# The TESS-Keck Survey XX: 15 New TESS Planets and a Uniform RV Analysis of
all Survey Targets

Alex S. Polanski IPAC Visiting Graduate Research Fellow  Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA  Jack Lubin Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA  Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  Corey Beard NASA FINESST Fellow  Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA  Joseph M. Akana Murphy NSF Graduate Research Fellow  Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95060, USA  Ryan Rubenzahl NSF Graduate Research Fellow  Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Michelle L. Hill Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA  Ian J. M. Crossfield  Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA  Ashley Chontos Henry Norris Russell Fellow  Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08540, USA  Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA  Paul Robertson Department of Physics and Astronomy, University of California, Irvine, CA 92697, 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  David R. Ciardi NASA Exoplanet Science Institute/Caltech-IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA  Natalie M. Batalha Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95060, USA  Courtney Dressing Department of Astronomy, University of California Berkeley, Berkeley CA 94720, USA  Benjamin Fulton NASA Exoplanet Science Institute/Caltech-IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA  Andrew W. Howard Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, 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  Erik A. Petigura Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  Lauren M. Weiss Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN, 46556, USA  Isabel Angelo Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA  Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles, CA 90095, USA  Aida Behmard Department of Astrophysics, American Museum of Natural History, 200 Central Park West, Manhattan, NY 10024, USA  Sarah Blunt Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  CIERA, Northwestern University, Evanston IL 60201  Casey L. Brinkman Institute for Astronomy, University of Hawai’i, Honolulu, HI 96822, USA  Fei Dai Division of Geological and Planetary Science, California Institute of Technology, 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 95060, 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  Lea A. Hirsch University of Toronto Mississauga, 3359 Mississauga Road Mississauga ON L5L 1C6 Canada  Rae Holcomb Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA  Molly R. Kosiarek NSF Graduate Research Fellow  Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA  Andrew W. Mayo Department of Astronomy, University of California Berkeley, Berkeley CA 94720, 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  Daria Pidhorodetska Department of Earth and Planetary Sciences, University of California, Riverside, CA 92521, USA  Malena Rice Department of Astronomy, Yale University, New Haven, CT 06511, USA  Lee J. Rosenthal  Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Nicholas Scarsdale Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95060, USA  Emma V. Turtelboom Department of Astronomy, University of California Berkeley, Berkeley CA 94720, USA  Dakotah Tyler Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA  Judah Van Zandt Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA  Samuel W. Yee Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08540, USA  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  51 Pegasi b Fellow  David R. Coria Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA  Shannon D. Dulz Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN, 46556, USA  Joel D. Hartman Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08540, USA  Aaron Householder Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Sarah Lange Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA  Andrew Langford NSF Graduate Research Fellow  Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK  School of Aeronautical and Astronautical Engineering, Purdue University, West Lafayette, IN, USA  Emma M. Louden Department of Astronomy, Yale University, New Haven, CT 06511, USA  Jared C. Siegel Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08540, USA  Emily A. Gilbert Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA  Erica J. Gonzales NSF Graduate Research Fellow  Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA  Joshua E. Schlieder  NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 22071, USA  Andrew W. Boyle Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA  Jessie L. Christiansen NASA Exoplanet Science Institute/Caltech-IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA  Catherine A. Clark Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA  NASA Exoplanet Science Institute/Caltech-IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA  Rachel B. Fernandes President’s Postdoctoral Fellow  Department of Astronomy & Astrophysics, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802, USA  Center for Exoplanets and Habitable Worlds, 525 Davey Laboratory, The Pennsylvania State University, University Park, PA 16802, USA  Michael B. Lund NASA Exoplanet Science Institute/Caltech-IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA  Arjun B. Savel Department of Astronomy, University of Maryland, College Park, MD 20742, USA  Holden Gill Department of Astronomy, University of California Berkeley, Berkeley CA 94720, USA  Charles Beichman  NASA Exoplanet Science Institute/Caltech-IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA  Rachel Matson  U.S. Naval Observatory, 3450 Massachusetts Avenue NW, Washington, D.C. 20392, USA  Elisabeth C. Matthews Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany  E. Furlan NASA Exoplanet Science Institute/Caltech-IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA  Steve B. Howell NASA Ames Research Center, Moffett Field, CA 94035, USA  Nicholas J. Scott NASA Ames Research Center, Moffett Field, CA 94035, USA  Mark E. Everett NSF’s National Optical-Infrared Astronomy Research Laboratory, 950 N. Cherry Ave., Tucson, AZ 85719, USA  John H. Livingston Astrobiology Center, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Astronomical Science Program, Graduate University for Advanced Studies, SOKENDAI, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan  Irina O. Ershova Faculty of Space Research, Moscow State University, 1 Leninskie Gory, bld. 52, Moscow, Russia  Dmitry V. Cheryasov Sternberg Astronomical Institute, Lomonosov Moscow State University, 119992, Universitetskij prospekt 13, Moscow, Russia  Boris Safonov  Sternberg Astronomical Institute, Lomonosov Moscow State University, 119992, Universitetskij prospekt 13, Moscow, Russia  Jorge Lillo-Box Centro de Astrobioloía, CSIC-INTA, ESAC Campus, Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain  David Barrado Centro de Astrobioloía, CSIC-INTA, ESAC Campus, Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain  María Morales-Calderón Centro de Astrobioloía, CSIC-INTA, ESAC Campus, Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain

###### Abstract

The Transiting Exoplanet Survey Satellite (TESS) has discovered hundreds of
new worlds, with TESS planet candidates now outnumbering the total number of
confirmed planets from Kepler. Owing to differences in survey design, TESS
continues to provide planets that are better suited for subsequent follow-up
studies, including mass measurement through radial velocity (RV) observations,
compared to Kepler targets. In this work, we present the TESS-Keck Survey’s
(TKS) Mass Catalog: a uniform analysis of all TKS RV survey data which has
resulted in mass constraints for 126 planets and candidate signals. This
includes 58 mass measurements that have reached $\geq 5\sigma$ precision. We
confirm or validate 32 new planets from the TESS mission either by significant
mass measurement (15) or statistical validation (17), and we find no evidence
of likely false positives among our entire sample. This work also serves as a
data release for all previously unpublished TKS survey data, including 9,204
RV measurements and associated activity indicators over our three year survey.
We took the opportunity to assess the performance of our survey, and found
that we achieved many of our goals including measuring the mass of 38 small
($<4\mbox{R${}_{\earth}$}$) planets, nearly achieving the TESS mission’s basic
science requirement. In addition, we evaluated the performance of the
Automated Planet Finder (APF) as survey support and observed meaningful
constraints on system parameters due to its more uniform phase coverage.
Finally, we compared our measured masses to those predicted by commonly used
mass-radius relations and investigated evidence of systematic bias.

exoplanet, mass-radius

††journal: Astrophysical Journal Supplements††facilities: Keck:I(HIRES),
Lick:APF(Levy), TESS, Exoplanet Archive††software: RadVel (Fulton & Petigura,
2018), Lightkurve (Lightkurve Collaboration et al., 2018), triceratops
(Giacalone et al., 2021)

May 23, 2024

##  1 Introduction

The Kepler (Borucki et al., 2010) mission revealed a rich exoplanet landscape
showing that planets with short orbital periods (P$<$100 days) between the
size of Earth and Neptune (1–4 R⊕) are ubiquitous in our galaxy (Dressing &
Charbonneau, 2013; Fulton & Petigura, 2018). However, the stars Kepler
targeted are mostly too distant, and hence too faint, for precise RV follow
up. In contrast, the Transiting Exoplanet Survey Satellite (TESS, Ricker et
al., 2015) mission was designed to preferentially discover planets around
brighter, closer host stars that are highly amenable to follow up efforts,
including known planetary systems (Kane et al., 2009, 2021). The current era
of precise RV mass measurements is beginning to reveal structure within the
mass-radius distribution of small planets. For cool M dwarfs, Luque & Pallé
(2022) found that the dichotomy of sub-Neptunes and super-Earths may indeed be
a trichotomy composed of rocky, icy, and gaseous planets. While the connection
between these groups and specific formation scenarios is debated (Rogers et
al., 2023), resolving nuances in this region of mass-radius space is a
significant motivator to expand the sample of planets around FGK stars with
precisely determined masses.

Understanding the processes that result in the observed planet population
hinges not only on well-characterized planets, but also on the mitigation of
bias and non-astrophysical scatter in datasets. This is especially important
for the derivation of mass-radius relations. For example, publication bias
(Burt et al., 2018) can not only bias a mass-radius relation to higher masses
but may also artificially decrease intrinsic scatter. Additionally, uniform
analyses have the power to eliminate scatter that may be inherent in
heterogeneous data sets such as those compiled from various literature
sources. Previous derivations of mass-radius relations have found evidence for
more scatter in planet masses than can be described by measurement error alone
(Weiss & Marcy, 2014; Wolfgang et al., 2016). Some of this intrinsic scatter
arises from the diversity of exoplanet compositions, but some may also be due
to heterogeneous datasets. Mass-radius relations derived from homogeneous
samples have the potential to more clearly distinguish between scatter caused
by real compositional diversity as opposed to differences in analysis and
target selection (Teske et al., 2021).

The plethora of planets now accessible with ground-based spectrographs has
given rise to large collaborations that are able to pool many nights of
telescope time together to follow up these targets and amass RV time series
data. The TESS Follow-up Observing Program
effort111https://tess.mit.edu/followup/ is a global collaboration encompassing
many different efforts to confirm planet candidates including transit
recovery, high contrast imaging, and RV follow up. Within RV follow up, large
collaborations include the GAPS programme (Covino et al., 2013), the HARPS-N
Rocky Planet Search (Motalebi et al., 2015), the CARMENES search for
exoplanets around M dwarfs (Reiners et al., 2018), the Magellan-TESS survey
(Teske et al., 2021), and many others. Another major RV follow-up effort,
which is the focus of this work, is the TESS-Keck Survey (TKS).

TKS is an RV follow-up program that targeted TESS-discovered systems with
Keck/HIRES and APF/Levy. The main goals of TKS, as well as our target
selection function, are detailed in full by Chontos et al. (2022, hereafter
TKS0), with the primary goal being to measure 100 planet masses over a 3 year
time span. Our target selection
process222https://github.com/ashleychontos/sort-a-survey identified TESS
Objects of Interest (TOIs) that were valuable across both complementary and
competing science cases. This resulted in a final target list of 108
transiting planet candidates in 86 systems333Targets in this work are
sometimes referred to by their TKS ID which is the name used in the California
Planet Search queue system. For reference, stars in the Henry Draper catalog
are referred to by their numerical designation (e.g. HD 95072 $\rightarrow$
95072) while TOIs are given a short-hand reference (e.g. TOI–1776
$\rightarrow$ T001776) . While many TKS publications have focused on the
detailed characterization of individual systems, in this work we combines the
homogeneous stellar properties of MacDougall et al. (2023) with a uniform
analysis of all RV survey data to compile a catalog of planet masses,
eccentricities, and densities. This includes a reanalysis of RV data for
previously confirmed planets in addition to 32 unpublished TESS systems.

The paper is organized as follows. §2 describes our data collection for high
resolution imaging and RV. §3 details the algorithm we developed for
homogeneously derived masses for all planets in our sample and we expand upon
caveats to this algorithm in §4. In §5, we compare our measured masses with
those previously published in TKS and in the wider literature. In §6 we
discuss how well our survey met its original goals, assess the contribution of
APF to our survey, and in §7 we review the ability of commonly used mass-
radius relations to predict a planet’s mass.

##  2 Observations

###  2.1 Radial Velocities

All of our spectroscopic data used in this analysis were taken entirely by the
High Resolution Echelle Spectrometer (HIRES, Vogt et al., 1994) on the Keck-I
telescope at W. M. Keck Observatory, and the Levy Spectrometer located on the
Automated Planet Finder (APF, Vogt et al., 2014a) telescope. HIRES is an
echelle spectrometer with a resolving power of $\sim$67,000 depending on the
slit used and a wavelength range spanning from 374–970 nm. We extracted RVs
from the spectroscopic data (reduced using the standard procedure described in
Howard et al. 2010), using the iodine cell method outlined in Butler et al.
(1996). The APF is a robotic telescope operated at Lick Observatory (Vogt et
al., 2014b). The Levy spectrograph has a resolving power of 100,000, and also
utilizes the same iodine cell method to extract precise RVs as for HIRES. The
APF has the same wavelength span as HIRES; 374–970 nm.

The total survey includes 7,894 HIRES RVs taken over the course of 974 Keck
observing nights when including archival RVs. Narrowing to only HIRES RVs
taken during TKS observing programs, we collected 4,943 HIRES RVs over 301
observing nights. We also use 5,989 APF RVs taken over the course of 1,205 APF
observing nights. Again, narrowing to only observations taken during TKS-
affiliated observing semesters, we acquired 4,261 APF RVs over 710 observing
nights.

Observational baseline is a key component of RV surveys, as a long baseline
allows for improved sensitivity to long-period, non-transiting companions.
When utilizing archival HIRES RVs, our maximum survey baseline was 6,502 days,
and our minimum was 59 days. The average RV baseline of the survey was 1,427
days. A more detailed breakdown by instrument is visible in Table 1. In
addition, many of the stars in our survey have RVs from other instruments, but
for this work we do not include non-TKS data.

In general, the TKS survey was broken down into a number of different science
cases with different observation and cadence goals, and such science cases
were the primary drivers in our observing strategy. Rather than detail all of
the TKS science cases here, we refer the interested reader to Chontos et al.
(2022), which describes our strategies in detail.

Table 1: Observation Statistics Statistic | HIRES (w/ archival) | APF (w/ archival) | HIRES (TKS only) | APF (TKS only)
---|---|---|---|---
NRV | 7894 | 5989 | 4943 | 4261
Nights Observed | 974 | 1205 | 301 | 710
Longest Baseline (days) | 6502 | 3391 | 1076 | 1249
Shortest Baseline (days) | 59 | 0 | 59 | 0
Average Baseline (days) | 1427 | 965 | 828 | 745

###  2.2 High Resolution Imaging

High resolution imaging (HRI) is an important step in validating planet
candidates due to its ability to resolve additional stars not resolved by
Gaia. Visual binary companions, regardless of whether they are gravitationally
bound or not, can dilute the TESS lightcurve leading to underestimated planet
radii (Ciardi et al., 2015). In this section, we describe the observations
taken of the systems that are newly validated in this work and discuss the
presence of a companion to TOI-1443. Since many of our TOIs were observed by
multiple instruments, in Table 7 we provide a summary of the imaging
observations made.

####  2.2.1 Keck-NIRC2

NIRC2 is an adaptive optics enabled imaging camera on the on the 10 m Keck II
telescope. Narrow angle mode was used, providing a pixel scale of around 0.01
″px-1 and full field of view of about 10″. Observations were taken in either
the Br-$\gamma$, K, or K’ filters. Observations were taken using the natural
guide star AO system in the standard three-point dither pattern to avoid the
lower-left quadrant of the detector, which is typically noisier than the other
three quadrants. The dither pattern has a step size of 3″. Each dither
position was observed three times, with 0.5″ positional offsets between each
observation, for a total of nine frames.

####  2.2.2 Palomar-PHARO

PHARO is an adaptive optics enabled imaging camera on the 5.1 m Hale telescope
with a pixel scale of 0.025 ″px-1 and a full field of view of around 25″.
Observations were taken in the Br-$\gamma$ and acquired using the natural
guide star AO system P3K (Dekany et al., 2013) in the standard five-point
quincunx dither pattern with steps of 5″. Each dither position was observed
three times, with 0.5″ positional offsets between each observation, for a
total of 15 frames.

####  2.2.3 Shane-ShARCS

ShARCS is an adaptive optics enabled camera on the Shane 3 m telescope at Lick
Observatory (Kupke et al., 2012; Gavel et al., 2014; McGurk et al., 2014).
Observations were taken with the Shane adaptive optics system in natural guide
star mode in order to search for nearby, unresolved stellar companions. We
used a variety of filters including $K_{s}$ ($\lambda_{0}=2.150$ $\mu$m,
$\Delta\lambda=0.320$ $\mu$m) and $J$ ($\lambda_{0}=1.238$ $\mu$m,
$\Delta\lambda=0.271$ $\mu$m). Information about our observing strategy can be
found in Savel et al. (2020). We reduced the data using the publicly available
SImMER pipeline (Savel et al., 2022).444https://github.com/arjunsavel/SImMER.
Further information about these data can be found in Dressing et al. (in prep)
and on ExoFOP.

####  2.2.4 Gemini-NIRI

NIRI (Hodapp et al., 2003) is an apdative optics enabled imaging camera on the
Gemini North 8 m telescope. In each case we observed using the Br$\gamma$
filter centered on 2.166$\micron$, and collected 9 individual frames,
dithering the telescope in a grid-pattern between each frame. Integration
times for individual frames were calculated based on the stellar magnitude,
and were 4.4s, 6.6s and 4s respectively for TOI–1184, TOI–1443, and TOI–1451.
To process the data, we first constructed a sky background by median-combining
the dithered science frames. We then removed bad pixels, flat fielded, and
subtracted the sky background. Cleaned frames were aligned by fitting the
stellar PSF in each frame, and coadded. Sensitivity of each observation was
calculated as a function of radius by injecting fake companions and scaling
their background so they could be redetected at 5$\sigma$. For visual
companions identified in the Gemini-NIRI data, we calculated astrometry
relative to the host-star by fitting a Gaussian to each of the star and
companion, and then applying the pixel scale of 0.021″/pixel. We performed
aperture photometry on both the star and the visual companion in our reduced
images, using a small aperture around the position determined in the previous
section.

For each target, we reached contrast sensitivities of at least 5mag beyond
$\sim$300mas, and at least 7mag in the background limited regime beyond
$\sim$1″; images have a field of view of 26$\times$26″, though sensitivity is
reduced in the outermost $\sim$3″where fewer dithered images are being
combined.

Figure 1: Contrast curves for TOI-1443 from Gemini-NIRI (blue) and SAI Speckle
Polarimeter (black). The 1$\sigma$ error for the NIRI contrast curve is given
as the blue envelope. A companion is observed for TOI-1443 at $\sim$0.5″that
is not detected in Gaia DR3.

####  2.2.5 Gemini-’Alopkeke & Zorro

‘Alopeke and Zorro are high-resolution optical speckle instruments mounted on
the Gemini North and South 8 m telescopes respectively. ‘Alopeke and Zorro are
identical instruments which provide simultaneous speckle imaging in two bands,
usually operated using narrow-band filters centered at 562nm and 832
nm555https://www.gemini.edu/sciops/instruments/alopeke-zorro/. Speckle imaging
consists of obtaining many thousands of very short exposures (typically 60
msec/frame at Gemini) which are then combined and subjected to Fourier
analysis in our standard reduction pipeline (see Howell et al., 2011; Horch et
al., 2012). Output data products include a reconstructed image in each filter
and determination of robust 5$\sigma$ contrast limits on companion detections
in each bandpass. If a close (0.02-1.2″) companion source is discovered, its
position angle, separation, and flux ratio are reported. The instruments are
described in detail in Scott et al. (2021).

####  2.2.6 WIYN-NESSI

The NESSI speckle imager (Scott, 2019) is mounted on the 3.5 m WIYN telescope
at Kitt Peak. NESSI simultaneously acquires data in two bands centered at 562
nm and 832 nm using high speed electron-multiplying CCDs (EMCCDs). We
collected and reduced the data following the procedures described in Howell et
al. (2011). The resulting reconstructed images achieved contrast of
$\Delta\mathrm{mag}\sim 6$ at a separation of 1″ in the 832 nm band.

####  2.2.7 Speckle Polarimeter

The Speckle Polarimeter (Safonov et al., 2017) is mounted on the the 2.5 m
telescope at the Caucasian Observatory of Sternberg Astronomical Institute
(SAI) of Lomonosov Moscow State University. Electron Multiplying CCD Andor
iXon 897 was used as a detector. For each target we accumulated 4000 frames
with 30 ms exposure times. The detector has a pixel scale of $20.6$ mas
pixel-1, and the angular resolution was 89 mas. For all targets except
TOI–1443 we did not detect any stellar companions.

####  2.2.8 AstraLux

The AstraLux instrument (Hormuth et al., 2008) is mounted on the 2.2 m
telescope of the Calar Alto Observatory (Almería, Spain). AstraLux uses the
lucky-imaging technique, obtaining a large number of very short exposures
(shorter than the coherence time of the atmospheric turbulence) that are
subsequently selected and combined. The datacube is then processed by the
automatic observatory pipeline (Hormuth et al., 2008), which besides doing the
basic reduction of the individual frames, selects the 10% with the highest
Strehl ratio (Strehl, 1902) and combines them into a final high-spatial
resolution image. All images were obtained in the SDSSz bandpass (peak of the
instrument resolution) with an individual exposure time of 10 or 20 ms
(depending on the source and weather conditions) and a field-of-view windowed
to $6\times 6$ ″. This final image is used to compute the sensitivity limits
(also known as the contrast curve). Such limits are computed by using our own
developed astrasens package666https://github.com/jlillo/astrasens with the
procedure described in Lillo-Box et al. (2012, 2014).

####  2.2.9 A Companion to TOI–1443

The only target in our sample where a diluting star is seen is TOI-1443, which
was imaged with Gemini-NIRI and the SAI speckle polarimeter (Figure 1).
TOI–1443 was imaged with the speckle polarimeter in four epochs: 2020–12–26,
2022–06–03, 2023–09–23, 2023–09–29 in the Ic band. Each time the object was
resolved, the binarity parameters were determined by approximation of the
average power spectrum with the model of binary star Strakhov et al. (2023).
The separation and position angle of secondary companion for these epochs was
found to be $518\pm 6$ mas and $68.2^{\circ}\pm 0.4$, $531\pm 6$ mas and
$69.3^{\circ}\pm 0.3$, $537\pm 5$ mas and $68.6^{\circ}\pm 0.4$, $507\pm 4$
mas and $68.2^{\circ}\pm 0.4$. Total proper motion reported by Gaia DR3 for
TOI–1443 is 90.511 mas/yr. This would yield a total relative shift of 249.54
mas between first and last epoch, if the secondary companion was a background
star. We conclude that this binary is a gravitationally bound system. We
additionally note that, while orbital motion is statistically detected through
these observations, they are not sufficient to provide meaningful orbital
constraints.

From Monet et al. 2003, TOI–1443 has Ic = 9.75 giving the primary an V-Ic
color of 1.08 mag. Interpolating Table 5 of Pecaut & Mamajek 2013, this gives
an effective temperature around 5300 K (spectral type of K0V), consistent with
its spectroscopically derived parameters. The Speckle Polarimeter gives an
average magnitude difference between the components of $\Delta$Ic = 5.0 mag
while NIRI gives $\Delta$K = 3.64$\pm$0.01 mag. From these values we obtain a
K-Ic color of 2.47 mag for the secondary component. Again interpolating Table
5 of Pecaut & Mamajek 2013 provides an approximate effective temperature of
3100 K, consistent with an M4.5V spectral type. A $\Delta$Ic of 5.0 mag
results in $\sim$0.5% contamination, assuming the planet transits the primary.

We also observed a significant RV trend of $0.029\pm 0.0044$ m s-1 d-1. Using
ethraid (Van Zandt & Petigura, 2024)777https://github.com/jvanzand/ethraid, we
use the RV trend and the NIRI sensitivity curve to constrain the combinations
of mass and semi-major axis of an object that could be responsible for the
trend. We find that an M4.5V dwarf (M${}_{*}\sim 0.18$ M⊙) at the observed
angular separation is a plausible explanation for the observed trend in our
RVs lending additional support to a bound scenario.

##  3 Methods

In this section, we describe the analysis of our survey data. In an effort to
achieve homogeneity, we outline the standardized decision tree that informed
our RV fits. We also describe the uniform set of priors used. In the few
instances where RVs from Keck/HIRES and/or APF exist prior to the inception of
our survey, we do include those in this analysis. This decision is motivated
by a desire to release these data, and by the fact that the existence of RVs
on a given target was a favorable metric in our target selection efforts
(Chontos et al., 2022).

Figure 2: A flowchart of our algorithm for homogeneous determination of planet
masses.

###  3.1 Radial Velocity Fitting

A schematic of our methodology is shown in Figure 2. We searched for signals
in each RV data set using RVSearch (Rosenthal et al., 2021a), which uses an
iterative approach to fit candidate signals, as determined by False Alarm
Probability, FAP > 1%, and then compare against an N vs N-1 planet model. We
seeded the search with parameters of known, transiting planets in each system
taken from the TKS Systems Properties Catalog (MacDougall et al., 2023).

Once all candidate signals within the RV dataset are identified by RVSearch,
we begin our RV fit. Using RadVel (Fulton & Petigura, 2018), we adopt a top-
down approach whereby we assume a maximally complex RV model where all
parameters (see below) are initially included. Free parameters included
Keplerian signal parameters ($P_{i}$, $T_{0,i}$, $K_{i}$,
$\sqrt{e_{i}}\sin{(\omega_{i})}$, $\sqrt{e_{i}}\cos{(\omega_{i})}$) for all
known planets (transiting and non-transiting), and candidate signals, linear
($\dot{\gamma}$) and quadratic ($\ddot{\gamma}$) trend terms, and
offset/jitter terms ($\gamma$, $\sigma$) specific to each instrument.

We ran RadVel in the fitting basis described above and explored the posterior
parameter space using Markov-chain Monte Carlo (MCMC) sampling (emcee,
Foreman-Mackey et al., 2013). This basis reparametrizes e (eccentricity) and
$\omega$ (argument of periastron) into $\sqrt{e}\cos{(\omega)}$ and
$\sqrt{e}\sin{(\omega)}$ for better MCMC performance. The MCMC was run until
the chains were well-mixed; a G-R statistic less than 1.001 (Gelman & Rubin,
1992; Ford, 2006) and the number of independent samples was greater than 1000
for all free parameters for at least five consecutive checks. We then
determined which combination of model parameters was justified using the
Akaike Information Criterion (AIC) with the preferred model being the one with
the smallest AIC. In cases where the lowest model AIC values differed by $<2$,
the model with the fewest free parameters was selected. One exception is when
model selection rejects a signal of a known, transiting planet. In these cases
we instead accept the model with lowest AIC score that still includes all
transiting planets.

We aimed to uniformly derive mass estimates for as many planets as possible.
For systems with high planet multiplicity and/or especially active host stars,
our methodology may not return the best planet parameters. Nonetheless, the
primary goal of this analysis is the homogeneous derivation of masses, not
necessarily the best derivation of masses. Similarly, in cases where
additional data from other instruments exists, a more precise mass could be
determined. We discuss caveats to our uniform fits in §4 and compare our
masses to literature values in §5.1.

###  3.2 Selection of Priors

We implemented a homogeneous set of priors for every planet in the sample
detailed in Table 2. Parameters such as trend, curvature, and jitter were
given broad, uniform priors. For transiting planets, the priors applied to
their period and time of conjunction were Gaussian, with centers and widths
equal to the posteriors of the transit fits performed in MacDougall et al.
(2023). Non-transiting planets were given broad Jeffrey’s priors (Jeffreys,
1946) on their orbital period with the initial guess sourced from the RVsearch
results. These planets were also given a broad, uniform prior on time of
conjunction, with lower and upper bounds extending half of the orbital period.
All other free parameters, including K-amplitude, K, were unrestricted and
allow for negative values.

###  3.3 Gaussian Processes

A Gaussian process (GP) model can often be very effective at accounting for
stellar activity from RV datasets (e.g., Haywood et al., 2014; López-Morales
et al., 2016). GPs are flexible, however, and can overfit on sparse datasets
(e.g., Blunt et al., 2023). A GP is used on a TKS systems if (1) $\log
R^{\prime}_{HK}>$ -4.9, and (2) if Nobs $>$ 30\. The first condition is to
ensure that stellar activity modeling is indeed warranted, as $\log
R^{\prime}_{HK}$ values are found to positively correlate with increased
stellar activity (Wright, 2005; Isaacson & Fischer, 2010; Hillenbrand et al.,
2015). The second condition is intended to prevent overfitting while using a
GP.

We used the QuasiPeriodic GP kernel to model activity (Haywood et al., 2014;
López-Morales et al., 2016). The covariance between observations taken at
times $t_{i}$ and $t_{j}$ is given as

$\centering
C_{i,j}=\eta_{1}^{2}*exp(\frac{-|t_{i}-t_{j}|^{2}}{\eta_{2}^{2}}-\frac{\sin^{2}(\frac{\pi|t_{i}-t_{j}|}{\eta_{3}})}{2\eta_{4}^{2}}).\@add@centering$
(1)

An advantage of the QuasiPeriodic GP kernel is the interpretability of its
hyperparameters, as most correspond, at least approximately, with a physical
parameter. $\eta_{1}$ is the GP amplitude in m s-1, and corresponds to the
amplitude of the stellar variability. $\eta_{2}$ is the exponential decay
length, and approximately represents the lifetime of a stellar spot.
$\eta_{3}$ is the recurrence timescale, which is usually well represented by
the rotation period of a star. $\eta_{4}$ is the periodic scale length, which
varies from 0 to 1 and approximately controls how periodic the structure of
the GP signal is.

Similar to planet parameters, we strove for homogeneous priors on GP
hyperparameters (Table 2). The GP amplitude $\eta_{1}$ is not known a-priori,
and we adopt a broad Jeffreys prior. We also use a broad Jeffreys prior for
$\eta_{2}$, though we prevent the value from falling below the system rotation
period, $\eta_{3}$, as recommended by Kosiarek & Crossfield (2020). $\eta_{3}$
is informed by either a periodogram of the photometry or S-values. Finally, we
restrict $\eta_{4}$ using a Gaussian prior recommended by López-Morales et al.
(2016). This is to prevent overfitting with the GP, which can happen for small
values of $\eta_{4}$.

Even when a GP is included in our maximally complex initial fit, if the GP is
not favored in model comparison, it is not included in our final fit. The
fitted values for our GP hyperparameters are given in Table 6.

###  3.4 Derivation of Physical Parameters

The stellar and transit properties for this work are taken from MacDougall et
al. (2023). In summary, stellar spectroscopic properties ($T_{\text{{eff}}}$,
[Fe/H], $\log{(g)}$) were derived from HIRES spectra using SpecMatch
(Petigura, 2015; Yee et al., 2017) while M∗ and R∗ were obtained using
isoclassify (Huber et al., 2017; Berger et al., 2020, 2023) with the
spectroscopic parameters used to inform input priors. Similarly, the
transiting planet parameters are from the same study’s analysis of TESS
lightcurves. In MacDougall et al. (2023), stellar parameter uncertainties do
not account for systematic errors in model isochrones (Tayar et al., 2022) but
do provide a recommendation to inflate stellar parameter uncertainties. In the
following derivation of physical properties, we make the recommended
corrections.

We derive the parameters listed in Table 4 by multiplying the MCMC chains from
each fit. For the planet mass we use the equation:

$\centering\frac{\text{m}_{p}\sin{(i)}}{\text{M}_{J}}=\frac{\text{K}}{\text{K}_{0}}\sqrt{1-e^{2}}\left(\frac{\text{M}_{*}}{\text{M}_{\odot}}\right)^{2/3}\left(\frac{P}{1\text{yr}}\right)^{1/3}\@add@centering$
(2)

where $\text{K}_{0}$ = 28.4329$\text{m s}^{-1}$. The semi-major axis, $a$, is
calculated using Kepler’s 3rd law in the form:

$\centering
a=\left(\frac{P^{2}~{}G~{}\text{M}_{Total}}{4\pi^{2}}\right)^{1/3}\@add@centering$
(3)

The majority of the planets in our sample are transiting allowing us to derive
the true mass with knowledge of the planet’s inclination. We calculate the
inclination of the transiting planets using888The precise definition of impact
parameter includes a factor of $(1-e^{2})/(1+e\sin{\omega})$, but given that
transiting planets have near-zero $\cos{i}$ this factor usually has a
negligible contribution to the derived mass.:

$\centering b=\frac{a}{\text{R}_{*}}\cos{(i)}\@add@centering$ (4)

where $a$ is taken from Equation 3 and both R∗ and $b$ are from MacDougall et
al. (2023). For R∗, we assume Gaussian distributed uncertainties, however, the
posterior distribution for the impact parameter in transit analyses is
typically non-Gaussian. To reflect this, we use the MCMC chains from
MacDougall et al. (2023)999The chains for each transit fit are available at
https://github.com/mason-macdougall/tks_system_properties and use sklearn’s
Kernel Density Estimation function to construct the impact parameter’s
distribution. We sample the resulting distribution to obtain a chain of
samples for $b$ of equal length to those used in our RadVel analyses. The
chains for $b$, R∗, and $a$ are used to derive $i$. For each derived parameter
in Table 4 we list the median value with the 15.6% and 84.1% percentiles as
uncertainties.

Figure 3: Mass-radius diagram for the full TKS sample (blue) in comparison to
the all known exoplanets with a $\geq 3\sigma$ mass. Markers are scaled
according to the mass precision (size $\propto M/\sigma_{M}$) while triangles
represent 3 $\sigma$ upper limits. Points outlined in gold represent newly
confirmed and validated planets in our sample. The region outlined in black
represents the region of M-R space shown in more detail in Figure 4. Table 2:
Survey Priors

Parameter Name | Prior | Units | Description
---|---|---|---
Transiting Planets:
Porb | $\mathcal{N}^{a}(\mu_{M23}^{*},sd_{M23})$ | days | Period
Tc | $\mathcal{N}(\mu_{M23},sd_{M23})$ | BJD (days) | Time of Inferior Conjunction
$\sqrt{e}\cos\omega$ | $\mathcal{U}^{b}(-1,1)$ | … | Eccentricity Reparametrizationd
$\sqrt{e}\sin\omega$ | $\mathcal{U}(-1,1)$ | … | Eccentricity Reparametrization
K | $\mathcal{U}(-\infty,+\infty)$ | m s-1 | Velocity Semi-amplitude
Non-Transiting Planets:
Porb | $\mathcal{J}^{c}(1,\rm{ObservationBaseline})$ | days | Period
Tc | $\mathcal{U}(T_{c}-\frac{P_{orb}}{2},T_{c}+\frac{P_{orb}}{2})$ | BJD (days) | Time of Inferior Conjunction
$\sqrt{e}\cos\omega$ | $\mathcal{U}(-1,1)$ | … | Eccentricity Reparametrization
$\sqrt{e}\sin\omega$ | $\mathcal{U}(-1,1)$ | … | Eccentricity Reparametrization
K | $\mathcal{U}(-\infty,+\infty)$ | m s-1 | Velocity Semi-amplitude
Trend and Curvature:
$\dot{\gamma}$ | $\mathcal{U}(-\infty,+\infty)$ | m s-1 d-1 | Linear Trend
$\ddot{\gamma}$ | $\mathcal{U}(-\infty,+\infty)$ | m s-1 d-2 | Quadratic Curvature
GP Hyperparameters
$\eta_{1}$ | $\mathcal{J}(0.1,100)$ | m s-1 | GP Amplitude
$\eta_{2}$ | $\mathcal{J}(\eta_{3},10000)$ | days | Exponential Scale Length
$\eta_{3}$ | $\mathcal{N}(\mu_{GLS},sd_{GLS})$ | days | Periodic Term
$\eta_{4}$ | $\mathcal{N}(0.5,0.05)$ | … | Periodic Scale Length
Instrumental Parameters
$\gamma_{\rm{HIRES}}$ | $\mathcal{U}(-\infty,+\infty)$ | m s-1 | HIRES offset
$\gamma_{\rm{APF}}$ | $\mathcal{U}(-\infty,+\infty)$ | m s-1 | APF offset
$\sigma_{\rm{HIRES}}$ | $\mathcal{U}(0.0,+\infty)$ | m s-1 | Instrumental Jitter, HIRES
$\sigma_{\rm{APF}}$ | $\mathcal{U}(0.0,+\infty)$ | m s-1 | Instrumental Jitter, APF

aafootnotetext: $\mathcal{N}$ is a normal prior with $\mathcal{N}$(mean,
standard deviation)

bbfootnotetext: $\mathcal{U}$ is a uniform prior with
$\mathcal{U}$(lower,upper)

ccfootnotetext: $\mathcal{J}$ is a Jeffreys prior with
$\mathcal{J}$(lower,upper)

ddfootnotetext: Reparameterization of eccentricity is motivated by Anderson et
al. (2011) and Eastman et al. (2013). Here, $\omega$ is the argument of
periapsis of the star’s orbit in a left-handed coordinate system.

**footnotetext: $\mu_{M23}$ and $sd_{M23}$ refers to the mean and standard
deviation of the posterior taken from MacDougall et al. (2023).

##  4 Caveats To a Homogeneous RV Fit

We developed our fitting methodology to be applicable to most systems. However
there were some instances where we departed from the steps stated in §3. In
the interest of reproducibility, here we clarify decisions made for three
systems.

###  4.1 TOI–1444

TOI–1444 hosts a confirmed ultra-short period planet (b) at 0.47 days along
with a candidate non-transiting companion (c) at $\sim$ 16 days (Dai et al.,
2021a). Since the publication of this system, we collected 20 RVs in addition
to the existing 56; however, these additional observations did not
significantly increase in the detection significance for this signal.
Curiously, when both the ‘b’ and ‘c’ components are removed, RVSearch reveals
a strong peak at 89 days. When only removing the ‘b’ component, neither the 16
day or 89 day signals are confidently detected. According to our methodology,
the 89 day signal would be included as a candidate signal, but since its
detection is dependent on the removal of a signal that has yet to be
definitively confirmed, we decide to exclude it from our fits. 89 days is also
close to the 90 day alias seen in HIRES data (Rosenthal et al., 2021b).

###  4.2 TOI–1726

TOI–1726 is a young Sun-like star that hosts two super-Earths of comparable
size (Damasso et al., 2023) with a rotation period of $\sim$6.4 days that is
clearly seen in periodograms of both our RVs and our activity indicators. This
rotation period happens to be close to the orbital period of TOI–1726 b at 7.1
days which, combined with the low expected semi-amplitude for both planets,
motivated us to stop observing this target well before it hit its 100
observations quota. According to our methodology, we placed an informative
prior on the periodic component of the GP informed by the rotation period of
the star resulting in a mass constraint for the c planet of 17.3$\pm
9.9\mbox{M${}_{\earth}$}$ which is in agreement with the previous publication
of this system. However, we obtain a mass for the ‘b’ planet of $37\pm
9.6\mbox{M${}_{\earth}$}$ which is significantly higher than both the estimate
from Damasso et al. (2023) and the masses of all other sub-Neptunes of similar
size.101010Hadden & Lithwick (2014)’s transit timing analysis of Kepler
planets found sub-Neptunes comparable in mass to our estimate for TOI–1726 c.
However they are still consistent with the highest RV-determined sub-Neptune
mass within their uncertainties. Given the similarity between the rotation and
orbital period we suspect the GP might be over-fitting and possibly inflating
the RV semi-amplitude for the ‘b’ planet to some degree. We keep this result
in the catalog for completeness but caution accepting it at face value.

###  4.3 TOI–1759

TOI–1759 is an M0V dwarf with moderate levels of activity
($\log{R^{\prime}_{HK}}=-4.69$) that hosts a $\sim 3~{}\mbox{R${}_{\earth}$}$
planet (Espinoza et al., 2022; Martioli et al., 2022a). A stellar rotation
period of 35.65 days was identified through SPIRou polarized spectra. Though
this signal was not clearly seen in either the CARMENES or SPIRou RVs, it is
prominent in the HIRES RVs. This could be due to the different band passes of
the instruments and the expected spot temperatures. Additionally, this signal
is absent in both our $S_{HK}$ timeseries and the TESS photometry. Given our
methodology for building RV fits, this stellar signal would have been treated
as Keplerian with a blind GP applied. In this case, we chose to place a
Gaussian prior on the rotation term in the GP. While we are only able obtain
an upper limit for the mass, a reanalysis of this system using additional new
data sets is underway (Polanski et. al in prep).

Figure 4: The mass-radius space for planets below 4 R⊕ in the TKS sample.
Points are color-coded based on the planets’ equilibrium temperature while the
size is scaled according their mass significance: larger points having a more
precise mass measurement. Points outlined in gold are planets where their mass
constraints are newly published in this work. Blue contours represent a
Gaussian Kernel Density Estimate (KDE) of all known exoplanets around FGK
stars. We show the composition tracks for pure iron, an Earth-like
composition, and a 50/50 water-silicate mix (Zeng et al., 2019). In addition,
we include the photo-evaporation mass-radius distributions from Rogers et al.
(2023).

##  5 Results

We report mass estimates or upper limits for a total of 126 planets and
candidate signals across 86 planetary systems. 112 of these planets transit
their host star. In Figure 3 we show our full sample in comparison to all
known exoplanets with a significant mass measurement,111111From the NASA
Exoplanet Archive as of Sept. 2023 while in Figure 4 we show a detailed view
of the mass-radius space for small planets. In Table 5 we report values for
all fitted parameters while Table 4 lists the derived mass, density and semi-
major axis for each candidate along with the previously published mass
estimate (where available).

In this section we compare our results to previously published measurements,
present newly confirmed planetary systems, and statistically validate planets
that did not reach a mass detection significance threshold of 3$\sigma$ (see
§5.3).

###  5.1 Comparison with Confirmed Planets

Figure 5: A comparison of mass measurements for the 62 planets in our sample
for which masses had been published previously. Black stars indicate the
literature value comes from a TKS publication while blue circles indicate a
mass publication outside of our survey. The insets show the comparison for
objects exceeding 500M⊕(upper left) and a zoomed-in view of the dense region
between 5 and 14 M⊕(lower right).

Figure 5 compares our derived masses with literature masses for 62 planets in
33 previously confirmed TESS systems. For the majority of planets, we find
that our approach produces consistent results with most measurements within
1$\sigma$.

Of the 11 planets where we were only able to determine an upper limit, 5 of
them were in the TOI–1136 system where both multiplicity and stellar activity
conspired to require a much more comprehensive analysis (Dai et al., 2023,
Beard et al. in review). Although expected, this highlights the difficulty in
homogeneous mass measurements for multiplanet systems which is exacerbated by
high levels of activity. Many of our mass measurements with the largest
measurement error ($M/\sigma_{M}<3\sigma$) in Figure 5 come from such systems
(e.g TOI–561, HD 191939, TOI–1136). In two cases, HD 25463 c and HD 12572 c,
only an upper limit was obtained in both this work and in their dedicated TKS
publication despite a more in-depth joint RV-transit fit (Akana Murphy et al.,
2023a), suggesting these planets require additional data. Conversely, for 24
previously published planets, we are able to obtain a more precise mass
measurement than previous literature values, with an average improvement in
the mean mass uncertainty of 20%.

###  5.2 New RV Confirmation of TOIs

We achieve a mass significance of $\geq 3\sigma$ for 15 previously unconfirmed
candidate planets. Given the vetting performed on these targets in Chontos et
al. (2022), we confirm these as bona fide planets. While a periodogram
analysis of the RV data for each of these systems all reveal some amount of
power at the candidate’s period, 8 had a false alarm probability less than 1%.
For the remaining 7 systems, we take the additional step of statistically
validating them (§5.3). Individual descriptions of these newly confirmed
planetary systems are given in this section and our periodogram analyses and
RV fits can be found in Appendix A.

####  5.2.1 TOI–260 b

TOI–260 b (HIP 1532) is a super-Earth (1.47${}^{+0.12}_{-0.08}$ R⊕) orbiting a
K type star (4050$\pm 109$ K) with an orbital period of $\sim$13.5 days. Our
S-index timeseries contains a stellar activity signal at $\sim$37 days which
is also seen in our RVs; however, we note that this is significantly different
from the rotation period of $\sim$15 days obtained through TESS photometry by
Howard et al. (2021). An RV fit (Fig 11) with a GP included allows us to
modestly constrain the mass of the transiting planet to 3.3$\pm 1.1$ M⊕,
placing it between the Earth-like and 50/50 water world composition curves,
although it is consistent with an Earth-like composition within the mass
error. With an RV semi-amplitude of 1.3 m s-1, a mass measurement for this
planet lies at the extreme end of HIRES’ capabilities, and the system would
benefit from additional observations with higher precision spectrographs.

####  5.2.2 TOI–1173 b

TOI–1173 b is a Saturn-sized (9.02${}^{+0.16}_{-0.15}$ R⊕) planet orbiting a G
type star (5414$\pm 125$ K) with an orbital period of $\sim$7.1 days. We were
able to obtain a 7$\sigma$ mass constraint of $28.3\pm 4.0$ M⊕ (Fig 12) with
28 RVs, giving TOI–1173 b a bulk density of $0.21\pm 0.04$ $\text{g cm}^{-3}$
which is a third of that of Saturn. TOI-1173 has an estimated TSM of 182,
making it a valuable target for transmission spectroscopy.

####  5.2.3 TOI–1184 b

TOI–1184 b is a sub-Neptune (2.41${}^{+0.10}_{-0.14}$ R⊕) orbiting a K type
star (4616$\pm 104$ K) with an orbital period of $\sim$5.7 days. Our RV fits
(Fig 13) were able to constrain the planet mass to 6.8$\pm 2.3$ M⊕, making it
one of the least dense sub-Neptunes in the TKS sample.

####  5.2.4 TOI–1194 b

TOI–1194 b is a Saturn sized (8.72${}^{+0.16}_{-0.15}$ R⊕) planet orbiting a G
type star (5393$\pm 124$ K) with an orbital period of $\sim$2.3 days. We were
able to obtain a 30$\sigma$ mass constraint of 120$\pm 6$ M⊕ (Fig 14) with 32
RVs corresponding to a density slightly higher than that of Saturn. The
shorter period of TOI–1194 b places it at the upper edge of the Neptune desert
and its high density could be the result of past or ongoing atmospheric
erosion.

####  5.2.5 TOI–1248 b

TOI–1248 b is a sub-Saturn sized (6.81${}^{+0.12}_{-0.12}$ R⊕) planet orbiting
a K type star (5205$\pm 120$ K) with an orbital period of $\sim$4.4 days.
Similar to TOI–1173 b, our RVs (Fig 15) constrain the mass to 27.4$\pm 3.6$
M⊕, giving it a density of 0.47$\pm 0.1$ $\text{g cm}^{-3}$.

####  5.2.6 TOI–1279 b

TOI–1279 b is a sub-Neptune (2.66${}^{+0.14}_{-0.11}$ R⊕) orbiting a G type
star (5457$\pm 127$ K) with an orbital period of $\sim$9.6 days. We obtain a
4$\sigma$ mass constraint of 10.6$\pm 2.5$ M⊕ (Fig 16) placing this planet in
a region of the mass-radius diagram where many of the sub-Neptunes in our
sample are concentrated. We also measure a significant downward RV trend of
-0.0079$\pm$0.0020 m s-1 d-1 that does not correlate with activity indicators,
suggesting the possible presence of a long period companion. Additionally,
TOI–1279 b is the only single-TOI system where MacDougall et al. (2023) detect
significant transit timing variations.

####  5.2.7 TOI–1451 b

TOI–1451 b is a sub-Neptune (2.61${}^{+0.13}_{-0.10}$ R⊕) orbiting a G type
star (5800$\pm 139$ K) with an orbital period of $\sim$16.5 days. We measure a
5$\sigma$ mass of 15.2$\pm 2.8$ M⊕ (Fig 17) placing TOI–1451 b in a region of
the mass-radius diagram where many of the sub-Neptunes in our sample are
concentrated (see Fig. 4). Our periodogram analysis of the RVs after
subtraction of the transiting planet also reveals a strong peak at $\sim$90
days that is not seen in the activity indicators. We treat this signal with
caution since multiple $\sim$90 day aliases were seen in the California Legacy
Survey data (Rosenthal et al., 2021a). A periodogram of the window function
for all RV data reveals no strong peak near 90 days, however, when considering
the window function of only HIRES data, multiple peaks at integer fractions of
a year are seen, including at 90 days. Because of this, we consider the 90 day
signal to be an alias in the HIRES data.

####  5.2.8 TOI–1472 b

TOI–1472 b is a Neptune analog (4.16${}^{+0.16}_{-0.13}$ R⊕) orbiting a K type
star with a period of $\sim$6.4 days. Our RV fits constrain the mass to
16.5$\pm 5.1$ M⊕ (Fig. 18), giving it a mass also comparable to that of
Neptune.

####  5.2.9 HD 156141 b (TOI–1742 b)

HD 156141 b (TOI–1742 b) is a sub-Neptune (2.37${}^{+0.06}_{-0.05}$ R⊕)
orbiting a G type star (5814$\pm 137$ K) with an orbital period of $\sim$21.3
days. We obtain a nearly 5.5$\sigma$ mass constraint of 9.7$\pm 1.9$ M⊕ (Fig.
19), placing this planet in a region of the mass-radius diagram where many of
the sub-Neptunes in our sample are concentrated. Our RVs also constrain the
orbit of the planet to a modest eccentricity of 0.3$\pm 0.1$, making this the
second highest eccentricity small (R$<4\mbox{R${}_{\earth}$}$) planet in the
TKS sample after TOI–1751 b. We also detect a significant amount of curvature
in our RV time series that correlates with our activity indicators.

####  5.2.10 TOI–1753 b

TOI-1753 b is a sub-Neptune (2.34${}^{+0.08}_{-0.06}$ R⊕) orbiting a G type
star (5620$\pm 134$ K) with an orbital period of $\sim$5.3 days. Our RV fits
(Fig. 20) constrain the mass of the transiting planet to 16.6$\pm 5.2$ M⊕. It
falls in the relatively common population of sub-Neptunes, though its mass and
radius, consistent with either a large H/He envelope, or some water enrichment
(see Fig. 4). A more precise mass would be required to disambiguate different
planetary compositions.

####  5.2.11 TOI–1775 b

TOI–1775 b is a Saturn sized (8.05${}^{+0.14}_{-0.13}$ R⊕) planet orbiting a
late G/early K type star (5283$\pm 116$ K) with an orbital period of $\sim
10.2$ days. We are obtain over a 6$\sigma$ (Fig. 21) mass constraint of 96$\pm
15$ M⊕ , giving TOI–1775 b a mass consistent with that of Saturn.

####  5.2.12 HD 77946 b (TOI–1778 b)

HD 77946 b (TOI–1778 b) is a sub-Neptune
(2.9${}^{+0.19}_{-0.14}\mbox{R${}_{\earth}$}$) planet orbiting an F type star
(6000$\pm 147$ K) with an orbital period of $\sim$10.2 days. We obtain a
nearly 6.5$\sigma$ (Fig. 22) mass constraint of 10.9$\pm 1.7$ M⊕, placing this
planet in a region of the mass-radius diagram where many of the sub-Neptunes
in our sample are concentrated (see Fig. 4). Our RVs obtain a 3$\sigma$
constraint on the orbital eccentricity of 0.21$\pm 0.07$, also placing this
among highest eccentricity small (R$<4\mbox{R${}_{\earth}$}$) planets in the
TKS sample. We also find evidence of curvature in our RV time series which
does not correlate with our activity indices, suggesting the potential
presence of a long period companion.

####  5.2.13 TOI–1798 b & c

TOI–1798 is a K type star (5106$\pm 115$ K) that hosts two transiting planets,
the first being TOI–1798 b, a 2.76${}^{+0.13}_{-0.1}\mbox{R${}_{\earth}$}$
sub-Neptune with a period of $\sim$8.0 days. RV fits (Fig 23) constrain the
mass to 6.5$\pm 2$ M⊕.

The second planet is TOI–1798 c, a
1.4${}^{+0.06}_{-0.07}\mbox{R${}_{\earth}$}$ super-Earth with a period of
$\sim$0.44 days, making this another ultra-short period planet in the TKS
sample. We were able to obtain an 8$\sigma$ mass of 5.6$\pm 0.7$ M⊕ , giving
this planet a high density of 11.5$\pm 2.0$ $\text{g cm}^{-3}$. Dai et al.
(2021a) compiled all known USPs with a mass at the time and observed a
correlation between planet mass and disk surface density of solid material
($10^{\text{[Fe/H]}}\times M_{*}$), suggesting that planet mass increases with
the availability of planetary building blocks within 1 AU. Estimating the
surface density of solids available in the protoplanetary disk as
$10^{\text{[Fe/H]}}\times M_{*}$, we find TOI–1798 c is placed comfortably
within the population of USPs studied in Dai et al. (2021a). TOI–1798 is the
third system in the TKS sample to host an inner USP accompanied by a longer
period, sub-Neptune-mass, companion.

####  5.2.14 TOI–1823 b

TOI-1823 b is a sub-Saturn sized (7.54${}^{+0.33}_{-0.25}$ R⊕) planet orbiting
a K type star (4926$\pm 113$ K) with an orbital period of $\sim$38.8 days. We
obtain an 8$\sigma$ mass constraint of 67.4$\pm 8.2$ M⊕ (Fig. 24) with 32 RVs,
giving it a density slightly higher than that of Saturn.

###  5.3 Statistical Validation of TOIs

For the 30 systems that either did not reach $\geq 3\sigma$ mass significance
or did not have a clear and independent periodogram detection, we used
TRICERATOPS (Giacalone et al., 2021) to calculate the false positive and
nearby false positive probabilities (FPP/NFPP) and statistically validate
these targets. Statistical validation attempts to rule out astrophysical false
positive scenarios such as eclipsing binaries. While statistical validation
has been employed since the Kepler era (Borucki et al., 2012; Crossfield et
al., 2016) with packages such as BLENDER (Torres et al., 2004) and VESPA
(Morton, 2015), we opt to use TRICERATOPS since it is actively maintained and
designed specifically for use on TESS candidates (Morton et al., 2023).

We began by pulling the TOI’s short cadence lightcurve from the MAST database
using Lightkurve (Lightkurve Collaboration et al., 2018) and then use transit
information from the TKS Systems Properties catalog (MacDougall et al., 2023)
to phase fold the data. We bin the timeseries data down to 100 bins in the
interest of computational
speed.121212https://triceratops.readthedocs.io/en/latest/tutorials/example.html
The apertures used in the SPOC pipeline are pulled and used as input to
TRICERATOPS. High resolution imaging data is also incorporated; however,
TRICERATOPS can only run with a single HCI dataset at a time so we chose the
imaging set with the best available contrast (§2.2).

When calculating the NFPP, we remove any NFPP candidates flagged by the TESS
Input Catalog (TIC, Stassun et al., 2018) as ‘artifact’ to avoid biasing the
NFPP value. If the TIC is missing stellar parameters for NFPP candidates, we
use the candidate’s Bp-Rp color to estimate $T_{\text{eff}}$, $M_{*}$, and
$R_{*}$ from Pecaut & Mamajek (2013).

To obtain an accurate estimate of the FPP and NFPP, we run TRICERATOPS 20
times per candidate planet and report the average and standard deviation in
Table 3. Typically, for a planet to be validated it must satisfy FPP $<$ 0.015
and NFPP $<$ 0.001, In this work, we compute the average and standard
deviation of the FPP and NFPP from the 20 runs and require a candidate to
clear those thresholds to 3$\sigma$ to be considered validated. In total we
graduate 17 candidates to validated planets, while six targets, TOI–1436.01,
1438.01, 1438.02, 1269.02, 1716.01, 2114.01 did not reach the requisite
threshold for validation and remain planetary candidates. That said, 1436.01
and 2114.01 have low enough FPP/NFPP to be considered likely planets
(Giacalone et al., 2021). In all cases, the most likely scenario was a planet
transiting the target star followed by a planet transiting the primary star
but with unresolved bound companions or unresolved background stars. Two
targets, TOI–1279.01 and TOI–1742.01, have FPPs of 26% and 1.8%, respectively,
which would place them in the likely planet category. However, given the
significant mass obtained for both of these planets (4$\sigma$ and 5$\sigma$
constraints, respectively), we consider them confirmed. Additionally, the low
NFPP across all of our targets suggests that none of the planets we targeted
are likely to be nearby false positives.

Table 3: TRICERATOPS Results

TOI | No. Sectors | Imaging Used | FPP | NFPP | Disposition
---|---|---|---|---|---
260.01 | 2 | Keck/NIRC2 Br$\gamma$ | 0.0003$\pm$0.0003 | $<10^{-4}$ | Confirmed Planet
1184.01 | 26 | Gemini/NIRI K | 0.0001$\pm$0.0001 | $<10^{-4}$ | Confirmed Planet
1279.01* | 6 | Palomar/PHARO Br$\gamma$ | 0.2631$\pm$0.0855 | $<10^{-4}$ | Confirmed Planet
1472.01 | 3 | Keck/NIRC2 Br$\gamma$ | 0.0001$\pm$0.0001 | $<10^{-4}$ | Confirmed Planet
1742.01* | 26 | Keck/NIRC2 Br$\gamma$ | 0.0184$\pm$0.0792 | $<10^{-4}$ | Confirmed Planet
1753.01 | 26 | Palomar/PHARO Br$\gamma$ | 0.0005$\pm$0.0002 | $<10^{-4}$ | Confirmed Planet
1798.01 | 5 | Gemini/’Alopeke 832 nm | 0.0003$\pm$0.0001 | $<10^{-4}$ | Confirmed Planet
1180.01 | 11 | WIYN/NESSI 832 nm | 0.0035$\pm$0.0032 | $<10^{-4}$ | Validated Planet
1244.01 | 26 | Keck/NIRC2 K | $<10^{-4}$ | $<10^{-4}$ | Validated Planet
1249.01 | 7 | Gemini/’Alopeke 832 nm | 0.0083$\pm$0.0016 | 0.0007$\pm$0.0001 | Validated Planet
1269.01 | 29 | Palomar/PHARO Br$\gamma$ | 0.0013$\pm$0.0004 | $<10^{-4}$ | Validated Planet
1269.02 | 29 | Palomar/PHARO Br$\gamma$ | 0.0091$\pm$0.0012 | 0.0064$\pm$0.001 | Candidate
1438.01 | 26 | Gemini/’Alopeke 832 nm | 0.0047$\pm$0.0027 | 0.0016$\pm$0.0014 | Candidate
1691.01 | 5 | Gemini/’Alopeke 832 nm | 0.0001$\pm$0.0003 | $<10^{-4}$ | Validated Planet
1716.01 | 3 | Gemini/’Alopeke 832 nm | 0.0018$\pm$0.0002 | 0.001$\pm$0.0001 | Candidate
1723.01 | 3 | Shane/ShARCS K-short | 0.0006$\pm$0.0001 | $<10^{-4}$ | Validated Planet
1758.01 | 7 | Gemini/’Alopeke 832 nm | 0.0002$\pm$0.0002 | $<10^{-4}$ | Validated Planet
1794.01 | 5 | Palomar/PHARO H-continuous | 0.0002$\pm$0.0001 | $<10^{-4}$ | Validated Planet
1799.01 | 2 | Palomar/PHARO Br$\gamma$ | 0.001$\pm$0.0001 | $<10^{-4}$ | Validated Planet
2128.01 | 3 | Palomar/PHARO H-continuous | $<10^{-4}$ | $<10^{-4}$ | Validated Planet
1174.01 | 7 | Gemini/’Alopeke 832 nm | 0.0012$\pm$0.0004 | $<10^{-4}$ | Validated Planet
1347.02 | 27 | Keck/NIRC2 K’ | 0.0097$\pm$0.0007 | $<10^{-4}$ | Validated Planet
1436.01 | 6 | Keck/NIRC2 Br$\gamma$ | 0.063$\pm$0.002 | $<10^{-4}$ | Likely Planet
1438.02 | 26 | Gemini/’Alopeke 832 nm | 0.0067$\pm$0.0017 | 0.0045$\pm$0.0014 | Candidate
1443.01 | 21 | Gemini/NIRI K | 0.0003$\pm$0.0002 | $<10^{-4}$ | Validated Planet
1467.01 | 3 | Keck/NIRC2 K | $<10^{-4}$ | $<10^{-4}$ | Validated Planet
1669.01 | 8 | Gemini/’Alopeke 832 nm | 0.0021$\pm$0.0004 | $<10^{-4}$ | Validated Planet
1776.01 | 2 | Palomar/PHARO Br$\gamma$ | 0.0029$\pm$0.0003 | $<10^{-4}$ | Validated Planet
2088.01 | 28 | WIYN/NESSI 832 nm | 0.003$\pm$0.004 | $<10^{-4}$ | Validated Planet
2114.01 | 2 | Palomar/PHARO Br$\gamma$ | 0.019$\pm$0.022 | $<10^{-4}$ | Likely Planet

Note. — The break in the table separates TOIs with a $\geq 3\sigma$ mass
measurement (top) those with a $1-3\sigma$ mass measurement (middle) and those
with only an upper limit (bottom). Validated planets satisfy FPP $\leq$ 0.015
and NFPP $\leq$ 0.001. Likely planets satisfy FPP $\leq$ 0.5 and NFPP $\leq$
0.001. * Indicates a target that would be considered a likely planet but is
still confirmed through a significant mass measurement.

##  6 Survey Performance

The overarching goal of TKS was to measure precise (5$\sigma$) planet masses
(Chontos et al., 2022). We use this section to assess the success of TKS as
well as reflect on how well we were able to our reach observing quotas. We
additionally discuss how effective we were at allocating resources to each
individual science case. While detailed information on each science case (SC)
can be found in Chontos et al. (2022), we provide a brief description here:
SC1 is dedicated to measuring bulk compositions, SC2 is dedicated to probing
system architectures, SC3 is dedicated to measuring masses of possible future
atmospheric targets, and SC4 is dedicated to measuring masses of planets
orbiting evolved stars.

###  6.1 Observation and Cadence Goals

We intended to get a maximum of 60 RVs for the majority of targets in our
survey. However, three notable exceptions include: those designated as
interesting multi-planet systems (100 RVs), those orbiting particularly active
hosts (100 RVs), and those in the Distant Giant survey (15 RVs).Figure 6 shows
a breakdown of number of observations per target in the survey and Figure 7
(top) shows the number of observations broken down by science case.

Figure 6: The number of observations acquired for each target by instrument.
Vertical dashed lines are at the 15, 60, and 100 observation thresholds set
for the several TKS science cases. Figure 7: Top: The number of observations
obtained broken down by science case. The vertical dashed lines represent the
$N_{\text{obs}}$ targets set in Chontos et al. (2022). Bottom: The median time
difference between observations (cadence) for our targets broken down by
science case.

In total, 62 stars received more observations than their stated goal. Of the
22 targets that did not meet their observing quota, 14 of the targets had
surpassed a $\geq 5\sigma$ mass and therefore, no more observations were
needed. At the extreme ends, there were 8 stars that missed their stated goal
of observations by greater than 40 observations. TOI–1136 is an activity
target, which was intended to get 100 observations. Instead, we opted to pool
all the time allocated to the stellar activity case (Technical Outcomes B; TB)
into this high interest target, and so we got 157 total observations. Out of
86 TOIs, only 3 were dropped131313Targets were dropped for various reasons
including higher than expected rotational broadening and stellar rotation
periods that coincided with planet orbital periods.: HD 63433 (TOI–1726,
§4.2), TOI–2045, and TOI–2114. Other targets, HD 63935 (TOI–509) and HD 235088
(TOI–1430), received more than 100 observations, despite being initially
designated 60, due to increased interest in the target: HD 63935 later
presented a second transiting planet and HD 235088 was a high priority
atmospheres target which displayed increased stellar activity.

To determine our attained cadence, we computed the time difference for every
observation of a given target (eliminating differences less than 0.85 days to
avoid intra-night cadence), and took the median time difference. In Figure 7
(bottom) we break down the observational cadence of targets by their SC. Note
that many targets are represented in multiple science cases. We find that the
Bulk Compositions, Atmospheres, and Evolved Hosts have median cadences between
3 and 4 days, while the System Architectures saw a spread of cadences. The 3rd
panel from the bottom of the lower plot in Figure 7 shows the lower RV cadence
required by the Distant Giants program ($\sim$30 days between observations)
which is part of the Architectures SC. The distribution of cadences achieved
for different science cases shows what is possible with a multi-year RV survey
and may be used in simulating observations for future TKS-like programs.

###  6.2 Mass Significance Achieved

It is similarly straight-forward to assess our performance of measured mass
significance. We measure at least a $5\sigma$ mass for 58 planets. This
increases to 77 planets for $\geq 3\sigma$ masses; see Figure 8 for a
histogram of mass significances of our survey. Breaking this down a bit
further, if we filter by planets with masses below 30 $M_{\oplus}$, then we
have measured 30 planets to $5\sigma$ mass or better and 44 planets to
$3\sigma$ mass. Through these numbers, given the over-arching goal of TKS of
measuring many precise planet masses, we believe our survey has been very
successful.

We can go further by acknowledging that our survey was driven by some science
cases that either were not interested in the transiting TOIs (Distant Giants,
SC2A) or intentionally made it challenging to measure a precise mass (Stellar
Activity, TB). In Figure 8 we highlight this group of targets and find that
many of our "under-performing" targets are in either of these categories. For
TOIs with radii $<4~{}\mbox{R${}_{\earth}$}$, we were able to reach at least a
3$\sigma$ mass for 38 of them. To put this number in context, the baseline
science requirement of the TESS Follow-up Program (TFOP) was to measure masses
for 50 TESS-discovered planets less than 4 R⊕
radii141414https://tess.mit.edu/followup/. Our survey alone was nearly able to
achieve this goal.

Figure 8: A histogram of the mass significance of each planet in our sample
(blue). We highlight TOIs that were part of either the Distant Giants (SC2A)
or Stellar Activity (TB) science cases, i.e programs where the transiting
planet was not of primary interest, in the light blue, hashed histogram.

###  6.3 APF as Survey Support

The use of the Automated Planet Finder in our survey was intended to provide
additional RVs to bright (V <10) targets. To that end, we conducted
complementary APF observations of 28 TOIs, which account for nearly half the
RV measurements presented in this work. In order to assess APF’s contribution
to the goals of the survey, we select a subset of the 28 TOIs, and re-analyze
these systems excluding APF data. This subset includes massive targets for
which a 5$\sigma$ mass was obtained without reaching the requisite 60
observations, targets that had their observations halted at 60 HIRES data
points, and targets that received considerable attention from APF, making up
$\sim$2/3 of their datasets.

A straightforward test of APF’s contribution to the survey is its effect on
mass precision. In Figure 9 we show the mass constraints for the TOIs
reanalyzed without APF data. Masses measured from the full RV dataset were
generally larger than those obtained with only HIRES data, though the
difference is often statistically insignificant. For two systems, TOI–1710 b
and HIP97166 c, APF had a significant impact on the mass significance
achieved. With TOI–1710 b, a 3$\sigma$ mass was only obtained due to APF RVs,
while without APF the non-transiting HIP97166 c would not have been detected
in a periodogram of HIRES-only data. In most cases, targets saw slight
reductions in their mass error after the inclusion of APF RVs.

For the magnitude range of these stars (V$\sim$8.5-11), APF is a comparably
lower precision instrument, with average per-datum uncertainties being $\sim$2
times greater than the RV errors attained with HIRES. This means that mass
constraints will generally be dominated by HIRES data. However, APF’s
contribution should not be assessed on mass precision alone. The higher
cadence of APF observations (Table 1) allowed for more uniform phase coverage,
and for HD 332231 b, HIP 97166 b, and HD 156141 b this resulted in
significantly improved constraints on the eccentricity of these planets, with
all three cases seeing a reduction in the eccentricity uncertainty by a factor
of two.

Figure 9: Comparisons of the mass constraints for a sample of systems observed
with both HIRES and APF. Blue errorbars denote the mass obtained with both
datasets while black is without APF data. Generally, APF contributed only
slightly to the mass significance for each system, with the exception of
TOI–1710 b and HIP97166 c.

TOI–1736, HD 146757, and HD 191939 are also systems that benefited greatly
from the inclusion of APF data. In TOI–1736’s case we were able to pick up the
acceleration of the system due to an outer companion through the initial 60
observations allocated to the single-TOI system. Additional observations made
with APF were able to extend the baseline and critically catch two passages of
the companion through periastron (Akana Murphy et al., 2023a, Figure 25). APF
provided continual cadence, which wasn’t feasible with HIRES, resulting strong
constraints on both the orbital period and orbital eccentricity of TOI–1736
b’s companion.

HD 146757 (Desai et al., 2024) benefited from APF data through the
identification of an alias in the HIRES data. This case highlights APF’s
strength as a sanity check when searching for long period, massive companions
with limited primary survey instrument data.

Finally, APF observations of HD 191939 during March through May 2020 (22
observations), at a time when few other observatories were taking data due to
COVID-19 shutdowns, were crucial for early detection of planet e, the 101 day
Saturn-mass planet (Lubin et al., 2022). Without these observations, the
signal may not have been recognized until much later, and possibly at an
aliased period. Subsequent APF data continued to fill the phase space of the
companion at a cadence higher than would have been possible with HIRES alone.
HD 146757 benefited from APF data through the identification of an alias in
the HIRES data.

APF’s contribution to the goals of TKS should not be understated. Our
understanding of the architecture of exoplanet systems hinges on both a high
degree of phase coverage to determine the eccentricity, and long baselines to
detect companions. For surveys with limited time allocations, these criteria
create opposing interests. Supplementing the observations of the primary
survey instrument with those made with instruments with less demand not only
helps to allocate more time to targets that require a greater density of
higher precision data, but also serves to extend the scientific productivity
of previous generation instruments. Future TKS-like surveys should seriously
consider using APF-like instruments to extend their observational baseline and
obtain denser phase coverage for eccentric planets. Additionally, support
instruments can also be used to conduct observations ahead of the primary
survey to identify systems that may be more interesting to certain science
cases (e.g. Distant Giants) than would be expected based on the presence of a
transiting planet alone.

##  7 Expected vs. Measured Masses

In Chontos et al. (2022), the expected RV semi-amplitude for each planet in
our sample was calculated using theoretical masses derived from mass-radius
relations. The relations used were Weiss & Marcy (2014) (WM14) for planets
with R < $4\mbox{R${}_{\earth}$}$ and Chen & Kipping (2017) (CK17) for planets
with $4\leq$ R $<11.3~{}\mbox{R${}_{\earth}$}$, both of which are empirically
derived. Figure 10 shows the masses we measure compared to their expected
values, with the error in the predicted mass being propagated from the radius
uncertainty. It can immediately be seen that across the mass range sampled
there is significant scatter around the one-to-one mass comparison line. This
scatter is not surprising: we should not expect simple power law mass-radius
relationships to be able to capture the compositional diversity of planets at
a given radius.

Deriving a new mass-radius relation from the TKS sample is beyond the scope of
this paper: we are using a limited sample of planets and not using all the RV
data available for these systems. But, here we examine how our measured masses
compare to what was predicted by these commonly used relations. We restrict
this discussion to planets below $11.3~{}\mbox{R${}_{\earth}$}$ since beyond
this threshold the theoretical mass was assumed to be a Jupiter mass.

###  7.1 Weiss and Marcy 2014

In their analysis, WM14 report an RMS scatter of 2.7 M⊕ and 4.3 M⊕ for planets
with R < $1.5~{}\mbox{R${}_{\earth}$}$ and $1.5\leq$ R
$<4~{}\mbox{R${}_{\earth}$}$, respectively, and $\chi^{2}$ values that cannot
be explained by mass measurement error alone. For the TKS sample, we find the
RMS scatter to be comparable: 1.2 M⊕ and 5.3 M⊕ for the same radius bins
(noting that our sample contains far fewer planets with R <
$1.5~{}\mbox{R${}_{\earth}$}$).

We then check if the WM14 M-R relation appropriately predicted the planet
masses, i.e. if the mass residual is centered around zero. For planets with
$1.5\leq$ R $<4~{}\mbox{R${}_{\earth}$}$, we find that a slight bias towards
under-predicted masses of $\sim 10$% while masses predicted from WM14 for the
smallest planets (R < $1.5~{}\mbox{R${}_{\earth}$}$) are in agreement with
what we measure from RVs. Exploring this further, we also recalculate mass
predictions using the modified version of WM14 that only includes planet
masses derived through RVs (as opposed to masses derived from RVs and transit
timing variations) and find that this largely mitigates the difference. This
suggests that the WM14 M-R relations, which were based primarily on Kepler
planets, may still be relied on to approximate the masses of planets coming
from TESS.

###  7.2 Chen and Kipping 2017

For planets with masses predicted from CK17 ($4\leq$ R
$<11.3~{}\mbox{R${}_{\earth}$}$) we report a higher RMS scatter of 32 M⊕ , but
also find this M-R relation produces the largest mass discrepancies, with an
average percent difference of 24%. Considering planets in this category had an
average measurement uncertainty of $11\%$ this represents an appreciable
difference. We also use the complete CK17 M-R relation to include planets
below $4~{}\mbox{R${}_{\earth}$}$ to check if this underestimation persists
for smaller worlds. This extends the Neptunian relation down to $\sim$1.24 R⊕
at which point it transitions to the Terran world relation. The predicted
masses from these relations show a percentage difference comparable to the
RV+TTV WM14 relation with the exception that this underestimation in mass is
more prevalent for the smallest planets. Below 1.5 R⊕, the mean percentage
difference increases to 28%, although we note that we have few planets in this
radius space and the average measurement uncertainty for these planets is 37%.

Figure 10: Left: A comparison of RV-measured masses to those predicted by the
empirical mass-radius relations Weiss & Marcy 2014 and Chen & Kipping 2017.
Blue points highlight planets that achieved a 5$\sigma$ mass significance
while the unfilled point represent the full sample. Right: The mass residual
(measured minus predicted) as a function of stellar and planetary parameters
(from top): RV semi-amplitude, planetary insolation flux, stellar mass, and
stellar metallicity. Pearson and Spearman correlation coefficients are given
for both the 5$\sigma$ sample and the full sample (in brackets).

###  7.3 Comparison to Non-TKS TESS Planets

We also perform a similar analysis for both M-R relations with the 169 TESS-
discovered exoplanets with a mass measurement151515From the NASA Exoplanet
Archive as of Sept. 2023. For WM14, we find a similar RMS scatter and, again,
a slight positive bias in the mass residual that disappears once the RV-only
relation is used.

With CK17, the underestimation of mass persists for the greater TESS sample.
Between 1.5 and 4 R⊕, the percent difference nearly doubles from 13% in just
the TKS sample to 20% for all TESS-discovered planets. Beyond 4 R⊕ , the
difference is comparable to the TKS sample at 27% suggesting that on average
CK17 underestimates planet masses by around a quarter and, in extreme cases,
by one half. However, we do note that below R $\sim
1.5~{}\mbox{R${}_{\earth}$}$, the mass residual reduces to 0.5 M⊕ for the
entire TESS-discovered sample. In contrast to WM14, CK17 has fewer “Neptunian”
worlds with the bulk of their sample having radii larger than $\sim
10~{}\mbox{R${}_{\earth}$}$. Therefore, this sample may not be appropriately
describing the lower mass population of planets, which comprises the majority
of worlds discovered to date.

###  7.4 Sources of M-R Relation Bias and Implications

Empirical M-R relations tend to rely on planets that are well-characterized in
both radius and mass space. This is especially true for CK17 who instituted a
3$\sigma$ mass significance threshold for their sample thereby not taking into
account selection effects or survey bias. Historically, more massive planets
have been easier to reach a high mass significance, and subsequent M-R
relations based on these samples may be biased to higher masses (known as
publication bias, Burt et al., 2018; Montet, 2018).

Comparing measured masses to their predicted values, we see the opposite trend
in parts of the TKS sample. Restricting ourselves to planets that reached a
$5\sigma$ mass (blue points in Fig. 5), we see that they are mainly the higher
mass planets for a given radius bin showing that M-R relations based on “well-
characterized” samples will indeed be biased towards higher mass. Weiss &
Marcy (2014) mitigated this bias by allowing for “negative” masses. It is
possible that if we were able to obtain greater mass significance on the
remaining under-performing planets, the average mass residual for the well-
characterized sample would move towards zero for the WM14 relation.

We may also expect the affect of publication bias to grow with decreasing RV
semi-amplitude as the noise floor of the instrument is approached. The right
panel of Figure 5 shows the mass residual of our sample as a function of
select planetary and stellar parameters. Interestingly, the mass residual
increases with larger RV semi-amplitude. HIRES is more than capable of
measuring semi-amplitudes above 5 m s-1 and planet masses in this range,
primarily predicted with CK17, should not be affected by a stopping criteria
based on mass significance. This implies that the CK17 M-R relation, at least
for planets between 1.5 and $\sim 11$ R⊕ , is not necessarily affected by
publication bias.

Another explanation is that the CK17 relations may simply be outdated. The
number of planets below 100 M⊕ has doubled since CK17’s study providing a far
more diverse data set from which to derive relationships between planet
properties. The vast majority of CK17’s sample were Jovian worlds with few
planets between 1 and 10 R⊕. A consequence of this, perhaps resulting from the
3$\sigma$ threshold criteria, is that the transition point between Terran and
Neptunian worlds is placed at 2 M⊕. In a recent reassessment of the M-R
relation, Baron et al. 2023 find that a transition nearer to $\sim 8$M⊕ more
appropriately describes the current sample of exoplanets. A higher mass
transition point results in a steeper M-R slope predicting higher masses for a
given radius. While Baron et al. 2023 also institute a quality cut on planet
mass and radius, their analysis still benefits from the significant increase
in well-characterized small planets.

Similarly, Edmondson et al. 2023 also find discrepancies between measurements
and CK17’s predictions. When used to predict planetary radius, a scenario that
will become increasingly important with the discovery of more non-transiting
planets, CK17 tends to overestimate planet radius in agreement with our
underestimate in mass.

M-R relations serve an important role in not only helping us to understand the
population of exoplanets we are presented with today but also for highlighting
targets that are particularly valuable for future follow up. The transit
spectroscopy metric (TSM, Kempton et al., 2018) estimates the expected signal-
to-noise ratio of an atmosphere signal obtained with JWST, and it depends on
the mass of the planet. Studies that use M-R relations to calculate the TSM
can be crucial for bringing planets with high potential to be well-
characterized to the forefront (Hord et al., 2023). However, care should be
employed with which M-R relations to use, and these empirical trends should
not be treated as a substitute for obtaining actual mass measurements. In
particular, TSMs calculated with masses predicted from CK17 may be higher than
expected, especially for planets larger than $\sim
1.5~{}\mbox{R${}_{\earth}$}$, producing exaggerated scale heights and
overestimated TSM values.

##  8 Conclusions

In this work we present a uniform analysis of 9,204 RV measurements taken as
part of the TESS-Keck Survey. Ultimately, we obtain masses or mass upper
limits on a total of 112 transiting and 15 non-transiting planets marking the
culmination of 3 years of observations from Keck/HIRES and the Automated
Planet Finder. We conclude with our results and main findings:

  * •

The TESS-Keck Survey has generated a wealth of RV data that, with this paper,
is now public (§2.1). This includes 5,110 Keck/HIRES RVs and activity
indicators in addition to 4,534 RVs from the Automated Planet Finder covering
an average baseline of nearly 4 years (inclusive of archival data).

  * •

We uniformly fit all the data in our survey (§3) to produce the largest
homogeneously analyzed RV dataset of TESS-discovered planets to date. We also
incorporate updated stellar and planetary parameters from the TKS System
Properties Catalog (MacDougall et al., 2023).

  * •

We confirm or validate, through RV measurements and statistical validation, 32
new planets of varying size, adding to the many previously published systems
in our survey (§5.2 & 5.3). This ensures that future mass-radius relations
derived with the TKS sample can incorporate mass upper limits on bona fide
planets.

  * •

We assess the performance of our survey (§6) and find that we were able to
achieve our observing goals (Chontos et al., 2022) for the majority of our
targets. In total, we were able to achieve a $\geq 5\sigma$ mass significance
for 58 planets in our sample, increasing to 77 planets at $\geq 3\sigma$
significance. We measured masses for 38 small planets below 4 R⊕to 3$\sigma$,
nearly achieving the TESS Follow-up Program’s base science requirement of 50
small planets with masses in a single survey.

  * •

We gauged the benefit of using the Automated Planet Finder as survey support
(§6.3). APF data played a crucial role in filling out the phase space for many
planets. This resulted in longer baselines for these systems, more precise
constraints in the eccentricity of 3 TOIs, and the identification of an
observing alias that would have been mistaken as a distant companion.

  * •

We compare our masses to those predicted using empirical mass-radius relations
(§7). We find that the Weiss & Marcy (2014) mass-radius relationship under-
predicts the planet masses when compared to our data set. However this
discrepancy largely disappears when using the version of their MR relation
that excludes masses derived from TTVs. Similarly, masses from Chen & Kipping
(2017) seem to be underestimated by factors of 1/4 to 1/2 compared to our
measurements suggesting this mass-radius relation may be outdated and is not
able to accurately describe the planet population we observe today.

The derived masses for our sample can be found in Table 4 and the fitted
parameters for each system in Table 5. This work represents another set of
uniformly analyzed planet masses for TESS-discovered planets, making this the
second work to do so (Teske et al., 2021). Our survey contributes to the
legacy of HIRES as a prolific instrument for planet detection and mass
measurement as we enter an era of sub-m/s RV precision pushing down to smaller
planet masses and longer orbital periods.

Table 4: Masses and Derived Parameters  TOI | TKS ID | Mass | Mass Provenance | Density | a | Literature Mass | Reference
---|---|---|---|---|---|---|---
|  | (M⊕) |  | ($\text{g cm}^{-3}$) | (AU) | (M⊕) |
260.01 | HIP1532 | $3.3^{+1.1}_{-1.0}$ | Mass | $5.6^{+2.02}_{-2.83}$ | $0.091^{+0.002}_{-0.002}$ | - | -
266.01 | HIP8152 | $8.9^{+1.7}_{-1.7}$ | Mass | $2.97^{+0.81}_{-1.08}$ | $0.093^{+0.002}_{-0.002}$ | $7.8^{+1.8}_{-1.8}$ |  Akana Murphy et al. (2023b)*
266.02 | HIP8152 | $10.7^{+2.1}_{-2.2}$ | Mass | $3.63^{+1.02}_{-1.38}$ | $0.139^{+0.003}_{-0.002}$ | $9.4^{+2.2}_{-2.2}$ |  Akana Murphy et al. (2023b)*
329.01 | T000329 | $40.4^{+3.8}_{-3.7}$ | Mass | $1.84^{+0.41}_{-0.55}$ | $0.0638^{+0.0012}_{-0.0013}$ | $40.7^{+3.7}_{-3.6}$ |  Chontos et al. (2024)*
465.01 | WASP156 | $41.8^{+2.9}_{-2.9}$ | Mass | $1.05^{+0.18}_{-0.23}$ | $0.0458^{+0.0008}_{-0.0009}$ | $40.7^{+3.2}_{-2.9}$ | Demangeon et al. (2018)
469.01 | 42813 | $5.9^{+2.0}_{-2.0}$ | Mass | $0.8^{+0.29}_{-0.35}$ | $0.11^{+0.002}_{-0.002}$ | $5.8^{+2.4}_{-2.4}$ |  Akana Murphy et al. (2023b)*
480.01 | 39688 | $20.8^{+4.4}_{-4.2}$ | Mass | $4.91^{+1.3}_{-1.65}$ | $0.077^{+0.001}_{-0.001}$ | $15.8^{+2.2}_{-2.1}$ |  Chontos et al. (2024)*
509.01 | 63935 | $10.5^{+1.6}_{-1.5}$ | Mass | $2.32^{+0.5}_{-0.65}$ | $0.083^{+0.002}_{-0.002}$ | $10.8^{+1.8}_{-1.8}$ |  Scarsdale et al. (2021)*
509.02 | 63935 | $11.1^{+2.0}_{-1.9}$ | Mass | $2.11^{+0.49}_{-0.62}$ | $0.148^{+0.003}_{-0.003}$ | $11.1^{+2.4}_{-2.4}$ |  Scarsdale et al. (2021)*
554.01 | 25463 | $8.7^{+2.7}_{-2.6}$ | Mass | $2.87^{+0.95}_{-1.2}$ | $0.076^{+0.001}_{-0.001}$ | $8.5^{+3.1}_{-3.1}$ |  Akana Murphy et al. (2023b)*
554.02 | 25463 | $4.3^{+1.9}_{-1.9}$ | Mass | $9.09^{+4.32}_{-5.87}$ | $0.0443^{+0.0008}_{-0.0008}$ | $<4.1$ |  Akana Murphy et al. (2023b)*
561.01 | T000561 | $3.0^{+0.45}_{-0.45}$ | Mass | $5.3^{+1.2}_{-1.51}$ | $0.0104^{+0.0002}_{-0.0002}$ | $2.24^{+0.2}_{-0.2}$ |  Brinkman et al. (2023)*
561.02 | T000561 | $6.9^{+1.3}_{-1.2}$ | Mass | $1.5^{+0.39}_{-0.51}$ | $0.087^{+0.002}_{-0.002}$ | $6.6^{+0.73}_{-0.73}$ |  Brinkman et al. (2023)*
561.03 | T000561 | $11.0^{+1.8}_{-1.8}$ | Mass | $2.97^{+0.7}_{-0.91}$ | $0.156^{+0.003}_{-0.003}$ | $12.15^{+1.1}_{-1.1}$ |  Brinkman et al. (2023)*
561.04 | T000561 | $8.2^{+3.0}_{-3.2}$ | Mass | - | $0.327^{+0.008}_{-0.008}$ | $13.6^{+1.4}_{-1.4}$ |  Brinkman et al. (2023)*
669.01 | T000669 | $10.0^{+1.4}_{-1.4}$ | Mass | $3.17^{+0.73}_{-0.95}$ | $0.048^{+0.001}_{-0.001}$ | $9.8^{+1.5}_{-1.5}$ |  Akana Murphy et al. (2023b)*
849.01 | T000849 | $41.8^{+2.5}_{-2.4}$ | Mass | $5.6^{+0.76}_{-0.92}$ | $0.0155^{+0.0003}_{-0.0003}$ | $39.09^{+2.66}_{-2.55}$ | Armstrong et al. (2020)
1136.01 | T001136 | $7.6^{+5.1}_{-5.0}$ | Mass | $1.93^{+1.29}_{-1.44}$ | $0.067^{+0.001}_{-0.001}$ | $6.0^{+1.3}_{-1.7}$ |  Beard et al. (2024)*
1136.02 | T001136 | $12.3^{+6.8}_{-7.0}$ | Mass | $0.68^{+0.38}_{-0.43}$ | $0.107^{+0.002}_{-0.002}$ | $8.35^{+1.8}_{-1.6}$ |  Beard et al. (2024)*
1136.03 | T001136 | $<24.0$ | Mass | $<8.0$ | $0.14^{+0.002}_{-0.002}$ | $6.07^{+1.09}_{-1.01}$ |  Beard et al. (2024)*
1136.04 | T001136 | $<32.0$ | Mass | $<3.0$ | $0.175^{+0.003}_{-0.003}$ | $9.7^{+3.9}_{-3.7}$ |  Beard et al. (2024)*
1136.05 | T001136 | $<31.0$ | Mass | $<25.0$ | $0.0514^{+0.0009}_{-0.0009}$ | $3.5^{+0.8}_{-0.7}$ |  Beard et al. (2024)*
1136.06 | T001136 | $12.2^{+9.3}_{-9.6}$ | Mass | $4.11^{+3.18}_{-3.37}$ | $0.23^{+0.004}_{-0.004}$ | $5.6^{+4.1}_{-3.2}$ |  Beard et al. (2024)*
1173.01 | T001173 | $28.3^{+4.1}_{-4.0}$ | Mass | $0.21^{+0.04}_{-0.05}$ | $0.071^{+0.001}_{-0.001}$ | - | -
1174.01 | T001174 | $<32.0$ | Mass | $<11.0$ | $0.08^{+0.001}_{-0.001}$ | - | -
1180.01 | T001180 | $10.0^{+5.3}_{-5.4}$ | Mass | $1.93^{+1.07}_{-1.25}$ | $0.082^{+0.002}_{-0.002}$ | - | -
1181.01 | T001181 | $377.0^{+17.0}_{-17.0}$ | Mass | $0.49^{+0.08}_{-0.11}$ | $0.0364^{+0.0006}_{-0.007}$ | $375.0^{+44.0}_{-44.0}$ | Kabáth et al. (2022)
1184.01 | T001184 | $6.8^{+2.3}_{-2.3}$ | Mass | $2.63^{+0.98}_{-1.24}$ | $0.056^{+0.001}_{-0.001}$ | - | -
1194.01 | T001194 | $120.0^{+5.6}_{-5.7}$ | Mass | $0.99^{+0.16}_{-0.21}$ | $0.034^{+0.0006}_{-0.0006}$ | - | -
1244.01 | T001244 | $6.6^{+3.8}_{-3.7}$ | Mass | $2.66^{+1.52}_{-1.78}$ | $0.061^{+0.001}_{-0.001}$ | - | -
1246.01 | T001246 | $5.4^{+1.9}_{-1.9}$ | Mass | $0.73^{+0.28}_{-0.33}$ | $0.132^{+0.003}_{-0.003}$ | $5.3^{+1.7}_{-1.7}$ |  Turtelboom et al. (2022)*
1246.02 | T001246 | $8.0^{+1.2}_{-1.1}$ | Mass | $1.84^{+0.42}_{-0.54}$ | $0.049^{+0.001}_{-0.001}$ | $8.1^{+1.1}_{-1.1}$ |  Turtelboom et al. (2022)*
1246.03 | T001246 | $9.1^{+1.3}_{-1.2}$ | Mass | $3.39^{+0.78}_{-1.02}$ | $0.061^{+0.001}_{-0.001}$ | $8.8^{+1.2}_{-1.2}$ |  Turtelboom et al. (2022)*
1246.04 | T001246 | $14.5^{+2.3}_{-2.3}$ | Mass | $1.83^{+0.47}_{-0.65}$ | $0.212^{+0.004}_{-0.004}$ | $14.8^{+2.2}_{-2.2}$ |  Turtelboom et al. (2022)*
1246.05 | T001246 | $31.4^{+4.5}_{-4.3}$ | mp$\sin{(i)}$ | - | $0.389^{+0.008}_{-0.008}$ | $25.6^{+3.6}_{-3.6}$ |  Turtelboom et al. (2022)*
1247.01 | 135694 | $6.1^{+1.8}_{-1.8}$ | Mass | $2.05^{+0.68}_{-0.8}$ | $0.12^{+0.002}_{-0.002}$ | $5.7^{+2.1}_{-2.1}$ |  Akana Murphy et al. (2023b)*
1248.01 | T001248 | $27.4^{+3.6}_{-3.5}$ | Mass | $0.47^{+0.1}_{-0.12}$ | $0.051^{+0.001}_{-0.001}$ | - | -
1249.01 | T001249 | $11.9^{+5.2}_{-5.1}$ | Mass | $1.84^{+0.85}_{-1.11}$ | $0.109^{+0.002}_{-0.002}$ | - | -
1255.01 | HIP97166 | $19.1^{+1.6}_{-1.5}$ | Mass | $6.86^{+1.26}_{-1.58}$ | $0.091^{+0.002}_{-0.002}$ | $20.0^{+1.5}_{-1.5}$ |  MacDougall et al. (2021)*
1255.02 | HIP97166 | $8.0^{+1.6}_{-1.6}$ | mp$\sin{(i)}$ | - | $0.124^{+0.002}_{-0.002}$ | $9.9^{+1.8}_{-1.8}$ |  MacDougall et al. (2021)*
1269.01 | T001269 | $6.4^{+3.0}_{-2.9}$ | Mass | $2.53^{+1.22}_{-1.42}$ | $0.0496^{+0.0009}_{-0.001}$ | - | -
1269.02 | T001269 | $6.8^{+4.4}_{-4.3}$ | Mass | $3.15^{+2.05}_{-2.29}$ | $0.083^{+0.001}_{-0.002}$ | - | -
1272.01 | T001272 | $27.0^{+2.7}_{-2.5}$ | Mass | $2.09^{+0.44}_{-0.59}$ | $0.0417^{+0.0007}_{-0.0007}$ | $24.6^{+2.3}_{-2.3}$ |  MacDougall et al. (2022)*
1272.02 | T001272 | $21.7^{+3.6}_{-3.6}$ | mp$\sin{(i)}$ | - | $0.079^{+0.001}_{-0.001}$ | $26.7^{+3.1}_{-3.1}$ |  MacDougall et al. (2022)*
1279.01 | T001279 | $10.6^{+2.5}_{-2.5}$ | Mass | $3.05^{+0.88}_{-1.14}$ | $0.085^{+0.002}_{-0.002}$ | - | -
1288.01 | T001288 | $44.1^{+2.7}_{-2.6}$ | Mass | $1.97^{+0.34}_{-0.44}$ | $0.0374^{+0.0007}_{-0.0008}$ | $42.0^{+3.0}_{-3.0}$ | Knudstrup et al. (2023)
1288.02 | T001288 | $85.7^{+12.1}_{-11.7}$ | mp$\sin{(i)}$ | - | $1.07^{+0.03}_{-0.03}$ | $84.0^{+7.0}_{-7.0}$ | Knudstrup et al. (2023)
1294.01 | T001294 | $63.9^{+4.7}_{-4.5}$ | Mass | $0.34^{+0.06}_{-0.08}$ | $0.051^{+0.001}_{-0.001}$ | $62.1^{+4.8}_{-4.6}$ |  Chontos et al. (2024)*
1294.02 | T001294 | $147.0^{+15.0}_{-14.0}$ | mp$\sin{(i)}$ | - | $0.61^{+0.02}_{-0.02}$ | $148.5^{+17.0}_{-15.8}$ |  Chontos et al. (2024)*
1296.01 | T001296 | $95.3^{+4.7}_{-4.6}$ | Mass | $0.19^{+0.03}_{-0.04}$ | $0.051^{+0.001}_{-0.001}$ | $94.7^{+1.4}_{-1.4}$ | Moutou et al. (2021)
1298.01 | T001298 | $99.0^{+6.0}_{-6.0}$ | Mass | $0.6^{+0.1}_{-0.13}$ | $0.057^{+0.001}_{-0.001}$ | $113.0^{+10.0}_{-10.0}$ | Moutou et al. (2021)
1339.01 | 191939 | $9.6^{+0.9}_{-0.9}$ | Mass | $1.34^{+0.25}_{-0.33}$ | $0.079^{+0.002}_{-0.002}$ | $10.0^{+0.7}_{-0.7}$ |  Orell-Miquel et al. (2023)*
1339.02 | 191939 | $6.1^{+1.3}_{-1.3}$ | Mass | $1.03^{+0.27}_{-0.34}$ | $0.171^{+0.003}_{-0.003}$ | $8.0^{+1.0}_{-1.0}$ |  Orell-Miquel et al. (2023)*
1339.03 | 191939 | $2.2^{+1.3}_{-1.3}$ | Mass | $0.4^{+0.23}_{-0.26}$ | $0.209^{+0.004}_{-0.004}$ | $2.8^{+0.6}_{-0.6}$ |  Orell-Miquel et al. (2023)*
1339.04 | 191939 | $116.0^{+5.0}_{-5.0}$ | mp$\sin{(i)}$ | - | $0.4^{+0.008}_{-0.008}$ | $112.2^{+4.0}_{-4.0}$ |  Orell-Miquel et al. (2023)*
1339.05 | 191939 | - | mp$\sin{(i)}$ | - | - | $<660.0$ |  Orell-Miquel et al. (2023)*
1339.06 | 191939 | - | mp$\sin{(i)}$ | - | - | $<13.5$ |  Orell-Miquel et al. (2023)*
1347.01 | T001347 | $12.2^{+1.6}_{-1.5}$ | Mass | $11.17^{+2.46}_{-3.2}$ | $0.0171^{+0.0003}_{-0.0003}$ | $11.1^{+1.2}_{-1.2}$ |  Rubenzahl et al. (2024)*
1347.02 | T001347 | $<9.0$ | Mass | $<11.0$ | $0.0546^{+0.0009}_{-0.001}$ | $<6.4$ |  Rubenzahl et al. (2024)*
1386.01 | T001386 | $45.8^{+5.8}_{-5.7}$ | Mass | $1.04^{+0.21}_{-0.27}$ | $0.173^{+0.003}_{-0.003}$ | - | -
1386.02 | T001386 | $75.2^{+15.3}_{-15.0}$ | mp$\sin{(i)}$ | - | $0.75^{+0.03}_{-0.02}$ | - | -
1410.01 | T001410 | $12.5^{+1.1}_{-1.0}$ | Mass | $2.3^{+0.53}_{-0.74}$ | $0.0207^{+0.0004}_{-0.0004}$ | $12.4^{+0.5}_{-0.5}$ | Livingston et al. in review
1410.02 | T001410 | $27.0^{+3.3}_{-3.2}$ | mp$\sin{(i)}$ | - | $0.239^{+0.004}_{-0.005}$ | $27.2^{+1.7}_{-1.7}$ | Livingston et al. in review
1411.01 | GJ9522A | $2.0^{+1.2}_{-1.1}$ | Mass | $6.36^{+3.71}_{-4.14}$ | $0.02122^{+0.0004}_{-0.0004}$ | - | -
1422.01 | T001422 | $12.1^{+4.5}_{-4.5}$ | Mass | $1.08^{+0.42}_{-0.5}$ | $0.108^{+0.002}_{-0.002}$ | $9.0^{+2.3}_{-2.0}$ | Naponiello et al. (2022)
1430.01 | 235088 | $4.2^{+2.4}_{-2.4}$ | Mass | $2.58^{+1.47}_{-1.66}$ | $0.071^{+0.001}_{-0.001}$ | - | -
1436.01 | T001436 | $<8.0$ | Mass | $<12.0$ | $0.0164^{+0.0003}_{-0.0003}$ | - | -
1437.01 | 154840 | $10.4^{+2.6}_{-2.6}$ | Mass | $3.91^{+1.11}_{-1.4}$ | $0.139^{+0.003}_{-0.003}$ | $9.6^{+3.9}_{-3.3}$ | Pidhorodetska et al. in review*
1438.01 | T001438 | $10.9^{+5.9}_{-5.9}$ | Mass | $2.47^{+1.4}_{-1.85}$ | $0.056^{+0.001}_{-0.001}$ | - | -
1438.02 | T001438 | $5.6^{+5.0}_{-5.1}$ | Mass | $1.7^{+1.51}_{-1.85}$ | $0.084^{+0.002}_{-0.002}$ | - | -
1439.01 | T001439 | $38.5^{+5.7}_{-5.6}$ | Mass | $2.76^{+0.64}_{-0.85}$ | $0.192^{+0.004}_{-0.004}$ | $38.2^{+5.6}_{-5.7}$ |  Chontos et al. (2024)*
1443.01 | T001443 | $<30.0$ | Mass | $<14.0$ | $0.147^{+0.003}_{-0.003}$ | - | -
1444.01 | T001444 | $3.58^{+0.76}_{-0.75}$ | Mass | $6.84^{+1.78}_{-2.27}$ | $0.0116^{+0.0002}_{-0.0002}$ | $3.87^{+0.71}_{-0.71}$ |  Dai et al. (2021b)*
1444.02 | T001444 | $10.2^{+2.7}_{-2.9}$ | mp$\sin{(i)}$ | - | $0.123^{+0.002}_{-0.002}$ | $11.8^{+2.9}_{-2.9}$ |  Dai et al. (2021b)*
1451.01 | T001451 | $15.2^{+2.8}_{-2.8}$ | Mass | $4.67^{+1.18}_{-1.55}$ | $0.127^{+0.003}_{-0.003}$ | - | -
1456.01 | 332231 | $74.1^{+5.6}_{-5.4}$ | Mass | $0.55^{+0.1}_{-0.12}$ | $0.145^{+0.003}_{-0.003}$ | $77.6^{+6.7}_{-6.7}$ |  Dalba et al. (2020)*
1467.01 | T001467 | $<9.0$ | Mass | $<11.0$ | $0.0495^{+0.0009}_{-0.0009}$ | - | -
1471.01 | 12572 | $8.3^{+1.7}_{-1.7}$ | Mass | $0.81^{+0.21}_{-0.25}$ | $0.145^{+0.003}_{-0.003}$ | $8.4^{+2.0}_{-2.0}$ |  Akana Murphy et al. (2023b)*
1471.02 | 12572 | $<7.0$ | Mass | $<1.0$ | $0.269^{+0.005}_{-0.005}$ | $<7.9$ |  Akana Murphy et al. (2023b)*
1472.01 | T001472 | $16.5^{+5.1}_{-5.1}$ | Mass | $1.24^{+0.41}_{-0.51}$ | $0.065^{+0.001}_{-0.001}$ | - | -
1473.01 | 6061 | $10.0^{+2.5}_{-2.5}$ | Mass | $3.82^{+1.1}_{-1.39}$ | $0.06^{+0.001}_{-0.001}$ | $10.8^{+2.7}_{-2.7}$ |  Akana Murphy et al. (2023b)*
1601.01 | T001601 | $387.0^{+16.0}_{-17.0}$ | Mass | $0.74^{+0.14}_{-0.18}$ | $0.069^{+0.001}_{-0.001}$ | $388.0^{+10.0}_{-10.0}$ |  Chontos et al. (2024)*
1611.01 | 207897 | $14.8^{+1.5}_{-1.4}$ | Mass | $6.29^{+1.32}_{-1.78}$ | $0.117^{+0.002}_{-0.002}$ | $14.4^{+1.6}_{-1.6}$ | Heidari et al. (2022)
1669.01 | T001669 | $<13.0$ | Mass | $<6.0$ | $0.0376^{+0.0007}_{-0.0007}$ | - | -
1669.02 | T001669 | $191.0^{+25.0}_{-24.0}$ | mp$\sin{(i)}$ | - | $1.27^{+0.03}_{-0.03}$ | $182.0^{+24.0}_{-24.0}$ |  Van Zandt et al. (2023)*
1691.01 | T001691 | $14.6^{+5.4}_{-5.3}$ | Mass | $1.76^{+0.68}_{-0.8}$ | $0.126^{+0.003}_{-0.003}$ | - | -
1694.01 | T001694 | $31.3^{+2.7}_{-2.5}$ | Mass | $1.13^{+0.21}_{-0.26}$ | $0.045^{+0.0008}_{-0.0008}$ | $26.1^{+1.1}_{-1.1}$ |  Van Zandt et al. (2023)*
1694.02 | T001694 | $297.0^{+16.0}_{-16.0}$ | mp$\sin{(i)}$ | - | $0.1^{+0.02}_{-0.02}$ | $334.0^{+16.0}_{-16.0}$ |  Van Zandt et al. (2023)*
1710.01 | T001710 | $22.4^{+4.1}_{-4.0}$ | Mass | $0.87^{+0.2}_{-0.25}$ | $0.166^{+0.003}_{-0.0013}$ | - | -
1716.01 | 237566 | $4.8^{+2.0}_{-2.1}$ | Mass | $1.09^{+0.49}_{-0.59}$ | $0.081^{+0.002}_{-0.002}$ | - | -
1723.01 | T001723 | $10.4^{+5.2}_{-4.8}$ | Mass | $1.6^{+0.79}_{-0.91}$ | $0.114^{+0.002}_{-0.002}$ | - | -
1726.01 | 63433 | $37.3^{+9.6}_{-9.6}$ | Mass | $20.15^{+5.89}_{-7.15}$ | $0.072^{+0.001}_{-0.001}$ | $2.4^{+3.0}_{-1.8}$ | Damasso et al. (2023)
1726.02 | 63433 | $17.2^{+10.3}_{-9.3}$ | Mass | $5.43^{+3.13}_{-3.47}$ | $0.146^{+0.003}_{-0.003}$ | $18.9^{+7.0}_{-6.9}$ | Damasso et al. (2023)
1736.01 | T001736 | $12.3^{+1.5}_{-1.4}$ | Mass | $2.09^{+0.43}_{-0.56}$ | $0.073^{+0.001}_{-0.001}$ | $11.9^{+1.6}_{-1.6}$ |  Akana Murphy et al. (2023b)*
1736.02 | T001736 | $2441.0^{+97.0}_{-99.0}$ | mp$\sin{(i)}$ | - | $1.37^{+0.03}_{-0.03}$ | $2477.0^{+118.0}_{-118.0}$ |  Akana Murphy et al. (2023b)*
1742.01 | 156141 | $9.7^{+1.9}_{-1.9}$ | Mass | $4.0^{+0.98}_{-1.21}$ | $0.154^{+0.003}_{-0.003}$ | - | -
1751.01 | 146757 | $19.5^{+3.5}_{-3.4}$ | Mass | $4.13^{+0.99}_{-1.26}$ | $0.215^{+0.004}_{-0.004}$ | $20.9^{+4.5}_{-4.2}$ |  Desai et al. (2024)*
1753.01 | T001753 | $16.6^{+5.2}_{-5.2}$ | Mass | $5.95^{+2.06}_{-2.49}$ | $0.059^{+0.001}_{-0.001}$ | - | -
1758.01 | T001758 | $6.9^{+6.2}_{-6.3}$ | Mass | $0.83^{+0.75}_{-0.83}$ | $0.138^{+0.003}_{-0.003}$ | - | -
1759.01 | T001759 | $<15.0$ | Mass | $<3.0$ | $0.115^{+0.002}_{-0.002}$ | $6.8^{+2.0}_{-2.0}$ | Martioli et al. (2022b)
1775.01 | T001775 | $96.0^{+15.0}_{-15.0}$ | Mass | $1.01^{+0.22}_{-0.27}$ | $0.08^{+0.002}_{-0.002}$ | - | -
1776.01 | 95072 | $1.4^{+1.1}_{-1.0}$ | Mass | $4.13^{+3.13}_{-3.79}$ | $0.0378^{+0.0007}_{-0.0008}$ | - | -
1778.01 | 77946 | $10.9^{+1.8}_{-1.7}$ | Mass | $2.44^{+0.61}_{-0.83}$ | $0.073^{+0.001}_{-0.01}$ | - | -
1794.01 | T001794 | $8.7^{+4.1}_{-4.0}$ | Mass | $1.31^{+0.62}_{-0.76}$ | $0.082^{+0.002}_{-0.002}$ | - | -
1797.01 | 93963 | $18.4^{+3.2}_{-3.1}$ | Mass | $3.31^{+0.8}_{-1.01}$ | $0.04726^{+0.0008}_{-0.0009}$ | $19.2^{+4.1}_{-4.1}$ | Serrano et al. (2022)
1797.02 | 93963 | $2.8^{+2.3}_{-2.3}$ | Mass | $4.81^{+3.91}_{-4.36}$ | $0.02061^{+0.0004}_{-0.0004}$ | $7.8^{+3.2}_{-3.2}$ | Serrano et al. (2022)
1798.01 | T001798 | $6.5^{+2.0}_{-2.0}$ | Mass | $2.61^{+0.9}_{-1.11}$ | $0.074^{+0.001}_{-0.001}$ | - | -
1798.02 | T001798 | $5.6^{+0.8}_{-0.7}$ | Mass | $11.17^{+2.5}_{-3.39}$ | $0.0107^{+0.0002}_{-0.0002}$ | - | -
1799.01 | 96735 | $4.0^{+1.7}_{-1.8}$ | Mass | $7.51^{+3.45}_{-4.4}$ | $0.071^{+0.001}_{-0.001}$ | - | -
1801.01 | HIP57099 | $<16.0$ | Mass | $<12.0$ | $0.075^{+0.001}_{-0.001}$ | - | -
1807.01 | HIP65469 | $2.44^{+0.6}_{-0.57}$ | Mass | $3.98^{+1.18}_{-1.53}$ | $0.0122^{+0.0002}_{-0.0002}$ | $2.57^{+0.5}_{-0.5}$ | Nardiello et al. (2022)
1823.01 | TIC142381532 | $67.4^{+8.1}_{-8.3}$ | Mass | $0.86^{+0.18}_{-0.24}$ | $0.212^{+0.004}_{-0.004}$ | - | -
1824.01 | T001824 | $16.0^{+2.6}_{-2.6}$ | Mass | $4.24^{+0.96}_{-1.21}$ | $0.151^{+0.003}_{-0.003}$ | $18.5^{+3.2}_{-3.2}$ | Lange et al. in prep*
1836.01 | 148193 | $24.7^{+6.1}_{-5.9}$ | Mass | $0.24^{+0.07}_{-0.08}$ | $0.157^{+0.003}_{-0.003}$ | $29.2^{+4.7}_{-4.8}$ |  Chontos et al. (2024)*
1836.02 | 148193 | $<8.0$ | Mass | $<3.0$ | $0.03089^{+0.0005}_{-0.0005}$ | - | -
1842.01 | T001842 | $89.4^{+7.8}_{-7.8}$ | Mass | $0.26^{+0.05}_{-0.06}$ | $0.1^{+0.002}_{-0.002}$ | $89.8^{+7.4}_{-7.4}$ |  Chontos et al. (2024)*
1898.01 | 83342 | $129.0^{+7.0}_{-8.0}$ | Mass | $0.85^{+0.15}_{-0.2}$ | $0.269^{+0.005}_{-0.005}$ | $127.0^{+7.0}_{-7.0}$ |  Chontos et al. (2024)*
2019.01 | T002019 | $34.4^{+4.4}_{-4.4}$ | Mass | $1.25^{+0.28}_{-0.37}$ | $0.128^{+0.003}_{-0.003}$ | $34.7^{+4.2}_{-4.1}$ |  Chontos et al. (2024)*
2045.01 | T002045 | $211.0^{+21.0}_{-20.0}$ | Mass | $0.55^{+0.11}_{-0.14}$ | $0.093^{+0.002}_{-0.002}$ | - | -
2076.01 | T002076 | $16.1^{+8.3}_{-8.2}$ | Mass | $4.1^{+2.14}_{-2.52}$ | $0.088^{+0.002}_{-0.002}$ | - | -
2076.02 | T002076 | $<55.0$ | Mass | $<6.0$ | $0.142^{+0.003}_{-0.003}$ | - | -
2076.03 | T002076 | $<29.0$ | Mass | $<4.0$ | $0.199^{+0.004}_{-0.004}$ | - | -
2088.01 | T002088 | $<37.0$ | Mass | $<2.0$ | $0.472^{+0.009}_{-0.009}$ | - | -
2114.01 | T002114 | $<199.0$ | Mass | $<0.0$ | $0.075^{+0.001}_{-0.001}$ | - | -
2128.01 | 155060 | $4.5^{+2.0}_{-2.0}$ | Mass | $2.68^{+1.24}_{-1.48}$ | $0.127^{+0.003}_{-0.003}$ | - | -
2145.01 | HIP86040 | $1767.0^{+71.0}_{-72.0}$ | Mass | $5.06^{+0.86}_{-1.11}$ | $0.111^{+0.002}_{-0.002}$ | $1672.0^{+121.0}_{-118.0}$ | Rodriguez et al. (2023)

##  9 Acknowledgements

The authors thank the anonymous referee whose thorough review greatly
increased the quality of this publication. We also thank the time assignment
committees of the University of California, the California Institute of
Technology, NASA, and the University of Hawaii for supporting the TESS-Keck
Survey with observing time at Keck Observatory and on the Automated Planet
Finder. We thank NASA for funding associated with our Key Strategic Mission
Support project. We gratefully acknowledge the efforts and dedication of the
Keck Observatory staff for support of HIRES and remote observing. We recognize
and acknowledge the cultural role and reverence that the summit of Maunakea
has within the indigenous Hawaiian community. We are deeply grateful to have
the opportunity to conduct observations from this mountain. We thank Ken and
Gloria Levy, who supported the construction of the Levy Spectrometer on the
Automated Planet Finder. We thank the University of California and Google for
supporting Lick Observatory and the UCO staff for their dedicated work
scheduling and operating the telescopes of Lick Observatory.

We thank Johanna Teske for her encouragement and for providing helpful advice
on the initial scope of this project.

This research is partially funded through the Caltech-IPAC Visiting Graduate
Research Fellowship (VGRF).

This research is based on data collected by the TESS mission. Funding for the
TESS mission is provided by the NASA Explorer Program.

This research has made use of the NASA Exoplanet Archive, which is operated by
the California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.

This research was carried out in part at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration (80NM0018D0004).

This work was partially support by the Future Investigators in NASA Earth and
Space Science and Technology (FINESST) program Grant No. 80NSSC22K1754.

J.V.Z. acknowledges support from the Future Investigators in NASA Earth and
Space Science and Technology (FINESST) grant 80NSSC22K1606.

E.A.P. acknowledges the support of the Alfred P. Sloan Foundation.

L.M.W. is supported by the Beatrice Watson Parrent Fellowship and NASA ADAP
Grant 80NSSC19K0597.

D.H. acknowledges support from the Alfred P. Sloan Foundation, the National
Aeronautics and Space Administration (80NSSC21K0652) and the Australian
Research Council (FT200100871).

I.J.M.C. acknowledges support from the NSF through grant AST-1824644.

A.B. is supported by the NSF Graduate Research Fellowship, grant No. DGE
1745301.

R.A.R. is supported by the NSF Graduate Research Fellowship, grant No. DGE
1745301.

C. D. D. acknowledges the support of the Hellman Family Faculty Fund, the
Alfred P. Sloan Foundation, the David & Lucile Packard Foundation, and the
National Aeronautics and Space Administration via the TESS Guest Investigator
Program (80NSSC18K1583).

J.M.A.M. is supported by the NSF Graduate Research Fellowship, grant No.
DGE-1842400. J.M.A.M. also acknowledges the LSSTC Data Science Fellowship
Program, which is funded by LSSTC, NSF Cybertraining Grant No. 1829740, the
Brinson Foundation, and the Moore Foundation; his participation in the program
has benefited this work.

M.R. acknowledges support from Heising-Simons Foundation Grant #2023-4478

##  Appendix A Radial Velocity Fits

In this appendix, we show the periodogram analysis of our RV, activity
indicators, and window function for each of the systems we were able to
confirm through mass measurements (§5.2). We also show the fits to the RV data
points.

Figure 11: Top: Periodogram analysis of all RVs for HIP 1532 b in our dataset
first subtracting any offsets and the Gaussian process, then removing the best
fit planet signal (first three panels). We also show a periodogram of the
S-indices and the RV window function (last two panels). The planet period is
given is shown with the blue vertical line while the rotation period of the
star is in purple. The 1% false alarm probability (FAP) is the horizontal blue
dashed line. Middle: The best fit Keplerian orbital plus Gaussian process
model (blue line). We add in quadrature the jitter terms in Table 5 with the
measurement errors for each RV. Residuals to the 1-planet fit are show in the
bottom panel. Bottom: RVs phase-folded to the orbital ephemeris of planet b.
Figure 12: Top: Periodogram analysis of all RVs for TOI–1173 b in our dataset
first subtracting any offsets, then removing the best fit planet signal (first
two panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 13: Top:
Periodogram analysis of all RVs for TOI–1184 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 14: Top:
Periodogram analysis of all RVs for TOI–1194 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 15: Top:
Periodogram analysis of all RVs for TOI–1248 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 16: Top:
Periodogram analysis of all RVs for TOI–1279 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 17: Top:
Periodogram analysis of all RVs for TOI 1451 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. The vertical red line denotes the location of a known HIRES
alias at $\sim 90$ days. Middle: The best fit Keplerian orbital model (blue
line). We add in quadrature the jitter terms in Table 5 with the measurement
errors for each RV. Residuals to the 1-planet fit are show in the bottom
panel. Bottom: RVs phase-folded to the orbital ephemeris of planet b. Figure
18: Top: Periodogram analysis of all RVs for TOI–1472 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 19: Top:
Periodogram analysis of all RVs for HD 156141 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 20: Top:
Periodogram analysis of all RVs for TOI–1753 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 21: Top:
Periodogram analysis of all RVs for TOI–1775 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 22: Top:
Periodogram analysis of all RVs for HD 77946 b in our dataset first
subtracting any offsets, then removing the best fit planet signal (first two
panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The planet period is given is shown with the blue
vertical line while the 1% false alarm probability (FAP) is the horizontal
blue dashed line. Middle: The best fit Keplerian orbital model (blue line). We
add in quadrature the jitter terms in Table 5 with the measurement errors for
each RV. Residuals to the 1-planet fit are show in the bottom panel. Bottom:
RVs phase-folded to the orbital ephemeris of planet b. Figure 23: Top:
Periodogram analysis of all RVs for TOI–1798 b and c in our dataset first
subtracting any offsets, then removing the best fit planet signals (first
three panels). We also show a periodogram of the S-indices and the RV window
function (last two panels). The periods of planet b and c are shown with the
blue and orange vertical lines respectively. The 1% false alarm probability
(FAP) is the horizontal blue dashed line. Middle: The best fit Keplerian
orbital model (blue line). We add in quadrature the jitter terms in Table 5
with the measurement errors for each RV. Residuals to the 2-planet fit are
shown in the bottom panel. Bottom: RVs phase-folded to the orbital ephemeris
of planet b and planet c. Figure 24: Top: Periodogram analysis of all RVs for
TOI–1823 b in our dataset first subtracting any offsets, then removing the
best fit planet signal (first two panels). We also show a periodogram of the
S-indices and the RV window function (last two panels). The planet period is
given is shown with the blue vertical line while the 1% false alarm
probability (FAP) is the horizontal blue dashed line. Middle: The best fit
Keplerian orbital model (blue line). We add in quadrature the jitter terms in
Table 5 with the measurement errors for each RV. Residuals to the 1-planet fit
are show in the bottom panel. Bottom: RVs phase-folded to the orbital
ephemeris of planet b.

=10mm  TOI (TKS ID) $P$ $T_{\text{0}}$ $K$ $e$ $\omega$ $\dot{\gamma}$
$\ddot{\gamma}$ $\gamma_{\text{HIRES}}$ $\gamma_{\text{APF}}$
$\sigma_{\text{HIRES}}$ $\sigma_{\text{APF}}$ (days) (BJD) (m s-1) (radians)
(m s-1 d-1) (m s-1 d-2) (m s-1) (m s-1) (m s-1) (m s-1) TOI 260 (HIP1532) - -
- - - $\equiv 0.0$ $\equiv 0.0$ -1.17(0.91) - 1.84(0.32) - b
13.475815(4.7e-05) 1392.2944(0.0021) 1.32(0.43) $\equiv 0.0$ $\equiv\pi/2$ - -
- - - - TOI 266 (HIP8152) - - - - - $\equiv 0.0$ $\equiv 0.0$ -1.47(0.36) -
3.12(0.29) - b 10.751014(5.5e-05) 1393.0855(0.0031) 2.71(0.51) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - c 19.60562(0.00025) 1398.2869(0.0064) 2.76(0.55)
0.2(0.1) 2.0(2.8) - - - - - - TOI 329 (T000329) - - - - - $\equiv 0.0$ $\equiv
0.0$ 0.03(0.86) - 4.93(0.69) - b 5.70439(0.00013) 2090.7955(0.0038) 15.1(1.3)
0.39(0.033) 3.0(3.0) - - - - - - TOI 465 (WASP156) - - - - - $\equiv 0.0$
-1.3e-05(1.1e-05) 1.23(0.98) - 3.04(0.74) - b 3.8361623(1.5e-06)
1414.13606(0.00031) 18.7(1.1) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 469
(42813) - - - - - 0.0144(0.0046) 2.08e-05(6.1e-06) 0.37(0.73) - 3.01(0.29) - b
13.630828(2.4e-05) 1474.569(0.001) 1.63(0.56) $\equiv 0.0$ $\equiv\pi/2$ - - -
- - - TOI 480 (39688) - - - - - $\equiv 0.0$ $\equiv 0.0$ -2.7(0.85) -
6.4(0.63) - b 6.866196(1.4e-05) 1469.5659(0.0015) 5.9(1.2) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 509 (63935) - - - - - 0.0055(0.0031)
-1.17e-05(4.5e-06) -1.23(0.43) 1.53(0.82) 3.55(0.29) 9.61(0.77) b
9.058807(1.5e-05) 1494.44674(0.00094) 3.37(0.48) $\equiv 0.0$ $\equiv\pi/2$ -
- - - - - c 21.4027(0.0018) 1504.13(0.064) 2.66(0.45) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 554 (25463) - - - - - $\equiv 0.0$ $\equiv 0.0$
-1.47(0.51) - 7.7(0.4) - b 7.0491423(9.5e-06) 1442.61823(0.00084) 2.49(0.76)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - c 3.04405(1e-05) 1438.473(0.002)
1.6(0.73) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 561 (T000561) - - - - -
0.00197(0.00086) $\equiv 0.0$ -2.2(0.5) - 2.78(0.25) - b 10.778849(3.2e-05)
1527.0606(0.0023) 2.41(0.42) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
0.44656895(7.8e-07) 1517.94528(0.00072) 2.99(0.43) $\equiv 0.0$ $\equiv\pi/2$
- - - - - - d 25.71255(0.00014) 1521.8815(0.0041) 2.86(0.45) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - e 77.9(1.5) 1536.2(7.3) 1.48(0.54) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 669 (T000669) - - - - - $\equiv 0.0$ $\equiv
0.0$ -2.26(0.43) - 2.95(0.35) - b 3.945152(1.8e-05) 1546.1419(0.0025)
4.26(0.56) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 849 (T000849) - - - - -
$\equiv 0.0$ $\equiv 0.0$ -2.02498874322401(0.0) - 0.0(3.5) - b
0.765548(5.3e-05) 1871.6812(0.0083) 29.7(1.5) $\equiv 0.0$ $\equiv\pi/2$ - - -
- - - TOI 1136 (T001136) - - - - - $\equiv 0.0$ $\equiv 0.0$ 8.6(6.5) 0.4(0.8)
12.5(2.4) 21.8(1.8) b 4.17278(0.00022) 1684.7(0.1) 3.2(2.7) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - c 6.2569(0.0002) 1688.71(0.11) 2.6(1.7) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - d 12.51861(1.1e-05) 1686.0628(0.00043) 3.3(1.9)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - e 18.80693(0.00011) 1697.7299(0.0032)
1.4(1.5) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - f 26.317822(5.3e-05)
1699.3777(0.0011) 1.5(1.7) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - g
39.5387(0.0035) 2423.6705(0.0033) 2.2(1.7) $\equiv 0.0$ $\equiv\pi/2$ - - - -
- - TOI 1173 (T001173) - - - - - $\equiv 0.0$ $\equiv 0.0$ -1.49(0.99) -
3.59(0.88) - b 7.06456(2.5e-06) 1688.71523(0.00021) 9.8(1.3) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1174 (T001174) - - - - - -0.068(0.011)
0.0001(4e-05) -12.7(4.9) - 0.0(8.3) - b 8.953458(2.1e-05) 1690.057(0.001)
0.3(3.5) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1180 (T001180) - - - - -
$\equiv 0.0$ $\equiv 0.0$ -0.5(1.5) - 6.0(1.2) - b 9.686753(1.2e-05)
1691.0488(0.00085) 3.6(1.9) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1181
(T001181) - - - - - $\equiv 0.0$ $\equiv 0.0$ -2.9(2.7) - 19.0(2.0) - b
2.10319365(4.1e-07) 1957.82136(0.00011) 145.8(3.9) $\equiv 0.0$ $\equiv\pi/2$
- - - - - - TOI 1184 (T001184) - - - - - $\equiv 0.0$ $\equiv 0.0$ -0.07(0.77)
- 5.72(0.58) - b 5.748432(3.9e-06) 1684.35945(0.00047) 3.0(1.0) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1194 (T001194) - - - - - $\equiv 0.0$ $\equiv
0.0$ 9.3(1.1) - 5.07(0.79) - b 2.3106446(5.4e-07) 1684.92352(0.00014)
58.4(1.6) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1244 (T001244) - - - - -
$\equiv 0.0$ $\equiv 0.0$ 0.85(0.89) - 3.2(3.1) - b 6.4003(1.3e-05)
1684.9485(0.0016) 2.7(1.6) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1246
(T001246) - - - - - 0.0009(0.0012) 2.2e-05(5.4e-06) -1.5(0.5) - 2.81(0.29) - b
4.307438(4.9e-05) 1686.56608(0.00074) 3.42(0.48) $\equiv 0.0$ $\equiv\pi/2$ -
- - - - - c 5.904137(1.4e-05) 1683.4663(0.0018) 3.48(0.47) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - d 18.654874(5.5e-05) 1688.975(0.002) 1.41(0.49)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - e 37.92548(0.00016) 1700.6958(0.0035)
3.0(0.46) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - f 94.0(0.2) 1702.2(3.8)
5.0(0.72) 0.263(0.098) -0.74(0.37) - - - - - - TOI 1247 (135694) - - - - -
0.0032(0.0012) $\equiv 0.0$ -0.6(0.5) -0.61(0.66) 3.82(0.36) 7.42(0.52) b
15.92346(3.8e-05) 1687.6496(0.0011) 1.66(0.49) $\equiv 0.0$ $\equiv\pi/2$ - -
- - - - TOI 1248 (T001248) - - - - - $\equiv 0.0$ $\equiv 0.0$ -2.2(0.9) -
3.44(0.85) - b 4.3601561(1.1e-06) 1687.12116(0.00016) 11.5(1.4) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1249 (T001249) - - - - - 0.016(0.0063)
2.6e-05(1.3e-05) -1.4(1.3) - 4.25(0.89) - b 13.079151(5.4e-05)
1694.3804(0.0021) 3.2(1.4) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1255
(HIP97166) - - - - - 0.0079(0.0011) $\equiv 0.0$ -5.6(0.68) -54.03(0.83)
2.7(0.3) 5.92(0.41) b 10.288914(6.4e-06) 1691.65438(0.00037) 6.18(0.45)
0.29(0.072) 1.71(0.18) - - - - - - c 16.432(0.041) 1694.0(1.3) 2.12(0.41)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1269 (T001269) - - - - - $\equiv
0.0$ $\equiv 0.0$ 0.87(0.96) - 2.7(3.7) - b 4.2529913(6.8e-06)
1686.60586(0.00092) 2.7(1.2) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
9.237885(2.6e-05) 1685.977(0.0022) 2.2(1.4) $\equiv 0.0$ $\equiv\pi/2$ - - - -
- - TOI 1272 (T001272) - - - - - $\equiv 0.0$ $\equiv 0.0$ 1.6(1.3) - 6.0(2.0)
- b 3.31599(1.8e-05) 1713.02552(0.00036) 13.5(1.3) 0.35(0.055) 2.46(0.27) - -
- - - - c 8.6811(0.0069) 1885.39(0.29) 7.4(1.2) 0.12(0.0) -1.57(0.0) - - - - -
- TOI 1279 (T001279) - - - - - -0.0079(0.0021) $\equiv 0.0$ 0.44(0.64) -
3.1(0.53) - b 9.61419(4e-05) 1717.4814(0.0022) 3.5(0.82) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1288 (T001288) - - - - - $\equiv 0.0$ $\equiv
0.0$ 3.22(0.69) - 3.43(0.54) - b 2.6998279(4.9e-06) 1712.35877(0.00025)
20.89(0.93) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c 416.0(12.0) 1894.4(17.0)
7.54(0.99) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1294 (T001294) - - - - -
-0.002(0.016) -0.000113(3.1e-05) 15.4(1.9) - 4.77(0.81) - b 3.915292(1.5e-05)
2393.00711(0.00066) 23.4(1.3) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
159.9(2.5) 2194.4(3.1) 15.7(1.3) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI
1296 (T001296) - - - - - $\equiv 0.0$ $\equiv 0.0$ 4.71(0.74) - 3.18(0.64) - b
3.9443736(1.6e-06) 1930.75531(0.00022) 35.0(1.1) 0.025(0.016) -0.01(0.91) - -
- - - - TOI 1298 (T001298) - - - - - $\equiv 0.0$ $\equiv 0.0$ -7.9(1.2) -
4.64(0.96) - b 4.537143(3e-06) 1934.12245(0.00032) 33.6(1.6) 0.027(0.027)
-1.0(2.0) - - - - - - TOI 1339 (191939) - - - - - 0.1306(0.0032)
-6.53e-05(3.3e-06) -36.8(0.6) -39.28(0.73) 2.27(0.22) 4.62(0.35) b
8.8803232(4.5e-06) 1715.35572(0.00028) 3.4(0.3) $\equiv 0.0$ $\equiv\pi/2$ - -
- - - - c 28.579889(3.4e-05) 1726.05528(0.00066) 1.46(0.31) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - d 38.352562(8.4e-05) 1743.553(0.0011) 0.47(0.29)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - e 101.723(0.078) 2044.15(0.31)
18.06(0.31) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1347 (T001347) - - - -
- $\equiv 0.0$ $\equiv 0.0$ -0.5(3.5) - 5.55(0.64) - b 0.84742431(5.8e-07)
1683.55882(0.00036) 8.6(1.1) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
4.841968(2.5e-05) 1683.3485(0.0027) 0.2(1.1) $\equiv 0.0$ $\equiv\pi/2$ - - -
- - - TOI 1386 (T001386) - - - - - 0.0053(0.0066) -5e-05(2.1e-05) 0.9(1.3) -
5.16(0.57) - b 25.8401(0.0031) 1752.321(0.003) 9.7(1.2) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - c 232.0(9.3) 1750.9(34.0) 8.4(1.7) 0.38(0.17)
-1.24(0.53) - - - - - - TOI 1410 (T001410) - - - - - -0.0034(0.0038)
-1.1e-06(6.8e-06) -2.06(0.73) - 2.84(0.36) - b 1.21687(3e-05)
1739.72931(0.00071) 8.67(0.63) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
47.56(0.15) 1980.4(1.2) 5.57(0.63) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI
1411 (GJ9522A) - - - - - 0.0065(0.0056) 2.7e-05(1.3e-05) -4.0(1.2) - 4.2(0.52)
- b 1.4520527(1.7e-06) 1739.47404(0.00046) 1.55(0.93) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1422 (T001422) - - - - - 0.0131(0.0029) $\equiv
0.0$ 2.1(1.3) - 4.77(0.73) - b 12.9967(0.0017) 1745.9221(0.0035) 3.3(1.2)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1430 (235088) - - - - -
0.0148(0.0057) -7e-05(2e-05) 4.0(1.0) 4.1(2.7) 3.9(2.5) 7.2(5.3) b
7.434151(1.8e-05) 1713.08113(0.00087) 1.53(0.87) $\equiv 0.0$ $\equiv\pi/2$ -
- - - - - TOI 1436 (T001436) - - - - - $\equiv 0.0$ $\equiv 0.0$ -0.12(0.74) -
6.2(0.59) - b 0.867617(3e-06) 1711.8963(0.0013) 0.0(2.0) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1437 (154840) - - - - - $\equiv 0.0$ $\equiv
0.0$ -0.2(0.5) -0.22(0.83) 4.33(0.39) 6.4(0.84) b 18.84078(0.00012)
1700.7353(0.0026) 2.5(0.6) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1438
(T001438) - - - - - 0.0824(0.0057) $\equiv 0.0$ -1.5(1.4) - 5.0(1.1) - b
5.1396625(7.1e-06) 1683.6265(0.00071) 4.4(2.4) $\equiv 0.0$ $\equiv\pi/2$ - -