# The TESS-Keck Survey XXI:
13 New Planets and Homogeneous Properties for 21 Subgiant Systems

Ashley Chontos Henry Norris Russell Fellow  Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA  Daniel Huber Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia  Samuel K. Grunblatt Department of Physics and Astronomy, Johns Hopkins University, 3400 N Charles St, Baltimore, MD 21218, USA  Nicholas Saunders Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  NSF Graduate Research Fellow  Joshua N. Winn Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA  Mason McCormack Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL 60637, USA  Emil Knudstrup Department of Space, Earth and Environment, Chalmers University of Technology, 412 93, Gothenburg, Sweden  Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark  Simon H. Albrecht Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark  Ian J. M. Crossfield  Department of Physics & Astronomy, University of Kansas, 1082 Malott, 1251 Wescoe Hall Dr., Lawrence, KS 66045, USA  Joseph E. Rodriguez Center for Data Intensive and Time Domain Astronomy, Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA  David R. Ciardi Caltech/IPAC-NASA Exoplanet Science Institute, 770 S. Wilson Avenue, Pasadena, CA 91106, USA  Karen A. Collins Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Jon M. Jenkins NASA Ames Research Center, Moffett Field, CA 94035, USA  Allyson Bieryla Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Natalie M. Batalha Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95060, USA  Corey Beard NASA FINESST Fellow  Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA  Fei Dai Division of Geological and Planetary Sciences, 1200 E California Blvd, Pasadena, CA, 91125, USA  Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  NASA Sagan Fellow  Paul A. Dalba Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA  Tara Fetherolf Department of Physics, California State University, San Marcos, CA 92096, USA  Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA  Steven Giacalone NSF Astronomy and Astrophysics Postdoctoral Fellow  Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Michelle L. Hill NASA FINESST Fellow  Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA  Andrew W. Howard Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Howard Isaacson Department of Astronomy, University of California Berkeley, Berkeley CA 94720, USA  Centre for Astrophysics, University of Southern Queensland, Toowoomba, QLD, Australia  Stephen R. Kane Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA  Jack Lubin Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  Department of Physics & Astronomy, The University of California Irvine, Irvine, CA 92697, USA  Mason G. MacDougall Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  Teo Močnik Gemini Observatory/NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, HI 96720, USA  Joseph M. Akana Murphy NSF Graduate Research Fellow  Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA  Erik A. Petigura Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  Daria Pidhorodetska Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA  Alex S. Polanski Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA  Paul Robertson Department of Physics & Astronomy, University of California Irvine, Irvine, CA 92697, USA  Ryan A. Rubenzahl NSF Graduate Research Fellow  Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Emma V. Turtelboom Department of Astronomy, 501 Campbell Hall, University of California, Berkeley, CA 94720, USA  Lauren M. Weiss Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN 46556, USA  Judah Van Zandt Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  George R. Ricker Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Roland Vanderspek Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  David W. Latham Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Sara Seager Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Samuel N. Quinn Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Avi Shporer Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Nora L. Eisner Flatiron Research Fellow  Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA  Robert F. Goeke  Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Alan M. Levine Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Eric B. Ting NASA Ames Research Center, Moffett Field, CA 94035, USA  Steve Howell  NASA Ames Research Center, Moffett Field, CA 94035, USA  Joshua E. Schlieder  NASA Goddard Space Flight Center, 8800 Greenbelt Rd., Greenbelt MD, 22071, USA  Paul Benni Acton Sky Portal private observatory, Acton, MA, USA  Andrew W. Boyle Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Tianjun Gan Department of Astronomy, Tsinghua University, Beijing 100084, People’s Republic of China  Eric Girardin Grand-Pra Observatory, 1984 Les Hauderes, Switzerland  Erica Gonzalez University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95065, USA  Joao Gregorio Crow Observatory, Portalegre, Portugal  Keith Horne SUPA Physics and Astronomy, University of St. Andrews, Fife, KY16 9SS Scotland, UK  John Livingston  Michael B. Lund Caltech/IPAC-NASA Exoplanet Science Institute, 770 S. Wilson Avenue, Pasadena, CA 91106, USA  Christopher R. Mann National Research Council Canada, Herzberg Astronomy & Astrophysics Research Centre, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada  Bob Massey Villa ’39 Observatory, Landers, CA 92285, USA  Elisabeth C. Matthews Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany  Kim K. McLeod Department of Astronomy, Wellesley College, Wellesley, MA 02481, USA  Enric Palle Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206, La Laguna, Tenerife, Spain  Adam Popowicz Silesian University of Technology, Department of Electronics, Electrical Engineering and Microelectronics, Akademicka 16, 44-100 GLiwice, Poland  Howard M. Relles Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Richard P. Schwarz Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Ramotholo Sefako South African Astronomical Observatory, P.O. Box 9, Observatory, Cape Town 7935, South Africa  Gregor Srdoc  Kotizarovci Observatory, Sarsoni 90, 51216 Viskovo, Croatia  Thiam-Guan Tan Perth Exoplanet Survey Telescope, Perth, Western Australia  Gavin Wang Tsinghua International School, Beijing 100084, China  Carl Ziegler Department of Physics, Engineering and Astronomy, Stephen F. Austin State University, TX 75962, USA Ashley Chontos<EMAIL_ADDRESS>
###### Abstract

We present a dedicated transit and radial velocity survey of planets orbiting
subgiant stars observed by the TESS Mission. Using $\sim$16 nights on
Keck/HIRES, we confirm and characterize 12 new transiting planets – TOI-329 b,
HD 39688 b (TOI-480), TOI-603 b, TOI-1199 b, TOI-1294 b, TOI-1439 b, TOI-1605
b, TOI-1828 b, HD 148193 b (TOI-1836), TOI-1885 b, HD 83342 b (TOI-1898),
TOI-2019 b – and provide updated properties for 9 previously confirmed TESS
subgiant systems (TOI-197, TOI-954, TOI-1181, TOI-1296, TOI-1298, TOI-1601,
TOI-1736, TOI-1842, TOI-2145). We also report the discovery of an outer, non-
transiting planet, TOI-1294 c ($P=160.1\pm 2.5$ d, $M_{\mathrm{p}}$
$=148.3^{+18.2}_{-16.4}$ $M_{\oplus}$), and three additional stars with long-
term RV trends. We find that at least 19$\pm$8% of subgiants in our sample of
21 stars have outer companions, comparable to main-sequence stars. We perform
a homogeneous analysis of the stars and planets in the sample, with median
uncertainties of 3%, 8% and 15% for planet radii, masses and ages, doubling
the number of known planets orbiting subgiant stars with bulk densities
measured to better than $10\%$. We observe a dearth of giant planets around
evolved stars with short orbital periods, consistent with tidal dissipation
theories that predict the rapid inspiral of planets as their host stars leave
the main sequence. We note the possible evidence for two distinct classes of
hot Jupiter populations, indicating multiple formation channels to explain the
observed distributions around evolved stars. Finally, continued RV monitoring
of planets in this sample will provide a more comprehensive understanding of
demographics for evolved planetary systems.

††facilities: APF, Hale (PHARO), HARPS, Keck:I (HIRES), Keck:II (NIRC2), MAST,
TESS††software: We made use of the following publicly-available Python
modules: astroquery, emcee (Foreman-Mackey et al., 2013), ktransit, evolstate
(Huber et al., 2017; Berger et al., 2018), pySYD (Chontos et al., 2021a, b)
and tesspoint.

##  1 Introduction

The existence of exoplanets orbiting stars in advanced evolutionary stages
such as helium-core burning red giants (Hon et al., 2023), white dwarfs
(Vanderburg et al., 2020) and pulsars (Wolszczan & Frail, 1992) suggests that
planets are able to withstand extreme environments present at the latest
stages of stellar evolution. Most known exoplanets will face a similar fate as
their host stars eventually evolve off the main-sequence (Kane, 2023), yet the
planet populations around post-main-sequence stars remain poorly understood.

The subgiant branch is a rapid phase in stellar evolution, causing stars with
small differences in mass and age to have significantly different temperatures
and radii. Both temperature and radii can now be precisely measured for most
exoplanet host stars by combining photometry, spectroscopy and Gaia parallaxes
(e.g. Berger et al., 2018), allowing subgiants to be well characterized and
thus used to explore post-main-sequence planet demographics. For example,
precise planet densities (which require precise knowledge of stellar radii and
masses) are important to infer both the bulk compositions and atmospheric
properties of exoplanets (Batalha et al., 2019). Indeed, while the number of
planets orbiting subgiants is relatively small ($\sim$$15\%$), they are
statistically over-represented ($\sim$$32\%$) when only considering planets
with the most precisely measured densities.

Precise ages are valuable for placing observational constraints on the
timescales of important processes affecting exoplanets. Previous studies
suggested that the timescales for processes like tidal circularization and
inward migration through tidal dissipation are strongly dependent on the
orbital distance and stellar radius (Zahn, 1977; Hut, 1981; Zahn, 1989). As
the stellar radius rapidly changes for subgiant stars, stellar evolution is
expected to affect tidal circularization timescales of close-in giant planets,
producing a transient population of midly eccentric planets orbiting evolved
stars (Villaver & Livio, 2009). Kepler and K2 data have yielded intriguing
evidence which supports this theory, but were based on a small sample of
planets (Van Eylen et al., 2016; Grunblatt et al., 2018; Chontos et al., 2019;
Vissapragada et al., 2022).

Table 1: TESS Subgiant Planet Sample System | TOI | RA $[^{o}]$ | Dec $[^{o}]$ | $V_{\mathrm{mag}}$ | $T_{\mathrm{mag}}$
---|---|---|---|---|---
New TESS systems
TOI-329 | 329 | 351.32 |  $-$15.63 | 11.3 | 10.7
HD 39688 | 480 | 88.38 |  $-$16.27 | 7.3 | 6.8
TOI-603 | 603 | 141.11 |  $+$5.77 | 10.3 | 9.7
TOI-1199 | 1199 | 166.88 |  $+$61.35 | 11.1 | 10.4
TOI-1294 | 1294 | 223.09 |  $+$70.48 | 11.3 | 10.9
TOI-1439 | 1439 | 241.76 |  $+$67.88 | 10.6 | 10.0
TOI-1605 | 1605 | 54.48 |  $+$33.08 | 10.2 | 9.6
TOI-1828 | 1828 | 241.56 |  $+$69.62 | 11.6 | 11.1
HD 148193 | 1836 | 245.91 |  $+$54.69 | 9.8 | 9.3
TOI-1885 | 1885 | 304.67 |  $+$66.16 | 12.7 | 12.0
HD 83342 | 1898 | 144.56 |  $+$23.55 | 7.9 | 7.4
TOI-2019 | 2019 | 234.43 |  $+$48.96 | 10.3 | 9.6
Updated TESS systems
HD 221416 | 197 | 353.03 |  $-$21.80 | 8.2 | 7.4
TOI-954 | 954 | 61.94 |  $-$25.21 | 10.3 | 9.8
TOI-1181 | 1181 | 297.22 |  $+$64.35 | 10.6 | 10.1
TOI-1296 | 1296 | 256.77 |  $+$70.24 | 11.4 | 10.8
TOI-1298 | 1298 | 241.32 |  $+$70.19 | 11.9 | 11.0
TOI-1601 | 1601 | 38.36 |  $+$41.01 | 10.7 | 10.1
TOI-1736 | 1736 | 43.44 |  $+$69.10 | 8.9 | 8.3
TOI-1842 | 1842 | 201.96 |  $+$9.03 | 9.8 | 9.3
TOI-2145 | 2145 | 263.76 |  $+$40.70 | 9.1 | 8.6

Early radial velocity (RV) surveys aimed to probe the sensitivity of gas-giant
planet occurrence to stellar mass using subgiant host stars (Johnson et al.,
2007; Bowler et al., 2010; Johnson et al., 2013; Wolthoff et al., 2022).
Additionally, Kepler and TESS have identified individual planets that transit
subgiants for which masses could be measured (Chontos et al., 2019; Huber et
al., 2019; Addison et al., 2021; Rodriguez et al., 2021; Saunders et al.,
2022; Grunblatt et al., 2022, 2023). However, a systematic transit and radial
velocity survey of subgiants has not yet been performed. In this paper we
present a homogeneous population of TESS planets orbiting subgiant stars
acquired as part of the TESS-Keck Survey (TKS; Chontos et al., 2022). Further
RV monitoring of planets in this sample will provide a more comprehensive
understanding of planet demographics for evolved systems.

##  2 Survey Description

###  2.1 Initial Target List

In order to select the most promising targets in a programmatic way, we
assembled a master target list starting with the catalog of TESS Objects of
Interest (TOI; Guerrero et al., 2021) and combined it with additional
resources. The summary statistics for the TESS planet candidates were
downloaded from the publicly-available database111https://tev.mit.edu/.

We queried the TESS Input Catalog (version 8, TICv8; Stassun et al., 2019) for
stellar properties (e.g., radius, etc.) and available photometry (i.e. Johnson
$V$ and 2-MASS $JHK$) for the current list of TOIs, as well as corresponding
$Gaia$ (Gaia Collaboration et al., 2016, 2018) source IDs. The source IDs were
then used to gather additional astrometric (i.e. RUWE) and photometric
information from $Gaia$ that were not directly accessible via TICv8. The
California Planet Search (CPS) RV archive222https://jump.caltech.edu/ was
queried for targets since many of the bright TESS stars already have archival
HIRES data available. As a final query, TOI dispositions were updated with the
TESS Follow-up Observing Program (TFOP) Working
Group333https://tess.mit.edu/followup/ (WG) Sub Group 1 (hereafter referred to
as SG1).

The evolutionary state of the star was determined with
evolstate444https://github.com/danxhuber/evolstate/, given its effective
temperature and surface gravity (Huber et al., 2017; Berger et al., 2018).
Here, stellar parameters were first drawn from HIRES-derived spectroscopic
parameters and then TICv8 if those were not available. In the event that
parameters were not available from either of these sources, the parameters
provided in the original TOI table were used.

Figure 1: Stellar size and distance for stars that host exoplanets with
measured densities according to the NASA Exoplanet
Archive666https://exoplanetarchive.ipac.caltech.edu, colored by their
approximate evolutionary state (i.e. Section 2.1). Markers are inversely sized
by their visual magnitudes (i.e. bigger is brighter) and filled in for stars
that host planets with the most precise ($\geq 4\sigma$) planet densities. The
subgiant hosts in the present sample (highlighted with a thick, black outline)
are, on average, closer and brighter than other known subgiant planet hosts.

###  2.2 Target Selection

When the survey was initially constructed, the maximum TOI number available
was TOI-2145. From these candidates, we first removed TOIs with unfavorable or
ambiguous SG1 dispositions (i.e. APC, BEB, FA, FP, NEB, PNEB, EB, SB1,
SB2)777Ambiguous planet candidate (APC), blended eclipsing binary (BEB), false
alarm (FA), false positive (FP), nearby eclipsing binary (NEB), probable
nearby eclipsing binary (PNEB), eclipsing binary (EB), single-lined
spectroscopic binary (SB1), double-lined spectroscopic binary (SB2). False
positive and unfavorable dispositions accounted for $\sim 25\%$ of the sample
(514 TOIs). We excluded targets at low declinations ($\delta<-40^{o}$) that
would not be accessible with Keck and also targets with a high $Gaia$ re-
normalized unit weight error888https://gea.esac.esa.int/archive/ (RUWE $>2$),
indicative of an unresolved companion (Belokurov et al., 2020; Evans, 2018).

Finally, we performed a search for close companions for the remaining targets
using their $Gaia$ DR2 coordinates and the MAST (Mikulski Archive for Space
Telescopes)
Portal999https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html. Any
target with a relatively close ($<2"$), bright ($\Delta V<5$) companion or any
companion within $1"$ were not considered for further follow-up, because of
the danger that high-resolution spectroscopy would be compromised by flux
contamination from the secondary star during sub-optimal observing conditions.
The final cut required a subgiant (SG) evolutionary state and brought the
final sample down to 93 TOIs.

###  2.3 Target Vetting

Before being followed up with precise radial velocity (PRV) observations, the
sample was subjected to one final round of vetting. The vetting described here
was originally adapted from the TESS-Keck Survey (TKS) target selection work
presented in Chontos et al. (2022) and is briefly summarized here.

Data validation (DV) reports from the SPOC (Science Processing Operations
Center; Jenkins et al., 2016; Twicken et al., 2018; Li et al., 2019) and QLP
(Quick Look Pipeline; Huang et al., 2020a, b) pipelines were downloaded and
inspected. Careful consideration was given to standard diagnostics for
threshold crossing events that indicate possible false positive scenarios such
as significant odd-even differences or large centroid offsets. Full DV reports
were downloaded to examine the best-fit model and model parameters to identify
any possible inconsistencies or other concerning features.

After passing the photometric vetting, targets were queued for reconnaissance
(or recon) spectra to check for spectroscopic false positives (FP). All recon
spectra were processed by ReaMatch (Kolbl et al., 2015) to search for and
identify faint stellar companions in double-lined spectroscopic binaries.
Systemic radial velocities, computed according to Chubak et al. (2012), were
compared to those from $Gaia$ to identify any large discrepancies which are
indicative of single-lined spectroscopic binaries (SB1). Targets for which the
recon and $Gaia$ RV differed by more than 5 $\rm km\,s^{-1}$ typically failed
this vetting step. However for more ambiguous cases near this cutoff, a second
recon spectrum was taken to test for significant linear trends which provide
additional evidence of the SB1-like nature.

###  2.4 Final Survey Sample

Our survey goal was to maximize the number of precise mass and density
measurements of evolved TESS planets that could be obtained within the given
16-night Keck/HIRES allocation. Thus brighter targets and targets with
existing HIRES data, both which would require less telescope time to achieve
this goal, were typically prioritized to be vetted and followed up first. The
final sample is provided in Table 1, which consists of 21 subgiant stars that
have at least one transiting TESS planet candidates.

Figures 6 and 2 contextualize the sample with the current population of single
stars that host planets with measured bulk densities. As expected with TESS,
the stars in this sample are on average closer and brighter than other
subgiant stars known to be transiting planet hosts. The stars in the sample
also span a wide range of masses and ages, as expected for subgiant stars.

Figure 2: Same as Figure 6 but in a Kiel diagram, plotted with surface gravity
and effective temperature. Here, markers also indicate stars of different
evolutionary states. MIST solar-metallicity tracks are added for reference.

##  3 Observations

###  3.1 TESS Photometry

Table 2: Number of sectors of available TESS data

System | TOI | 20s | 120s | 600s | 1800s
---|---|---|---|---|---
HD 221416 | 197 | 1 | 2∗ | 1 | 1
TOI-329 | 329 | – | 2∗ | 2 | 1
HD 39688 | 480 | – | 2∗ | 1 | 1
TOI-603 | 603 | 1 | 4∗ | 3 | 1
TOI-954 | 954 | – | 1∗ | 1 | 2
TOI-1181 | 1181 | – | 19∗ | 10 | 12
TOI-1199 | 1199 | – | 2∗ | 2 | 2
TOI-1294 | 1294 | – | 5∗ | 5 | 6
TOI-1296 | 1296 | 5 | 18∗ | 8 | 12
TOI-1298 | 1298 | – | 19∗ | 10 | 13
TOI-1439 | 1439 | – | 19∗ | 10 | 13
TOI-1601 | 1601 | – | – | – | 1∗
TOI-1605 | 1605 | 1 | 1 | – | 1∗
TOI-1736 | 1736 | 3 | 6∗ | 1 | 3
TOI-1828 | 1828 | – | 20∗ | 10 | 13
HD 148193 | 1836 | 1 | 7∗ | 4 | 4
TOI-1842 | 1842 | – | 2∗ | 1 | 1
TOI-1885 | 1885 | – | 10∗ | 3 | 8
HD 83342 | 1898 | – | 4∗ | 3 | 1
TOI-2019 | 2019 | – | 3∗ | 1 | 3
TOI-2145 | 2145 | – | 4∗ | 3 | 2

∗Indicates the data used for the joint fits (Section 5.3).

We downloaded all available light curve products for each target by using the
MAST101010Mikulski Archive for Space Telescopes (MAST)
https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html Portal, which
primarily came from the SPOC and QLP pipelines. In order to decide which light
curves would be used in the joint transit and RV analysis (Section 5.3), we
inspected all available light curve data to look for systematics or other
undesirable features as a result of differences in data reduction methods.
Table 2 summarizes the TESS data that was available for the sample during the
analysis, including how many sectors a given target was observed for, at which
cadence(s) and which data was used for further analyses.

For the planet fits we typically used the specially curated TESS light curves,
corresponding to the PDC-SAP (pre-search data conditioning; Smith et al.,
2012; Stumpe et al., 2012, 2014) flux from the SPOC pipeline and the KSP-SAP
(for Kepler spline) flux from the QLP pipeline. Light curves were then
processed following the methodology in Chontos et al. (2019). To summarize,
light curve processing included rejecting points with poor quality flags,
clipping outliers by using a sliding two-day filter at the 5$\sigma$ level,
and flattening out-of-transit data by applying a median boxcar filter. As a
final step, only data within $\pm 1.5$ times the transit duration (centered on
the mid-transit times) was retained to speed up the planet-fitting routine.

Table 3: Summary of RV observations taken of the sample. All RVs in this work are made publicly available in Table 4. System | TOI |  $N$ RVs (unbinned) | Instrument | First Observation [UT] | Last Observation [UT] | Baseline$\,\,\mathrm{[yr]}$
---|---|---|---|---|---|---
HD 221416 | 197 | 57 (64) | HIRES | 2018 Nov 3 | 2021 Dec 25 | 3.1
TOI-329 | 329 | 43 | HIRES | 2020 Jun 3 | 2021 Dec 25 | 1.6
HD 39688 | 480 | 62 (181) | HIRES | 2019 Dec 27 | 2021 Dec 26 | 2.0
HD 39688 | 480 | 20 (33) | HARPS-N | 2019 Sep 26 | 2023 Feb 20 | 3.4
TOI-603 | 603 | 12 | HIRES | 2020 Oct 31 | 2022 May 13 | 1.5
TOI-954 | 954 | 28 | HIRES | 2020 Aug 27 | 2021 Nov 26 | 1.2
TOI-1181 | 1181 | 50 (87) | HIRES | 2019 Dec 2 | 2022 May 16 | 2.5
TOI-1199 | 1199 | 16 | HIRES | 2019 Dec 10 | 2022 May 13 | 2.4
TOI-1294 | 1294 | 32 | HIRES | 2020 Mar 10 | 2022 May 13 | 2.2
TOI-1296 | 1296 | 24 | HIRES | 2019 Nov 28 | 2022 May 16 | 2.5
TOI-1298 | 1298 | 22 | HIRES | 2020 Jun 3 | 2022 May 13 | 1.9
TOI-1439 | 1439 | 53 | HIRES | 2020 Mar 10 | 2022 May 13 | 2.2
TOI-1601 | 1601 | 37 | HIRES | 2020 Feb 25 | 2022 Dec 31 | 1.8
TOI-1605 | 1605 | 44 | HIRES | 2020 Aug 26 | 2022 Sep 2 | 1.3
TOI-1736 | 1736 | 77 (79) | HIRES | 2020 Aug 2 | 2022 Jan 19 | 2.0
TOI-1736 | 1736 | 35 (37) | HARPS-N | 2020 Oct 10 | 2023 Feb 20 | 2.3
TOI-1828 | 1828 | 19 | HIRES | 2020 Jun 12 | 2022 May 13 | 1.9
HD 148193 | 1836 | 53 | HIRES | 2020 May 26 | 2022 May 13 | 2.0
HD 148193 | 1836 | 45 | HARPS-N | 2021 Feb 13 | 2021 Jul 21 | 0.5
TOI-1842 | 1842 | 38 | HIRES | 2020 May 26 | 2022 May 9 | 1.2
TOI-1885 | 1885 | 15 | HIRES | 2020 Jun 10 | 2022 May 13 | 1.9
HD 83342 | 1898 | 48 | HIRES | 2020 Jun 10 | 2022 May 13 | 2.1
TOI-2019 | 2019 | 43 | HIRES | 2020 Jun 24 | 2022 May 13 | 1.9
TOI-2145 | 2145 | 40 | HIRES | 2020 Aug 25 | 2022 May 13 | 1.7

###  3.2 HIRES Radial Velocities

The survey results presented here were conducted over 16 nights in 2020 and
2021 using the High-Resolution Echelle Spectrometer (HIRES; Vogt et al.,
1994), which is mounted on the 10-m Keck I telescope on Maunakea in Hawai‘i.
Observations were acquired as part of the TESS-Keck Survey (TKS), where
baselines for program targets are on average $\sim$2 years. HIRES operates in
the spectral range of $0.3-1.0$ microns and uses an iodine cell configuration
that when placed in the light path imprints a dense forest of absorption lines
and thus serves as a robust wavelength calibration from which Doppler shifts
can be measured (Butler et al., 1996).

Every target presented in this sample has two iodine-free observations: 1) a
low S/N recon spectrum and 2) a high S/N template. A recon spectrum is an
iodine-free exposure with an S/N of $\approx 40/\mathrm{pixel}$ to check for
false positives as part of the vetting procedure discussed in Section 2.3. A
“template” is also an iodine-free exposure but typically obtained at a very
high S/N, since this is used to compute the rest of the RVs for a given
target. The rest of the iodine-in observations were reduced according to the
well-tested procedures of the California Planet Search documented in Howard et
al. (2010).

###  3.3 HARPS-N Radial Velocities

We acquired high-resolution ($R=115000$) spectra of HD 148193 with the High
Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N;
Cosentino et al., 2012) mounted on the 3.58 m Telescopio Nazionale Galileo
(TNG) located on Roque de los Muchachos, La Palma, Spain. A total of 46
spectra were collected between UT 2021 February 13 and UT 2021 June 21. We set
the exposure time to 900 s, which led to a median SNR of $\sim$75 per pixel at
550 nm. We used the second fibre of the instrument to monitor the sky
background. The HARPS-N spectra were reduced and extracted using the dedicated
Data Reduction Software (DRS; Lovis & Pepe, 2007) available at the telescope.

Ground-based RV observations for the sample are summarized in Table 3,
including the number of observations per target, the first and last
observation date and current baseline coverage. All radial velocity data used
in the analysis are provided in Table 4.

Table 4: All radial velocities used in this work.

System | Time | RV | RV Unc. | Instrument
---|---|---|---|---
| [BJD] | $\rm[ms^{-1}]$ | $\rm[ms^{-1}]$ |
$\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$
TOI-329 | 2459028.108213 | $-9.74$ | 2.15 | HIRES
$\cdots$ | $\cdots$ | $\cdots$ | $\cdots$ | $\cdots$

(This table is available in machine-readable form.)

Table 5: Summary of high-resolution imaging observations (Section 3.4) for new TESS systems presented in this work. System | Instrument | Observation Date | Filter | Resolution | Contrast at $0.^{{}^{\prime\prime}}5$
---|---|---|---|---|---
|  | [UT] |  | [FWHM] | [$\Delta$ mag]
TOI-329 | Palomar/PHARO | 2019 Jul 13 | Br-$\gamma$ | $0.^{{}^{\prime\prime}}10$ | 7.0
HD 39688 | Keck/NIRC2 | 2019 Mar 25 |  $K$-cont | $0.^{{}^{\prime\prime}}05$ | 8.4
TOI-603 | Keck/NIRC2 | 2019 Jun 09 |  $K$-cont | $0.^{{}^{\prime\prime}}05$ | 7.5
TOI-1199 | Palomar/PHARO | 2020 Jan 08 | Br-$\gamma$ | $0.^{{}^{\prime\prime}}13$ | 6.2
TOI-1294 | Keck/NIRC2 | 2020 May 28 |  $K$-cont | $0.^{{}^{\prime\prime}}05$ | 7.9
TOI-1439 | Keck/NIRC2 | 2020 May 28 | Br-$\gamma$ | $0.^{{}^{\prime\prime}}05$ | 7.9
TOI-1605 | Keck/NIRC2 | 2020 Sep 09 | Br-$\gamma$ | $0.^{{}^{\prime\prime}}05$ | 6.8
TOI-1605 | Keck/NIRC2 | 2020 Sep 09 |  $J$-cont | $0.^{{}^{\prime\prime}}03$ | 6.9
HD 148193 | Palomar/PHARO | 2021 June 22 | Br-$\gamma$ | $0.^{{}^{\prime\prime}}09$ | 6.8
HD 148193 | Palomar/PHARO | 2021 June 22 |  $H$-cont | $0.^{{}^{\prime\prime}}08$ | 7.8
HD 83342 | Palomar/PHARO | 2020 Dec 04 | Br-$\gamma$ | $0.^{{}^{\prime\prime}}14$ | 6.1
TOI-2019 | Keck/NIRC2 | 2020 Sep 09 | $Ks$ | $0.^{{}^{\prime\prime}}05$ | 7.3

###  3.4 High-resolution Imaging

Table 5 summarizes the high-resolution imaging observations acquired for
targets that are being published for the first time. Our targets HD 39688 and
TOIs 603, 1294, 1439, 1605, and 2019 were all observed using Keck/NIRC2
natural guide star adaptive optics imaging in the 2.2$\mu$m Brackett-$\gamma$
(Br-$\gamma$) filter. We obtained the data in narrow-angle mode to provide a
pixel scale of $\sim$0.01” and a total field of view of $\sim$10”. We used
NIRC2’s standard three-point, 3”-step dither pattern to avoid the noisy,
lower-left detector quadrant. We acquired three sets of dithers for each
target, with 0.5 positional offsets between each observation. Data were
analyzed following Furlan et al. (2017).

No companions were detected for our sample, with the exception of TOI-1836,
which was observed using the PHARO (Palomar High Angular Resolution Observer)
instrument on the 5-m Hale telescope at the Palomar Observatory in California.
The observations of TOI-1836 were taken on (UT) 2021-06-22 with the narrowband
Br-$\gamma$ filter. The sensitivity curve and image preview is shown in Figure
3, revealing a companion at a separation of $\rho=0.819^{\prime\prime}$ with
$\Delta m=5.722$. The zoomed out image on the right of Figure 3 shows a
$0.2^{\prime\prime}$ binary (TIC 207468069) approximately 10” away that is
astrometrically associated with TOI-1836. We include the analysis and results
from the joint fits discussed in Section 5.3 but later remove TOI-1836 b from
the discussion in Section 7.

##  4 Host Star Characterization

###  4.1 High-resolution Spectroscopy

Figure 3: High-resolution image of TOI-1836 taken by the PHARO instrument at
Palomar on UT 2021-06-22 in the narrowband Br-$\gamma$ filter. Imaging
revealed a multiple star system in an interesting heirarchy, the primary star
which is orbited by a single star in addition to a well-separated binary at a
projected separation of $10^{\prime\prime}$.

Spectroscopic stellar parameters ($\rm{[Fe/H]}$, $T_{\mathrm{eff}}$, $v\sin
i$, $\log g$) were derived using SpecMatch. SpecMatch derives parameters
either from synthetic model atmospheres (i.e. SpecMatch-Synth; Petigura 2015)
or empirically from a library of HIRES templates (i.e. SpecMatch-Emp; Yee et
al. 2017), the latter of which was primarily developed for later-type cool
dwarfs.

Initial inspections of recon spectra for the sample reported effective
temperatures in the range $5080\,$K $<$ $T_{\mathrm{eff}}$ $<6600\,$K.
Therefore, we adopted the derived spectroscopic values from SpecMatch-Synth
for the entire sample. These values are subjected to uncertainties of
$\sigma_{T_{\mathrm{eff}}}=100$ K in effective temperature,
$\sigma_{\mathrm{log}g}=0.1$ dex in surface gravity,
$\sigma_{\mathrm{[Fe/H]}}=0.06$ dex in metallicity, and $\sigma_{v\sin i}=1.0$
$\rm km\,s^{-1}$ in projected velocity.

###  4.2 Broadband Photometry and Gaia Parallax

We derived fundamental stellar properties from MIST (MESA Isochrones and
Stellar Tracks; Choi et al., 2016) model grids, as implemented in
isoclassify111111https://github.com/danxhuber/isoclassify (Huber et al.,
2017). Given a set of observables (i.e., photometry, spectroscopy, etc.),
isoclassify interpolates the stellar grids to derive properties like their
masses, luminosities, radii, densities and ages.

Table 6: Summary of subgiant host star properties

| Spectroscopy∗ | Derived parameters${}^{\dagger}\,$
---|---|---
TOI | TIC |  $T_{\mathrm{eff}}$ [K] |  $\log g$ [cgs] | $\rm{[Fe/H]}$ | $v\sin i$ |  $R_{\star}$[$R_{\odot}$] |  $M_{\star}$ [$M_{\odot}$] |  $\bar{\rho}_{\star}$ [g cm-3] | Age [Gyr]
197 | 441462736 | $5080\pm 90$ | $3.584\pm 0.010$ | $-0.08\pm 0.08$ |  $<$2.0 | $2.943\pm 0.064$ | $1.212\pm 0.074$ | $0.067\pm 0.001$ | $4.9\pm 1.1$
329 | 169765334 | 5635 | 4.00 |  $+$0.18 |  $<$2.0 | $1.52^{+0.04}_{-0.04}$ | $1.07^{+0.06}_{-0.04}$ | $0.300\pm 0.034$ | $8.3^{+1.4}_{-2.0}$
480 | 317548889 | 6224 | 4.23 |  $+$0.17 | 8.7 | $1.49^{+0.05}_{-0.03}$ | $1.28^{+0.03}_{-0.03}$ | $0.385\pm 0.032$ | $2.6^{+0.6}_{-0.6}$
603 | 262746281 | 5894 | 4.07 |  $+$0.20 | 4.0 | $1.58^{+0.03}_{-0.03}$ | $1.23^{+0.04}_{-0.07}$ | $0.309\pm 0.020$ | $4.2^{+1.6}_{-0.7}$
954 | 44792534 | 5788 | 3.85 |  $+$0.40 | 3.4 | $1.90^{+0.04}_{-0.04}$ | $1.37^{+0.03}_{-0.11}$ | $0.196\pm 0.015$ | $3.4^{+1.6}_{-0.4}$
1181 | 229510866 | 6107 | 4.02 |  $+$0.42 | 10.6 | $1.93^{+0.04}_{-0.04}$ | $1.47^{+0.03}_{-0.03}$ | $0.204\pm 0.014$ | $2.2^{+0.3}_{-0.3}$
1199 | 99869022 | 5619 | 3.92 |  $+$0.42 |  $<$2.0 | $1.46^{+0.03}_{-0.03}$ | $1.15^{+0.05}_{-0.06}$ | $0.366\pm 0.028$ | $6.2^{+2.0}_{-1.4}$
1294 | 219015370 | 5690 | 4.02 |  $+$0.27 |  $<$2.0 | $1.55^{+0.03}_{-0.03}$ | $1.16^{+0.07}_{-0.06}$ | $0.310\pm 0.025$ | $6.1^{+1.9}_{-1.5}$
1296 | 219854185 | 5562 | 3.88 |  $+$0.42 |  $<$2.0 | $1.68^{+0.04}_{-0.03}$ | $1.16^{+0.12}_{-0.04}$ | $0.241\pm 0.033$ | $6.9^{+1.1}_{-2.4}$
1298 | 237104103 | 5783 | 4.01 |  $+$0.41 | 2.6 | $1.45^{+0.03}_{-0.03}$ | $1.21^{+0.03}_{-0.06}$ | $0.395\pm 0.032$ | $4.3^{+1.8}_{-0.8}$
1439 | 232982558 | 5843 | 4.02 |  $+$0.22 | 2.6 | $1.61^{+0.03}_{-0.03}$ | $1.23^{+0.04}_{-0.09}$ | $0.291\pm 0.024$ | $4.5^{+1.8}_{-0.8}$
1601 | 139375960 | 6020 | 3.94 |  $+$0.36 | 5.7 | $2.20^{+0.06}_{-0.07}$ | $1.51^{+0.04}_{-0.05}$ | $0.140\pm 0.013$ | $2.3^{+0.4}_{-0.3}$
1605 | 101037590 | 5752 | 4.06 |  $+$0.00 |  $<$2.0 | $1.49^{+0.03}_{-0.03}$ | $1.04^{+0.05}_{-0.04}$ | $0.308\pm 0.030$ | $8.3^{+1.4}_{-1.4}$
1736 | 408618999 | 5724 | 4.21 |  $+$0.16 |  $<$2.0 | $1.41^{+0.03}_{-0.03}$ | $1.08^{+0.06}_{-0.05}$ | $0.382\pm 0.033$ | $7.3^{+1.8}_{-1.9}$
1828 | 232982938 | 5780 | 4.04 |  $+$0.14 |  $<$2.0 | $1.56^{+0.03}_{-0.03}$ | $1.17^{+0.06}_{-0.07}$ | $0.302\pm 0.023$ | $5.5^{+1.8}_{-1.3}$
1836 | 207468071 | 6198 | 4.18 |  $-$0.13 | 5.9 | $1.66^{+0.03}_{-0.03}$ | $1.22^{+0.03}_{-0.08}$ | $0.265\pm 0.018$ | $3.5^{+1.3}_{-0.5}$
1842 | 404505029 | 6084 | 3.98 |  $+$0.33 | 6.2 | $2.02^{+0.04}_{-0.04}$ | $1.47^{+0.03}_{-0.04}$ | $0.175\pm 0.013$ | $2.4^{+0.4}_{-0.3}$
1885 | 258510872 | 6617 | 4.31 |  $+$0.03 | 7.8 | $1.62^{+0.04}_{-0.04}$ | $1.19^{+0.05}_{-0.08}$ | $0.272\pm 0.024$ | $3.7^{+1.4}_{-0.6}$
1898 | 91987762 | 6241 | $4.18$ |  $-$0.10 | 7.0 | $1.62^{+0.03}_{-0.03}$ | $1.23^{+0.03}_{-0.06}$ | $0.283\pm 0.021$ | $3.4^{+1.0}_{-0.5}$
2019 | 159781361 | 5630 | 3.89 |  $+$0.41 | 1.6 | $1.73^{+0.03}_{-0.03}$ | $1.20^{+0.11}_{-0.04}$ | $0.233\pm 0.024$ | $6.0^{+1.0}_{-2.0}$
2145 | 88992642 | 6232 | 4.00 |  $+$0.29 | 17.8 | $2.69^{+0.06}_{-0.06}$ | $1.78^{+0.04}_{-0.05}$ | $0.091\pm 0.006$ | $1.2^{+0.1}_{-0.1}$

Note–
Values for TOI-197 were adopted from the asteroseismic analysis in Huber et
al. (2019).
${}^{*}\,$Spectroscopic parameters were derived with SpecMatch-Synth (Petigura
et al., 2017a) (see Section 4.1), which has the following systematic
uncertainties: $\sigma_{T_{\mathrm{eff}}}=100$ K in effective temperature;
$\sigma_{\mathrm{log}g}=0.1$ dex in surface gravity;
$\sigma_{\mathrm{[Fe/H]}}=0.06$ dex in metallicity; $\sigma_{v\sin i}=1.0$
$\rm km\,s^{-1}$ in projected velocity.
${}^{\dagger}\,$Derived stellar parameters were estimated from model grids
using isoclassify (Huber et al., 2017). Reported uncertainties are intrinsic
precisions of the sample. When comparing these values to other methods,
systematic errors as described in Tayar et al. (2022) should be considered.

We used the values of $T_{\mathrm{eff}}$ and $\rm{[Fe/H]}$ (discussed in the
previous section) as spectroscopic inputs, along with parallaxes from Gaia
Data Release 3 (DR3; Gaia Collaboration et al., 2021, 2023). In order to
further constrain the results and fit for extinction directly, we also
included Johnson $BV$ photometry, $JHK_{s}$ from 2MASS (Skrutskie et al.,
2006) and $GB_{p}R_{p}$ from Gaia (Gaia Collaboration et al., 2021, 2023). For
Gaia DR3 photometry, we adopted a systematic noise floor of 0.01 mag. A
summary of derived stellar parameters are provided in Table 6. We note that
the uncertainties on the reported masses, radii, densities and ages are
intrinsic precisions of the sample. When comparing these values to other
methods, systematic errors as described in Tayar et al. (2022) should be
considered.

##  5 Planet Characterization

###  5.1 System Confirmation

We fitted Keplerian orbits to all systems with significant RV variations that
are in phase with reported transits seen by TESS. Keplerian RV orbits are
described by the orbital period ($P$), argument of periastron ($\omega$),
orbital eccentricity ($e$), Doppler velocity semi-amplitude ($K$) as well as
the time of inferior conjunction ($T_{\mathrm{conj}}$). We also included
instrument-specific “jitter” ($\sigma$) and RV offset ($\gamma$) terms. RV
models can be further described by long-term properties which include linear
($\dot{\gamma}$) and quadratic ($\ddot{\gamma}$) acceleration terms, referred
to as trend and curvature respectively. The two parameters $\dot{\gamma}$ and
$\ddot{\gamma}$ capture additional Keplerian signals present in a time series
with periods longer than the timespan of the available data. We did not fit
for curvature in any system and linear trends were only added in systems that
required an additional parameter to reasonably fit the data, the latter which
is discussed in more detail in the following section.

Each system was fit with a single-planet model using radvel (Fulton et al.,
2018), which performs rigorous model fitting and selection using well-known
metrics (i.e. BIC, AIC, etc.). Since transits typically constrain periods
well, we placed strong Gaussian priors on the periods using the values and
uncertainties reported by TESS. For conjunction times we placed flat, uniform
priors and enforced positive Doppler semi-amplitudes ($K>0$). Finally, to
avoid implicit biases we used the default radvel fitting basis {$P$,
$T_{\mathrm{conj}}$, $\sqrt{e}\cos\omega$, $\sqrt{e}\sin\omega$, $K$}.

Table 7: Models used during joint transit and RV fits (Section 5.3). System | TOI | Model
---|---|---
HD 221416 | 197 | 1-planet model
TOI-329 | 329 | 1-planet model
HD 39688 | 480 | 1-planet model
TOI-603 | 603 | 1-planet model
TOI-954 | 954 | 1-planet model
TOI-1181 | 1181 | 1-planet model
TOI-1199 | 1199 | 1-planet model
TOI-1294 | 1294 | 2-planet model $+$ linear trend
TOI-1296 | 1296 | 1-planet model
TOI-1298 | 1298 | 1-planet model
TOI-1439 | 1439 | 1-planet model
TOI-1601 | 1601 | 1-planet model
TOI-1605 | 1605 | 1-planet model $+$ linear trend
TOI-1736 | 1736 | 2-planet model $+$ linear trend
TOI-1828 | 1828 | 1-planet model $+$ linear trend
HD 148193 | 1836 | 1-planet model
TOI-1842 | 1842 | 1-planet model
TOI-1885 | 1885 | 1-planet model
HD 83342 | 1898 | 1-planet model
TOI-2019 | 2019 | 1-planet model
TOI-2145 | 2145 | 1-planet model

For a given iteration, the system was initialized with all available
parameters and then radvel iterated through all combinations of free
parameters. In other words, we set the initial number of possible parameters,
which in the case of a single planet here is at most eight (i.e. $P_{b}$,
$K_{b}$, $e_{b}$, $\omega_{b}$, ${T_{\mathrm{conj}}}_{b}$, $\sigma_{i}$,
$\gamma_{i}$, $\dot{\gamma}$). Each system required several iterations of this
procedure in order to identify the best possible solution and ultimately,
confirm that we were recovering the same signal identified by TESS.

###  5.2 Searching for Additional Companions

With continued RV follow up, some systems exhibited significant scatter that
could not be explained by a single-planet model alone. Since it has been shown
that RV data can be systematically contaminated by stellar variability (Lubin
et al., 2021), we first estimated what the expected contribution would be from
the host star given its physical properties. This step was especially
important with our sample of evolved host stars, which are notoriously more
noisy than their main-sequence counterparts. We calculated the stellar
“jitter” using Equation 3 from Chontos et al. (2022), which includes noise
contributions from granulation and p-mode oscillations (Yu et al., 2018), as
well as rotation (Chontos et al., 2022) and activity (Isaacson & Fischer,
2010). We then use four categories to understand their long-term
characteristics:

Table 8: Priors used for the joint transit and RV fitting analysis discussed
in Section 5.3.

Parameter |  Symbol |  Units |  Prior
---|---|---|---
Default model parameters
Instrument-specific terms |  |  |
TESS zero-point offset |  $z$ |  ppm |  $\mathcal{U}[-\infty;+\infty]$
Keck/HIRES RV offset |  $\gamma$ |  $\rm m\,s^{-1}$ |  $\mathcal{U}[-\infty;+\infty]$
Transiting planet parameters |  |  |
Mean stellar density |  $\bar{\rho}_{\star}$ |  g cm-3 |  $\mathcal{U}[0;+\infty]$
Limb-darkening coefficient 1 |  $u_{1}$ |  |  $\mathcal{N}(x;0.6)[0,2]$
Limb-darkening coefficient 2 |  $u_{2}$ |  |  $\mathcal{N}(x;0.6)[-1,1]$
Orbital period |  $P$ |  days |  $\mathcal{U}[0;+\infty]$
Time of inferior conjunction |  $T_{\mathrm{c}}$ |  days |  $\mathcal{U}[-\infty;+\infty]$
Impact parameter |  $b$ |  |  $\mathcal{U}[0;1+R_{\mathrm{p}}/R_{\star}]$
Planet-to-star radius ratio |  $R_{\mathrm{p}}/R_{\star}$ |  |  $\mathcal{U}[0;+\infty]$
Eccentricity |  $e$ |  |  1/$e$
|  $\sqrt{e}\sin\omega$ |  |  $\mathcal{U}[-1;1]$
|  $\sqrt{e}\cos\omega$ |  |  $\mathcal{U}[-1;1]$
RV semiamplitude |  $K$ |  $\rm m\,s^{-1}$ |  $\mathcal{U}[0;+\infty]$
Optional model parameters
RV trends |  |  |
Linear RV trend∗ |  $\dot{\gamma}$ |  $\rm m\,s^{-1}$$\rm\,d^{-1}$ |  $\mathcal{U}[-\infty;+\infty]$
Nontransiting planet parameters |  |  |
Orbital period |  $P$ |  days |  $\mathcal{U}[0;0.5\times\mathrm{baseline}]$
Time of inferior conjunction |  $T_{\mathrm{c}}$ |  days |  $\mathcal{U}[-\infty;+\infty]$
Eccentricity |  $e$ |  |  1/$e$
|  $\sqrt{e}\sin\omega$ |  |  $\mathcal{U}[-1;1]$
|  $\sqrt{e}\cos\omega$ |  |  $\mathcal{U}[-1;1]$
RV semiamplitude |  $K$ |  $\rm m\,s^{-1}$ |  $\mathcal{U}[0;+\infty]$

∗Time reference was set to the RV baseline midpoint, which is provided in the
tables for each system that included a trend.

  1. 1.

Systems with observations that behaved as expected (observed scatter $\approx$
expected scatter). This included many of the known TESS systems in Figure 4,
including HD 221416, TOI-954, TOI-1296, TOI-1298, TOI-1601, and TOI-1842.
TOI-603, a new confirmation, also falls into this category but has a limited
number of RVs.

  2. 2.

Systems that show evidence for additional companions through significant
linear trends. Figure 6 shows 3 newly confirmed TESS systems, TOI-1294 (left),
TOI-1605 (middle) and TOI-1828 (right), all which showed significant RV
offsets between observing seasons that could only be explained by an
additional companion. The other system is TOI-1736, which also exhibits an
astrometric acceleration and therefore, may be affected by a distant but bound
stellar companion. For the systems that included a linear trend component,
time references were defined as the midpoint of the RV time series and are
included in the supplementary table(s).

  3. 3.

Systems with scatter higher than expected due to the presence of new non-
transiting companions detected in the RV observations. Here, we define “non-
transiting” as a planet with no reported detection of a transit in the TESS
photometry. For systems in this category, we implemented a blind search
approach by adding parameters for a second planet to the model, whose only
constraint was the orbital period, which was restricted to one half of the
total observation baseline. To facilitate the interpretation of various
models, the analysis was complemented by
rvsearch121212https://github.com/California-Planet-Search/rvsearch, which is a
tool to search for Keplerian signals in RV time series data (Rosenthal et al.,
2021). For example, we typically ranked a potential planet relatively high
when radvel converged on a fairly precise period which was then matched by a
significant period peak in the rvsearch results. In other words, rvsearch was
not used to enforce more strict priors but used as a second interpretation of
the system. Our three new, non-transiting planetary detections are discussed
in Section 6 in more detail.

  4. 4.

Systems with higher residual RV scatter than expected but no straightforward
model to best explain the current set of observations. For systems like
TOI-1181, TOI-1885 and TOI-2145, residual scatter exceeded 50 $\rm m\,s^{-1}$.
The residuals were also high for TOI-329, TOI-1199, TOI-1439, HD 148193
(TOI-1836), HD 83342 (TOI-1898) and TOI-2019 but did not exceed 50 $\rm
m\,s^{-1}$. In none of these systems was there an obvious way to reduce the
scatter with an additional companion and consequently, more RV observations
are needed to reveal the true nature of the systems.

###  5.3 Joint Transit & RV Fitting

Table 7 defines the models used for each system. We simultaneously fit TESS
photometry and RV data for each target, as indicated in Table 2 and Table 4,
respectively. For fitting we followed Chontos et al. (2019), who used the
ktransit131313https://github.com/mrtommyb/ktransit package, an implementation
of the analytical model by Mandel & Agol (2002). The analysis uses the
following parameters as model input: orbital period ($P$), mid-transit time
($T_{0}$), quadratic limb-darkening coefficients ($u_{1},u_{2}$), mean stellar
density ($\bar{\rho}_{\star}$), impact parameter ($b$), ratio of the planet
radius to the stellar radius ($R_{\mathrm{p}}/R_{\star}$) and Doppler
amplitude ($K_{\star}$). Other free parameters include the photometric ($z$)
and spectroscopic ($\gamma$) zero-point offsets, the eccentricity of the orbit
as well as the argument of periapsis, where $e$ and $\omega$ are re-
parameterized to avoid parameter biases.

Figure 4: Phase-folded transit and radial velocity data for previously
confirmed single-planet TESS systems: HD 221416 b (TOI-197; top left), TOI-954
b (top middle), TOI-1181 b (top right), TOI-1296 b (middle left), TOI-1298 b
(middle middle), TOI-1601 b (middle right), TOI-1842 b (bottom left), and
TOI-2145 b (bottom right). Best-fit joint models are overplotted in red,
including 100 samples randomly drawn from posterior distributions and plotted
in gray (with transparency) to show model uncertainties.

Table 8 defines the standard priors assigned in the joint transit and RV
fitting, which were generally flat, uninformative priors. We used weak priors
for quadratic limb-darkening coefficients (LDCs) $\\{u_{1},u_{2}\\}$ by
setting Gaussian priors with wide widths ($\sigma=0.6$) and centers set by
theoretical TESS band values from Claret (2016), which are interpolated in
$T_{\mathrm{eff}}$, $\log g$ and $\rm{[Fe/H]}$. Moreover, additional
constraints on $u_{1}$ and $u_{2}$ were implemented to prevent the limb-
darkening properties from taking nonphysical values (Burke et al., 2008;
Barclay et al., 2015). We also implemented the $\\{q_{1},q_{2}\\}$
parametrization from Kipping (2013) to more efficiently sample the two-
dimensional LDC parameter space. We sampled uniformly in $e\cos\omega$ and
$e\sin\omega$ and therefore also added an additional Jeffreys prior (1/$e$) to
effectively set a uniform prior on eccentricity (Eastman et al., 2013).

To sample the multi-dimensional parameter space, we used the affine-invariant
ensemble Markov Chain Monte Carlo (MCMC) sampler, emcee (Foreman-Mackey et
al., 2013). For joint global fits, we assumed a linear ephemeris and quadratic
limb darkening law. Every joint transit and RV fit initialized 50 walkers,
i.e., at least twice the maximum number of free parameters for a given system.
Each walker took $10^{4}$ steps and then implemented a burn-in phase of
$10^{3}$ steps before concatenating samples to obtain the final posterior
distributions for the parameters.

Table 9 summarizes the primary properties of interest for the full subgiant
planet sample, which uses HD designations where available and remaining
targets are assigned by their TOI number. More than half are newly confirmed
TESS systems, comprising TOI-329, HD 39688 (TOI-480), TOI-603, TOI-1199,
TOI-1294, TOI-1439, TOI-1605, TOI-1828, HD 148193 (TOI-1836), TOI-1885, HD
83342 (TOI-1898) and TOI-2019. We also provide updated, homogeneous parameters
for the 9 other known TESS systems in Table 1 (Huber et al., 2019; Rodriguez
et al., 2021; Sha et al., 2021; Kabáth et al., 2022; Wittenmyer et al., 2022;
Rodriguez et al., 2023; Akana Murphy et al., 2023).

###  5.4 Previously known TESS Systems

Our homogeneous sample of precise RVs combined with considerably longer time
baselines than previous studies provides the opportunity to better
characterize and understand evolved TESS systems. Figure 4 shows transit and
RV data for previously confirmed systems plotted with our global results, as
well as updated properties for each system in the supplementary tables. Here
we summarize any major differences we find in the updated properties for known
TESS systems.

Our most evolved system, HD 221416 (TOI-197), was the first asteroseismic host
discovered by TESS and sits at the base of the red giant branch. Our derived
mass of $M_{\mathrm{p}}$ $=44.6\pm 4.0$ $M_{\oplus}$ is nearly one third
smaller than the value of $M_{\mathrm{p}}$ $=60.5\pm 5.7$ $M_{\oplus}$
reported in Huber et al. (2019), highlighting the importance for long-term RV
monitoring. We also find a mild eccentricity ($e=0.167\pm 0.050$) that is
consistent with their reported value of $e=0.115\pm 0.032$. Combining the
eccentricity with the asteroseismic age, Huber et al. (2019) constrained the
planetary tidal quality to be near or larger than a lower limit of
$Q_{\mathrm{p}}\approx 3.2\times 10^{4}$, because otherwise the orbit would
have already circularized within its lifetime of $\sim$5 Gyr.

First identified by Sha et al. (2021), TOI-954 b is a short-period ($P=3.68$
days) Saturn-sized planet. Sha et al. (2021) reported a value of
$M_{\mathrm{p}}$ $=55.3\pm 5.6$ $M_{\mathrm{p}}$ while we found a mass that is
$4\sigma$ higher ($M_{\mathrm{p}}$ $=76.8\pm 5.6$ $M_{\oplus}$). Our median
eccentricity of $e=0.045$ is smaller than the value of $e=0.14$ reported by
Sha et al. (2021), but both estimates are consistent with zero. Finally, our
$10\sigma$ mass measurement improves the bulk planet density precision by a
factor of two, with $\bar{\rho}_{\mathrm{p}}$ $=0.50^{+0.06}_{-0.05}$ $\rm
g\,cm^{-3}$.

Rodriguez et al. (2021) reported a bimodal posterior probability distributions
for the mass and age of the TESS planet host TOI 1601, which they attributed
to the star’s relatively ambiguous location on an HR diagram given the
precision of their observations. Our analysis agrees with their younger, more
massive solution, with an age of $2.3\pm 0.4$ Gyr and mass of $1.51\pm 0.05$
$M_{*}$.

##  6 New TESS Systems

Phase-folded data and global fits are shown for all new, single-planet TESS
systems in Figure 5. New systems with significant RV trends, including
TOI-1294, TOI-1605 and TOI-1828, are shown in Figure 6. We discuss each of the
new TESS confirmations in the following subsections below. Planet properties
derived from the global fits are summarized in Table 9.

###  6.1 TOI-329

The $V$$=$$11.3$ subgiant star is a cool ($T_{\mathrm{eff}}$ $=5660\pm 75$ K),
low mass ($M_{\star}$ $=1.08\pm 1.03$ $M_{\odot}$) star with a moderate
metallicity of $\rm{[Fe/H]}$ $=+0.16\pm 0.05$. The TOI-329.01 $\sim$1 parts
per thousand (ppt) transit-like events were also detected twice by TFOP SG1
ground-based transit observations in Sloan $i^{\prime}$ band using 7.8”
photometric apertures that excluded the flux of all known Gaia DR3 stars. The
SPOC difference image analysis for TOI-329.01 constrained the host star to
within 1.2$\pm$3.3” of the location of the transit source.

Figure 5: Same as Figure 4 but for new TESS single-planet systems: TOI-329 b
(top left), HD 39688 b (TOI-480, top middle), TOI-603 b (top right), TOI-1199
b (middle left), TOI-1439 b (middle middle), HD 148193 b (TOI-1836; middle
right), TOI-1885 b (bottom left), HD 83342 b (TOI-1898; bottom middle), and
TOI-2019 (bottom right). Best-fit joint models are overplotted in red with 100
samples randomly drawn from posterior distributions and plotted in gray (with
transparency) to demonstrate the model uncertainties.

Follow-up RV measurements resolved the 5.7 day orbit, where the phase-folded
HIRES data in Figure 5 (top left) clearly demonstrate that the planet has a
significantly ($\sim$$13\sigma$) non-zero eccentricity. The planet is slightly
larger than Neptune at $R_{\mathrm{p}}$$\sim 4.7$ $R_{\oplus}$, which is a
rare planet type in the context of the observed planet radius distribution
(e.g., Fulton et al. 2017). We report a mass of $M_{\mathrm{p}}$ $=40.8\pm
3.6$ $M_{\oplus}$ and a bulk density of $\bar{\rho}_{\mathrm{p}}$ $=2.13\pm
0.54$ $\rm g\,cm^{-3}$. The combination of the relatively small separation
($a/R_{\star}$$\leq 10$) and older age ($8.3\pm 1.0$ Gyr) would suggest that
the orbit has had sufficient time to circularize via tidal interactions of the
planet with the host star. Yet the eccentricity is found to be moderate
($e=0.39\pm 0.03$), suggesting some other dynamical process as a potential
source for the non-zero eccentricity.

###  6.2 HD 39688 (TOI-480)

TFOP SG1 ground-based lightcurves ruled out nearby eclipsing binaries as the
source of the TOI-480.01 transit-like event detected in the TESS data.
However, HD 39688 ($V$$=$$7.3$) is a challenging system since the host star
has a rotational velocity of $\sim$8 $\rm km\,s^{-1}$ while the estimated
Doppler amplitude of the transiting $\sim$2.8 $R_{\oplus}$ candidate was 2.8
$\rm m\,s^{-1}$. The $\sigma_{\mathrm{RV}}-$$v\sin i$ relation of Chontos et
al. (2022) predicted an additional scatter of $\sim$2.6 $\rm m\,s^{-1}$ in the
time series due to the rotation. Therefore, during each visit to HD 39688 we
obtained three back-to-back observations to improve the per-visit uncertainty
by a factor of $\sqrt{3}$. The transit and RV observations indeed confirm the
planetary nature of HD 39688 b ($M_{\mathrm{p}}$$\,=15.7\pm 2.2$
$M_{\oplus}$), which has a bulk density consistent with a rocky, terrestrial
planet ($\rho_{\mathrm{p}}=4.4\pm 0.8$ gcc).

Due to the high $v\sin i$, we checked the raw TESS photometry (SAP-FLUX) for
evidence of stellar rotation via star spot modulation. We identified a
significant peak at a period of $P_{\mathrm{rot}}$ $\sim 6.92$ days, which if
due to the host star rotation, suggests that the system is either near or at
synchronous rotation with the transiting planet, which has an orbital period,
$P\sim 6.86$ days. The stellar inclination to the line of sight measured from
the observations (by combining $v\sin i$, $P_{\mathrm{rot}}$, $R_{\star}$) is
$\sim 52^{o}$, which suggests a probable misalignment of the orbital plane of
the planets with respect to the rotation axis of the star. In the event that
the misalignment is confirmed then synchronization would not be expected.

###  6.3 TOI-603

The effective temperature and age of TOI-603 are roughly consistent with those
of the Sun, with $T_{\mathrm{eff}}$ $=5850\pm 70$ K and an age of $4.9\pm 1.2$
Gyr. The subgiant star is larger and more massive though, with a size of
$R_{\star}$ $=1.56\pm 0.03$ $R_{\odot}$ and a mass of $M_{\star}$ $=1.20\pm
0.05$ $M_{\odot}$. With only 12 HIRES RVs, the mass measurement of
$M_{\mathrm{p}}$ $=47.5\pm 13.7$ $M_{\oplus}$ has the lowest statistical
significance of all new confirmations, but the $\sim$$3\sigma$ detection is
sufficient to confirm the planetary nature of the transiting planet, TOI-603
b.

TOI-603.01 is one example from the TESS Primary Mission where an alias of the
true period was reported; it was only observed for a single sector during the
nominal mission, and it was initially assumed that a transit occurred during
the data gap. Further TFOP efforts consistently confirmed that the period is
close to twice that of the previously reported period, which is supported by
the phase-folded HIRES RVs shown in Figure 5. Fortunately the target was re-
observed in 2-minute cadence in the first Extended Mission in sectors 35, 45
and 46, which provided more transits to better constrain the observed planet
properties (i.e. $R_{\mathrm{p}}$ $=7.93\pm 0.20$ $R_{\oplus}$, $P=16.17989\pm
0.00006$ days).

###  6.4 TOI-1199

TOI-1199 is one the smallest host stars in the sample, with $R_{\star}$
$=1.46\pm 0.02$ $R_{\odot}$, $T_{\mathrm{eff}}$ $=5630\pm 54$ K and an age of
$\sim 6.3$ Gyr. The transiting planet, TOI-1199 b, is a giant planet
($R_{\mathrm{p}}$ $=10.6\pm 0.3$ $R_{\oplus}$) on an approximately circular
orbit with a period of $P\sim 3.7$ days. Using 16 HIRES RVs, we report a
precise mass of $M_{\mathrm{p}}$ $=69.4\pm 5.7$ $M_{\oplus}$ and bulk density
of $\bar{\rho}_{\mathrm{p}}$ $=0.32\pm 0.04$ g cm-3.

Intriguingly, a total of 7 different threshold crossing events (TCEs) with
similar periods were all assigned to the same TIC, which we speculate is
evidence for transit timing variations (TTVs). We also found additional power
near the reported period in the residual RV periodogram after subtracting out
the single-planet model, which could be evidence for another planet in the
system. However given the small number of RVs, more observations are needed to
confirm the existence of any additional companions.

###  6.5 TOI-1294

TOI-1294 is a massive ($M_{\star}$ $=1.20\pm 0.05$ $M_{\odot}$) and metal-rich
($\rm{[Fe/H]}$ $=+0.28\pm 0.06$) host star, with an effective temperature of
$T_{\mathrm{eff}}$ $\sim 5770\pm 80$ K and age of $\sim 5.2^{+1.4}_{-0.9}$
Gyr. Achromatic $\sim$3 ppt transit-like events were also detected on target
by TFOP SG1 ground-based transit observations in Sloan $g^{\prime}$ and Sloan
$i^{\prime}$ bands using 5.8” or smaller photometric apertures that excluded
the flux of all known Gaia DR3 stars. Initial follow up RVs immediately
confirmed the planetary nature of the transiting, Saturn-sized
($R_{\mathrm{p}}$$\,=9.2\pm 0.3$) TOI-1294 b, with a mass of
$M_{\mathrm{p}}$$\,=62.2\pm 5.0$ $M_{\oplus}$ on a $\sim 3.9$-day orbit.

A significant offset was observed during the second observing season near the
2400 time stamp, seen in the bottom left panel of Figure 6, which could only
be explained by at least one additional companion. A blind RV search
unambiguously recovered a Keplerian signal at a period of $P=160.9\pm 2.5$
days, with a mass corresponding to $M_{\mathrm{p}}$$\,=148.3\pm 17.3$
$M_{\oplus}$, hereafter referred to as TOI-1294 c. The best-fit model also
exhibits an RV trend of $\dot{\gamma}=0.052\pm 0.007$ $\rm m\,s^{-1}\,d^{-1}$
($T_{\mathrm{ref}}=2459198.114897$), where further RV observations will enable
a more comprehensive understanding of the evolved, multi-planet TOI-1294
system.

Figure 6: Phase-folded TESS photometry (top) and Keck/HIRES RV time series
(bottom) with the joint transit and RV fit overplotted in red. The RV
observations presented here enabled the discovery of non-transiting planetary
companion, TOI-1294 c (Section 6.5), as well as three additional outer
companions observed via significant trends in TOI-1294 (left), TOI-1605
(middle) and TOI-1828 (right).

###  6.6 TOI-1439

TOI-1439 ($V$$=$$10.6$) has an effective temperature $T_{\mathrm{eff}}$
$=5857\pm 60$ K and metallicity of $\rm{[Fe/H]}$ $=+0.22\pm 0.06$. The radius
and mass of the subgiant host are $R_{\star}$ $=1.64$ $R_{\odot}$ and
$M_{\star}$ $=1.24$ $M_{\odot}$, respectively, and it has an intermediate age
of $\sim 4.5^{+1.6}_{-0.6}$ Gyr. The observed activity indicator from the RV
time series, $\log R_{HK}^{\prime}$ $=-5.26$, suggests that the star is
relatively inactive. This is further supported by back-to-back HIRES
observations obtained on UT 2020-07-27, which were separated by one hour and
showed very little jitter.

TOI-1439 b is a Neptune-sized ($R_{\mathrm{p}}$ $=4.1\pm 0.2$ $R_{\oplus}$)
planet on an orbit with a period of $P\sim 27.6$ days, which is slightly
longer than a single TESS sector. We measured a mass and bulk density
corresponding to $M_{\mathrm{p}}$ $=38.4\pm 5.5$ $M_{\oplus}$ and
$\bar{\rho}_{\mathrm{p}}$ $=2.9\pm 0.6$ $\rm g\,cm^{-3}$, respectively. After
subtracting the best-fit model from the RV time series, however, the residual
RVs still showed high scatter and given the relatively inactive host star,
could indicate the presence of additional planets in the system.

###  6.7 TOI-1605

TOI-1605 ($V$$=$$10.2$) has an effective temperature and metallicity which are
fully consistent with those of the Sun, with $T_{\mathrm{eff}}$ $=5774\pm 75$
K and $\rm{[Fe/H]}$ $=+0.03\pm 0.06$. The host star also has a radius of
$R_{\star}$ $=1.51\pm 0.03$ $R_{\odot}$, a mass of $M_{\star}$ $=1.05\pm 0.03$
$M_{\odot}$, and an age of $\sim 7.9\pm 1.0$ Gyr. Achromatic $\sim$5 ppt
transit-like events of TOI-1605.01 were detected by TFOP SG1 ground-based
transit observations in multiple bands spanning Sloan $g^{\prime}$ through
Pan-STARRS $z$-short bands.

TOI-1605 b is currently challenging to characterize, given the limited
availability of TESS photometry and the high impact parameter that is implied
by the v-shaped transit shown in Figure 6 (middle). The Jupiter-sized planet
($R_{\mathrm{p}}$ $=10.34\pm 0.64$ $R_{\oplus}$) has a mass of
$M_{\mathrm{p}}$ $=221.3\pm 7.7$ $M_{\oplus}$ and is on an eccentric
($e=0.28\pm 0.01$) orbit, which is interesting given the short orbital period
($<10$ days). As seen in the bottom of Figure 6, the RV observations also
indicate the presence of an outer companion ($\dot{\gamma}=-0.298\pm 0.006$
$\rm m\,s^{-1}\,d^{-1}$ using a time reference of
$T_{\mathrm{ref}}=2459497.065739$) that could be responsible for the observed
high eccentricity but more RVs are needed to characterize the outer companion.

###  6.8 TOI-1828

The host star TOI-1828 ($V$$=$$11.6$) is a subgiant with an effective
temperature of $T_{\mathrm{eff}}$ $=5680$ K, a radius of $R_{\star}$ $=1.60$
$R_{\odot}$, and a mass of $M_{\star}$ $=1.06$ $M_{\odot}$. TFOP SG1 ground-
based transit observations in Sloan $g^{\prime}$ and Sloan $i^{\prime}$ bands
also detected achromatic $\sim$3 ppt transit-like events of TOI-1828.01 using
7.8” or smaller photometric apertures that excluded the flux of all known Gaia
DR3 stars. The SPOC difference image analysis also constrained the host star
to within 0.12$\pm$2.4” of the location of the transit source.

The close-in ($P=9.094$ days), eccentric ($e=0.31\pm 0.03$) HJ is strikingly
similar to TOI-1605 b (discussed above), with the exception of the lower
planet mass of $M_{\mathrm{p}}$ $=58.5\pm 3.8$ (and bulk density of
$\bar{\rho}_{\mathrm{p}}$ $=0.50\pm 0.05$ $\rm g\,cm^{-3}$). The panels on the
right side in Figure 6 show the phase-folded TESS photometry (top) and RV time
series (bottom). The last RV observation clearly indicates an additional
companion in the system. As expected though, the single, most recent RV does
not constrain the slope well but the measured trend is significant
nevertheless, with $\dot{\gamma}=-0.147\pm 0.012$ $\rm m\,s^{-1}\,d^{-1}$
($T_{\mathrm{ref}}=2459445.570399$).

Table 9: Summary of derived planet properties from the joint transit and RV fits. Planet | $P\,\,\mathrm{[days]}$ | Epoch [BTJD] | $R_{p}\,\,[R_{\oplus}]$ | $M_{p}\,\,[M_{\oplus}]$ | $\rm\bar{\rho}_{{}_{p}}\,\,[g\,cm^{-3}]$ | $e$
---|---|---|---|---|---|---
HD 221416 b | $14.2790\pm 0.0027$ | $1357.0127\pm 0.0022$ | $9.36\pm 0.33$ | $44.6\pm 4.0$ | $0.30\pm 0.04$ | $0.17\pm 0.05$
TOI-329 b | $5.7044\pm 0.0001$ | $2090.7935\pm 0.0049$ | $4.72\pm 0.36$ | $40.8\pm 3.6$ | $2.13\pm 0.54$ | $0.39\pm 0.03$
HD 39688 b | $6.86588\pm 0.00001$ | $1469.5660\pm 0.0016$ | $2.69\pm 0.10$ | $15.7\pm 2.2$ | $4.42\pm 0.80$ | $0.10\pm 0.07$
TOI-603 b | $16.17989\pm 0.00006$ | $2268.0635\pm 0.0015$ | $7.93\pm 0.20$ | $47.5\pm 13.7$ | $0.52\pm 0.16$ | $0.22\pm 0.19$
TOI-954 b | $3.6843\pm 0.0002$ | $2145.2170\pm 0.0008$ | $9.47\pm 0.25$ | $76.8\pm 5.6$ | $0.50\pm 0.06$ | $0.05\pm 0.04$
TOI-1181 b | $2.1031937\pm 0.0000005$ | $1957.8213\pm 0.0001$ | $16.14\pm 0.34$ | $374.7\pm 8.9$ | $0.49\pm 0.03$ | $0.01\pm 0.01$
TOI-1199 b | $3.67147\pm 0.00001$ | $2611.4540\pm 0.0005$ | $10.60\pm 0.33$ | $69.4\pm 5.7$ | $0.32\pm 0.04$ | $0.05\pm 0.04$
TOI-1294 b | $3.91529\pm 0.00001$ | $2393.0110\pm 0.0033$ | $9.19\pm 0.31$ | $62.2\pm 5.0$ | $0.44\pm 0.06$ | $0.07\pm 0.04$
TOI-1294 c | $160.1\pm 2.5$ | $2349.0106\pm 5.7665$ | – | $148.3\pm 17.0$ | – | $0.10\pm 0.09$
TOI-1296 b | $3.944373\pm 0.000001$ | $1930.7553\pm 0.0002$ | $13.93\pm 0.30$ | $95.4\pm 5.35$ | $0.19\pm 0.02$ | $0.02\pm 0.02$
TOI-1298 b | $4.537143\pm 0.000003$ | $1929.5853\pm 0.0003$ | $9.64\pm 0.21$ | $98.3\pm 5.2$ | $0.60\pm 0.05$ | $0.03\pm 0.03$
TOI-1439 b | $27.643927\pm 0.000090$ | $1703.4752\pm 0.0023$ | $4.15\pm 0.18$ | $38.4\pm 5.5$ | $2.94\pm 0.57$ | $0.15\pm 0.07$
TOI-1601 b | $5.33206\pm 0.00034$ | $1793.2741\pm 0.0026$ | $14.07\pm 0.49$ | $361.4\pm 7.6$ | $0.71\pm 0.08$ | $0.07\pm 0.04$
TOI-1605 b | $8.7099\pm 0.0006$ | $2887.4759\pm 0.0766$ | $10.34\pm 0.64$ | $221.3\pm 7.7$ | $1.10\pm 0.21$ | $0.28\pm 0.01$
TOI-1736 b | $7.073091\pm 0.000008$ | $2740.5891\pm 0.0007$ | $3.05\pm 0.19$ | $11.9\pm 1.6$ | $2.30\pm 0.50$ | $0.04\pm 0.04$
TOI-1736 c | $571.3\pm 0.5$ | $2273.1\pm 0.4$ | – | $2477\pm 118$ | – | $0.37\pm 0.01$
TOI-1828 b | $9.0941045\pm 0.0000083$ | $1936.2770\pm 0.0007$ | $8.62\pm 0.19$ | $58.5\pm 3.8$ | $0.50\pm 0.05$ | $0.31\pm 0.03$
HD 148193 b | $20.38085\pm 0.000025$ | $1933.1655\pm 0.0008$ | $8.38\pm 0.19$ | $28.4\pm 4.3$ | $0.27\pm 0.04$ | $0.14\pm 0.11$
TOI-1842 b | $9.573922\pm 0.000013$ | $1933.3360\pm 0.0008$ | $12.29\pm 0.32$ | $73.4\pm 7.5$ | $0.22\pm 0.03$ | $0.18\pm 0.08$
TOI-1885 b | $6.544060\pm 0.000006$ | $1958.2553\pm 0.0008$ | $13.66\pm 0.41$ | $516.4\pm 32.7$ | $1.12\pm 0.12$ | $0.04\pm 0.03$
HD 83342 b | $45.522149\pm 0.000039$ | $1894.2540\pm 0.0005$ | $9.74\pm 0.22$ | $127.5\pm 6.6$ | $0.76\pm 0.07$ | $0.48\pm 0.04$
TOI-2019 b | $15.3444\pm 0.0055$ | $1958.2895\pm 0.0040$ | $5.66\pm 0.28$ | $34.6\pm 4.2$ | $1.05\pm 0.21$ | $0.09\pm 0.07$
TOI-2145 b | $10.26111\pm 0.00001$ | $2013.2807\pm 0.0006$ | $12.25\pm 0.30$ | $1810.2\pm 42.5$ | $5.42\pm 0.42$ | $0.21\pm 0.02$

###  6.9 HD 148193 (TOI-1836)

HD 148193 ($V$$=$$\,9.6$) is a young ($\sim$$3.3$ Gyr) and hot ($\sim$$6235$
K) star, and is one of the more metal-poor subgiants in the sample, with
$\rm{[Fe/H]}$ $=-0.16$. As discussed in Section 3.4, HD 148193 is the only
host star in the sample with any known stellar companions. High-resolution
imaging revealed a close ($<1^{\prime\prime}$, $\Delta m=5.7$) companion and a
$0.2^{\prime\prime}$ binary (TIC 207468069) that is $\sim$$10^{\prime\prime}$
away. TFOP SG1 ground-based transit observations in Pan-STARRS $z$-short band
and Cousins I band detected $\sim$2.5 ppt transit-like events on target. The
transiting $\sim$20-day planet HD 148193 b has a size of $R_{\mathrm{p}}$
$=8.38\pm 0.19$ $R_{\oplus}$ and a mass of $M_{\mathrm{p}}$ $=28.4\pm 4.3$
$M_{\oplus}$.

The SPOC pipeline more recently identified another candidate signal using data
from the extended mission. The candidate is interior to the confirmed planet,
with a radius of $R_{\oplus}$ $=2.5$ $R_{\oplus}$ and a period of $P=$ 1.77
days, but ultimately its confirmation is beyond the scope of this paper.

###  6.10 TOI-1885

TOI-1885 is a young ($2.0\pm 0.3$ Gyr) and hot ($T_{\mathrm{eff}}$ $=6527\pm
98$ K) host star with a solar-like metallicity ($\rm{[Fe/H]}$ $=0.02\pm$0.05).
Gaia DR3 also reported an effective temperature that is fully consistent with
the value of derived from the spectrum. The effective temperature of the star
places it on the hot side of the Kraft break (Kraft, 1967), suggesting that
the host star lacks a significant convective envelope.

Our analysis estimates a planet size of $R_{\mathrm{p}}$ $=13.66\pm 0.41$
$R_{\oplus}$ and mass of $M_{\mathrm{p}}$ $=516.4\pm 32.7$ $M_{\oplus}$ ($\sim
1.6$ $M_{\mathrm{J}}$), which together constrain the bulk density to
$\sim$$10\%$, with $\bar{\rho}_{\mathrm{p}}$$=1.12\pm 0.12$ $\rm g\,cm^{-3}$.
The close-in giant planet has an orbital period of $P=6.544$ days and appears
to be on a nearly circular orbit, but more RVs could better constrain the
eccentricity of the orbit.

Figure 7: Planet size versus orbital period (left) and incident flux (right)
for all planets with measured radii and masses. Evolutionary states of the
host stars are indicated by different colors: main-sequence (grey), subgiants
(cyan) and red giants (orange). Filled markers show planets with the most
precise densities ($\geq 4\sigma$). Our subgiant sample is highlighted with
thick black outlines, and positions for new non-transiting planets (i.e. with
no measured sizes) are shown by vertical, dashed lines.

###  6.11 HD 83342 (TOI-1898)

HD 83342 ($V$$=$$7.9$) was originally a community TESS object of interest due
to the single transit that occurred during the nominal mission. However the
target was reobserved for two additional sectors in the extended mission,
hence providing two additional transits to better constrain the orbital period
of the transiting candidate TOI-1898.01. The planet HD 83342 b is a warm
Jupiter ($P=45.5$ days) with a mass of $M_{\mathrm{p}}$ $=127.5\pm 6.6$
$M_{\oplus}$ and is on a highly eccentric orbit with $e=0.48\pm 0.04$, as
shown in the phase-folded RVs in the bottom left of Figure 5. The moderate
$v\sin i$ of the host star also makes the system an ideal target to measure
the sky-projected obliquity via Rossiter-McLaughlin or Doppler tomography
observations, and especially because the highly eccentric, warm Jupiter could
help elucidate gas giant formation and migration pathways.

###  6.12 TOI-2019

TOI-2019 is a cool ($\sim$$5590$ K), metal-rich ($\rm{[Fe/H]}$ $=+0.40\pm
0.06$) star with an age of $6.7\pm 0.6$ Gyr. Comparatively, the subgiant host
has a more moderate size, with $R_{\star}$ $=1.75\pm 0.03$ $R_{\odot}$ and a
mass of $M_{\star}$ $=1.17\pm 0.04$ $M_{\odot}$. The transiting planet,
TOI-2019 b, is a rare planet type in context with the current distribution of
planetary radii, with $R_{\mathrm{p}}$ $=5.7\pm 0.3$ $R_{\oplus}$, and is also
one of the longer period planets in our sample, with $P=15.35$ days. Our
measured mass is $M_{\mathrm{p}}$ $=34.60\pm 4.26$ $M_{\oplus}$, which
translates to a bulk planet density of $\bar{\rho}_{\mathrm{p}}$ $=1.05\pm
0.20$ $\rm g\,cm^{-3}$.

##  7 Discussion

###  7.1 Planet Sizes and Multiplicity

Figure 7 shows planet sizes versus orbital period and incident flux for all
planets with measured radii and masses, separated according to the
evolutionary state of the host star. Literature values were taken from the
NASA Exoplanet Archive141414https://exoplanetarchive.ipac.caltech.edu. Our
sample increases the number of known planets with measured radii and masses
orbiting subgiant stars by 25%, bringing the total population to $106$
planets. Further, our sample contribution increases to 50% when only
considering planets with the most precisely measured ($\leq 10\%$) densities.
Based on radius and incident flux, our sample consists mainly of warm and hot
Jupiters and sub-Saturns, and a handful of sub-Neptune sized planets.

Figure 7 shows that planets orbiting subgiants show the same broad demographic
features as planets orbiting main-sequence stars, including radius inflation
with incident flux for gas-giant planets (Burrows et al., 2000; Lopez &
Fortney, 2016) and a dearth of planets with high-incident fluxes and radii
between $\approx 3-8$ $R_{\oplus}$ (the sub-Neptune desert, Lundkvist et al.,
2016). Quantitatively, planets orbiting subgiants are on average hotter and
exclude the shortest orbital period planets. The former is consistent with
selection bias, while the latter is consistent with tidal orbital period decay
becoming more efficient as a star evolves off the main-sequence, causing short
period planets to be engulfed (Schlaufman & Winn, 2013).

Our sample includes 4 subgiants with outer non-transiting companions. Sample
targets have observations that span two years on average and therefore
assuming each target has equal sensitivity to such companions, corresponds to
an approximate occurrence rate of outer Jovian planets in subgiant systems of
19$\pm$8%. This fraction is consistent with the occurrence rate of Jovian
planets beyond the ice line from long-term RV surveys (Fernandes et al., 2019;
Fulton et al., 2021). Since subgiants are on average more massive than main-
sequence stars, this may imply that the correlation of stellar mass and gas-
giant planet occurrence does not extend to long orbital periods. We caution
that the above numbers are not based on a detailed occurrence rate study
(using injection/recovery tests), which is beyond the scope of this paper.

Figure 8: Same as Figure 7 but now showing planet radius versus planet mass
(left) and bulk density versus planet radius (right). Solar system planets are
shown by the black symbols.

###  7.2 Mass-Radius Relation

Figure 8 compares the mass-radius relation and density versus radius for our
sample with values for other planets drawn from the literature. For giant
planets ($>10$ $R_{\oplus}$) we observe that planets orbiting subgiant stars
follow largely the same distribution as planets orbiting main-sequence stars.
We observe a tentative lack of inflated, massive ($>1000$$M_{\oplus}$) planets
around subgiant stars. However, a K-S test shows that this is not significant,
likely due to the small sample size.

A large fraction of our newly confirmed planets fall in the region between
Neptune and sub-Saturn sized planets, for which radii increase as
$R_{P}\approx M_{P}^{0.6}$, and Jovian planets, for which radius is nearly
constant with mass (Weiss et al., 2013; Chen & Kipping, 2017). Sub-Saturn
sized planets (4–8 $R_{\oplus}$) around main-sequence stars show a wide
variety of masses, (6–60 $M_{\oplus}$), even at roughly fixed radius (Petigura
et al., 2017b; Van Eylen et al., 2018). Conversely, our sample of planets
orbiting subgiants appears to show a tighter mass range (35-50 $M_{\oplus}$),
and the smallest ($<4$ $R_{\oplus}$) planets found around subgiants are all
consistently more massive. We speculate that this could signify that the
atmospheres of low density planets are preferentially eroded away as the host
star evolves into a subgiant. An alternative explanation is that low-mass
planets are more difficult to confirm around subgiant stars, which exhibit
increased RV jitter due to granulation.

###  7.3 Eccentricity and Age

Orbital eccentricities of exoplanets provide valuable clues for how planetary
systems might have formed. For example, planet-planet scattering followed by
high eccentricity migration is one of the favored formation scenarios for gas-
giant planets on short orbits (Dawson & Johnson, 2018). Our sample is
particularly useful for investigations of such theories due to the precise age
constraints for subgiant host stars. Indeed, recent studies have found that
hot Jupiter occurrence decreases with stellar age (Hamer & Schlaufman, 2019;
Miyazaki & Masuda, 2023; Chen et al., 2023).

Figure 9 shows orbital eccentricity versus age for all hot Jupiters
($R_{\mathrm{p}}$ $>8$ $R_{\oplus}$, $P<10$ days) in our sample. Intriguingly,
some of the most eccentric planets in our sample are found orbiting around
some of the oldest stars. This suggests that planet-planet scattering, which
can lead to high eccentricities, may occur on $>$ Gyr timescales.
Alternatively, it suggests that tidal circularization can occur on
significantly slower timescales than orbital period decay, consistent with a
diversity of dissipation efficiencies.

Another clue for the dynamical architectures of these systems is the presence
of outer, non-transiting companions. Figure 9 shows that planets without outer
companions are preferentially young and on circular orbits. Conversely,
planets with outer companions are preferentially older and on eccentric
orbits. If confirmed, this would imply possible distinct formation pathways
for different hot Jupiter populations in which some undergo high-eccentricity
migration and circularize quickly, whereas those with outer companions
possibly gain their eccentricities through Kozai-Lidov oscillations (Fabrycky
& Tremaine, 2007). Additional systems will be required to confirm the
significance of this trend, given the small number statistics in this sample.

Figure 9: Orbital eccentricity versus age for all hot Jupiters (i.e.,
$R_{\mathrm{p}}$ $>8$ $R_{\oplus}$ and $P\leq 10$ days) in our sample. The
$y$-axis is scaled non-linearly to emphasize more moderate eccentricities. The
effective temperature of the host star is color coded and symbol size scales
with planet mass. Planets with non-transiting outer companions are shown as
squares.

##  8 Conclusions

We presented a dedicated transit and radial velocity survey of planets
orbiting subgiants observed by TESS. Our main conclusions can be summarized as
follows:

  * •

We measured radii and masses for the 23 planets orbiting 21 subgiant stars, 13
of which are new planet discoveries. Of the 21 transiting planets with
measured sizes, 19 planets have bulk densities measured to better than 25%,
including 6 with densities measured to better than 10%.

  * •

Our sample includes 4 subgiants with outer non-transiting companions,
corresponding to an approximate outer Jovian planet fraction of 19$\pm$8%.
This fraction is consistent with the occurrence rate of outer Jovian planets
orbiting main-sequence stars.

  * •

The mass-radius diagram for giant planets orbiting subgiant stars roughly
matches the observed distribution for main-sequence stars, with the exception
of a tentative lack of inflated, massive planets. We also observe that sub-
Saturn sized planets orbiting subgiants are systematically more massive than
similar sized planets around main-sequence stars, which may be related to
detection bias or preferential atmosphere stripping in low-density planets.

  * •

We find tentative evidence for two populations among close-in ($P<10$ days)
giant planets ($R_{\mathrm{p}}$ $>8\,$$R_{\oplus}$) orbiting our subgiant
sample: 1) “lonely” young ($\sim 2$ Gyr), circular HJs orbiting hot
($T_{\mathrm{eff}}$ $>6200$ K) stars, and 2) older ($\sim 8-10$ Gyr),
eccentric ($e\sim 0.3$) HJs orbiting stars with $T_{\mathrm{eff}}$ between
$5700-5900$ K where there is evidence for outer companions. Thus the observed
properties of hot Jupiters orbiting evolved stars are the likely consequence
of multiple formation channels.

Future characterization of planets in this sample will provide a more
comprehensive understanding of planet demographics for evolved systems. For
example, many of the host stars in this sample are rapidly rotating ($v\sin i$
$>5$ $\rm km\,s^{-1}$), facilitating the measurement of projected obliquities
via Rossiter-McLaughlin or Doppler tomography observations (Saunders et al.,
in prep; Knudstrup et al., in prep). Continued monitoring by TESS and RV
surveys will furthermore provide insights into additional planets in these
systems.

## Acknowledgements

The authors wish to recognize and acknowledge the very significant cultural
role and reverence that the summit of Maunakea has always had within the
Native Hawaiian community. We are most fortunate to have the opportunity to
conduct observations from this mountain.

We thank all the observers who spent time collecting data over the many years
at Keck/HIRES. We gratefully acknowledge the efforts and dedication of the
Keck Observatory staff for support of HIRES and remote observing. We thank the
University of California and Google for supporting Lick Observatory and the
UCO staff for their dedicated work scheduling and operating the telescopes of
Lick Observatory.

A.C. and D.H. acknowledge support from the National Aeronautics and Space
Administration (80NSSC21K0652). D.H. also acknowledges support from the Alfred
P. Sloan Foundation and the Australian Research Council (FT200100871). N.S.
acknowledges support by the National Science Foundation Graduate Research
Fellowship Program under Grant Number 2236415. E.K. and S.H.A. acknowledge
support from the Danish Council for Independent Research through Grant Number
2032-00230B. M.L.H. would like to acknowledge NASA support via the FINESST
Planetary Science Division, NASA award number 80NSSC21K1536. K.K.M.
acknowledges support from the New York Community Trust Fund for Astrophysical
Research). E.P. acknowledges financial support from the Agencia Estatal de
Investigación of the Ministerio de Ciencia e Innovación
MCIN/AEI/10.13039/501100011033 and the ERDF “A way of making Europe” through
project PID2021-125627OB-C32, and from the Centre of Excellence “Severo Ochoa”
award to the Instituto de Astrofisica de Canarias.…

This paper made use of data collected by the TESS mission and are publicly
available from the Mikulski Archive for Space Telescopes operated by the Space
Telescope Science Institute. 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 Program through the NASA Advanced Supercomputing Division
at Ames Research Center for the production of the SPOC data products. This
research has made use of the Exoplanet Follow-up Observation Program website,
which is operated by the California Institute of Technology, under contract
with the National Aeronautics and Space Administration under the Exoplanet
Exploration Program. This work has made use of observations (programme IDs:
A42/TAC22 and A43/TAC11) from the Italian Telescopio Nazionale Galileo, which
is operated on the island of La Palma by the Fundación Galileo Galilei of the
Istituto Nazionale di Astrofisica at the Spanish Observatorio del Roque de los
Muchachos of the Instituto de Astrofisica de Canarias.

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