution Imaging

Table 5: Summary of High-Resolution Imaging Observations  Figure 2: Speckle
sensitivity curve (solid line) and auto-correlation function (ACF, inset
image) from SOAR HRCam observations of TOI-2193. A nearby stellar companion is
detected at $1\farcs 89$, seen as the two bright points to the northwest and
southeast of the primary in the ACF image.  Figure 3: Same as Figure 2, but
for TOI-3331. A nearby stellar companion is detected at $2\farcs 663$, visible
in the inset image to the NE and SW of the primary star.

Figure 4: From top to bottom: SOAR HRCam speckle imaging, Palomar PHARO
Br$\gamma$ AO imaging, Palomar PHARO $H$-cont AO imaging of TOI-3540. The
close companion at $0\farcs 92$ is detected by all three observations. The
line plots in each panel show the sensitivity curves for the corresponding
observation.

We also obtained high angular-resolution imaging of all of our target systems,
in order to detect and characterize stellar companions that might have been
blended with the primary target in the TESS images. This allows us to assess
the spectroscopic follow-up potential of a target star, eliminate false-
positive scenarios, and evaluate the impact of any contamination on the fitted
planetary properties. Table 2.3 summarizes the observations made for each
system, which were coordinated by the TFOP High-Resolution Imaging Sub-Group 3
(SG3). Nearby companions were detected in three cases shown in Figures 2, 3
and 4 . No companions were found for the other targets down to detection
limits, and plots illustrating these observations can be found at the end of
this paper, in Figure 2.1.

TOI-2193, TOI-2207, TOI-2421, TOI-3331, and TOI-3540 were observed in the $I$
band with the High-Resolution Camera (HRCam; Tokovinin & Cantarutti 2008), a
speckle imaging instrument on the Southern Astrophysical Research (SOAR) 4.1m
telescope. The general observing strategy for TESS targets and data reduction
procedure are described in Ziegler et al. (2019, 2021) and Tokovinin (2018)
respectively, while an example SOAR observation for TOI-2193 is shown in
Figure 2. Nearby stellar companions were detected in the SOAR observations for
TOI-2193 (Sep. = $1\farcs 89$, $\Delta I=3.8$ mag); TOI-3331 (Sep. = $2\farcs
66$, $\Delta I=2.6$ mag); and TOI-3540 (Sep. = $0\farcs 92$, $\Delta I=1.8$
mag).

TOI-2570 was observed using the ShARCS camera on the Shane 3-m telescope at
Lick Observatory (Kupke et al., 2012; Gavel et al., 2014; McGurk et al.,
2014). Two sequences of observations were taken with the Shane adaptive optics
system in natural guide star mode, one with a $Ks$ filter ($\lambda_{0}=2.150$
$\mu$m, $\Delta\lambda=0.320$ $\mu$m) and one with a $J$ filter
($\lambda_{0}=1.238$ $\mu$m, $\Delta\lambda=0.271$ $\mu$m). The data were
reduced using the publicly available SImMER pipeline (Savel et al.,
2020).444https://github.com/arjunsavel/SImMER We found no evidence for stellar
companions within our detection limits.

TOI-2570 and TOI-3540 were also observed in the near-infrared with the Palomar
High Angular Resolution Observer (PHARO; Hayward et al. 2001) on the 200-in
Hale telescope at Palomar Observatory. Both targets were observed in the
Br$\gamma$ filters, while TOI-3540 was also observed in the $H$-cont filter.
These observations improved the bound for the lack of stellar companions to
TOI-2570, while also identifying the $0\farcs 92$ stellar companion to
TOI-3540, as seen in the SOAR speckle images.

We observed TOI-2236 and TOI-2567 with the Zorro and ’Alopeke imaging
instruments on the Gemini-South and Gemini-North telescopes respectively
(Scott & Howell, 2018; Scott et al., 2021). No companions were detected in
either set of observations, down to the instrumental detection limits.

Finally, the targets TOI-3693 and TOI-4137 were observed with the speckle
polarimeter on the 2.5m telescope at the Caucasian Observatory of Sternberg
Astronomical Institute (SAI) of Lomonosov Moscow State University (Safonov et
al., 2017). The observations were made in the $I$-band, and no stellar
companions were detected for either target.

###  2.4 High-Resolution Spectroscopy

We obtained high-resolution spectroscopy for each of the ten target systems to
measure precise relative radial-velocities (RVs) for each system, allowing us
to confirm the planetary nature of the transiting companion and measure its
mass. We sought to obtain 6–8 observation epochs per target, primarily at
orbital quadratures. We describe the instruments used and data analysis
procedures in the rest of this section, and summarize the observations for
each target in Table 2.4.

In addition to extracting RV measurements from each spectroscopic observation,
we measured the bisector inverse slope (BIS) of the spectral line profiles,
using the procedures described by Hartman et al. (2019), for the observations
from PFS, CHIRON, FEROS, HIRES and NEID. For spectra that were observed
through an iodine cell, we only used the iodine-free orders to perform this
measurement. The complete RV and BIS data for each target are presented in
Table 2.4, and plotted in Figures LABEL:fig:toi2193_multiplot and
LABEL:fig:toi2207_multiplot-LABEL:fig:toi4137_multiplot.

Table 6: Summary of Radial-Velocity Measurements  Table 7: Radial-Velocity
Measurements

Note. — The complete table of RV measurements is available in machine-readable
form. .

####  2.4.1 PFS Spectroscopy

We observed TOI-2193, TOI-2207 and TOI-3331 with the Planet Finder
Spectrograph (PFS) on the 6.5-meter Magellan II Clay Telescope at the Las
Campanas Observatory in Chile (Crane et al., 2006, 2008, 2010). PFS is a high-
resolution echelle spectrograph that uses an iodine absorption cell to produce
precise radial-velocities. We observed each target in the 3x3 binning mode
with the iodine cell in the optical path, choosing short exposure times of ten
minutes or less, which allowed us to attain a typical RV precision of about 5
$\mathrm{m}\,\mathrm{s}^{-1}$, well above the instrument’s demonstrated long-
term precision of $\lesssim 1$ $\mathrm{m}\,\mathrm{s}^{-1}$. The spectra were
reduced and velocities extracted with the custom pipeline described by Butler
et al. (1996). A high S/N, iodine-free, template spectrum was also obtained
for each target, as required for the RV extraction procedure.

####  2.4.2 CHIRON Spectroscopy

TOI-2207, TOI-2236, and TOI-2421 were observed with the CTIO High Resolution
Spectrometer (CHIRON; Tokovinin et al. 2013; Paredes et al. 2021) on the CTIO
1.5m telescope on Cerro Tololo in Chile. CHIRON is an optical, fiber-fed
echelle spectrometer with a spectral resolution of $R\approx$80,000 when used
with an image slicer. We observed with typical exposure times of 1200 to
1800s, bracketed by calibration observations of a ThAr lamp. The spectra were
flat-fielded, bias subtracted, and wavelength calibrated using the standard
CHIRON pipeline. Radial-velocities were extracted via least-squares
deconvolution of the spectra against synthetic templates (Donati et al., 1997;
Zhou et al., 2020), achieving a typical RV precision of 30-70
$\mathrm{m}\,\mathrm{s}^{-1}$. We also used the Stellar Parameter
Classification (SPC; Buchhave et al. 2012) code to derive atmospheric
properties from the spectra, with the results shown in Table 10.

####  2.4.3 FEROS Spectroscopy

TOI-2207 was also observed on six epochs with the FEROS spectrograph (Kaufer
et al., 1999) mounted on the MPG 2.2m telescope at the ESO La Silla
Observatory, in Chile, in the context of the Warm gIaNts with tEss
collaboration (WINE, Brahm et al., 2019; Trifonov et al., 2021). FEROS is a
stabilized fiber-fed high resolution spectrograph configured with a comparison
fiber to trace instrumental radial-velocity drift during the scientific
exposures. The six observations of TOI-2207 were performed between 2021-07-22
and 2021-10-24 with a typical exposure time of 1200 seconds, achieving an S/N
per resolution element ranging from 70 to 100. All FEROS data were processed
with the CERES pipeline (Brahm et al., 2017), which executed all steps
involved in obtaining high precision radial-velocities with the cross-
correlation technique, starting from the raw images. The typical radial-
velocity error of these observations was $\approx 10$ m/s. CERES also
estimates the stellar atmospheric parameters from the spectra, which are
tabulated in Table 10.

####  2.4.4 MINERVA-Australis Spectroscopy

We also obtained 11 observations of TOI-2421 between 2021-06-26 and 2021-08-16
using the Minerva-Australis telescope array (Wittenmyer et al., 2018; Addison
et al., 2019), located at Mt. Kent Observatory, Australia. Minerva-Australis
is an array of four identical 0.7 m telescopes linked via fiber feeds to a
single KiwiSpec echelle spectrograph at a spectral resolving power of
$R\sim$80,000 over the wavelength region of 5000-6300Å. The array is wholly
dedicated to radial-velocity follow-up of TESS planet candidates (e.g.,
Nielsen et al., 2019; Addison et al., 2021; Wittenmyer et al., 2018).
Simultaneous wavelength calibration is provided via two calibration fibers
illuminated by a quartz lamp through an iodine cell. The spectra were
extracted for each telescope individually and the radial-velocities were
extracted via the same techniques as those described above for the CHIRON
observations.

####  2.4.5 TRES Spectroscopy

We observed all five targets in the Northern hemisphere (TOI-2567, TOI-2570,
TOI-3540, TOI-3693, and TOI-4137) with the Tillinghast Reflector Echelle
Spectrograph (TRES; Fűrész 2008). TRES has a spectral resolution of $R\sim
44,000$ and is located on the FLWO 1.5m Tillinghast Reflector telescope on
Mount Hopkins, Arizona. The observations for each target were scheduled near
the two opposite quadratures, ensuring maximum sensitivity to the planet’s
orbital motion. Two TRES spectra were taken of each target except for
TOI-3693, for which we collected three observations. The data were reduced and
radial-velocities extracted using the pipeline described in Buchhave et al.
(2010) and Quinn et al. (2012).

The spectra were also analyzed with SPC to derive the stellar atmospheric
parameters $T_{\mathrm{eff}}$, $\log{g}$, $\mathrm{[Fe/H]}$, and $v\sin{i}$.
The results from each observation were weighted according to the cross-
correlation function and averaged together, with the final stellar properties
presented in Table 10.

####  2.4.6 HIRES Spectroscopy

We observed TOI-2567, TOI-3540 and TOI-3693 with the High Resolution Echelle
Spectrometer (HIRES; Vogt et al. 1994) on the Keck-I 10m telescope on
Maunakea, Hawaii. We obtained 6–9 observations for each target with an iodine
cell that provides a precise wavelength calibration and allows for radial-
velocity extraction. These observations were made through the queue system
operated by the California Planet Search (CPS), and reduced with the standard
CPS procedures (Howard et al., 2010; Howard & Fulton, 2016).

To reduce the observation time necessary to obtain a high-S/N, iodine-free
template spectrum, we used the matched template technique developed by Dalba
et al. (2020). Briefly, we first obtained an iodine-free but low S/N ($\sim
40$/pixel) reconnaissance spectrum, which was then matched against a library
of archival HIRES template spectra described in Yee et al. (2017). A
Deconvolved Stellar Spectral Template (DSST) was then derived for the target
using the high S/N spectrum of the best-matching library star, which could
then be used in the radial-velocity extraction procedure. For the slowly
rotating F and G dwarfs observed here, Dalba et al. (2020) found that the
technique introduced a median error of 4.7 $\mathrm{m}\,\mathrm{s}^{-1}$ to
the RV measurements, compared with obtaining a high-S/N template of the target
star. We included this introduced error by adding it in quadrature to the
internal RV precision of the observations. For the massive planets targeted by
our work, this additional error should not significantly affect the
characterization of the planetary systems, especially given that we chose
observation exposure times of $\lesssim 10$ minutes to yield an RV precision
of a similar magnitude, $5$–$10$ $\mathrm{m}\,\mathrm{s}^{-1}$.

####  2.4.7 NEID Spectroscopy

TOI-2570 and TOI-4137 were observed with the NEID spectrograph on the WIYN
3.5m telescope at Kitt Peak National Observatory (KPNO). NEID is a newly
commissioned stabilized, fiber-fed optical spectrograph with a resolving power
of $R\approx$110,000 spanning the wavelength range from 3800 to 9300 Å.
(Schwab et al., 2016; Halverson et al., 2016). The data were reduced and RVs
extracted using v1.1.2 of the standard NEID Data Reduction Pipeline (NEID-
DRP)555https://neid.ipac.caltech.edu/docs/NEID-DRP, which derives velocities
through cross-correlation with a weighted numerical stellar mask based on
spectral type (Baranne et al., 1996; Pepe et al., 2002). We used relatively
short exposure times for our observations, obtaining RV precisions of about 5
$\mathrm{m}\,\mathrm{s}^{-1}$ for TOI-2570 and 15
$\mathrm{m}\,\mathrm{s}^{-1}$ for the relatively fainter TOI-4137.

##  3 Stellar Characterization

We collected literature photometry and astrometry of each of the planet host
stars from the TESS Input Catalog (TIC; Stassun et al., 2018, 2019), Gaia EDR3
(Brown et al., 2021; Riello et al., 2021; Lindegren et al., 2021), 2MASS
(Cutri et al., 2003), WISE (Cutri, 2012), and Tycho-2 (Høg et al., 2000)
catalogs. These properties are displayed in Tables 3.1 and 9, and were used in
our global modelling of each system (§4).

###  3.1 Spectroscopic Parameters

For each system, we further characterized the host star properties using the
high resolution stellar spectra obtained as part of our spectroscopic follow-
up program. In the case of systems observed with the stabilized spectrographs
CHIRON and NEID, we used a spectrum from a single epoch with the highest
signal-to-noise ratio (S/N). For systems observed with PFS, we used the high
S/N iodine-free template spectrum. For those observed with HIRES, we used the
low S/N iodine-free reconnaissance spectrum.

We used the publicly available code SpecMatch-Emp (Yee et al.,
2017)666https://github.com/samuelyeewl/specmatch-emp to obtain a homogeneous
set of stellar properties for our targets. This code works by comparing a
target spectrum to a library of observed high-resolution ($R\approx$60,000),
high S/N ($\mathrm{S/N}\approx 150$/pixel) spectra from Keck/HIRES. The
library stars have well-determined empirical stellar properties from a variety
of sources, including asteroseismology, interferometry, and spectrophotometry.
The code finds the five library spectra that best match the target, accounting
for rotational broadening, and interpolates between those stars’ properties to
derive ($T_{\mathrm{eff}}$, $R_{\star}$, $\mathrm{[Fe/H]}$) for the target,
with uncertainties of $\sigma(T_{\mathrm{eff}})=100$ K, $\sigma(\Delta
R_{\star}/R_{\star})=15\%$, $\sigma(\mathrm{[Fe/H]})=0.09$ dex, which are
robust even when the S/N is as low as 20/pixel.

While SpecMatch-Emp was developed for use with Keck/HIRES spectra, it has been
successfully used with spectra from other instruments (e.g., Teske et al.,
2018). To account for the narrow line spread functions of the other
spectrographs used compared with that of HIRES, we modified the code to allow
the target star’s spectrum to be broadened relative to the library spectra. We
found that this produced sharper $\chi^{2}$ minima, and a better match to the
target spectrum. Previous testing of this approach using a cross-validation
technique with the library Keck/HIRES spectra showed no degradation in the
accuracy of the derived parameters. We compared the SpecMatch-Emp-derived
parameters to those derived from the TRES reconnaissance spectra when
available (§2.4.5), and found them to be within 1-$\sigma$ agreement.

We measured $v\sin{i}$ for each of the targets using the SpecMatch-
Synth777https://github.com/petigura/specmatch-syn (Petigura, 2015) code. This
code works similarly to SpecMatch-Emp, but matches the target spectrum to a
synthetic spectral library from Coelho et al. (2005) instead. A set of eight
best-matching spectra are selected from the synthetic library, which spans a
range of $T_{\mathrm{eff}}$, $\log{g}$, and $\mathrm{[Fe/H]}$. These are then
combined using trilinear interpolation and convolved with a rotational-
macroturbulent profile and Gaussian instrumental profile to create a better
match to the target spectrum. During this process, the macroturbulent
broadening is assumed to follow the relationship from Valenti & Fischer
(2005):

$v_{\mathrm{mac}}=\left(3.98-\frac{T_{\mathrm{eff}}-5770\,\mathrm{K}}{650\,\mathrm{K}}\right)\,\mathrm{km}\,\mathrm{s}^{-1}.$
(1)

The code optimizes over the interpolation weights and $v\sin{i}$ to derive the
target stellar atmospheric properties. We report only the $v\sin{i}$ from this
code, but we found that the other parameters were typically within 1-$\sigma$
agreement with those derived by SpecMatch-Emp, which is more robust for low
S/N spectra. We report $T_{\mathrm{eff}}$, $\log{g}$, and $\mathrm{[Fe/H]}$
from SpecMatch-Emp, and $v\sin{i}$ and $v_{\mathrm{mac}}$ from SpecMatch-Synth
in Table 10.

For those targets with observations from TRES, we also used SPC (Buchhave et
al., 2012) to derive stellar atmospheric properties. SPC cross-correlates an
observed spectrum against a grid of synthetic spectra from Kurucz (1993),
allowing $T_{\mathrm{eff}}$, $\log{g}$, $\mathrm{[Fe/H]}$, and $v\sin{i}$ to
be determined. The SPC stellar parameters are also tabulated in Table 10, and
we found that in all cases, the derived properties did not differ from those
from SpecMatch by more than 1.5-$\sigma$. For targets with CHIRON spectra, we
derived stellar properties by matching the spectra against a library of
$\sim$10,000 observed spectra previously classified by SPC. This procedure is
described in more detail in Rodriguez et al. (2021), with results shown in
Table 10. Finally, for TOI-2207, we used the CERES code (Brahm et al., 2017)
to estimate stellar properties from the FEROS spectra. In all cases, the
stellar properties derived by these different codes do not differ
significantly, giving us greater confidence in these results. For consistency,
we used the SpecMatch results for $T_{\mathrm{eff}}$, $R_{\star}$ and
$\mathrm{[Fe/H]}$ for all targets as prior constraints in our EXOFASTv2 fits,
as described in Section 4.

=1.5in

Table 8: Catalog Photometry and Astrometry of Planet Host Stars

Target | TOI-2193 | TOI-2207 | TOI-2236 | TOI-2421 | TOI-2567 | Source
---|---|---|---|---|---|---
Identifiers
TIC | 401604346 | 90850770 | 394722182 | 70524163 | 258920431 |
GAIA EDR3 | 6373308503181838592 | 6675883485986480256 | 4613145315172329984 | 4968289907406396160 | 2254929887069708160 |
2MASS | 20544592-7248166 | 20302318-4453150 | 01203986-8658476 | 02123692-3523272 | 19135180+6620524 |
Tycho-2 | 9329-00167-1 | 7962-00808-1 | 9498-00283-1 | 7009-01148-1 | – |
WISE | J205445.92-724816.8 | J203023.20-445315.2 | J012039.88-865847.8 | J021236.95-352327.2 | J191351.77+662052.5 |
Astrometric Measurements
R.A. (J2000) | 20:54:45.895 | 20:30:23.207 | 01:20:39.841 | 02:12:36.966 | 19:13:51.759 | 1
Decl. (J2000) | -72:48:16.71 | -44:53:15.44 | -86:58:47.88 | -35:23:27.31 | +66:20:52.58 | 1
$\mu_{{\alpha}}\cos{\delta}$ (mas yr-1) | -2.465 $\pm$ 0.009 | 15.782 $\pm$ 0.021 | -3.653 $\pm$ 0.017 | 29.004 $\pm$ 0.012 | -16.973 $\pm$ 0.011 | 1
$\mu_{{\delta}}$ (mas yr-1) | -0.911 $\pm$ 0.011 | -25.806 $\pm$ 0.018 | -7.860 $\pm$ 0.015 | -3.689 $\pm$ 0.017 | 9.021 $\pm$ 0.011 | 1
Parallax (mas) | 2.896 $\pm$ 0.009 | 2.626 $\pm$ 0.020 | 2.837 $\pm$ 0.012 | 3.055 $\pm$ 0.020 | 1.929 $\pm$ 0.009 | 1
$b$ (∘) | -34.782 | -35.849 | -30.123 | -70.835 | 22.507 | 1
$l$ (∘) | 320.935 | 355.480 | 302.488 | 243.467 | 97.326 | 1
Photometric Measurements
$T$ (mag) | 11.400 $\pm$ 0.006 | 10.965 $\pm$ 0.006 | 10.867 $\pm$ 0.006 | 10.692 $\pm$ 0.006 | 11.749 $\pm$ 0.008 | 2
$G$ (mag) | 11.806 $\pm$ 0.003 | 11.352 $\pm$ 0.003 | 11.289 $\pm$ 0.003 | 11.157 $\pm$ 0.003 | 12.210 $\pm$ 0.003 | 1
$G_{\mathrm{{BP}}}$ (mag) | 12.109 $\pm$ 0.003 | 11.637 $\pm$ 0.003 | 11.601 $\pm$ 0.003 | 11.510 $\pm$ 0.003 | 12.573 $\pm$ 0.003 | 1
$G_{\mathrm{{RP}}}$ (mag) | 11.331 $\pm$ 0.004 | 10.906 $\pm$ 0.004 | 10.806 $\pm$ 0.004 | 10.637 $\pm$ 0.004 | 11.683 $\pm$ 0.004 | 1
$B_{T}$ (mag) | 12.857 $\pm$ 0.202 | 12.519 $\pm$ 0.207 | 12.267 $\pm$ 0.135 | 12.149 $\pm$ 0.089 | – | 3
$V_{T}$ (mag) | 12.057 $\pm$ 0.143 | 11.422 $\pm$ 0.102 | 11.664 $\pm$ 0.105 | 11.488 $\pm$ 0.068 | – | 3
$J$ (mag) | 10.767 $\pm$ 0.024 | 10.438 $\pm$ 0.024 | 10.261 $\pm$ 0.023 | 10.090 $\pm$ 0.024 | 11.118 $\pm$ 0.021 | 4
$H$ (mag) | 10.462 $\pm$ 0.023 | 10.201 $\pm$ 0.023 | 10.006 $\pm$ 0.023 | 9.752 $\pm$ 0.024 | 10.764 $\pm$ 0.019 | 4
$K_{s}$ (mag) | 10.383 $\pm$ 0.021 | 10.133 $\pm$ 0.023 | 9.960 $\pm$ 0.021 | 9.667 $\pm$ 0.021 | 10.717 $\pm$ 0.017 | 4
$W1$ (mag) | 10.343 $\pm$ 0.023 | 10.091 $\pm$ 0.022 | 9.900 $\pm$ 0.023 | 9.624 $\pm$ 0.024 | 10.659 $\pm$ 0.023 | 5
$W2$ (mag) | 10.354 $\pm$ 0.021 | 10.149 $\pm$ 0.020 | 9.925 $\pm$ 0.020 | 9.678 $\pm$ 0.020 | 10.714 $\pm$ 0.020 | 5
$W3$ (mag) | 10.361 $\pm$ 0.068 | 10.191 $\pm$ 0.069 | 9.884 $\pm$ 0.037 | 9.623 $\pm$ 0.040 | 10.629 $\pm$ 0.054 | 5

References. — (1) - Gaia EDR3 (Brown et al., 2021); (2) - TESS Input Catalog
(Stassun et al., 2019); (3) - Tycho-2 (Høg et al., 2000); (4) - 2MASS (Cutri
et al., 2003); (5) - WISE (Cutri, 2012).

Note. — The catalog photometry presented here has not been corrected for
contamination by nearby stellar companions (§3.2).

The data in this table is available in machine-readable form.

=1.5in

Table 9: Catalog Photometry and Astrometry of Planet Host Stars  Target | TOI-2570 | TOI-3331 | TOI-3540 | TOI-3693 | TOI-4137 | Source
---|---|---|---|---|---|---
Identifiers
TIC | 239816546 | 194795551 | 17865622 | 240823272 | 417646390 |
GAIA EDR3 | 3445148131761842944 | 4042548116644168832 | 1896138833241139584 | 404433018447476096 | 497750842338402560 |
2MASS | 05484513+3205028 | 18051781-3406254 | 21553871+2810460 | 01023706+5118143 | 05102703+7023279 |
Tycho-2 | – | 7399-00615-1 | – | 3275-01223-1 | 4346-00736-1 |
WISE | J054845.12+320502.6 | J180517.84-340624.5 | J215538.71+281045.9 | J010237.05+511814.1 | J051027.06+702327.9 |
Astrometric Measurements
R.A. (J2000) | 05:48:45.129 | 18:05:17.800 | 21:55:38.729 | 01:02:37.054 | 05:10:27.093 | 1
Decl. (J2000) | +32:05:02.55 | -34:06:25.82 | +28:10:46.20 | +51:18:14.00 | +70:23:27.88 | 1
$\mu_{{\alpha}}\cos{\delta}$ (mas yr-1) | -6.531 $\pm$ 0.014 | 0.445 $\pm$ 0.032 | 6.306 $\pm$ 0.044 | -6.962 $\pm$ 0.016 | 19.686 $\pm$ 0.013 | 1
$\mu_{{\delta}}$ (mas yr-1) | -15.848 $\pm$ 0.009 | -17.028 $\pm$ 0.022 | -1.296 $\pm$ 0.043 | -21.307 $\pm$ 0.014 | -3.005 $\pm$ 0.015 | 1
Parallax (mas) | 2.765 $\pm$ 0.014 | 4.446 $\pm$ 0.026 | 3.541 $\pm$ 0.040 | 5.656 $\pm$ 0.018 | 2.891 $\pm$ 0.017 | 1
$b$ (∘) | 2.207 | -6.219 | -20.456 | -11.529 | 17.587 | 1
$l$ (∘) | 177.656 | 357.625 | 82.170 | 124.715 | 141.500 | 1
Photometric Measurements
$T$ (mag) | 11.977 $\pm$ 0.006 | 11.321 $\pm$ 0.006 | 10.954 $\pm$ 0.007 | 11.419 $\pm$ 0.006 | 10.856 $\pm$ 0.009 | 2
$G$ (mag) | 12.450 $\pm$ 0.003 | 11.824 $\pm$ 0.003 | 11.428 $\pm$ 0.003 | 11.955 $\pm$ 0.003 | 11.246 $\pm$ 0.003 | 1
$G_{\mathrm{{BP}}}$ (mag) | 12.821 $\pm$ 0.003 | 12.212 $\pm$ 0.003 | 11.674 $\pm$ 0.003 | 12.386 $\pm$ 0.003 | 11.534 $\pm$ 0.003 | 1
$G_{\mathrm{{RP}}}$ (mag) | 11.915 $\pm$ 0.004 | 11.255 $\pm$ 0.004 | 10.835 $\pm$ 0.005 | 11.357 $\pm$ 0.004 | 10.797 $\pm$ 0.004 | 1
$B_{T}$ (mag) | – | 12.989 $\pm$ 0.372 | – | 12.783 $\pm$ 0.174 | 12.243 $\pm$ 0.093 | 3
$V_{T}$ (mag) | – | 11.753 $\pm$ 0.204 | – | 12.025 $\pm$ 0.120 | 11.395 $\pm$ 0.058 | 3
$J$ (mag) | 11.303 $\pm$ 0.022 | 10.348 $\pm$ 0.026 | 10.237 $\pm$ 0.021 | 10.657 $\pm$ 0.022 | 10.314 $\pm$ 0.023 | 4
$H$ (mag) | 10.960 $\pm$ 0.021 | 10.068 $\pm$ 0.029 | 9.899 $\pm$ 0.022 | 10.246 $\pm$ 0.023 | 10.048 $\pm$ 0.031 | 4
$K_{s}$ (mag) | 10.905 $\pm$ 0.020 | 9.914 $\pm$ 0.026 | 9.784 $\pm$ 0.017 | 10.151 $\pm$ 0.020 | 10.004 $\pm$ 0.022 | 4
$W1$ (mag) | 10.860 $\pm$ 0.023 | 9.565 $\pm$ 0.022 | 9.742 $\pm$ 0.023 | 10.132 $\pm$ 0.023 | 9.957 $\pm$ 0.023 | 5
$W2$ (mag) | 10.918 $\pm$ 0.020 | 9.653 $\pm$ 0.020 | 9.792 $\pm$ 0.019 | 10.178 $\pm$ 0.020 | 9.999 $\pm$ 0.021 | 5
$W3$ (mag) | 11.178 $\pm$ 0.167 | 9.895 $\pm$ 0.075 | 9.678 $\pm$ 0.062 | 10.141 $\pm$ 0.049 | 9.930 $\pm$ 0.093 | 5

=1in

Table 10: Spectroscopic Stellar Properties  Target | TOI-2193 | TOI-2207 | TOI-2236 | TOI-2421 | TOI-2567 | Target | TOI-2570 | TOI-3331 | TOI-3540 | TOI-3693 | TOI-4137
---|---|---|---|---|---|---|---|---|---|---|---
Code | SpecMatch | SpecMatch | CERES | SpecMatch | SPC | SpecMatch | SPC | SpecMatch | SPC | Code | SpecMatch | SPC | SpecMatch | SpecMatch | SPC | SpecMatch | SPC | SpecMatch | SPC
Instrument | PFS | PFS | FEROS | CHIRON | CHIRON | CHIRON | CHIRON | HIRES | TRES | Instrument | NEID | TRES | PFS | HIRES | TRES | HIRES | TRES | NEID | TRES
$T_{\mathrm{eff}}$ (K) | 5974 $\pm$ 110 | 6075 $\pm$ 110 | 6050 $\pm$ 150 | 6228 $\pm$ 110 | 6164 $\pm$ 50 | 5645 $\pm$ 110 | 5577 $\pm$ 50 | 5609 $\pm$ 110 | 5650 $\pm$ 50 |  | 5756 $\pm$ 110 | 5765 $\pm$ 50 | 5521 $\pm$ 110 | 5865 $\pm$ 110 | 5969 $\pm$ 50 | 5246 $\pm$ 110 | 5274 $\pm$ 50 | 6125 $\pm$ 110 | 6134 $\pm$ 50
$R_{\star}$ ($R_{\odot}$) | 1.21 $\pm$ 0.18 | 1.49 $\pm$ 0.22 | – | 1.66 $\pm$ 0.25 | – | 1.92 $\pm$ 0.29 | – | 1.83 $\pm$ 0.27 | – |  | 1.35 $\pm$ 0.20 | – | 1.06 $\pm$ 0.16 | 1.34 $\pm$ 0.20 | – | 0.85 $\pm$ 0.13 | – | 1.65 $\pm$ 0.25 | –
$\log{g}$ (cgs) | – | – | 4.20 $\pm$ 0.20 | – | 4.17 $\pm$ 0.10 | – | 3.82 $\pm$ 0.10 | – | 4.15 $\pm$ 0.10 |  | – | 4.43 $\pm$ 0.10 | – | – | 4.40 $\pm$ 0.10 | – | 4.61 $\pm$ 0.10 | – | 4.13 $\pm$ 0.10
$[\mathrm{Fe/H}]$ (dex) | -0.04 $\pm$ 0.09 | 0.15 $\pm$ 0.09 | 0.10 $\pm$ 0.10 | 0.08 $\pm$ 0.09 | 0.00 $\pm$ 0.10 | 0.18 $\pm$ 0.09 | 0.01 $\pm$ 0.10 | 0.24 $\pm$ 0.09 | 0.41 $\pm$ 0.08 |  | 0.18 $\pm$ 0.09 | 0.22 $\pm$ 0.08 | 0.12 $\pm$ 0.09 | 0.18 $\pm$ 0.09 | 0.30 $\pm$ 0.08 | 0.12 $\pm$ 0.09 | -0.09 $\pm$ 0.08 | 0.08 $\pm$ 0.09 | 0.14 $\pm$ 0.08
$v\sin{i}$ (km/s)aaFlux has been normalized such that the mean out-of-transit flux has a baseline of 1.0, but is not yet detrended.Median instrumental RV uncertainty for each target and instrument. | 4.6 $\pm$ 1.0 | 6.9 $\pm$ 1.0 | 7.5 $\pm$ 2.0 | 9.8 $\pm$ 1.0 | 10.2 $\pm$ 0.5 | 4.2 $\pm$ 1.0 | 5.2 $\pm$ 0.5 | 2.5 $\pm$ 1.0 | 4.6 $\pm$ 0.5 |  | 2.3 $\pm$ 1.0 | 4.0 $\pm$ 0.5 | 3.5 $\pm$ 1.0 | 3.9 $\pm$ 1.0 | 6.3 $\pm$ 0.5 | 4.4 $\pm$ 1.0 | 5.1 $\pm$ 0.5 | 8.8 $\pm$ 1.0 | 9.2 $\pm$ 0.5
$v_{\mathrm{mac}}$ (km/s)bbThe detrend variables are as listed in Table 2.2. | 3.6 $\pm$ 0.2 | 3.8 $\pm$ 0.2 | – | 3.2 $\pm$ 0.2 | – | 4.1 $\pm$ 0.2 | – | 4.1 $\pm$ 0.2 | – |  | 4.2 $\pm$ 0.2 | – | 4.1 $\pm$ 0.2 | 3.7 $\pm$ 0.2 | – | 4.7 $\pm$ 0.2 | – | 5.0 $\pm$ 0.2 | –

###  3.2 SED Fitting for Stars with Nearby Companions

Table 11: Observed Properties of Stellar Companions

TOI-3331 Gaia EDR3 ID 4042548116644168832 4042548120990244096 TIC ID 194795551
1565174683 Ang. Sep. ($"$) – 2.663 PA (∘) – 48 $\Delta I$ (mag) – 2.6 Parallax
(mas) $4.577\pm 0.057$ $5.388\pm 0.171$ $\mu_{\alpha}\cos{\delta}$ (mas/yr)
$0.421\pm 0.118$ $10.766\pm 0.604$ $\mu_{\delta}$ (mas/yr) $-16.943\pm 0.090$
$-22.713\pm 0.475$ RV (km/s) $-46.5\pm 0.6$ – $G$ (mag) $11.831\pm 0.001$
$14.264\pm 0.002$ $G_{\mathrm{BP}}$ (mag) $12.249\pm 0.003$ $14.999\pm 0.004$
$G_{\mathrm{RP}}$ (mag) $11.268\pm 0.002$ $13.301\pm 0.014$ TOI-3540 Gaia EDR3
ID 1896138833241139584 – TIC ID 17865622 – Ang. Sep. ($"$) – 0.917 PA (∘) –
200 $\Delta I$ (mag) – 1.8 $\Delta\mathrm{Br}\gamma$ (mag) – 1.022 $\Delta
H\mathrm{cont}$ (mag) – 1.144 Parallax (mas) $3.633\pm 0.259$ –
$\mu_{\alpha}\cos{\delta}$ (mas/yr) $5.722\pm 0.496$ – $\mu_{\delta}$ (mas/yr)
$-4.567\pm 0.592$ – RV (km/s) $-4.1\pm 0.7$ – $G$ (mag) $11.404\pm 0.003$ –
$G_{\mathrm{BP}}$ (mag) $11.698\pm 0.002$ – $G_{\mathrm{RP}}$ (mag) $10.839\pm
0.003$ –

Figure 5: Multi-component SED fits for the systems TOI-2193 (top), TOI-3331
(middle), and TOI-3540 (bottom), for which we detected nearby stellar
companions. The green points show the best-fit model for the primary, while
the orange points show the model for the secondary, as derived from isochrone
fitting. The blue points show the combined model fluxes from both components,
while the red points with error bars show the observed catalog fluxes.
Extinction-corrected atmospheric models from Kurucz (1993) are plotted for the
two stellar components for illustration, though these are not used directly in
the fit, which is performed with the MIST bolometric correction tables. The
lower panel of each plot shows the residuals of the combined observed fluxes
to the combined model fit, in units of the uncertainty on each measurement.
Table 12: Secondary Properties from SED Fit

Three of the target systems (TOI-2193, TOI-3331, TOI-3540) had nearby
companions detected in high-resolution imaging (§2.3, Figures 2–4). The
magnitude difference and angular separation of the primary and secondary
derived from this imaging are presented in Table 3.2. In the case of TOI-2193
and TOI-3331, these companions were also detected by Gaia as they are
relatively bright and at separations $\gtrsim 1\farcs 0$, which Gaia can
reliably resolve.

To correct the catalog photometry and photometric timeseries data for
contamination by these companions, we used the isochrones package (Morton,
2015) to perform a multi-component Spectral Energy Distribution (SED) fit. For
each system, we fitted the blended catalog photometry, together with the
$\Delta$mag between the primary and secondary stars obtained from high-
resolution imaging, to synthetic photometry derived from the MIST isochrones
(Dotter, 2016; Choi et al., 2016). We placed an error floor of 0.02 mag for
the Gaia and 2MASS photometry, and 0.03 mag for the WISE photometry, to
account for possible systematic errors in the isochrones in reproducing the
broad-band photometry measurements. The fit was additionally constrained by
the parallax measurements from Gaia, the spectroscopic parameters derived for
the primary in Section 3.1, and an upper limit on the line-of-sight extinction
from Schlegel et al. (1998) and Schlafly & Finkbeiner (2011).

We provide the best-fit stellar properties and MIST isochrone synthetic
photometry for the secondary, along with corresponding uncertainties from a
Markov Chain Monte Carlo analysis, in Table 3.2. We then subtracted the
synthetic photometry from the blended catalog photometry (as listed in Tables
3.1 and 9), and use these corrected fluxes for our global modelling (§4). We
also computed flux dilution factors (defined in §4) for each band in which
time-series photometry was obtained, to correct for the contribution from the
nearby stars to the light-curve. These dilution factors were used in the
global ExoFAST fits.

In addition, as a further check that the spectroscopic parameters derived in
Section 2.4 were not biased by possible contamination of the observed spectrum
by the companion, we performed a series of tests on the SpecMatch-Emp code. We
injected a diluted spectrum matching the companion’s spectral type into the
target spectrum and performed the stellar characterization procedure. We found
that even if the companion was responsible for contaminating the target
spectrum by up to 10%, the derived stellar properties did not vary by more
than the uncertainties. Furthermore, contamination down to $\sim$1% would be
detected in the residuals as a poor $\chi^{2}$ match, which was not the case
for these three targets.

We discuss each of these three targets in more detail in the rest of this
section.

####  3.2.1 TOI-2193 Companion

The TOI-2193 system contains two stars (TOI-2193A and TOI-2193B) separated by
$1\farcs 885$ and a magnitude difference of $\Delta I=3.8$ mag. The Gaia EDR3
catalog (Brown et al., 2021; Riello et al., 2021) contains astrometry for both
components, as well as 3-band photometry ($G,G_{\mathrm{BP}},G_{\mathrm{RP}}$)
for the primary and $G$-band photometry for the secondary. The parallaxes and
proper motions for the two components are identical within the uncertainties,
suggesting that they are a bound system with a projected separation of
$\approx 640$ AU (Table 3.2). We therefore performed the isochrone fit
assuming that the two stars have the same age and had the same initial
metallicity.

The best-fit SED model found the secondary to have a mass of
$M_{\star}=0.54\pm 0.01M_{\odot}$, and the estimated fluxes are shown in the
top panel of Figure 5. We used this best-fit model to correct the 2MASS and
WISE catalog photometry, but not the Gaia and TIC photometry, since the two
components were resolved in Gaia as well as the TESS Input Catalog (TIC;
Stassun et al. 2018, 2019). For the same reason, we do not impose an
additional dilution factor for the TESS light-curve, since it was already
accounted for in the crowding corrections performed by the TESS SPOC.

####  3.2.2 TOI-3331 Companions

In the case of the TOI-3331 system, SOAR imaging detected a nearby star with
an angular separation of $2\farcs 663$ and $\Delta I=2.6$ mag. This system was
also resolved by Gaia. The Gaia EDR3 catalog gives a parallax of
$\Pi_{2}=5.39\pm 0.17$ for the secondary, compared with $\Pi_{1}=4.577\pm
0.057$ for the primary. The proper motions for the two stars differ
significantly (Table 3.2). Thus, the two stars are most likely a chance
alignment along the line of sight. Gaia photometry also resolved a third star
at an angular separation of $4\farcs 89$, but we ignored this object in our
fit due to its faintness ($G=20.1$). In our isochrone fit, we model the two
stars with independent ages and metallicities, with individual parallaxes as
constrained by Gaia, and show the results in the middle panel of Figure 5. As
with the previous case, we did not correct the Gaia and TESS photometry, as
the secondary was resolved in those catalogs.

####  3.2.3 TOI-3540 Companion

For TOI-3540, SOAR speckle imaging as well as PHARO AO imaging both detected a
companion at $0\farcs 917$, with $\Delta I=1.8$ mag. This companion was not
resolved by Gaia, so we do not have parallax or proper motion measurements for
this object. However, studies (e.g., Horch et al., 2014; Matson et al., 2018)
have shown that most nearby companions within $1"$ are likely to be bound,
leading us to assume that this is the case for TOI-3540. This would give the
pair of stars a projected separation of $\approx 250$ AU. We then performed
the isochrone fit under this assumption, finding that the catalog photometry
is well-described by a two-component system in which the secondary has a mass
of $M_{\star}=0.79\pm 0.02M_{\odot}$. We corrected the fluxes in all
photometric bands, and computed the appropriate dilution factors for the TESS
and ground-based time-series photometry.

##  4 Planetary System Characterization

We characterized each planetary system with the exoplanet fitting code
EXOFASTv2 (Eastman et al., 2013, 2019). This software models the star and
planet in a self-consistent manner, fitting transit and radial-velocity
observations as well as the broad-band photometry, with constraints on the
stellar properties from the MIST stellar evolutionary models (Dotter, 2016;
Choi et al., 2016). EXOFASTv2 uses a differential evolution Markov Chain Monte
Carlo (DE-MCMC) algorithm to explore the posterior distribution and determine
uncertainties of each fitted parameter.

In this section, we first describe our general fitting strategy, before
describing some deviations from the general strategy for specific targets. We
imposed Gaussian priors on the stellar spectroscopic properties
$T_{\mathrm{eff}}$, $R_{\star}$, and $\mathrm{[Fe/H]}$ based on the SpecMatch-
Emp characterization described in §3.1. For the SED fit, we used broadband
photometry from the Gaia EDR3 (Brown et al., 2021; Riello et al., 2021),
Tycho-2 (Høg et al., 2000), 2MASS (Cutri et al., 2003), and WISE (Cutri, 2012)
catalogs. We imposed a minimum uncertainty of 0.02 mag for the Gaia and 2MASS
photometry, and 0.03 mag for the WISE photometry. We also imposed a Gaussian
prior on the parallax from Gaia EDR3, corrected for the parallax zero-point as
described in Lindegren et al. (2021)888https://gitlab.com/icc-
ub/public/gaiadr3_zeropoint, as well as an upper limit on line-of-sight
extinction from Schlegel et al. (1998) and Schlafly & Finkbeiner (2011).

We fitted the available radial-velocities with an independent RV offset
$\gamma$ and jitter $\sigma_{\mathrm{jit}}$ terms for each instrument and
target. For those targets with only two observations from TRES (TOI-2567,
-2570, -3540, -4137), we did not include the TRES RVs in the fit, as the
introduction of two additional per-instrument free parameters did not justify
their inclusion. In all cases however, we find that the TRES measurements are
consistent with the modelled RV semiamplitude from the global fit (Figures
LABEL:fig:toi2567_multiplot, LABEL:fig:toi2570_multiplot,
LABEL:fig:toi3540_multiplot & LABEL:fig:toi4137_multiplot), giving us
additional confidence in our results. We did not allow for any long-term
radial-velocity trends, because our initial testing showed that trends were
not required to achieve a good fit to the data for any of our systems,
especially given the relatively short baseline of our RV observations.

We used both the TESS and ground-based time-series photometry to constrain the
transit model. EXOFASTv2 fits an analytic transit model from Mandel & Agol
(2002) and Agol et al. (2020) to the transit light-curve, with quadratic limb-
darkening coefficients in each band constrained by the stellar properties and
the tables from Claret & Bloemen (2011) and Claret (2017). EXOFASTv2 ensures
that the constraint on the stellar mean density implicit in the transit model
is consistent with the mean density implied by the MIST stellar evolution
model. We also fit for a separate flux baseline $F_{0}$ and added variance
$\sigma^{2}$ for each transit light-curve.

While the fluxes from TESS are already corrected for dilution from neighboring
stars in the TESS Input Catalog (TIC; Stassun et al. 2018, 2019), we still
fitted for a dilution factor $A_{D}$, to account for any inaccuracies and to
propagate uncertainties, as recommended by Eastman et al. (2019). Here,
$A_{D}=F_{2}/(F_{1}+F_{2})$ is the fractional contribution to the total flux
($F_{1}+F_{2}$) from all neighboring stars ($F_{2}$). We imposed a Gaussian
prior on this dilution factor centered at zero and with a width equal to 10%
the contamination ratio found in the TIC. For the ground-based photometry, we
simultaneously detrended against the detrending vectors listed in Table 2.2.
We normalized the detrend parameters to be between $[-1,+1]$, and used an
additive detrending model for the light-curve. The final light-curve model at
time $i$ is then

$\mathrm{Model}_{i}=F_{0}\left(T_{i}(1-A_{D})+A_{D}\right)+\sum C_{j}d_{i,j},$
(2)

where $T_{i}$ is the transit model with an out-of-transit baseline of 1,
$d_{i,j}$ is the $j$-th detrending parameter at time $i$, and $C_{j}$ the
additive coefficient for the $j$-th parameter. For the TESS long-cadence data,
this model is integrated over the 30-minute or 10-minute exposure time to
account for smearing of the light-curve over each exposure.

We performed our initial fits requiring circular orbits for each planet. We
also performed a second fit in which the eccentricity was allowed to be a free
parameter. In EXOFASTv2 , the eccentricity is parameterized in terms of
$\sqrt{e}\cos{\omega}$ and $\sqrt{e}\sin{\omega}$. In all but one case
(TOI-2207 b), the data are consistent with a circular orbit. As such, we adopt
the results from the circular fit for these objects, but also report
1-$\sigma$ upper limits on the eccentricity from the fit where we allowed
eccentricity to float. For TOI-2207 b, our eccentric fit found that the median
of the posterior distribution was more than $3$-$\sigma$ above zero,
suggesting that this planet, with an orbital period of $P\approx 8.00$ days,
has a detectably eccentric orbit. We adopt the results from the eccentric fit
for this target.

We ran the EXOFASTv2 DE-MCMC algorithm using the convergence criteria
suggested by Eastman et al. (2019), requiring the Gelman-Rubin statistic
(Gelman & Rubin, 1992) to be $<1.01$, as well as $>1{,}000$ independent draws
in each parameter. Tables 13 and 14 contain the median and 68% confidence
intervals of the marginalized one-dimensional posterior probability
distributions for the fitted parameters, from the adopted fit. We also provide
the full results from both circular and eccentric fits for all targets as a
machine-readable companion to those tables. The best-fit model for the
transit, radial-velocities, and SED for each system are shown in Figures
LABEL:fig:toi2193_multiplot and LABEL:fig:toi2207_multiplot through
LABEL:fig:toi4137_multiplot.

###  4.1 Target-Specific Notes

In the case of TOI-2207 b, our eccentric fit found that the median of the
posterior distribution was more than $3$-$\sigma$ above zero, suggesting that
this planet, with an orbital period of $P\approx 8.00$ days, has a detectably
eccentric orbit. As such, in Table 13, we report the median and 68% confidence
intervals for the eccentric fit for all parameters listed.

The objects TOI-2193A b and TOI-3540A b appear to be on orbits wherein the
planetary transits graze the stellar limb. In this regime, there is a strong
degeneracy between the planet-to-star radius ratio $R_{p}/R_{\star}$ and the
transit impact parameter $b$. The resulting posterior distributions for these
parameters have long tails allowing for extremely large and unphysical planet
radii. In these cases, we placed an upper limit of $R_{p}/R_{\star}<0.5$
during the fit to ensure convergence of the MCMC fits within these limits. As
the medians of the posterior distributions would be heavily skewed by the long
tails, we report the mode of the posterior distributions and the 95% lower
limit on the planet radius and 95% upper limit on the orbital inclination
(note that these limits also depend on the cutoff chosen during the fit).

In general, we did not fit for any dilution factors in the transit light-
curves, except for the TESS data, where we allowed $A_{D}$ to vary within a
small range around zero. However, for the targets described in Section 3.2
that have stellar companions, we also allowed for dilution of the ground-based
light-curves, since the apertures used also contained the stellar companions.
In these cases, we used the best-fit multi-component SED model to derive
dilution factors for each photometric filter to correct the light-curves,
imposing a Gaussian prior with width equal to 10% of the dilution factor
around the mean value.

For targets observed in multiple TESS sectors, we generally fit each sector of
data separately, with a separate baseline flux $F_{0}$ and variance
$\sigma^{2}$ per sector. TOI-2567 was observed by TESS in a total of 15
sectors (14–26, 40, 41), which would greatly increase the dimensionality of
the fit were we to include these two additional free parameters for each. In
this case, we fit the Sectors 14–26 data, which were all at 30-min cadence, as
a single light-curve. The sectors 40 and 41 data were taken at 2-min cadence,
and we fit these as a single light-curve too. In general, our fitted values
for $F_{0}$ and $\sigma^{2}$ for the TESS data are close to 1.0 and 0.0
respectively, indicating minimal baseline offsets between sectors, so
combining these consecutive sectors of data should not have had a significant
impact on the fit.

###  4.2 Potential False-Positive Scenarios

Various astrophysical phenomena can lead to light-curves that appear similar
to planetary transits, leading to false-positive planet detections (e.g.
Collins et al. 2018). The goal of our ground-based follow-up observations was
to help rule out or reduce the likelihood of such scenarios. For each of our
ten hot Jupiter systems, the seeing-limited ground-based photometry confirm
that the transits occur on the target stars, as opposed to being nearby
eclipsing binaries that contaminate the TESS photometric aperture. The
measured RV semi-amplitudes for all companions are also consistent with
planetary mass objects, rather than brown dwarfs, which can have similar radii
despite their significantly larger masses. Furthermore, the spectra of each
target showed no indications of secondary spectral lines. To check for the
possibility of unresolved blended eclipsing binaries causing line-profile
variations that may appear as RV variations, we computed the Pearson-$r$
coefficient to check for correlations between the measured RV and the spectral
line BIS. For each of the ten target systems, we found no statistically
significant correlations ($p>0.1$).

Given the extensive ground-based follow-up observations and lack of BIS
variations, we are confident that all of our targets are confirmed as true
planets. However, we chose to pay closer attention to the two systems TOI-2193
and TOI-3540, which exhibit grazing transits and have close resolved stellar
companions. Although the measured RV reflex motions measured on the primary
stars are indicative of planetary mass objects orbiting them, there may be
concern that these may actually be blended eclipsing binary (EB) false
positives, where the diluted light of the companion is the source of both the
transit and apparent radial-velocity variations. In the case of TOI-2193, the
nearby companion TOI-2193B is $1\farcs 885$ away. A small aperture measurement
($1\farcs 2$) of the LCO-CTIO light-curve taken on UT 2021-07-26 confirmed
that the source of the transit signal is indeed TOI-2193A. For TOI-3540, the
companion star is just $0\farcs 917$ away and could not be resolved by seeing-
limited photometry.

In order to definitively rule out such scenarios for these two objects, we
carried out a detailed blend modeling of each system following the procedures
described in Hartman et al. (2019), which is based on the work of Torres et
al. (2004). In each case we jointly model the available TESS and ground-based
light curves, catalog broadband photometry, Gaia parallaxes, and
spectroscopically determined atmospheric parameters. We include the resolved
stellar companions in the modelling, jointly fitting for the masses,
metallicities, distances, and ages of all stars that we assume contribute to
the blended (or resolved) measurements, and we include the measured magnitude
differences from high-resolution-imaging as observations to be fit in the
modelling. We use the MIST stellar models to constrain the properties of the
stars. For TOI-2193 we force the resolved stellar companion to have the same
age, distance and metallicity as the primary star, while for TOI-3540 we allow
the components to have independent values.

For each system we consider four scenarios: (1) the primary object in the
resolved pair is a single star with a transiting planet, while the secondary
object is also a single star; (2) the primary object in the resolved pair is a
single star, while the secondary object is a two-component stellar eclipsing
binary system; (3) the primary object in the resolved pair is itself an
unresolved hierarchical triple consisting of a bright non-eclipsing star and a
fainter stellar eclipsing binary, and the secondary object in the resolved
pair is a single star; and (4) the primary object in the resolved pair is an
unresolved blend between a bright non-eclipsing star and a line-of-sight
background eclipsing binary, while the secondary object in the resolved pair
is a single star. For both TOI-2193 and TOI-3540 we find that scenario (1)
provides the best (lowest $\chi^{2}$) fit to the observations, despite using
the fewest model parameters. In both cases the combination of the photometry
and Gaia parallax measurements favors scenarios where each of the resolved
point sources is itself a single star, while the transit duration and depth,
and the lack of secondary eclipses or ellipsoidal variations in the light
curves favors a transiting planet around the primary star over scenarios
involving eclipsing stellar binaries. For both TOI-2193 and TOI-3540 we find
that scenario (4) is the next-best-fitting scenario, and that this scenario
has $\Delta\chi^{2}\approx 70$, and $\Delta\chi^{2}\approx 9$ compared to
scenario (1) for TOI-2193 and TOI-3540, respectively. The relative inability
of the blend-models to fit the photometric data, together with the significant
RV variations consistent with transiting giant planet companions, and the lack
of any significant BIS variation in phase with the transit ephemerides, leads
us to conclude that both TOI-2193A b and TOI-3540A b have been confirmed as
transiting planets.

=-1in =2.3in

Table 13: Median Values and 68% Confidence Intervals for Fitted Stellar and
Planetary Parameters

|  | TOI-2193 b | TOI-2207 b | TOI-2236 b | TOI-2421 b | TOI-2567 b
---|---|---|---|---|---|---
Planet Parameters
$P$ (days) | Period | $2.1225735\pm 0.0000016$ | $8.001968^{+0.000024}_{-0.000025}$ | $3.5315902\pm 0.0000026$ | $4.3474032^{+0.0000079}_{-0.0000078}$ | $5.983944\pm 0.000013$
$T_{c}$ (BJDTDB) | Time of conjunction | $2459052.42122\pm 0.00021$ | $2459283.82747\pm 0.00046$ | $2459011.45704\pm 0.00023$ | $2458957.02765^{+0.00064}_{-0.00063}$ | $2459007.78085\pm 0.00052$
$T_{14}$ (days) | Transit duration | $0.06862^{+0.00087}_{-0.00084}$ | $0.1930^{+0.0015}_{-0.0013}$ | $0.127\pm 0.001$ | $0.2026\pm 0.0017$ | $0.2274\pm 0.0016$
$\tau$ (days) | Ingress/egress duration | $0.03431^{+0.00043}_{-0.00042}$ | $0.01230^{+0.00140}_{-0.00047}$ | $0.0219\pm 0.0012$ | $0.0125^{+0.0011}_{-0.0014}$ | $0.01365^{+0.00120}_{-0.00083}$
$a/R_{\star}$ | Planet-star separation | $5.71^{+0.17}_{-0.13}$ | $11.7\pm 0.4$ | $6.84^{+0.16}_{-0.15}$ | $6.67^{+0.34}_{-0.24}$ | $8.64^{+0.24}_{-0.31}$
$\left(R_{P}/R_{\star}\right)^{2}$ | Transit depth | $0.0191\,(>0.0169)$ | $0.004273^{+0.000098}_{-0.000090}$ | $0.007011^{+0.000092}_{-0.000090}$ | $0.002949^{+0.000071}_{-0.000075}$ | $0.003537^{+0.000073}_{-0.000068}$
$i$ (deg) | Inclination | $79.96\,(<80.57)$ | $88.84^{+0.79}_{-0.85}$ | $83.58^{+0.26}_{-0.25}$ | $86.49^{+1.30}_{-0.76}$ | $88.30^{+1.10}_{-0.82}$
$K$ (m/s) | RV semi-amplitude | $136^{+25}_{-26}$ | $55.8^{+8.3}_{-10.0}$ | $172\pm 43$ | $37.8^{+8.6}_{-8.9}$ | $20.6^{+3.2}_{-3.1}$
$a$ (AU) | Semimajor axis | $0.03319^{+0.00052}_{-0.00051}$ | $0.0854^{+0.0015}_{-0.0016}$ | $0.05009^{+0.00080}_{-0.00082}$ | $0.0543^{+0.0021}_{-0.0010}$ | $0.0672^{+0.0024}_{-0.0012}$
$R_{P}$ ($R_{\mathrm{J}}$) | Planet radius | $1.77\,(>1.55)$ | $0.995^{+0.028}_{-0.027}$ | $1.282^{+0.032}_{-0.031}$ | $0.925^{+0.035}_{-0.034}$ | $0.975^{+0.031}_{-0.029}$
$M_{P}$ ($M_{\mathrm{J}}$) | Planet mass | $0.94\pm 0.18$ | $0.64^{+0.10}_{-0.12}$ | $1.58^{+0.40}_{-0.39}$ | $0.333\pm 0.079$ | $0.201^{+0.034}_{-0.031}$
$\rho_{P}$ (g cm-3) | Planet density | $0.060\,(<0.321)$ | $0.80\pm 0.16$ | $0.93^{+0.25}_{-0.24}$ | $0.52^{+0.15}_{-0.13}$ | $0.269^{+0.052}_{-0.051}$
$\log{g_{P}}$ (cgs) | Planet surface gravity | $2.81\,(<3.00)$ | $3.203^{+0.071}_{-0.092}$ | $3.38^{+0.10}_{-0.12}$ | $2.98^{+0.10}_{-0.12}$ | $2.720^{+0.071}_{-0.080}$
$b\equiv a\cos{i}/R_{\star}$ | Transit impact parameter | $0.990\,(>0.967)$ | $0.20^{+0.16}_{-0.14}$ | $0.766^{+0.013}_{-0.014}$ | $0.409^{+0.071}_{-0.130}$ | $0.26^{+0.11}_{-0.16}$
$e$ | Eccentricity | 0.0 (fixed) | $0.174^{+0.048}_{-0.052}$ | 0.0 (fixed) | 0.0 (fixed) | 0.0 (fixed)
$e_{\mathrm{lim}}$aaThe $v\sin{i}$ in the SpecMatch column was computed from SpecMath-Synth.We did not correct the catalog photometry for the secondary fluxes in these bands, as the primary and secondary were resolved in the Gaia catalog. | 1-$\sigma$ upper limit on eccentricity | $<0.063$ | – | $<0.135$ | $<0.136$ | $<0.080$
$\tau_{\mathrm{circ}}$ (Gyr)bb$v_{\mathrm{mac}}$ is assumed based on effective temperature and the relation from Valenti & Fischer (2005). | Tidal circularization timescale | $0.00036\,(<0.00908)$ | $13.2^{+5.6}_{-4.6}$ | $0.40^{+0.12}_{-0.11}$ | $0.94^{+0.37}_{-0.28}$ | $1.78^{+0.44}_{-0.43}$
$\langle F\rangle$ (Gerg s-1 cm-2) | Incident flux | $2.20\pm 0.11$ | $0.553^{+0.026}_{-0.024}$ | $1.846^{+0.085}_{-0.088}$ | $1.257^{+0.065}_{-0.088}$ | $0.759^{+0.042}_{-0.041}$
$T_{\mathrm{eq}}$ (K) | Planet equilibirum temperature | $1763^{+21}_{-22}$ | $1259^{+16}_{-15}$ | $1688^{+19}_{-21}$ | $1534^{+20}_{-28}$ | $1352^{+18}_{-19}$
Stellar Parameters
$M_{\star}$ ($M_{\odot}$) | Stellar mass | $1.082^{+0.052}_{-0.049}$ | $1.296^{+0.069}_{-0.072}$ | $1.343^{+0.066}_{-0.065}$ | $1.131^{+0.130}_{-0.064}$ | $1.130^{+0.130}_{-0.059}$
$R_{\star}$ ($R_{\odot}$) | Stellar radius | $1.248^{+0.026}_{-0.028}$ | $1.564^{+0.041}_{-0.040}$ | $1.573\pm 0.033$ | $1.750^{+0.051}_{-0.049}$ | $1.686^{+0.043}_{-0.044}$
$\log{g_{\star}}$ (cgs) | Stellar surface gravity | $4.278^{+0.030}_{-0.024}$ | $4.161^{+0.034}_{-0.036}$ | $4.172\pm 0.024$ | $4.005^{+0.059}_{-0.037}$ | $4.044^{+0.036}_{-0.037}$
$\rho_{\star}$ (g cm-3) | Stellar density | $0.781^{+0.072}_{-0.052}$ | $0.476^{+0.050}_{-0.047}$ | $0.486^{+0.034}_{-0.031}$ | $0.297^{+0.048}_{-0.031}$ | $0.340^{+0.030}_{-0.036}$
$L_{\star}$ ($L_{\odot}$) | Stellar luminosity | $1.779^{+0.075}_{-0.084}$ | $3.05\pm 0.11$ | $3.41^{+0.14}_{-0.18}$ | $2.729^{+0.095}_{-0.091}$ | $2.54\pm 0.11$
$T_{\mathrm{eff}}$ (K) | Stellar effective temperature | $5966^{+73}_{-72}$ | $6101^{+75}_{-73}$ | $6248^{+72}_{-77}$ | $5607\pm 68$ | $5611^{+62}_{-65}$
$[\mathrm{Fe/H}]$ (dex) | Metallicity | $0.027^{+0.066}_{-0.052}$ | $0.181\pm 0.086$ | $0.119^{+0.081}_{-0.078}$ | $0.190^{+0.083}_{-0.085}$ | $0.241^{+0.078}_{-0.079}$
$[\mathrm{Fe/H}]_{0}$ (dex)ccfootnotemark:  | Initial metallicity | $0.082^{+0.060}_{-0.052}$ | $0.245\pm 0.081$ | $0.222\pm 0.072$ | $0.210^{+0.076}_{-0.083}$ | $0.258^{+0.071}_{-0.073}$
Age (Gyr) | Stellar age | $5.5^{+1.9}_{-1.7}$ | $3.3^{+1.3}_{-1.1}$ | $2.52^{+0.89}_{-0.82}$ | $7.5^{+1.7}_{-2.8}$ | $7.6^{+1.8}_{-2.7}$
EEPddfootnotemark:  | Equal evolutionary phase | $404^{+16}_{-28}$ | $383^{+30}_{-33}$ | $360^{+30}_{-15}$ | $455.6^{+4.5}_{-37.0}$ | $452.6^{+5.2}_{-33.0}$
$A_{V}$ (mag) | Visual extinction | $0.113^{+0.045}_{-0.060}$ | $0.049^{+0.031}_{-0.032}$ | $0.305^{+0.040}_{-0.064}$ | $0.024^{+0.013}_{-0.015}$ | $0.074^{+0.030}_{-0.042}$
d (pc) | Distance | $345.3\pm 1.1$ | $380.6\pm 2.9$ | $352.4\pm 1.5$ | $328.1^{+4.2}_{-4.0}$ | $505.2^{+7.7}_{-7.4}$

Note. — This table contains the fit results from the preferred fit for each
target: circular fits ($e$ fixed at 0.0) for all targets apart from TOI-2207
b, and an eccentric fit for TOI-2207 b. The results from both fits for each
target are available as a machine-readable table.

For TOI-2193A b and TOI-3540A b, we provide the posterior mode and 95% lower
limits for the $(R_{p}/R_{\star})^{2}$, $R_{p}$, and $b$, and the posterior
mode and 95% upper limits for $i$, $\rho_{P}$,$\log{g_{P}}$, and
$\tau_{\mathrm{circ}}$.

a-d Additional notes are provided following Table 14.

=2.3in

Table 14: Median Values and 68% Confidence Intervals for Fitted Stellar and
Planetary Parameters (continued)

|  | TOI-2570 b | TOI-3331 b | TOI-3540 b | TOI-3693 b | TOI-4137 b
---|---|---|---|---|---|---
Planet Parameters
$P$ (days) | Period | $2.9887615\pm 0.0000022$ | $2.0180231^{+0.0000043}_{-0.0000044}$ | $3.1199990\pm 0.0000079$ | $9.088516^{+0.000026}_{-0.000027}$ | $3.8016122\pm 0.0000065$
$T_{c}$ (BJDTDB) | Time of conjunction | $2459393.14532\pm 0.00021$ | $2459371.6530\pm 0.0002$ | $2459109.14114\pm 0.00089$ | $2458806.68164^{+0.00032}_{-0.00031}$ | $2458990.46651\pm 0.00033$
$T_{14}$ (days) | Transit duration | $0.12527^{+0.00097}_{-0.00091}$ | $0.08846^{+0.00085}_{-0.00083}$ | $0.0792^{+0.0026}_{-0.0025}$ | $0.1482^{+0.0012}_{-0.0011}$ | $0.1429\pm 0.0013$
$\tau$ (days) | Ingress/egress duration | $0.01423^{+0.00093}_{-0.00089}$ | $0.01397^{+0.00087}_{-0.00084}$ | $0.0396\pm 0.0013$ | $0.01937^{+0.00100}_{-0.00052}$ | $0.0167^{+0.0012}_{-0.0011}$
$a/R_{\star}$ | Planet-star separation | $8.13^{+0.23}_{-0.22}$ | $7.09^{+0.18}_{-0.17}$ | $7.51^{+0.26}_{-0.25}$ | $22.13^{+0.30}_{-0.47}$ | $7.80\pm 0.24$
$\left(R_{P}/R_{\star}\right)^{2}$ | Transit depth | $0.01304\pm 0.00026$ | $0.01559\pm 0.00033$ | $0.023\,(>0.015)$ | $0.02134^{+0.00041}_{-0.00039}$ | $0.00749\pm 0.00014$
$i$ (deg) | Inclination | $87.73^{+0.75}_{-0.57}$ | $85.40^{+0.38}_{-0.36}$ | $81.93\,(<83.11)$ | $89.57^{+0.29}_{-0.28}$ | $85.7\pm 0.4$
$K$ (m/s) | RV semi-amplitude | $111.2^{+6.9}_{-7.5}$ | $360\pm 21$ | $155^{+17}_{-16}$ | $109^{+26}_{-24}$ | $156^{+17}_{-15}$
$a$ (AU) | Semimajor axis | $0.04145^{+0.00081}_{-0.00086}$ | $0.03144^{+0.00048}_{-0.00055}$ | $0.04289^{+0.00092}_{-0.00093}$ | $0.0813^{+0.0011}_{-0.0012}$ | $0.05222^{+0.00089}_{-0.00096}$
$R_{P}$ ($R_{\mathrm{J}}$) | Planet radius | $1.217^{+0.035}_{-0.034}$ | $1.158\pm 0.043$ | $2.10\,(>1.44)$ | $1.124^{+0.029}_{-0.023}$ | $1.211^{+0.040}_{-0.039}$
$M_{P}$ ($M_{\mathrm{J}}$) | Planet mass | $0.820^{+0.063}_{-0.065}$ | $2.27\pm 0.16$ | $1.18\pm 0.14$ | $1.02^{+0.24}_{-0.22}$ | $1.44^{+0.17}_{-0.15}$
$\rho_{P}$ (g cm-3) | Planet density | $0.563^{+0.069}_{-0.063}$ | $1.82^{+0.24}_{-0.21}$ | $0.065\,(<0.512)$ | $0.89^{+0.22}_{-0.20}$ | $1.01^{+0.17}_{-0.15}$
$\log{g_{P}}$ (cgs) | Planet surface gravity | $3.137^{+0.041}_{-0.043}$ | $3.624\pm 0.041$ | $2.64\,(<3.17)$ | $3.300^{+0.095}_{-0.110}$ | $3.387^{+0.057}_{-0.058}$
$b\equiv a\cos{i}/R_{\star}$ | Transit impact parameter | $0.32^{+0.07}_{-0.10}$ | $0.569^{+0.030}_{-0.034}$ | $1.073\,(>0.936)$ | $0.17^{+0.10}_{-0.11}$ | $0.584^{+0.035}_{-0.038}$
$e$ | Eccentricity | 0.0 (fixed) | 0.0 (fixed) | 0.0 (fixed) | 0.0 (fixed) | 0.0 (fixed)
$e_{\mathrm{lim}}$aafootnotemark:  | 1-$\sigma$ upper limit on eccentricity | $<0.039$ | $<0.188$ | $<0.164$ | $<0.054$ | $<0.246$
$\tau_{\mathrm{circ}}$ (Gyr)bbfootnotemark:  | Tidal circularization timescale | $0.111^{+0.022}_{-0.018}$ | $0.071^{+0.015}_{-0.012}$ | $0.0027\,(<0.0897)$ | $22.3^{+6.0}_{-5.4}$ | $0.66^{+0.16}_{-0.13}$
$\langle F\rangle$ (Gerg s-1 cm-2) | Incident flux | $0.951^{+0.066}_{-0.060}$ | $1.114^{+0.096}_{-0.083}$ | $1.145^{+0.069}_{-0.066}$ | $0.0934^{+0.0064}_{-0.0056}$ | $1.379^{+0.092}_{-0.082}$
$T_{\mathrm{eq}}$ (K) | Planet equilibirum temperature | $1431^{+24}_{-23}$ | $1488^{+31}_{-29}$ | $1498\pm 22$ | $801^{+13}_{-12}$ | $1570^{+25}_{-24}$
Stellar Parameters
$M_{\star}$ ($M_{\odot}$) | Stellar mass | $1.063^{+0.063}_{-0.065}$ | $1.016^{+0.047}_{-0.052}$ | $1.081^{+0.071}_{-0.069}$ | $0.867^{+0.036}_{-0.037}$ | $1.313^{+0.068}_{-0.071}$
$R_{\star}$ ($R_{\odot}$) | Stellar radius | $1.095^{+0.026}_{-0.025}$ | $0.952\pm 0.029$ | $1.228\pm 0.033$ | $0.791^{+0.017}_{-0.014}$ | $1.438^{+0.039}_{-0.038}$
$\log{g_{\star}}$ (cgs) | Stellar surface gravity | $4.385^{+0.030}_{-0.031}$ | $4.487^{+0.022}_{-0.023}$ | $4.293\pm 0.036$ | $4.581^{+0.014}_{-0.021}$ | $4.240^{+0.031}_{-0.032}$
$\rho_{\star}$ (g cm-3) | Stellar density | $1.138^{+0.100}_{-0.091}$ | $1.65^{+0.13}_{-0.12}$ | $0.823^{+0.090}_{-0.079}$ | $2.48^{+0.10}_{-0.16}$ | $0.621^{+0.059}_{-0.055}$
$L_{\star}$ ($L_{\odot}$) | Stellar luminosity | $1.199^{+0.086}_{-0.079}$ | $0.807^{+0.081}_{-0.068}$ | $1.549^{+0.079}_{-0.080}$ | $0.453^{+0.034}_{-0.030}$ | $2.75^{+0.20}_{-0.17}$
$T_{\mathrm{eff}}$ (K) | Stellar effective temperature | $5771^{+89}_{-87}$ | $5609^{+92}_{-87}$ | $5810\pm 79$ | $5321^{+86}_{-82}$ | $6202^{+94}_{-90}$
$[\mathrm{Fe/H}]$ (dex) | Metallicity | $0.191\pm 0.083$ | $0.148\pm 0.084$ | $0.176\pm 0.089$ | $0.071^{+0.079}_{-0.076}$ | $0.182^{+0.083}_{-0.085}$
$[\mathrm{Fe/H}]_{0}$ (dex)ccfootnotemark:  | Initial metallicity | $0.193\pm 0.075$ | $0.13\pm 0.08$ | $0.204^{+0.077}_{-0.078}$ | $0.050^{+0.078}_{-0.075}$ | $0.247\pm 0.068$
Age (Gyr) | Stellar age | $4.4^{+3.3}_{-2.6}$ | $2.1^{+2.7}_{-1.5}$ | $6.0^{+3.0}_{-2.5}$ | $3.0^{+3.8}_{-2.1}$ | $2.1^{+1.3}_{-1.0}$
EEPddfootnotemark:  | Equal evolutionary phase | $366^{+35}_{-32}$ | $328^{+21}_{-38}$ | $406^{+20}_{-37}$ | $323^{+22}_{-36}$ | $347^{+37}_{-18}$
$A_{V}$ (mag) | Visual extinction | $0.255^{+0.089}_{-0.092}$ | $0.21^{+0.14}_{-0.13}$ | $0.130^{+0.043}_{-0.065}$ | $0.2\pm 0.1$ | $0.132^{+0.081}_{-0.072}$
d (pc) | Distance | $361.7\pm 1.8$ | $224.6\pm 1.3$ | $282.6^{+3.2}_{-3.1}$ | $176.5^{+1.5}_{-1.4}$ | $333.6^{+4.2}_{-4.1}$

Note. — Table 3 in Eastman et al. (2019) provides a detailed description of
all derived and fitted parameters.

a For those targets where we adopt a circular fit, we also provide the 68%
upper limit on eccentricity derived from the eccentric fits.

b The tidal circularization timescale is computed with Equation (3) of Adams &
Laughlin (2006), assuming a tidal quality factor $Q_{S}=10^{6}$.

c The stellar metallicity when the star was formed, that define the grid
points for the MIST stellar evolutionary tracks.

d The equal evolutionary phase (EEP) corresponds to specific points in the
stellar evolutionary tracks, as described in Dotter (2016).

##  5 Discussion

Figure 6: Gaia absolute $G$-magnitude and $G_{\mathrm{BP}}-G_{\mathrm{RP}}$
color-magnitude diagram for known hot Jupiter hosts . The colored circles are
the ten systems presented in this paper, identified by the color bar on the
right (these colors are consistent with the following figures). The navy blue
squares show hot Jupiter systems discovered by TESS, while the gray circles
show the remaining hot Jupiter systems. The black lines show the MIST
evolutionary tracks at a metallicity of $\mathrm{[Fe/H]}=+0.15$, close to the
median metallicity of our sample, for stellar masses between 0.8 and 1.30
$M_{\odot}$. The points have not been corrected for interstellar extinction.
Figure 7:  Mass-radius distribution for the systems presented in this paper
(colored circles). For TOI-2193A b and TOI-3540 b, we plot the mode and lower
limits on the planet radii. The navy blue squares show hot Jupiter systems
discovered by TESS, while the gray circles show the masses and radii of all
planets from the NASA Exoplanet Archive with masses determined to better than
50% and radii to better than 20%.

The ten planets presented in this paper have orbital periods between 2 and 10
days, and masses between 0.2 and 2.2 $M_{\mathrm{J}}$. To put these newly-
discovered planets into context, we downloaded data from the NASA Exoplanet
Archive (NASA Exoplanet Archive,
2022)999https://exoplanetarchive.ipac.caltech.edu/, accessed 14 Feb 2022 .

In Figure 6, we show the distribution of the stellar hosts of our ten planets
in color-magnitude space, in the context of other hot Jupiter hosts (orbital
period $P<10$ days, planet radius $8\,R_{\oplus}<R_{p}<24\,R_{\oplus}$). Our
ten planets orbit F and G stars, and all of the stars have metallicities
similar to that of the Sun or higher, with a median $\mathrm{[Fe/H]}$ of
$+0.18$. This is in line with the well-known preference for hot Jupiters to
exist around stars with super-solar metallicities (Santos et al., 2004;
Valenti & Fischer, 2005).

The planets in our sample have masses and radii generally consistent with the
previously known population of hot Jupiters (Figure 7). The new planets are
also consistent with the previously noted trend that hot Jupiters with higher
incident fluxes tend to have larger radii (Figure 8; see also Demory & Seager
2011).

###  5.1 Two Inflated Saturns

Figure 8:  Distribution of planet radius (top panel) and mass (lower panel) as
a function of planet insolation, expressed as the equilibrium temperature at
the planet’s orbital distance, assuming no albedo and perfect heat
redistribution. The two least massive planets in our sample, TOI-2421 b and
TOI-2567 b, lie on the lower edge of the distribution of known hot Jupiters,
just above the hot Neptune desert (Mazeh et al., 2016). The navy blue squares
and gray circles represent the same previously known systems as described in
Figure 7.  Figure 9:  Bulk density of the planets in our sample, excluding the
grazing planets TOI-2193A b and TOI-3540 b. The gray circles represent the
same previously known systems as described in Figure 7.

Two of the host stars (TOI-2421, TOI-2567) appear to have recently evolved off
the terminal age main sequence, with stellar radii $R_{\star}=1.75\pm 0.05$
$R_{\odot}$ and $1.69\pm 0.04$ $R_{\odot}$ respectively. Their masses are both
about 1.13 $M_{\odot}$. These two stars also host the lowest-mass planets in
our sample – TOI-2421 b is a Saturn-mass planet, with a mass of $M_{p}=0.33\pm
0.08M_{\mathrm{J}}$, and TOI-2567 b is a sub-Saturn ($M_{p}=0.20\pm
0.03M_{\mathrm{J}}$). The two planets lie on the upper boundary of the hot
Neptune desert (Mazeh et al., 2016), as shown in the lower panel of Figure 8.

Both planets are inflated, with radii of
$R_{p}=0.925^{+0.035}_{-0.034}R_{\mathrm{J}}$ and
$0.975^{+0.031}_{-0.029}R_{\mathrm{J}}$ respectively. Indeed, TOI-2567 b has a
bulk density of just $0.27\pm 0.05$$\mathrm{g}\,\mathrm{cm}^{-3}$, making it
one of the least dense planets known for its mass (Figure 9). The two planets
join a small but growing collection of hot Saturns orbiting slightly evolved
stars, including TOI-954 b (Sha et al., 2021), TOI-1296 b (Moutou et al.,
2021) and TOI-1842 b (Wittenmyer et al., 2022). Such planets can help test
models of radius reinflation around evolved stars (e.g. Lopez & Fortney 2016;
Thorngren et al. 2021) by helping to place constraints on the timescale of
reinflation, and via comparison with such trends for their more massive
counterparts (e.g. Hartman et al. 2016).

###  5.2 Planet Eccentricities

Figure 10:  Measured eccentricities and upper limits for the planets in our
sample. Here, we show the 68% confidence interval measured for the
eccentricity of TOI-2207 b, along with 68% upper limits on the eccentricity
for TOI-2193 b, TOI-2570 b, and TOI-3693 b, for which we can place a
constraint better than $e<0.1$ from the current data. The gray circles show
the measured eccentricities of previously known giant exoplanets
($R_{p}>8R_{\oplus}$) with eccentricities at least 2-$\sigma$ greater than
zero, while gray triangles at the bottom of the plot show planets on orbits
consistent with circular.

While the shortest period hot Jupiters are expected to be on circular orbits
due to tides raised by the star on the planet, the tidal circularization
timescale increases rapidly with orbital distance. Tidal circularization might
be too slow to have affected planets with periods approaching 10 days or
longer, with an extreme example being the recently discovered TOI-3362 b, a
potential proto-hot Jupiter on a $P=18.1$ day, $e=0.82$ orbit (Dong et al.,
2021). Indeed, the two longest period planets in our sample, TOI-2207 b
($P=8.00$ days) and TOI-3693 b ($P=9.09$ days) have theoretical tidal
circularization timescales of $12\pm 5$ and $22\pm 6$ Gyr, based on Equation 3
of Adams & Laughlin (2006) which extended the work from Goldreich & Soter
(1966), and assuming a tidal quality factor of $Q_{P}=10^{6}$.

The measured orbital eccentricity of TOI-2207 b is
$e=0.174^{+0.048}_{-0.052}$, which is greater than zero by more than
3-$\sigma$, although the significance of this result may be affected by the
Lucy-Sweeney bias (Lucy & Sweeney, 1971). Given that the estimated stellar age
is 4 Gyr, which is of the same order of magnitude as the theoretical
circularization timescale, the current eccentricity might be a remnant of a
high-eccentricity migration formation pathway for this planet.

In contrast, TOI-3693 b, which has a longer orbital period, appears to have a
more circular orbit. The 68% and 95% upper limits for the eccentricity of this
planet are $e<0.054$ and $e<0.13$ respectively. More data, including the
possible timing and detection of a secondary eclipse, would be required to
obtain a more secure measurement of the planet eccentricity, but TOI-3693 b is
not likely to have an orbital eccentricity similar to that of TOI-2207 b or
some other warm Jupiters (e.g. TOI-640 b (Rodriguez et al., 2021), TOI-559 b
(Ikwut-Ukwa et al., 2021)).

These two longer period hot Jupiter systems are also potential targets for
stellar obliquity measurements with the Rossiter-McLaughlin (RM) effect
(Rossiter, 1924; McLaughlin, 1924). The expected RM amplitudes for the two
systems are $\approx 30$ $\mathrm{m}\,\mathrm{s}^{-1}$ for TOI-2207 b and
$\approx 90$ $\mathrm{m}\,\mathrm{s}^{-1}$ for TOI-3693 b (Gaudi & Winn,
2007), which should be measurable on a large telescope given the relatively
bright host stars ($V=11.4,12.0$ respectively). The large planet-star
separations of the two planets ($a/R_{\star}\approx 12$ and $22$ respectively)
result in long tidal realignment timescales. Thus, misaligned orbits in these
systems, particularly when correlated with orbital eccentricity, could be
indicative of a high-eccentricity formation pathway, although they could also
result from perturbations by an outer planets in the system.

##  6 Conclusions

We presented the discovery and characterization of ten new hot Jupiters around
F and G stars from NASA’s TESS mission. These planets orbit relatively bright
stars ($G<12.5$) and are potential targets for atmospheric characterization,
measurements of stellar obliquity, and other follow-up observations. While we
have drawn attention to some of the notable features of the new planets,
including the low density of the sub-Saturn TOI-2567 b and the detectable
eccentricity of TOI-2207 b, the larger and longer-term purpose of the survey
is to allow for more general conclusions to be drawn about the hot Jupiter
population. This will require more observations to detect and confirm new
planets (the “numerator” of demographic calculations) as well as a detailed
examination of the TESS selection function and survey characteristics (the
“denominator”). Based on the forecast of Yee et al. (2021), to assemble a
sample of 400 hot Jupiters (an order-of-magnitude more planets than the Kepler
sample), a magnitude-limited survey would need to be complete down to
$G=12.5$. The ten planets described here, along with the other new TESS hot
Jupiters that have been described in the literature (Rodriguez et al., 2019;
Zhou et al., 2019; Brahm et al., 2020; Davis et al., 2020; Nielsen et al.,
2020; Ikwut-Ukwa et al., 2021; Rodriguez et al., 2021; Sha et al., 2021; Wong
et al., 2021; Knudstrup et al., 2022; Rodriguez et al., 2022, e.g.,) are steps
toward realizing the promise of TESS for hot Jupiter demographics.

We thank the anonymous reviewer whose comments helped improve the manuscript.
S.W.Y. thanks Gummi Stefansson for helpful conversations regarding the NEID
observations. This paper includes data collected by the TESS mission that are
publicly available from the Mikulski Archive for Space Telescopes (MAST).
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 at the TESS Science Processing Operations Center.
Resources supporting this work were provided by the NASA High-End Computing
(HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames
Research Center for the production of the SPOC data products. We also
acknowledge the use of data from 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 research made use of Lightkurve, a Python
package for Kepler and TESS data analysis (Lightkurve Collaboration et al.,
2018). 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 the
National Aeronautics and Space Administration. The Observatory was made
possible by the generous financial support of the W. M. Keck Foundation. Keck
telescope time was granted by NOIRLab (Prop. ID 2021B-0162, PI: Yee) through
the Mid-Scale Innovations Program (MSIP). MSIP is funded by NSF. The authors
wish to recognize and acknowledge the very significant cultural role and
reverence that the summit of Maunakea has always had within the indigenous
Hawaiian community. We are most fortunate to have the opportunity to conduct
observations from this mountain. This paper contains data taken with the NEID
instrument, which was funded by the NASA-NSF Exoplanet Observational Research
(NN-EXPLORE) partnership and built by Pennsylvania State University. NEID is
installed on the WIYN telescope, which is operated by the National Optical
Astronomy Observatory, and the NEID archive is operated by the NASA Exoplanet
Science Institute at the California Institute of Technology. NN-EXPLORE is
managed by the Jet Propulsion Laboratory, California Institute of Technology
under contract with the National Aeronautics and Space Administration. Data
presented herein were obtained at the WIYN Observatory from telescope time
allocated to NN-EXPLORE through the scientific partnership of the National
Aeronautics and Space Administration, the National Science Foundation, and
NOIRLab. This work was supported by a NASA WIYN PI Data Award, administered by
the NASA Exoplanet Science Institute. The authors thank Sarah Logsdon and
Heidi Schweiker for help with the NEID observations. The authors are honored
to be permitted to conduct astronomical research on Iolkam Du’ag (Kitt Peak),
a mountain with particular significance to the Tohono O’odham. This paper
includes data gathered with the 6.5 meter Magellan Telescopes located at Las
Campanas Observatory, Chile. This research has used data from the CTIO/SMARTS
1.5m telescope, which is operated as part of the SMARTS Consortium by RECONS
(www.recons.org) members Todd Henry, Hodari James, Wei-Chun Jao, and Leonardo
Paredes. At the telescope, observations were carried out by Roberto Aviles and
Rodrigo Hinojosa. The CHIRON data were obtained from telescope time allocated
under the NN-EXPLORE program with support from the National Aeronautics and
Space Administration. Some of the data presented herein were obtained at the
Minerva-Australis facility from telescope time allocated under the NN-EXPLORE
program with support from the National Aeronautics and Space Administration.
Minerva-Australis is supported by Australian Research Council LIEF Grant
LE160100001, Discovery Grants DP180100972 and DP220100365, Mount Cuba
Astronomical Foundation, and institutional partners University of Southern
Queensland, UNSW Sydney, MIT, Nanjing University, George Mason University,
University of Louisville, University of California Riverside, University of
Florida, and The University of Texas at Austin. We respectfully acknowledge
the traditional custodians of all lands throughout Australia, and recognise
their continued cultural and spiritual connection to the land, waterways,
cosmos, and community. We pay our deepest respects to all Elders, ancestors
and descendants of the Giabal, Jarowair, and Kambuwal nations, upon whose
lands the Minerva-Australis facility at Mt Kent is situated. 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. This paper makes use of data from the MEarth Project, which
is a collaboration between Harvard University and the Smithsonian
Astrophysical Observatory. The MEarth Project acknowledges funding from the
David and Lucile Packard Fellowship for Science and Engineering, the National
Science Foundation under grants AST-0807690, AST-1109468, AST-1616624 and
AST-1004488 (Alan T. Waterman Award), the National Aeronautics and Space
Administration under Grant No. 80NSSC18K0476 issued through the XRP Program,
and the John Templeton Foundation. Adam Popowicz and Slawomir Lasota were
responsible for data processing and automation of observations at SUTO
observatories and were financed by grant BK-246/RAu-11/2022. AJ acknowledges
support from ANID – Millennium Science Initiative – ICN12_009 and FONDECYT
project 1210718. J.H acknowledges support from NASA grants 80NSSC19K0386,
80NSSC19K1728, and 80NSSC21K0335. in
2193,2207,2236,2421,2567,2570,3331,3540,3693,4137 =2193

Figure 11: Same as Figure LABEL:fig:toi2193_multiplot, but for TOI- b.

Figure 12: High-Resolution imaging of hot Jupiter hosts described in this
paper. From top to bottom, left to right: Row 1: SOAR HRCam Observation of
TOI-2207; Gemini-South Zorro Observation of TOI-2236; Row 2: SOAR HRCam
Observation of TOI-2374; SOAR HRCam Observation of TOI-2421; Row 3: Gemini-
North ’Alopeke Observation of TOI-2567; ShaneAO/SHARCS Observation($J$-band)
of TOI-2570; ShaneAO/SHARCS Observation($K_{s}$-band) of TOI-2570; Row 4:
SAI-2.5m Speckle Polarimeter Observation of TOI-3693; SAI-2.5m Speckle
Polarimeter Observation of TOI-4137. No companions were detected down to the
instrumental detection limits for any of these targets.

##  Appendix A Additional Fit Parameters

We present in Table A the median and 68% confidence intervals for additional
fit parameters not listed in Tables 13 and 14 for the adopted fits. These are
the linear and quadratic limb-darkening parameters $(u_{1},u_{2})$ in each
band; additional flux dilution from neighboring stars in each band $(D)$; the
relative RV offset for each instrument $\gamma_{\mathrm{rel}}$
($\mathrm{m}\,\mathrm{s}^{-1}$); and the RV jitter for each instrument
$\sigma_{J}$ ($\mathrm{m}\,\mathrm{s}^{-1}$).

Table 15: Additional Fit Parameters (Median and 68% Confidence Intervals)

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