# Two young planetary systems around field stars with ages between $20-320$
Myr from _TESS_

George Zhou Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Hubble Fellow  Samuel N. Quinn Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Jonathan Irwin  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Chelsea X. Huang Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.  Karen A. Collins Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Luke G. Bouma  Department of Astrophysical Sciences, Princeton University, NJ 08544, USA.  Lamisha Khan  Cambridge Rindge and Latin High School  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Anaka Landrigan  Cambridge Rindge and Latin High School  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Andrew M. Vanderburg Department of Astronomy, The University of Texas at Austin, Austin, TX 78712, USA.  Joseph E. Rodriguez Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  David W. Latham Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Guillermo Torres  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Stephanie T. Douglas  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Allyson Bieryla  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Gilbert A. Esquerdo Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Perry Berlind  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Michael L. Calkins  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Lars A. Buchhave DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 328, DK-2800 Kgs. Lyngby, Denmark  David Charbonneau  Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Kevin I. Collins George Mason University, 4400 University Drive, Fairfax, VA, 22030 USA  John F. Kielkopf Department of Physics and Astronomy, University of Louisville, Louisville, KY 40292, USA  Eric L. N. Jensen Dept. of Physics & Astronomy, Swarthmore College, Swarthmore PA 19081, USA  Thiam-Guan Tan Perth Exoplanet Survey Telescope, Perth, Western Australia  Rhodes Hart  Centre for Astrophysics, University of Southern Queensland, Toowoomba, QLD, 4350, Australia  Brad Carter  Centre for Astrophysics, University of Southern Queensland, Toowoomba, QLD, 4350, Australia  Christopher Stockdale Hazelwood Observatory, Victoria, Australia  Carl Ziegler  Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, Ontario M5S 3H4, Canada  Nicholas Law  Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA  Andrew W. Mann Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA  Steve B. Howell NASA Ames Research Center, Moffett Field, CA 94035, USA  Rachel A. Matson NASA Ames Research Center, Moffett Field, CA 94035, USA  U.S. Naval Observatory, Washington, DC 20392 USA  Nicholas J. Scott NASA Ames Research Center, Moffett Field, CA 94035, USA  Elise Furlan  NASA Exoplanet Science Institute, Caltech/IPAC, Mail Code 100-22, 1200 E. California Blvd., Pasadena, CA 91125, USA  Russel J. White  IPAC, Mail Code 314-6, Caltech, 1200 E. California Boulevard, Pasadena, CA 91125, USA  Coel Hellier  Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK  David R. Anderson  Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK  Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK  Richard G. West  Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK  George Ricker  Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.  Roland Vanderspek  Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.  Sara Seager Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.  Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  Jon M. Jenkins  NASA Ames Research Center, Moffett Field, CA 94035, USA  Joshua N. Winn Department of Astrophysical Sciences, Princeton University, NJ 08544, USA.  Ismael Mireles Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Pamela Rowden School of Physical Sciences, The Open University, Milton Keynes MK7 6AA, UK  Daniel A. Yahalomi Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA.  Bill Wohler NASA Ames Research Center, Moffett Field, CA, 94035, USA  SETI Institute, Mountain View, CA 94043, USA  Clara. E. Brasseur Space Telescope Science Institute, USA  Tansu Daylan  Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.  Knicole D. Colón NASA Goddard Space Flight Center, Exoplanets and Stellar Astrophysics Laboratory (Code 667), Greenbelt, MD 20771, USA

###### Abstract

Planets around young stars trace the early evolution of planetary systems. We
report the discovery and validation of two planetary systems with ages
$\lesssim 300$ Myr from observations by the Transiting Exoplanet Survey
Satellite. TOI-251 is a $40-320$ Myr old G star hosting a
$2.74_{-0.18}^{+0.18}{}\,R_{\oplus}$ mini-Neptune with a $4.94$ day period.
TOI-942 is a $20-160$ Myr old K star hosting a system of inflated Neptune-
sized planets, with TOI-942b orbiting with a period of $4.32$ days, with a
radius of $4.81_{-0.20}^{+0.20}{}\,R_{\oplus}$, and TOI-942c orbiting in a
period of $10.16$ days with a radius of $5.79_{-0.18}^{+0.19}{}\,R_{\oplus}$.
Though we cannot place either host star into a known stellar association or
cluster, we can estimate their ages via their photometric and spectroscopic
properties. Both stars exhibit significant photometric variability due to spot
modulation, with measured rotation periods of $\sim 3.5$ days. These stars
also exhibit significant chromospheric activity, with age estimates from the
chromospheric calcium emission lines and X-ray fluxes matching that estimated
from gyrochronology. Both stars also exhibit significant lithium absorption,
similar in equivalent width to well-characterized young cluster members.
_TESS_ has the potential to deliver a population of young planet-bearing field
stars, contributing significantly to tracing the properties of planets as a
function of their age.

planetary systems — stars: individual (TOI-251, TIC224225541, TIC146520535,
TOI-942) techniques: spectroscopic, photometric

††journal: AJ††software: lightkurve (Barentsen et al., 2019), emcee (Foreman-
Mackey et al., 2013), Astropy (Astropy Collaboration et al., 2013,
2018),AstroImageJ(Collins et al., 2017a), PyAstronomy (Czesla et al., 2019),
TESSCut (Brasseur et al., 2019)

”

##  1 Introduction

The first few hundred million years of planet evolution sculpts the population
of exoplanetary systems we observe today. The properties of young planetary
systems help unravel the factors that shape the present-day population: in-
situ formation, migration, and photo-evaporation. Probing the timescales of
these mechanisms motivates us to search for planets within the first few
hundred million years of their birth.

Recent searches for young planets have yielded a handful of discoveries with
targeted radial velocity surveys and space-based transit monitoring. Dozens of
planets have been identified in the 600-800 Myr old Praesepe and Hyades
clusters (Quinn et al., 2012, 2014; Obermeier et al., 2016; Mann et al.,
2016a; Ciardi et al., 2018; Mann et al., 2017; Livingston et al., 2018; Mann
et al., 2018; Vanderburg et al., 2018; Rizzuto et al., 2018; Livingston et
al., 2019). These discoveries enabled estimates of planet occurrence rates in
million-year old cluster environments (e.g. Rizzuto et al., 2017).

To sample the earlier stages of planet evolution, transit searches have
focused on members of known young stellar associations, finding planets with
ages ranging from $\sim 10-150$ Myr. Observations from the _K2_ mission
revealed planets within the Upper Scorpius moving group (Mann et al., 2016b;
David et al., 2016) and Taurus-Auriga star-forming region (David et al.,
2019b, a).

With the library of all sky photometry made available by the Transiting
Exoplanet Survey Satellite (TESS, Ricker et al., 2016), planets around bright,
young stars have been identified (e.g. Newton et al., 2019; Rizzuto et al.,
2020; Mann et al., 2020, Plavchan et al. 2020, Newton et al. in-prep). These
are the first planets around bright young stars that are suitable for in-depth
characterizations, enabling the first obliquity measurements of newly formed
planets (Zhou et al., 2020; Montet et al., 2020), as well as atmospheric
studies in the near future.

However, star forming clusters begin to disperse within the first hundred
million years of formation (Krumholz et al., 2019). Left behind are relatively
young stars that can no longer be traced back to their source of origin. These
stars can still be identified by their signatures of youth. Mamajek &
Hillenbrand (2008) summarizes the activity signatures that can be used to
provide approximate ages of Sun-like stars. The rapid rotation of these young
stars lead to enhanced chromospheric activity and X-ray emission. Their
current rotation rates can help guide the age estimates via gyrochronology.
The abundance of lithium in the atmospheres of main-sequence Sun-like stars is
also a useful youth indicator. Recent efforts to trace young field stars have
made use of all-sky spectroscopic surveys to catalog large numbers of
chromospherically active (e.g. Žerjal et al., 2013) and lithium bearing (e.g.
Žerjal et al., 2019) stars.

These photometric and spectroscopic signatures of youth, however, are often
detrimental to our ability to identify and characterize the planets these
stars harbor. The photometric variations due to star spots and stellar
rotation make transit planet searches more difficult. The same spot activity
induces radial velocity variations on the $\sim 100\,\rm m\,s^{-1}$ level,
masking the planetary orbits. Despite these difficulties, Sanchis-Ojeda et al.
(2013) identified Kepler-63 b as a giant planet around a $\sim 300$ Myr young
field star, and made use of the spot activity to infer its orbital obliquity
via transit spot-crossing events. The small planets around K2-233 (David et
al., 2018b) and EPIC 247267267 (David et al., 2018a) are additional examples
of young field stars with ages of 100-700 Myr discovered by the _K2_ mission.

We report the discovery of a mini-Neptune around TOI-251, which we determine
to have an age of $40-320$ Myr based on its rotational, spectroscopic, and
X-ray properties. We also report the two inflated Neptunes around TOI-942,
with an age of $20-160$ Myr from its rotation, spectroscopic, and X-ray age
indicators. These planets were validated by a campaign of ground-based
photometric and spectroscopic observations. In particular, the ability to
predict future transit times degraded substantially over the year between the
_TESS_ discovery and subsequent follow-up efforts. Our ground based
photometric follow-up campaign demonstrates the effectiveness of small
telescopes in recovering the shallow 1 mmag transits that these small planets
exhibit. These young planets around field stars open an untapped population
that can help us construct the properties of planetary systems over time.

##  2 Candidate identification and follow-up observations

###  2.1 Identification of planet candidates by _TESS_

TIC 224225541 received _TESS_ 2 minute cadenced target pixel stamp
observations, as part of the TESS Candidate Target List (CTL Stassun et al.,
2018) during Sector 2, between 2018 August 08 and September 09, with the
target star being located on Camera 2, CCD 4 of the _TESS_ array. Light curves
and transit identification were made possible via the Science Processing
Observation Center (SPOC, Jenkins et al., 2016). The transits of the mini-
Neptune were detected as per Twicken et al. (2018) and Li et al. (2019), with
a multiple event statistic of 10.9, and were released to the community as
TOI-251b, with an orbital period of $4.94$ days. We make use of the Simple
Aperture Photometry made available for this star for further analysis (Twicken
et al., 2010; Morris et al., 2020). The _TESS_ light curve of TOI-251 is shown
in Figure 1, and individual transits of TOI-251b in Figure 2.

TIC 146520535 was observed during Sector 5 of the primary mission, between
2018 November 15 and December 11, by the Camera 2 CCD 2 Full Frame Images at
30 minute cadence. The MIT quicklook pipeline (Huang et al., 2019) identified
a set of transit events at 4.331 day with signal to pink noise ratio of 11.7,
and released as TOI-942b. In subsequent visual examinations of the light
curves, two single transits of slightly deeper depth than TOI-942b were
identified in the light curves spaced $10.16$ days apart. Further analysis
showed that these two single transits are identical in depth and duration, and
are due to a second planet candidate TOI-942c.

We then extracted the light curves for TOI-942 from the public Full Frame
Images (FFIs) made available on the MAST archive using the _lightkurve_
package (Barentsen et al., 2019). A $10\times 10$ pixel FFI cutout was
extracted around the target star using the TESScut function (Brasseur et al.,
2019). The photometric aperture was defined to encompass the brightest $68\%$
of pixels, within a maximum radius of 3 pixels from the target star
coordinates. Surrounding pixels without nearby stars are used for background
subtraction. The _TESS_ light curve of TOI-942 is shown in Figure 3,
individual transits of TOI-942b and c are shown in Figure 4 and 5
respectively.

Figure 1: The full _TESS_ light curve of TOI-251 during Sector 2 of short
cadence observations. The top panel shows the SPOC Simple Aperture Photometry
fluxes. The red ticks above the light curve mark the times of transit for
TOI-251b. The middle panel shows the light curve after removal of the stellar
activity signal as modeled via our global analysis. The bottom panel shows the
phased light curve around the transit of TOI-251b. The black points show the
binned light curve at phase intervals of 0.002. The best fit models are shown
in red in each panel. Figure 2: Individual transits of TOI-251b during the
_TESS_ observations. Each panel shows an individual transit, with the mid-
transit epoch labelled on the X-axis. The best fit model is overlaid in red,
showing the transit model and the stellar activity model. Figure 3: The _TESS_
light curve of TOI-942 from 30-minute cadence Full Frame Images during Sector
5 of observations. The panels are arranged as per Figure 1. The red ticks
above the light curve mark the times of transit for TOI-942b, the blue ticks
mark the transit times for TOI-942c. The phase folded transit of TOI-942b is
shown on the bottom left, and TOI-942c on the bottom right. The black points
show the binned light curve at phase intervals of 0.002.  Figure 4: Individual
transits of TOI-942b during the _TESS_ observations. Each panel shows an
individual transit, with hours from the mid-transit epoch labeled. The best
fit model is overlaid in red, showing the transit model and the stellar
activity model. Note that the vertical scales differ from transit to transit
due to the sharply varying stellar activity at each transit event.  Figure 5:
Individual transits of TOI-942c during the _TESS_ observations. Each panel
shows an individual transit. The best fit model is overlaid in red, showing
the transit model and the stellar activity model.

###  2.2 Spectroscopic follow-up

####  2.2.1 SMARTS 1.5 m / CHIRON

We obtained a series of spectroscopic observations with the CHIRON facility to
characterize the host star properties and constrain the masses of the planets
in each system. CHIRON is a high resolution spectrograph on the 1.5 m SMARTS
telescope, located at Cerro Tololo Inter-American Observatory (CTIO), Chile
(Tokovinin et al., 2013). CHIRON is fed through an image slicer via a fiber,
yielding a spectral resolving power of $\lambda/\Delta\lambda\equiv R=80,000$
over the wavelength region 4100 to $8700$ Å.

Radial velocities were extracted from CHIRON spectra by fitting the line
profiles derived from each spectra. The line profiles are measured via a
least-squares deconvolution of the observed spectra against synthetic
templates (following Donati et al., 1997), and are listed in Table 1 and Table
2, and plotted in Figures 6 and 7.

In addition to providing radial velocity and stellar atmosphere parameter
measurements, the CHIRON spectra also allow us to search for additional
blended spectral companions that may be indicative of other astrophysical
false positive scenarios for these systems. We perform a signal injection and
recovery exercise to determine the detection thresholds for any additional
spectroscopic stellar companion that may be blended in the spectrum. The
detectability of the blended source is determined by its flux ratio and
velocity separation to the target star, and its rotational broadening. As
such, we performed $\sim 10,000$ iterations of the injection, with different
combinations of these factors, to the averaged spectroscopic line profile for
each target star. The derived detection thresholds are shown in Figure 8. We
can rule out non-associated any stellar companions with $\Delta\mathrm{mag}<4$
for TOI-251, assuming they exhibit minimal rotational broadening and
substantial velocity separation between the target star and the blended
companion. Similarly, we can rule out blended, non-associated, slowly rotating
stellar companions with $\Delta\mathrm{mag}<3.5$ for TOI-942. Our ability to
detect such companions degrade significantly if they are rapidly rotating, or
if they have similar systemic velocities to the target star.

We also made use of the CHIRON observations to measure the projected
rotational velocity $v\sin{I_{\star}}$ of the host stars. Following Zhou et
al. (2018), we model the line profiles derived from the CHIRON spectra via a
convolution of kernels representing the rotation, radial-tangential
macroturbulence, and instrument broadening terms. The rotational and radial-
tangential macroturbulence kernels follow the prescription in Gray (2005),
while the instrument broadening kernel is represented by a Gaussian function
of width that of the instrument resolution. For TOI-251, we measured a
projected rotational broadening velocity of $v\sin{I_{\star}}=11.5\pm
1.0{}\,\rm km\,s^{-1}$, and macroturbulent velocity of
$v_{\mathrm{mac}}=7.9\pm 1.0{}\,\rm km\,s^{-1}$. For TOI-942, we measure
$v\sin{I_{\star}}=14.3\pm 0.5{}\,\rm km\,s^{-1}$, and $v_{\mathrm{mac}}=9.8\pm
3.4{}\,\rm km\,s^{-1}$. We note that for slowly rotating stars, there is
significant degeneracy between various line broadening parameters. These
degeneracies can systematically impact future observations, such as transit
spectroscopic obliquity observations, or estimates of the line-of-sight
inclination of the system.

Figure 6: Radial velocities of TOI-251 obtained with CHIRON. Top panel shows the radial velocities as a function of their observation. The plotted uncertainties are the quadrature addition of the per-point measurement uncertainty and stellar jitter. Bottom panel shows the velocities phase folded to the period of TOI-251b, with the transit occurring at phase 0. The dashed radial velocity model show the 3$\sigma$ mass upper limit that we can place on TOI-251b based on these velocities.  Figure 7: Radial velocities of TOI-942 obtained with CHIRON. Top panel shows the radial velocities as a function of their observation. The plotted uncertainties are the quadrature addition of the per-point measurement uncertainty and stellar jitter. Bottom panels show the velocities phased at the ephemerides of TOI-942b and TOI-942c, with the corresponding 3$\sigma$ upper limit for each planet marked by the dashed curve. Note that while the velocities of TOI-942b appear to phase well with its transit ephemeris, this should be attributed to the stellar activity signal being at a similar timescale to the orbital period.  Table 1: Radial Velocities for TOI-251 BJD-TDB | RV $(\rm km\,s^{-1})$ | RV Error $(\rm km\,s^{-1})$ | Inst
---|---|---|---
2458472.59427 | -2.323 | 0.031 | TRES
2458636.91068 | -2.087 | 0.013 | CHIRON
2458637.92204 | -1.933 | 0.019 | CHIRON
2458640.90185 | -2.058 | 0.024 | CHIRON
2458650.86649 | -2.087 | 0.018 | CHIRON
2458653.83789 | -2.188 | 0.050 | CHIRON
2458665.79446 | -2.134 | 0.013 | CHIRON
2458666.84512 | -2.004 | 0.010 | CHIRON
2458667.86580 | -2.080 | 0.006 | CHIRON
2458668.80856 | -1.983 | 0.019 | CHIRON
Table 2: Radial Velocities for TOI-942 BJD-TDB | RV $(\rm km\,s^{-1})$ | RV Error $(\rm km\,s^{-1})$ | Inst
---|---|---|---
2458579.51343 | 25.400 | 0.024 | CHIRON
2458751.87828 | 25.467 | 0.043 | CHIRON
2458774.79336 | 25.197 | 0.038 | CHIRON
2458775.80474 | 25.147 | 0.043 | CHIRON
2458782.85938 | 25.518 | 0.031 | CHIRON
2458785.79240 | 25.493 | 0.044 | CHIRON
2458787.72494 | 25.294 | 0.026 | CHIRON
2458789.71153 | 25.310 | 0.036 | CHIRON
2458791.77641 | 25.240 | 0.033 | CHIRON
2458775.91595 | 25.181 | 0.267 | TRES
2458786.92907 | 25.024 | 0.074 | TRES

TOI-251
TOI-942

Figure 8: Detection threshold for any blended spectroscopic companions to the
target stars via CHIRON observations. Colored regions show the excluded
parameter space for any blended stars, as a function of their magnitude
difference to the target star $\Delta\mathrm{mag}$, and their velocity
separation. Our ability to detect such companions depend on their rotational
line broadening. The simulation shows the detection thresholds for a blended
star of $v_{\mathrm{rot}}$ = 5, 15, and 25 $\mathrm{km\,s}^{-1}$, with the
detectability progressively worsening for more rapidly rotating companions.
The black regions show where no companions can be detected. For low velocity
separations, there is degeneracy between any blended companion and the target
star, and as such we are not sensitive to such scenarios. As the broadening
profiles have structured noise features, some velocities are systematically
more sensitive to secondary companions than other regions.

####  2.2.2 FLWO 1.5 m / TRES

We also obtained observations of TOI-251 and TOI-942 with the Tillinghast
Reflect Echelle Spectrograph (TRES, Fűrész, 2008) on the 1.5 m reflector at
the Fred Lawrence Whipple Observatory (FLWO), Arizona, US. TRES is a fiber-fed
echelle spectrograph with a resolution of $R\sim 44000$ over the spectral
region of $3850-9100\,\AA$. The observing strategy and reduction procedure are
outlined in Buchhave et al. (2012).

One observation was obtained for TOI-251, and two for TOI-942. These spectra
were used to measure the stellar atmospheric properties of the host stars via
the Stellar Parameter Classification pipeline (Buchhave et al., 2010),
subsequently used as priors in our global analyses (Section 5). We find
TOI-251 to be a Sun-like stellar surface effective temperature of $T_{\rm
eff}=5833\pm 143$ K, surface gravity of $\log g=4.49\pm 0.23$ dex, and
metallicity of $\mathrm{[m/H]}=-0.16\pm 0.13$ dex. TOI-942 is an early K star
with $T_{\rm eff}=5187\pm 52$ K, $\log g=4.59\pm 0.10$ dex, and
$\mathrm{[m/H]}=0.07\pm 0.08$ dex.

###  2.3 Photometric follow-up

Table 3:  Summary of photometric observations  Target | Facility | Date(s) | Number of Images aa Outlying exposures have been discarded.  | Cadence (s) bb Median time difference between points in the light curve. Uniform sampling was not possible due to visibility, weather, pauses.  | Filter
---|---|---|---|---|---
TOI-251 | WASP | 2006-05-15 – 2014-12-06 | 132002 | 37 | WASP
|  | (Over 8 observing campaigns) |  |  |
TOI-251 | _TESS_ | 2018-08-23 – 2018-09-20 | 18316 | 120 | $TESS$
TOI-251 | LCO-SSO | 2019-07-23 | 148 | 127 | $Y$
TOI-251 | MKO | 2019-07-28 | 168 | 89 | $i^{\prime}$
TOI-251 | MEarth | 2019-08-22 | 1749 | 12 | MEarth band
TOI-942 | WASP | 2006-09-15 – 2014-12-09 | 87361 | 30 | WASP
|  | (Over 10 observing campaigns) |  |  |
TOI-942 | _TESS_ | 2018-11-15 – 2018-12-11 | 1188 | 1799 | $TESS$
TOI-942 | MEarth | 2019-11-05 | 1680 | 10 | MEarth band
TOI-942 | MEarth | 2019-11-13 | 1791 | 10 | MEarth band
TOI-942 | MEarth | 2019-11-15 | 1814 | 11 | MEarth band
TOI-942 | MEarth | 2019-11-17 | 2346 | 6 | MEarth band
TOI-942 | MEarth | 2019-11-25 | 1974 | 10 | MEarth band
TOI-942 | MEarth | 2019-11-30 | 2049 | 11 | MEarth band
TOI-942 | MEarth | 2019-12-05 | 2488 | 10 | MEarth band
TOI-942 | MEarth | 2019-12-26 | 2223 | 5 | MEarth band

We obtained a series of ground-based photometric follow-up observations to
confirm that the transits are on-target, eliminate false-positive scenarios,
and refine the ephemeris and orbital parameters.

Full and partial transits of TOI-251b, TOI-942b, and TOI-942c were obtained by
an array of ground-based observatories. In particular, with only two transits
in the _TESS_ observations, the ephemeris uncertainty for TOI-942c was as
large as 5 hours, whilst the uncertainties for the shorter period planets
TOI-251b and TOI-942b were 2 hours. The first attempts at recovering the
transits of both planets failed due to these large uncertainties, but were
still useful in refining the transit predictions. Subsequent attempts
fortuitously captured partial transits, leading to the recovery of the
ephemeris.

####  2.3.1 Las Cumbres Observatory

Las Cumbres Observatory Global Telescope (LCOGT) is a global network of small
robotic telescopes (Brown et al., 2013). A full transit of TOI-251b was
observed by the 1 m LCOGT telescope located at Siding Spring Observatory,
Australia. The observations are scheduled via the TESS Transit Finder, which
is a customized version of the Tapir software package (Jensen, 2013). The
observations were obtained with the Sinistro camera, in the $Y$ band on the
night of 2019-07-23. The LCOGT images were calibrated by the standard LCOGT
BANZAI pipeline (McCully et al., 2018) and the photometric data were extracted
using the AstroImageJ (AIJ) software package (Collins et al., 2017a), showing
a likely detection of the 1 mmag transit event. Nearby stars were cleared for
signs of eclipsing binaries, showing that the transit event is on target to
within seeing limits. The observation is shown in Figure 9.

####  2.3.2 Mt. Kent Observatory

A full transit of TOI-251b was observed with the University of Louisville
Research Telescope at Mt. Kent Observatory, Queensland, Australia. The
University of Louisville Research Telescope is a PlaneWave Instruments CDK700
0.7 m telescope equipped with a 4 K$\times$4 K detector. The observation on
2019-07-28 was obtained in the $i^{\prime}$ band, spanning four hours, with an
average exposure time of $\sim 90\,s$. Photometry was extracted using
AstroImageJ (Collins et al., 2017b), showing a successful detection of the
transit event. The nearby stars were again checked for signatures of eclipsing
binaries, with none detected.

####  2.3.3 MEarth

The MEarth instruments are described in detail by Irwin et al. (2015) and for
brevity we do not repeat those details here.

For the majority of the MEarth observations listed in Table 3, we adopted a
standard observational strategy used for bright TOIs where all but one of the
available telescopes at a given observing site are operated defocused to
obtain photometry of the target star, and one telescope observes in focus with
the target star saturated to obtain photometry of any nearby contaminating
stars not properly resolved in the defocused observations. Once these stars
had been fully ruled out as the source of the transits, we simply used all
telescopes in defocused mode to obtain a slight improvement in sampling. This
was done for the observation of TOI-251 and for the last two observations of
TOI-942 (2019-12-05 and 2019-12-26) only.

With the exception of the observation of TOI-251 on 2019-11-17 which was
gathered from both MEarth-North and MEarth-South simultaneously (using a total
of 15 telescopes, 8 at MEarth-North and 7 at MEarth-South), all other
observations were gathered from MEarth-South using 7 telescopes. For TOI-942
exposure times were 60s on all telescopes and the defocused telescopes used a
half flux diameter (HFD) of 12 pixels. For TOI-942 we used a defocus setting
of 6 pixels HFD and an exposure time of 60s for the defocus telescopes and 30s
for the single in-focus telescope at MEarth-South, and 8 pixels HFD with all
telescopes using 60s exposure times at MEarth-North. These instruments use a
different model of CCD so have different pixel scales (0.84 arcsec/sec at
MEarth-South and 0.76 arcsec/sec at MEarth-North) and require slightly
different observational setups to achieve the same saturation limit.

Data were gathered continuously subject to twilight, zenith distance, and
weather constraints. Telescope 7 at MEarth-South used in the defocus ensemble
had a shutter stuck in the open position for all observations but this does
not appear to affect the light curves despite visible smearing during readout.
All data were reduced following standard procedures detailed in Irwin et al.
(2007); Berta et al. (2012). Photometric aperture radii for extraction of the
defocus time series of the target star were 24 pixels for TOI-251, 9.9 pixels
for TOI-942 at MEarth-South, and 12.7 pixels for TOI-251 at MEarth-North.

Figure 9: Ground based follow-up light curves of TOI-251b. The light curves from each facility are shown with an arbitrary vertical offset applied. The solid points mark the binned fluxes at phase intervals of 0.002. The observatory, date, and filter of each observation are labelled. Observations by the MEarth observatory were taken in the MEarth band. |
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Figure 10: Ground based follow-up light curve of TOI-942b Left and TOI-942c
Right are shown. The light curves are gathered by the MEarth observatory.

####  2.3.4 WASP archival observations

TOI-251 and TOI-942 also received multi-season monitoring by ground-based
transit surveys. The Wide Angle Search for Planets (WASP) Consortium (Pollacco
et al., 2006) observed both target stars with the Southern SuperWASP facility,
located at the Sutherland Station of the South African Astronomical
Observatory. Each SuperWASP station consists of arrays of eight commonly
mounted 200 mm f/1.8 Canon telephoto lenses, equipped with a
$2\mathrm{K}\times 2\mathrm{K}$ detector yielding a field of view of
$7.8^{\circ}\times 7.8^{\circ}$ per camera.

TOI-251 and TOI-942 received eight years of WASP observations, spanning 2006
to 2014. The $\sim 2\%$ spot modulation signal is clear in the WASP datasets
for both host stars. We made use of these observations in Section 4 to confirm
that the rotation period we measure from _TESS_ is robust and consistent with
that seen over the significantly longer timescales of the WASP observations.

###  2.4 High spatial resolution imaging

We obtained a series of high spatial resolution imagery of the target stars to
check for blended nearby stellar companions. Such companions can be the source
of false positive signals due to stellar eclipsing binaries, or dilute the
planetary transit signal leading to systematically smaller planet radius
measurements.

Observations of TOI-251 and TOI-942 were obtained as part of the Southern
Astrophysical Research (SOAR) _TESS_ survey (Ziegler et al., 2020). Speckle
imaging observations were obtained with the Andor iXon-888 camera on the 4.1 m
SOAR telescope. Observations of TOI-251 were obtained on 2019 May 18, and
TOI-942 on 2019 November 19. Each target star observation involved 400 frames
of $200\times 200$ binned pixels about the target, with a pixel scale of
$0\farcs 01575$, obtained over the course of 11 s. The observations were
reduced as per Tokovinin (2018). The speckle auto cross correlation functions
from these observations are shown in Figure 11. No stellar companions were
detected for either target star.

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Figure 11: SOAR speckle observations of TOI-251 (left) and TOI-942 (right).
The $5\sigma$ detection sensitivity to companions are shown in each figure.
The inserts show the auto correlation functions (ACF) for each observation. No
stellar companions were detected near either target star.

We also obtained speckle observations of TOI-942 with ′Alopeke at the 8 m
Gemini-North observatory, located on Mauna Kea, Hawaii. The observation,
obtained on 2019 October 14, incorporates a 1-minute integration involving
1000 60 ms exposures of $256\times 256$ pixel subarrays about the target star.
These observations have resulting spatial resolutions of $0.016\arcsec$ FWHM
in the blue, and $0.025\arcsec$ in the red, yielding an inner working angle of
$\sim$3 AU at the distance to TOI-942. The analysis and detection limits were
derived as per Howell et al. (2011) and Howell et al. (2016). The speckle
images and limits on companions are shown in Figure 12. Note that the
observations were obtained at relatively high airmass, and as such the blue
reconstructed image is adversely affected. No stellar companions are detected
in either channel.

Figure 12: Gemini-N ‘Alopeke speckle images of TOI-942, in the blue (top left)
and red (top right) channels. (Lower panel) The corresponding limiting
magnitudes for companions as a function of angular distance to the target
star.

##  3 Elimination of false positive scenarios

A number of astrophysical false positive scenarios can imitate the transit
signals of planetary systems. Eclipsing binaries in grazing geometries, or
nearby faint eclipsing binaries can exhibit transits of depths similar to that
of transiting super-Earths and Neptunes in extreme scenarios.

The possibility that our target stars are actually grazing eclipsing binaries
is extremely unlikely given their well-resolved box-shaped transits.
Nevertheless we obtained a series of radial velocity observations for both
target stars. Radial velocity variation at the $>1\,\rm km\,s^{-1}$ level can
be indicative of the companion being of stellar mass, or the target star being
spectroscopically blended with a background eclipsing binary.

We obtained nine spectra of each target star, and derived radial velocities
from each via a least-squares deconvolution analysis (Section 2.2.1). As
expected for young stars, these velocities exhibited significant astrophysical
jitter beyond their velocity uncertainties. The mean uncertainty of the
velocities for TOI-251 is $17\,\rm m\,s^{-1}$, while the velocity scatter is
significantly higher at $73\,\rm m\,s^{-1}$. Similarly, the mean uncertainty
in the velocities of TOI-942 is $35\,\rm m\,s^{-1}$, but the velocity scatter
is at $127\,\rm m\,s^{-1}$.

Nevertheless, the lack of a detectable radial velocity orbit to within $1\,\rm
km\,s^{-1}$ for both target stars rules out the possibility that they are
orbited by stellar companions. In section 5, we derive upper limits to the
masses of any orbiting companions around our target stars. The velocities of
each system are modeled assuming circular orbits for each planet; the stellar
activity is accounted for via a jitter term. We make no attempts at correcting
for the stellar jitter via decorrelation against stellar activity indicators,
nor make use of Gaussian processes to model possible rotational signals in the
velocities. Through this simple exercise, we find $3\sigma$ mass upper limits
of $<1.0{}\,M_{\mathrm{Jup}}$ for TOI-251b, $<2.6{}\,M_{\mathrm{Jup}}$ for
TOI-942b, and $<2.5{}\,M_{\mathrm{Jup}}$ for TOI-942c. Future examination
making use of stellar activity markers can further refine the masses of these
planets.

The $22\arcsec\,\mathrm{pixel}^{-1}$ plate scale of _TESS_ often makes it
difficult to distinguish the true source of transit signals in crowded fields.
Fainter eclipsing binaries whose depths are diluted by the flux from the
target star can often be misinterpreted as planet candidates. We obtained
ground-based follow-up photometric confirmation of all planet candidates
around TOI-251 (Figure 9) and TOI-942 (Figure 10). The on-target detection of
the transits shows that the transit signal originates from the target stars to
within the spatial resolution of $\sim 1\arcsec$ of our ground-based follow-up
facilities.

From the high spatial resolution speckle images presented in Section 2.4, we
can also eliminate the presence of any stellar companions with $\Delta M<4$
within $\sim 0.2\arcsec$ of our target stars. No _Gaia_ stars are catalogued
within $2\arcsec$ of these target stars. Similarly, no slowly rotating
spectroscopic blended companions were detected from our CHIRON observations
(Section 2.2.1) at $\Delta M<4$.

We can estimate the probability that a faint eclipsing binary lying unresolved
by our high resolution speckle images is causing the transit signals. The
transit shape, and the ratio between the ingress and totality timescales, can
inform us about the brightness of any diluted background eclipsing binary that
may be causing the transit signal (Seager & Mallén-Ornelas, 2003). We follow
Vanderburg et al. (2019) and estimate the brightest possible background
eclipsing binary that may be inducing our transit signal. The maximum
difference in magnitude is given by $\Delta m_{\mathrm{TESS}}\leq
2.5\log_{10}(T_{12}^{2}/T_{13}^{2}\delta)$, where $T_{12}$ is the duration of
ingress, $T_{13}$ is the duration between first and third contact, and
$\delta$ is the depth of the transit.

We find that for TOI-251b, the transit can only be caused by a background
eclipsing binary with $\Delta m_{\rm TESS}\leq 3.40$ and 3.0$\sigma$
significance. From our diffraction limited observations of TOI-251, we
excluded stellar blends within 0.2′′ to a brightness contrast of $\approx 3$
magnitudes. For a randomly chosen star in a direction near TOI-251, the
density of $2.0\leq\Delta m_{\rm TESS}\leq 3.4$ stars within the ground-based
exclusion radius of 0.2′′ is $<3\times 10^{-5}$. Though TOI-251 is not
randomly chosen, it is far from the galactic plane, where background eclipsing
binaries are expected to be roughly two orders of magnitude less common than
true planets (Sullivan et al., 2015, Figure 30). While not formally
impossible, the combined transit shape, lack of companions detectable by
diffraction limited imaging, lack of secondary spectroscopic lines, and line
of sight of TOI-251 lead background eclipsing binary scenarios to be highly
disfavored.

For TOI-942, a similar calculation yields that a background eclipsing binary
no fainter than 2.68 magnitudes is required to cause the transits of either
one of its two planets. If it were a randomly chosen star, then the chance of
there being another background star within $0.2$” is $<6\times 10^{-5}$ at
$\Delta m_{\mathrm{TESS}}<2.68$. The chance that two such background eclipsing
binaries exist inducing our multi-planet transiting signal is $<4\times
10^{-9}$. The low probability of such an occurrence, the multi-planet nature
of the system, and the lack of any companions from diffraction limited imaging
and spectroscopy, lead to eclipsing binary scenarios being disfavored.

##  4 Estimating the age of young field stars

It is notoriously difficult to estimate the ages of field stars. However,
young Sun-like stars exhibit rotational and activity induced photometric and
spectroscopic behavior that make it possible to approximate their ages. These
activity and rotation period properties can typically be calibrated via well-
characterized clusters (Mamajek & Hillenbrand, 2008) to provide age
relationships that can be used for dating purposes.

Sun-like stars spin down over their main-sequence lifetimes through mass loss
via stellar-wind processes. Whilst the Sun has a present-day rotation period
of 24 days, similar stars in the 120 Myr old Pleiades cluster have rotation
periods of $\sim 4$ days. The rapid rotation and consequentially stronger
dynamo of young stars excites strong spot and chromospheric activity.
Observable chromospheric activity indicators, such as emission in the core of
the calcium II lines, as well as X-ray emission, can be used as proxies for
rotation and age of young Sun-like stars. The element lithium is destroyed in
the cores of Sun-like stars through proton collisions. Through convective
mixing processes, this leads to a rapid depletion of lithium in the stellar
atmosphere within the first $\sim 500$ Myr of their lives. The strength of the
lithium 6708 Å absorption feature has traditionally being used as a youth
indicator for Sun-like stars.

We made use of these photometric and spectroscopic properties to estimate the
ages of TOI-251 and TOI-942. Though these estimates are imprecise given the
field nature of our target stars, they generally agree sufficiently for us to
place meaningful age constraints on these target stars.

###  4.1 Lithium depletion

The strength of atmospheric lithium absorption in the spectra of convective
envelope stars is also a commonly adopted age indicator. We make use of the Li
$6708\,\AA$ line as another age estimator for our targets. The Li line
equivalent widths are estimated by fitting three Gaussian profiles, accounting
for the Li doublet at $6707.76\,\AA$ and $6707.91\,\AA$, and the nearby Fe I
line at $6707.43\,\AA$ that is often blended with the Li features. Each line
is assumed to be of equal width, and the two Li lines are also assumed to be
of equal height. Using the TRES observations we obtained for both target
stars, we measured equivalent widths of the Li $6708\AA$ line to be $0.134\pm
0.017\,\AA$ for TOI-251, and $0.257\pm 0.054\,\AA$ for TOI-942.

To compare the lithium absorption feature of our target stars against stars in
well characterized clusters and associations, we obtained a series of spectra
of members of the IC 2602, IC 2391, Pleiades, and Praesepe groups. Spectra and
measurements of Pleiades and Praespe members come from long-term radial-
velocity surveys for planets in open clusters using the TRES spectrograph. Two
such surveys, in Praesepe and the Hyades, are described in Quinn et al. (2012)
and Quinn et al. (2014). With the goal of measuring low-amplitude RV
variation, the spectra are typically high SNR, and therefore support precise
measurement of Li equivalent widths. Li measurements for IC 2602 and IC 2391
members are adapted from Randich et al. (1997) and Randich et al. (2001).

Figure 13 shows the Li 6708 Å equivalent widths of the target stars, in
comparison with the same measurements for membership stars. The Li line
strength of TOI-251 agrees with that of Pleiades members, whilst TOI-942
exhibits significantly stronger Li absorption than equivalent stars in
Pleiades.

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Figure 13: Both TOI-251 and TOI-942 exhibit strong lithium absorption at 6708
Å. We fit this absorption feature with a Gaussian doublet at $6707.76\,\AA$
and $6707.91\,\AA$, and a single Fe I line at $6707.43\,\AA$. The absorption
features and best fit models of TOI-251 are shown in the left panel, TOI-942
on the middle panel. The bottom panel compares the equivalent widths of the
lithium feature against stars in the IC 2602, IC 2391, Pleiades, and Praesepe
clusters and associations. Measurements for Pleiades and Praesepe were
obtained as part of this work using the methodology described above.
Measurements for IC 2602 and IC 2391 are adopted from Randich et al. (1997)
and Randich et al. (2001).

###  4.2 Activity-age relationships

Both stars exhibit significant chromospheric emission in the near-ultraviolet
calcium II H and K lines and the near-infrared calcium II triplet. Both stars
are also detected in X-ray with the ROSAT all-sky survey, while TOI-942 is
detected in the GALEX NUV band. Chromospheric emission is a proxy for stellar
rotation, being generated due to the stronger magnetic dynamo of the rapidly
rotating young stars (e.g. Noyes et al., 1984). We make use of the Mount
Wilson $S_{HK}$ index to compare the chromospheric emission of our target
stars from the TRES spectra against literature activity-age relationships, as
explained in the next section.

####  4.2.1 Calcium II HK emission

Both calcium II H $(3969\,\AA)$ and K $(3934)$ lines are captured within TRES
echelle orders. We measure calcium II HK emission core emissions in a band
$1\,\AA$ wide centered about each line. The baseline flux is estimated from
$5\,\AA$ wide bands over the continuum regions on either side of the line
center. Figure 14 shows our calcium line strength measurements for Sun-like
stars $(5000<T_{\mathrm{eff}}<6000\,\mathrm{K})$ against that of catalog
$S_{HK}$ values of the same stars from the Mount Wilson Observatory HK Project
(Wilson, 1978; Vaughan et al., 1978; Duncan et al., 1991; Baliunas et al.,
1995). With the exception of a few active outlying stars, we find that our
line emission flux estimates can be translated to the $S_{HK}$ index with a
simple linear transformation, with an uncertainty of $\Delta S_{HK}=0.078$.
The calcium II HK line strength, as a function of the bolometric flux
$(R^{\prime}_{HK})$, is then calibrated using the relationship from Noyes et
al. (1984), via the _PyAstronomy_ (Czesla et al., 2019) _SMW_RHK_ function.
The $S_{HK}$ and $R^{\prime}_{HK}$ values for the target stars are listed in
Table 4. The uncertainties in these values are computed as the quadrature
addition of uncertainty in the TRES emission flux to $S_{HK}$ calibration, and
the scatter of the measurements between each observation.

The calcium II HK luminosity can be correlated with stellar age. We make use
of the calibration from Mamajek & Hillenbrand (2008) (Equation 3) to calculate
the calcium II HK ages of our target stars. TOI-251 has an age of
$27_{-13}^{+21}$ Myr, with a $3\sigma$ regime ranging from 3 to 170 Myr,
consistent with the gyrochronology estimate. TOI-942 is estimated to have an
age of $10_{-6}^{+12}$ Myr, with a $3\sigma$ upper limit of 100 Myr. The
activity age estimate is significantly younger than that from gyrochronology.
We note that with $\log R^{\prime}_{HK}=-4.019\pm 0.064$, the calcium II HK
emission from TOI-942 is near the limits of the calibrated range of the
Mamajek & Hillenbrand (2008) relations of $-5.0<\log R^{\prime}_{HK}<-4.0$,
corresponding to a lower age boundary of 8 Myr. Stars as young as TOI-942 have
saturated chromospheric emission features, making it difficult for us to
derive precise ages from these spectroscopic indicators.

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Figure 14: Calibrations for our measurements of the calcium II HK and infrared
triplet activity indices. Left panel shows the $S_{HK}$ index of Mount Wilson
stars as measured by TRES observations. We find agreement between our
measurements and those from literature to within $\Delta S_{HK}=0.078$. Right
panel shows the equivalent width measurements of the calcium II infrared
triplet core emission for stars that have both archival TRES observations and
were surveyed in Žerjal et al. (2017). We find that a linear transformation is
also sufficient to transform our measured values from TRES to those reported
in literature, with a resulting scatter in the equivalent widths of
$\Delta\mathrm{EW}_{\mathrm{IRT}}=0.053\,\AA$.

####  4.2.2 Infrared calcium II triplet emission

The infrared calcium II triplet at $8498\,\AA$, $8542\,\AA$ and $8662\,\AA$
also exhibit line core emission in active stars. Both TOI-251 and TOI-942
exhibit strong core emission in the infrared. The $8498\,\AA$ and $8542\,\AA$
lines are well placed within the TRES spectral orders. To measure the core
emission equivalent widths of these lines, we first fit and remove a synthetic
spectral template, and fit the residuals about the calcium lines with a
Gaussian profile. The synthetic template is an ATLAS9 (Castelli & Kurucz,
2004) atmosphere model, convolved with the instrumental and rotational
broadening kernel of the target star. The synthetic template is then
subtracted from the continuum normalized observed spectrum. The resulting
residuals about each calcium line are fitted with a Gaussian, with width
corresponding to the line broadening of the spectrum, and with centroid fixed
to the expected central wavelength of each line.

Figure 14 shows the equivalent widths as measured from TRES against the same
stars that were characterized by Žerjal et al. (2017). For Sun-like stars, a
linear transformation between our TRES observations and the literature values
is sufficient, with a scatter in the resulting relationship of
$\Delta\mathrm{EW}_{\mathrm{IRT}}=0.053\,\AA$.

We measure calcium II infrared triplet equivalent widths of
$\mathrm{EW}_{\mathrm{IRT}}=0.61\pm 0.10\,\AA$ for TOI-251 and $1.73\pm
0.17\,\AA$ for TOI-942. Žerjal et al. (2017) offers a qualitative age –
calcium triplet relationship from their calibration of cluster stars. The
infrared triplet emission of TOI-251 makes it compatible with similar stars in
the 100-1000 Myr range, whilst TOI-942 falls in the $<100$ Myr age range.

####  4.2.3 X-ray emission

Young, rapidly rotating stars are also known to exhibit X-ray emission.
TOI-251 is an X-ray source in The Second ROSAT Source Catalog of Pointed
Observations (Rosat, 2000), while TOI-942 is an X-ray source in the ROSAT all-
sky faint source catalog (Voges et al., 2000). Their X-ray count rates,
hardness ratios, and luminosities are provide in Table 4. We adopt the
calibration provided in Fleming et al. (1995) for the conversion between the
X-ray count rate $(CTS)$ to an X-ray luminosity $(L_{x})$, finding an X-ray
luminosity of $\log(L_{x}/L_{\mathrm{bol}})=-4.45\pm 0.36$ for TOI-251, and
$-3.12\pm 0.16$ for TOI-942. Using the age – X-ray luminosity relationship
from Mamajek & Hillenbrand (2008) (Equation A3), we derive an estimated age of
$280_{-180}^{+550}$ Myr for TOI-251, but the $3\sigma$ age upper limit is not
constraining due to the scatter in the distribution. For TOI-942, we find an
X-ray age of $7_{-4}^{+11}$ Myr, with a $3\sigma$ upper limit of 250 Myr. Like
our Ca II HK and infrared triplet estimates, the X-ray luminosity is saturated
for this calibration above $\log(L_{x}/L_{\mathrm{bol}})=4.0$ (corresponding
to an 8 Myr lower limit). TOI-942 is more active than the calibrated range of
the Mamajek & Hillenbrand (2008) relationships, so our age estimate is at best
qualitative.

####  4.2.4 NUV detection

Ultraviolet emission from active chromospheres can also be an indicator of
youth for Sun-like stars. TOI-942 has a measurable flux in the NUV band of the
GALEX all-sky catalogue (Bianchi et al., 2017). Findeisen et al. (2011)
calibrated a $NUV-J$ / $J-K$ colour-colour relationship using Hyades, Blanco
1, and moving group members, with a resulting scatter in the determined $\log$
ages of $0.39\,$dex. We adopt this relationship, and find an NUV age for
TOI-942 of $60_{-40}^{+130}$ Myr. We note that there is significant scatter in
the relationship between NUV flux and age, and as such the $3\sigma$ range of
the NUV age estimate is only constraining to $<1\,$Gyr.

###  4.3 Rotation Period and Gyrochronology

TOI-251 and TOI-942 exhibit significant spot-induced rotational modulation in
their _TESS_ light curves. These light curves, folded over the rotational
period, are shown in Figure 15. The periodograms from a Lomb-Scargle analysis
of the single sector of _TESS_ observations, as well as each observing
campaign of the WASP observations, are shown.

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Figure 15: Both TOI-251 and TOI-942 show significant spot modulation in their
light curves. The top panels show the Lomb-Scargle periodogram of the _TESS_
light curves (red) and each campaign of the WASP observations (grey). The
rotation period is consistently detected in the single sector of _TESS_
observations, and the eight years of monitoring from WASP. The bottom panels
show the _TESS_ light curve folded to the rotation period. Each rotation
period is over-plotted with a slightly different color gradient, such that it
is easier to discern the spot variations over the course of the _TESS_
observations.

From the _TESS_ light curves, we measure a rotation period for TOI-251 of
$3.84\pm 0.48$ days, while TOI-942 has a rotation period of $3.40\pm 0.37$
days. Similarly, the WASP observations yielded rotation periods of $3.799\pm
0.047$ days for TOI-251, and $3.41\pm 0.49$ for TOI-942. The longevity of this
activity signal from _TESS_ and WASP gives us confidence that the periodicity
we quote is the rotation period of the host stars.

We adopt a few gyrochronology relationships to estimate the ages of TOI-251
and TOI-942. These relationships were calibrated by interpolating the slow
rotating sequence in well characterized clusters. We note that by adopting
these relationships, we are making the assumption that TOI-251 and TOI-942
follow the age spin-down trends seen in slow rotators amongst Sun-like stars.
Many of these young clusters also show a spread in rotation at a given mass.
By Pleiades age, the rapid rotators are usually all binaries (e.g. Douglas et
al., 2016; Stauffer et al., 2018), but at the youngest ages, we cannot confirm
that our stars lie on the main sequence. If TOI-251 and TOI-942 are rapid
rotators for their age, then their ages will be difficult to estimate using
gyrochronology. Given that both stars exhibit significant chromospheric
activity and Lithium absorption, we think it is reasonable to assume these
stars are relatively young. By assuming that they are also slow rotators for
their age, we can apply gyrochronology relations to derive an additional age
constraint.

Using the relationship in Barnes (2007), we find an age $T_{\mathrm{gyro}}$ of
$110_{-60}^{+30}$ Myr for TOI-251, with a $3\sigma$ age range of 40-220 Myr.
TOI-942 is considerably younger at $50\pm 13$ Myr, with a $3\sigma$ age range
of 20-90 Myr. The uncertainties are the quadrature addition of the intrinsic
uncertainties in the gyrochronology relationship, as prescribed in Barnes
(2007), and the uncertainties resulting from the _TESS_ rotation period
measurements. Similarly, applying the age relationship from Mamajek &
Hillenbrand (2008), we get an age range of $70-318$ Myr for TOI-251, and
$41-155$ Myr for TOI-942.

Qualitatively, we can compare the rotation periods of our target stars against
those in known clusters and associations. Figure 16 shows the rotation periods
of the target stars against known members of the 120 Myr old Pleiades measured
by Rebull et al. (2016), and 800 Myr old Praesepe measured by Rebull et al.
(2017). For comparison, we also plot the rotation of members of the $h$ Persei
cluster, at an age of $13$ Myr from Moraux et al. (2013), to illustrate that
both TOI-251 and TOI-942 are older than some of the youngest cluster and
associations. The $h$ Persei members are marked by the blue squares in Figure
16. The colors of stars in $h$ Persei have been de-reddened according to the
3D dust maps via _dustmap_ (Green, 2018) using maps from Green et al. (2019).
In this qualitative comparison, the rotation period of TOI-251 agrees well
with the Pleiades population, supporting the gyrochronology estimate of $\sim
110$ Myr. TOI-942 is rotating faster than an equivalent star within the
Pleiades distribution, and as such supports our estimate of it being younger
than 100 Myr. We note though that there is a possibility for our targets to be
young, rapid rotators, as with stars in the significantly younger $h$ Persei
cluster.

Figure 16: A comparison between the rotation periods of TOI-251 and TOI-942
against stars from known clusters and associations. The blue squares mark
stars from the 13 Myr old $h$ Persei cluster as measured by Moraux et al.
(2013), with colors dereddened from 3D dust maps. The orange points show the
distribution of rotation periods for stars in the 120 Myr Pleiades cluster
from Rebull et al. (2016). The grey points show stars in the $\sim 800$ Myr
Praesepe cluster measured by Rebull et al. (2017). TOI-251 has rotation
periods similar to stars from the Pleiades. TOI-942 appears younger than the
majority of single stars from the Pleiades, but older than Sun-like stars near
the zero-age main sequence in the $h$ Persei cluster.

####  4.3.1 Infrared excess

The spectroscopic and gyrochronology age estimates described above have placed
meaningful upper age limits. Lower limits from these measurements are more
difficult for TOI-942 given that many of its activity indicators are
saturated.

A qualitative argument for the lower limits of both TOI-251 and TOI-942 can be
made due to their lack of any infrared excess in the WISE bands. The spectral
energy distribution of TOI-251 and TOI-942 are shown in Figure 19. Disks can
be traced by $H\alpha$ emission and infrared excess, and typically dissipate
by $\sim 5-10$ Myr (See reviews by Mamajek, 2009; Williams & Cieza, 2011). As
such, we adopt a lower limit of 10 Myr for the age of TOI-942.

####  4.3.2 Color-magnitude diagram

Further lower bound age limits may be inferred by comparing the colors and
magnitudes of the target stars against members of well known clusters. Figure
17 shows the Gaia color-magnitude diagram for TOI-251 and TOI-942. Stars from
the 120 Myr old Pleiades cluster (Lodieu et al., 2019) and 15 Myr old Upper
Sco association (Damiani et al., 2019) are shown for comparison.

TOI-251 is consistent with having an age similar to stars in the Pleiades
cluster, as per our spectroscopic and gyrochronology estimates above. Having
reached the main sequence, it is difficult to estimate its age from the
spectral energy distribution, and the ages from isochrone models provide no
further constraints to the age of the system.

TOI-942 lies marginally above the zero-age main sequence. The activity-based
age estimates described above have trouble placing an lower bound on the age
of TOI-942. From the color-magnitude diagram, TOI-942 clearly sits below stars
from the 15 Myr old Upper Sco association. As part of the global analysis, the
isochrone-fitted age from Section 5 provides a $3\sigma$ lower age limit of 23
Myr, consistent with that provided by gyrochronology.

Figure 17: The Gaia color-magnitude diagram of TOI-251 and TOI-942. For
comparison, stars from the 120 Myr old Pleiades cluster (Lodieu et al., 2019),
and the 15 Myr old Upper Sco association are shown (Damiani et al., 2019).
TOI-251 lies close to the distribution of stars in the Pleiades cluster.
TOI-942 lies marginally above stars in the Pleiades, but is clearly older than
the pre-main sequence stars in Upper Sco. For referece, the zero-age main
sequence from the MIST isochrones is marked by the black line (Dotter, 2016).

###  4.4 Kinematics

To the best of our knowledge, neither TOI 251 nor TOI 942 is a member of any
known coeval stellar population. To check, we searched the CDIPS target star
list (Bouma et al. 2019 Table 1), which is a concatenation of stars from
across the literature reported to be in known moving groups and open clusters.
This concatenation included large surveys ($>10^{5}$ cluster stars) such as
those of Kharchenko et al. (2013), Dias et al. (2014), Oh et al. (2017),
Cantat-Gaudin et al. (2018), Gaia Collaboration et al. (2018a), Zari et al.
(2018), Cantat-Gaudin et al. (2019), and Kounkel & Covey (2019). It also
included targetted surveys, for instance those of Röser et al. (2011), Rizzuto
et al. (2011), Kraus et al. (2014), Bell et al. (2017), Gagné et al. (2018a),
Gagné et al. (2018b), and Gagné & Faherty (2018). We also verified that we
could not place these targets into any known associations via the online
BANYAN $\Sigma$ tool (Gagné et al., 2018b).

###  4.5 Summary of age estimates

Figure 18 summarizes the ages of TOI-251 and TOI-942 as estimated from the age
indicators. For TOI-251, gyrochronology and chromospheric Ca II HK emissions
provide constraining age estimates. We adopt an estimated age range of 40-320
Myr for TOI-251, encompassing the $3\sigma$ upper range of both gyrochronology
relationships we tested, and the upper limit of chromospheric Ca II HK
emission estimates – the two age indicators that yielded constraining
estimates in our analysis. This age range also agrees with the estimates from
the less constraining Ca II infrared triplet and X-ray emission estimates,
which put the age of TOI-251 below 1 Gyr.

TOI-942 is clearly more active than TOI-251 and members of the Pleiades
cluster. Constraining measurements for the age of TOI-251 come from
gyrochronology, Ca II HK emissions, and the Ca II infrared triplet emissions,
placing a $3\sigma$ age range at $20-160$ Myr. The age estimates from X-ray
and NUV emissions are less constraining, but still consistent with a young age
for TOI-942. The fact that the rotation of the star is significantly slower
than similar stars in the 13 Myr $h$ Persei cluster at zero-age main sequence,
and the lack of infrared excess for TOI-942 allowed us to place an approximate
lower limit of 20 Myr.

Figure 18: A summary of the age-activity indicators for TOI-251 and TOI-942.
The $1\sigma$ (solid) and $3\sigma$ (lightened) age ranges from
gyrochronology, spectroscopic and photometric activity indicators are marked.
We adopt a final age estimate for TOI-251 of $40-320$ Myr, and for TOI-942 of
$20-160$ Myr.

##  5 System modeling

To derive accurate system parameters, we present a series of global models for
each system incorporating the _TESS_ discovery light curve, ground-based
follow-up light curves, radial velocities, spectroscopic and broadband
atmospheric parameters, and stellar isochrone constraints.

The light curves of young stars exhibit large variations due to spot
modulation. The variability signal often dwarfs the planetary transits, and as
such needs to be carefully considered so as to yield un-biased system
parameters. The modeling of spot activity is simplified by the quasi-
sinusoidal nature of the light curves, with well defined periods that can be
easily modeled. We adopt the _celerite_ package (Foreman-Mackey et al., 2017)
to model the stellar variability via its simple harmonic oscillator kernel,
with free parameters describing the frequency of the stellar variability
$\log\omega_{0}=\log 1/P_{\mathrm{rot}}$, the dampening factor $\log Q_{0}$,
and the power of the oscillator $\log S_{0}$. We impose a Gaussian prior on
$\log\omega_{0}$ based on the rotation period of each star, with the specific
limits shown in Table 5. Linear uniform priors were imposed for $\log Q_{0}$
and $\log S_{0}$. The follow-up light curves are also included in the global
analysis. These light curves are not modeled as part of the Gaussian process.
To account for any environmental systematics in the light curves, we instead
include a linear trend for each transit, a linear coefficient detrending
against airmass, and an additional offset term for meridian flips.

The transits are modeled via the _batman_ package (Kreidberg, 2015), with free
parameters defining the periods $P$, transit center ephemeris $T_{c}$, planet-
star radius ratio $R_{p}/R_{\star}$, and line of sight inclination $i$ for
each transiting planet. Limb darkening parameters are interpolated from Claret
& Bloemen (2011) and Claret (2017), and fixed through the modeling process.
The radial velocities are further modeled by circular orbits, with masses of
each planet $m_{p}$, and a jitter term $\sigma_{\mathrm{rv}}$ to account for
the radial velocity jitter. Given the large stellar-activity induced jitter
for these young stars, we only provide upper limits on the masses of the
planets reported here.

In addition, we model the stellar parameters simultaneously with the transits
and radial velocities. The stellar properties are modeled via the MESA
Isochrones & Stellar Tracks (MIST Dotter, 2016), interpolated using stellar
evolution tracks with ages below 1 Gyr and with initial masses
$0.6<M_{\star}<1.6\,M_{\odot}$. Free parameters include the stellar mass
$M_{\star}$, radius $R_{\star}$, and stellar metallicity [M/H]. These are
constrained by the spectroscopic effective temperature $T_{\mathrm{eff}}$,
surface gravity $\log g_{\star}$, and metallicity as measured by SPC from the
TRES spectra. We also incorporate photometric magnitudes from visual HIPPARCOS
(Perryman et al., 1997), _Gaia_ (Gaia Collaboration et al., 2018b) and near
infrared 2MASS bands (Skrutskie et al., 2006) in the modeling of the spectral
energy distribution. We incorporate de-biased _Gaia_ DR2 distance estimates
from Bailer-Jones et al. (2018) into the SED analysis. Though we have
estimates of the stellar age, we apply no age prior to the stellar evolution
modeling beyond limiting the ages to below 1 Gyr. The resulting age posteriors
are largely uninformative, allowing for all ages within the given range.

The final parameters for the host stars are presented in Table 4, and the
planet properties are presented in Table 5. The spectral energy distributions
are shown in Figure 19, with the best fit atmospheric model overlaid.

TOI-251

TOI-942

Figure 19: Spectral energy distributions (SED) of TOI-251 and TOI-942 over the HIPPARCOS (Perryman et al., 1997), _Gaia_ (Gaia Collaboration et al., 2018b), and 2MASS bands (Skrutskie et al., 2006) bands are plotted in navy. The MIST isochrone predicted fluxes in each band are marked by the open orange squares. The best fit ATLAS9 (Castelli & Kurucz, 2004) synthetic atmosphere model is overlaid in orange. The WISE $W_{1}$, $W_{2}$, and $W_{3}$ fluxes of the target stars are also shown, though they are not used to constrain the SED model.  Table 4:  Stellar parameters  Parameter | TOI-251 | TOI-942 | Source
---|---|---|---
Catalogue Information
TIC | 224225541 | 146520535 | Stassun et al. (2018)
Tycho-2 | 7520-00369-1 | 5909-00319-1 | Høg et al. (2000)
 _Gaia_ DR2 Source ID | 6539037542941988736 | 2974906868489280768 | Gaia Collaboration et al. (2018b)
 _Gaia_ RA (2015.5) | 23:32:14.9 | 05:06:35.91 | Gaia Collaboration et al. (2018b)
 _Gaia_ DEC (2015.5) | -37:15:21.11 | -20:14:44.21 | Gaia Collaboration et al. (2018b)
 _Gaia_ $\mu_{\alpha}$ $(\mathrm{mas}\,\mathrm{yr}^{-1})$ | $44.639\pm 0.074$ | $15.382\pm 0.034$ | Gaia Collaboration et al. (2018b)
 _Gaia_ $\mu_{\delta}$ $(\mathrm{mas}\,\mathrm{yr}^{-1})$ | $1.902\pm 0.070$ | $-3.976\pm 0.040$ | Gaia Collaboration et al. (2018b)
 _Gaia_ DR2 Parallax $(\mathrm{mas})$ | $10.019\pm 0.044$ | $6.524\pm 0.029$ | Gaia Collaboration et al. (2018b)
Systemic Radial Velocity ($\rm km\,s^{-1}$) aa Derived from the global
modeling described in Section 5, co-constrained by spectroscopic stellar
parameters and the _Gaia_ DR2 parallax.
| $-2.059_{-0.030}^{+0.026}$ | $25.321_{-0.032}^{+0.034}$ | …
U $(\rm km\,s^{-1})$ | $-19.454\pm 0.085$ | $-15.729\pm 0.030$ |
V $(\rm km\,s^{-1})$ | $-7.190\pm 0.045$ | $-22.347\pm 0.045$ |
W $(\rm km\,s^{-1})$ | $-4.550\pm 0.039$ | $-5.252\pm 0.040$ |
Stellar atmospheric properties
$T_{\rm eff\star}$ (K) | $5875_{-190}^{+100}$ | $4928_{-85}^{+125}$ |
$\rm[Fe/H]$ aa Derived from the global modeling described in Section 5, co-
constrained by spectroscopic stellar parameters and the _Gaia_ DR2 parallax.
| $-0.106_{-0.070}^{+0.079}$ | $-0.221_{-0.076}^{+0.131}$ |
$v\sin{I_{\star}}$ ($\rm km\,s^{-1}$) | $11.5\pm 1.0$ | $14.3\pm 0.5$ |
$v_{\mathrm{macro}}$ ($\rm km\,s^{-1}$) | $7.9\pm 1.0$ | $9.8\pm 3.4$ |
Stellar activity properties
$P_{\mathrm{rot}}$ (d) | $3.84\pm 0.48$ | $3.40\pm 0.37$ |
$S_{HK}\,(\AA)$ | $0.6160.083$ | $1.06\pm 0.15$ |
$\log R^{\prime}_{HK}$ | $-4.119\pm 0.066$ | $-4.019\pm 0.064$ |
Ca II IRT EW $(\AA)$ | $0.61\pm 0.10$ | $1.73\pm 0.17$ |
ROSAT X-ray Counts $CTS$ | $0.01477$ | $0.0446\pm 0.0130$ | Rosat (2000); Voges et al. (2000)
ROSAT X-ray Hardness Ratio $HR_{1}$ | $-0.39\pm 0.12$ | $0.17\pm 0.28$ | Rosat (2000); Voges et al. (2000)
X-ray luminosity $\log Lx/L_{\mathrm{bol}}$ | $-4.45\pm 0.36$ | $-3.12\pm 0.16$ |
Li 6708 EW $(\AA)$ | $0.134\pm 0.017$ | $0.257\pm 0.054$ |
Photometric properties
GALEX NUV (mag) |  | $18.507\pm 0.049$ | Bianchi et al. (2017)
TESS $T$ (mag) | $9.3258\pm 0.0061$ | $11.0462\pm 0.0066$ | Stassun et al. (2018)
 _Gaia_ $G$ (mag) | $9.7541\pm 0.0012$ | $11.6346\pm 0.0014$ | Gaia Collaboration et al. (2018b)
 _Gaia_ $Bp$ (mag) | $10.1070\pm 0.0030$ | $12.1468\pm 0.0034$ | Gaia Collaboration et al. (2018b)
 _Gaia_ $Rp$ (mag) | $9.2910\pm 0.0026$ | $10.9950\pm 0.0029$ | Gaia Collaboration et al. (2018b)
TYCHO $B$ (mag) | $10.528\pm 0.068$ | $12.783\pm 0.364$ | Perryman et al. (1997)
TYCHO $V$ (mag) | $9.8870\pm 0.0050$ | $11.982\pm 0.026$ | Perryman et al. (1997)
2MASS $J$ (mag) | $8.766\pm 0.020$ | $10.231\pm 0.022$ | Skrutskie et al. (2006)
2MASS $H$ (mag) | $8.498\pm 0.044$ | $9.747\pm 0.023$ | Skrutskie et al. (2006)
2MASS $K_{s}$ (mag) | $8.426\pm 0.027$ | $9.639\pm 0.023$ | Skrutskie et al. (2006)
WISE $W_{1}$ (mag) | $8.372\pm 0.024$ | $9.576\pm 0.024$ | Wright et al. (2010); Cutri & et al. (2013)
WISE $W_{2}$ (mag) | $8.399\pm 0.020$ | $9.609\pm 0.020$ | Wright et al. (2010); Cutri & et al. (2013)
WISE $W_{3}$ (mag) | $8.368\pm 0.022$ | $9.453\pm 0.039$ | Wright et al. (2010); Cutri & et al. (2013)
Stellar properties
$M_{\star}$ ($M_{\sun}$) | $1.036_{-0.009}^{+0.013}$ | $0.788_{-0.031}^{+0.037}$ |
$R_{\star}$ ($R_{\sun}$) | $0.881_{-0.047}^{+0.038}$ | $1.022_{-0.020}^{+0.018}$ |
$\log{g_{\star}}$ (cgs) | $4.560_{-0.046}^{+0.046}$ | $4.314_{-0.028}^{+0.028}$ |
$L_{\star}$ ($L_{\sun}$) | $0.831_{-0.072}^{+0.105}$ | $0.428_{-0.079}^{+0.166}$ |
Line of sight inclination $I_{*}\,(^{\circ})$ | $78_{-14}^{+7}\,(>43\,3\sigma)$ | $76_{-11}^{+9}\,(>45\,3\sigma)$ |
Age (Myr) | $40-320$ | $20-160$ |
Distance (pc) | $99.52_{-0.43}^{+0.44}$ | $152.76_{-0.71}^{+0.71}$ |
Table 5:  Orbital and planetary parameters  Parameter | TOI-251b | TOI-942b | TOI-942c
---|---|---|---
Light curve parameters
$P$ (days) | $4.937770_{-0.000029}^{+0.000028}$ | $4.324190_{-0.000030}^{+0.000030}$ | $10.156430_{-0.000079}^{+0.000069}$
$T_{c}$ (${\rm BJD-TDB}$) aa $T_{c}$: Reference epoch of mid transit that minimizes the correlation with the orbital period. $T_{14}$: total transit duration, time between first to last contact;  | $2458357.30548_{-0.0015}^{+0.0013}$ | $2458441.5762_{-0.0021}^{+0.0021}$ | $2458447.0563_{-0.0023}^{+0.0023}$
$T_{14}$ (days) aa $T_{c}$: Reference epoch of mid transit that minimizes the correlation with the orbital period. $T_{14}$: total transit duration, time between first to last contact;  | $0.0930_{-0.0020}^{+0.0026}$ | $0.1418_{-0.0018}^{+0.0025}$ | $0.07994_{-0.00088}^{+0.00082}$
$a/R_{\star}$ | $14.02_{-0.61}^{+0.82}$ | $10.12_{-0.18}^{+0.13}$ | $17.88_{-0.32}^{+0.22}$
$R_{p}/R_{\star}$ | $0.02858_{-0.0010}^{+0.0011}$ | $0.04322_{-0.0016}^{+0.0015}$ | $0.05202_{-0.0013}^{+0.0012}$
$b\equiv a\cos i/R_{\star}$ | $0.607_{-0.070}^{+0.047}$ | $0.05_{-0.04}^{+0.05}$ | $0.149_{-0.093}^{+0.119}$
$i$ (deg) | $87.52_{-0.31}^{+0.40}$ | $89.97_{-0.51}^{+0.34}$ | $89.54_{-0.42}^{+0.68}$
Limb-darkening and gravity darkening coefficients bb Values for a quadratic
law given separately for each of the filters with which photometric
observations were obtained. These values were adopted from the tabulations by
Claret & Bloemen (2011) according to the spectroscopic an initial estimate of
the stellar parameters.
$a_{i}^{\prime}$ | 0.3817 | … | …
$b_{i}^{\prime}$ | 0.3393 | … | …
$a_{Y}$ | 0.1428 | … | …
$b_{Y}$ | 0.3642 | … | …
$a_{\mathrm{Mearth}}$ | 0.1925 | 0.3201 | …
$b_{\mathrm{Mearth}}$ | 0.3552 | 0.2797 | …
$a_{\mathrm{TESS}}$ | 0.2831 | 0.4006 | …
$b_{\mathrm{TESS}}$ | 0.2873 | 0.2243 | …
RV parameters
$K$ ($\rm m\,s^{-1}$) | $<120$ | $<370$ | $<284$
$e$ | 0 (fixed) | 0 (fixed) | 0 (fixed)
RV jitter ($\rm m\,s^{-1}$) | $81_{-22}^{+34}$ | $86_{-29}^{+56}$ | …
Gaussian process hyperparameters
$\log\omega_{0}$ SHOT Frequency | $-1.26_{-0.14}^{+0.14}$ | $-1.19_{-0.11}^{+0.11}$ | …
| (Gaussian prior $\mu=-1.35,\sigma=0.13$) | (Gaussian prior $\mu=-1.22,\sigma=0.11$) |
$\log Q_{0}$ SHOT Quality factor | $-0.55_{-0.40}^{+0.57}$ | $-1.10_{-0.31}^{+0.43}$ | …
$\log S_{0}$ SHOT S | $-4.25_{-0.56}^{+0.56}$ | $-2.37_{-0.50}^{+0.48}$ | …
Planetary parameters
$R_{p}$ ($R_{\oplus}$) | $2.74_{-0.18}^{+0.18}$ | $4.81_{-0.20}^{+0.20}$ | $5.79_{-0.18}^{+0.19}$
$M_{p}$ ($M_{\mathrm{Jup}}$) | $<1.0$ | $<2.6$ | $<2.5$
$a$ (AU) | $0.05741_{-0.00017}^{+0.00023}$ | $0.04796_{-0.00065}^{+0.00073}$ | $0.0847_{-0.0011}^{+0.0012}$

##  6 Discussion

We report the discovery and validation of planets around TOI-251 and TOI-942.
The two systems of small planets orbiting relatively young field stars, with
TOI-251 estimated to be $40-320$ Myr old, and TOI-942 at $20-160$ Myr old. The
mini-Neptune TOI-251 b has an orbital period of $4.94$ days, and a radius of
$2.74_{-0.18}^{+0.18}$ $R_{\oplus}$. Two inflated Neptunes orbit TOI-942, with
TOI-942b in a $4.32$ day orbit with a radius of $4.81_{-0.20}^{+0.20}$
$R_{\oplus}$, and TOI-942c in a $10.16$ day orbit with a radius of
$5.79_{-0.18}^{+0.19}$ $R_{\oplus}$.

###  6.1 The radius-period diagram for young planets, and the detectability of
smaller planets

Discoveries of super-Earths and Neptunes around young stars give us a unique
opportunity to explore the evolution of small planets in their early stages of
evolution. Figure 20 shows the period-radius distribution of close-in small
planets, comparing the planets characterized by the _Kepler_ survey and those
subsequently discovered around stars younger than $500$ Myr. Photoevaporation
is key in sculpting this distribution, creating a sub-Saturn desert devoid of
close-in Neptunes and super-Earths (e.g. Lopez et al., 2012; Owen & Wu, 2013;
Owen & Lai, 2018) and carving the radius valley between rocky and gaseous
planets further out (e.g. Fulton et al., 2017; Owen & Wu, 2017).

TOI-251b straddles along the evaporation gap between solid cores and planets
still retaining their gaseous envelopes. It is amongst the smallest planets
known around stars younger than 500 Myr; only the planets around the Ursa
Major moving group member TOI-1726 (Mann et al., 2020) are smaller. The
planets around TOI-942 lie in the sub-Saturn radius regime, similar in radii
and periods to other young planetary systems at the $\sim 20-50$ Myr age
regime, such as DS Tuc Ab (Newton et al., 2019), and V1298 Tau c and d (David
et al., 2019a).

Figure 20: The period-radius distribution of close-in small planets. The
contours mark the distribution of planets from the _Kepler_ survey
characterized in Fulton et al. (2017), with a gap between rocky and gaseous
enveloped planets clearly seen. Planets around TOI-251 and TOI-942 are marked.
The detection limits of planets around each of these stars are marked by
horizontal lines. Planets around stars younger than 500 Myr old are shown in
cyan-colored points, including the planets around V1298 (David et al., 2019b,
a), K2-33b (Mann et al., 2016b; David et al., 2016), DS Tuc Ab (Newton et al.,
2019), Kepler-63b (Sanchis-Ojeda et al., 2013), HIP67522 b (Rizzuto et al.,
2020), and TOI1726 b and c (Mann et al., 2020).

The planets around TOI-251 and TOI-942, as well as most other planets found
around young stars, have larger radii than most in the _Kepler_ sample.
However, it may be difficult to compare this sample of planets around young,
active stars against those identified by the _Kepler_ sample around quiet
stars with higher precision light curves.

To see if smaller planets could be recovered from similar light curves, we
performed a signal injection and recovery exercise on the _TESS_ observations
of TOI-251 and TOI-942. Figure 20 shows the detection thresholds derived from
1000 injected planets across the radius-period space. Each injection is drawn
from a uniform distribution in period between 1 and 15 days, radius from 0.5
to 15 $R_{\oplus}$, and impact parameter from 0 to 1. A circular orbit is
assumed for every injected planet. The light curves are then detrended via a
cosine-filtering (Mazeh & Faigler, 2010) algorithm, and the transits recovered
via a BLS (Kovács et al., 2002) search. The injection and recovery exercise
shows that the planets we discovered are nearly the smallest detectable
planets. The detection thresholds worsen significantly for planets in orbits
longer than 10 days. Importantly, the predominant population of close-in small
planets with $R_{p}<2R_{\oplus}$, and those with $R_{P}<3R_{\oplus}$ and
orbital periods $>10$ days, would not be detectable around either star.
Similar injection and recovery exercises of previous analyses (e.g. Newton et
al., 2019; Rizzuto et al., 2020) show similar results, that our detectability
for planets smaller than $\sim 2-3\,R_{\oplus}$ is only complete at periods
shorter than 10 days.

###  6.2 Orbital eccentricity and prospects for obliquity measurements

One main tracer for the origins of close-in planets is the properties of the
orbits they currently inhabit. High eccentricity or highly oblique orbits can
be indicative of strong dynamical interaction in the early history of these
planets.

We modified our analysis (Section 5) to allow eccentricity, modeled as
$\sqrt{e}\cos\omega$ and $\sqrt{e}\sin\omega$, to be free during the global
modeling. To prevent the large jitter of radial velocities and systematic
effects from ground base transit observations from influencing our
eccentricity estimates, we make use of only the _TESS_ light curves and the
SED in this analysis.

Figure 21 and 22 show the resulting posteriors in eccentricity $e$ and
longitude of periastron $\omega$. For both systems, the eccentricity can only
be loosely constrained with existing datasets. We find $3\sigma$ upper limits
$e<0.64$ for TOI-251b, $<0.87$ for TOI-942b, and $<0.80$ for TOI-942c.

Figure 21: Eccentricity posterior for TOI-251b, as constrained by the _TESS_
transit duration and inferred stellar parameters. We find that the
eccentricity of TOI-251b can only be loosely constrained to $e<0.64$ at
$3\sigma$ significance.

Figure 22: Eccentricity posteriors for TOI-942b and c based on their _TESS_
transit durations and inferred host star parameters. The eccentricities are
poorly constrained with existing observations, with only highly eccentric
orbits ruled out. The eccentricity of TOI-942b is constrained to be $e<0.87$,
and $e<0.80$ for TOI-942c at $3\sigma$ significance.

Given the difficulty in measuring precise radial velocity orbits for these
planets around young, active stars, a potentially easier observational
constraint on their dynamical histories is their projected orbital obliquity
angles. The obliquity angle is the relative angle between the orbital planes
of the planets and the rotation axis of the host star. Planets that
experienced significant dynamical interactions in their past can often be
found in highly oblique orbits (e.g. Triaud, 2017).

The line of sight inclination of the host stars can be used to approximate the
orbital obliquity for the planets. Following Masuda & Winn (2020), we compute
the stellar inclination angle $I_{*}$ via the isochrone-derived stellar radius
$R_{\star}$, the spectroscopic rotational broadening velocity
$v\sin{I_{\star}}$, and the photometric rotation period $P_{\mathrm{rot}}$ of
each system. Though tight constraints cannot be placed with our existing
observations, TOI-251 and TOI-942 appear both to be well aligned, with
$3\sigma$ lower limits of $I_{\star}>45^{\circ}$ for both stars (see Table 4
for their precisely derived values).

A much more precise technique of measuring the orbital obliquities of these
transiting systems is to observe their spectroscopic transits via the
Rossiter-McLaughlin (Rossiter, 1924; McLaughlin, 1924) effect, or via the
Doppler tomographic transit shadow detection (Donati et al., 1997; Collier
Cameron et al., 2010). Based on our measured rotational broadening velocity,
TOI-251b should exhibit an in-transit velocity anomaly of $\sim 4\,\rm
m\,s^{-1}$, while TOI-942b and TOI-942c should exhibit significant velocity
variations at the levels of $20-30\,\rm m\,s^{-1}$. Planets around bright,
young, rapidly rotating stars are good targets for mapping the orbital
obliquity – age relationship, and determining the origins of the abundance of
small planets around Sun-like stars.

##  7 Conclusions

TOI-251 and TOI-942 are two field stars exhibiting photometric and
spectroscopic signatures of youth, hosting transiting Neptunes that were
identified by _TESS_ observations.

TOI-251b is a $2.74_{-0.18}^{+0.18}{}\,R_{\oplus}$ mini-Neptune in a $4.94{}$
day period around a G-type star. The period and transit ephemeris of the
system were refined by three ground-based follow-up observations that
successfully detected the 1 mmag transit events on the target star. We were
able to eliminate false positive scenarios with extensive spectroscopic
follow-up and speckle imaging of the host star, validating the planetary
nature of the transits.

We estimated the age of TOI-251 to be $40-320$ Myr, based on its photometric
rotation period, spectroscopic calcium II core emission in the HK and infrared
triplet lines, and the presence of X-ray emission from the ROSAT all-sky
survey. The rotation period and 6708 Å lithium absorption strength are
comparable to that of stars in the Pleiades cluster, agreeing with our age
estimates for the system.

TOI-942 hosts two Neptune sized planets around a K-type star. TOI-942b is a
$4.81_{-0.20}^{+0.20}{}\,R_{\oplus}$ planet in a $4.32{}$ day period orbit,
while TOI-942c has a radius of $5.79_{-0.18}^{+0.19}{}\,R_{\oplus}$ and an
orbital period of $10.16{}$ days. The transits of TOI-942b and c were both
successfully recovered by an extensive ground-based follow-up campaign with
the MEarth telescope array. The planetary nature of the system were further
validated by diffraction limited imaging and spectroscopic analyses.

The age of TOI-942 is significantly younger than TOI-251, estimated at
$20-160$ Myr. It exhibits strong X-ray and calcium emission that are stronger
and beyond the range of calibrated literature age-activity relationships. The
rotation period and lithium absorption strength of TOI-942 suggest that it has
an age younger than the Pleiades cluster, and more in agreement with younger
stellar associations.

TOI-251 and TOI-942 are examples of young planet hosting field stars that can
contribute significantly to characterizing the relationship between planet
properties and their ages. _TESS_ is likely to yield numerous systems like
TOI-251 and TOI-942, amenable to extensive follow-up observations that can
characterize the orbital and atmospheric properties of planets at early stages
of their evolutions.

The authors became aware of a parallel effort on the characterization of
TOI-942 by Carleo et al. in the late stages of the manuscript preparations.
The submissions are coordinated, and no analyses or results were shared prior
to submission. Work by G.Z. is supported by NASA through Hubble Fellowship
grant HST-HF2-51402.001-A awarded by the Space Telescope Science Institute,
which is operated by the Association of Universities for Research in
Astronomy, Inc., for NASA, under contract NAS 5-26555. The MEarth Team
gratefully acknowledges funding from the David and Lucile Packard Fellowship
for Science and Engineering (awarded to D.C.). This material is based upon
work supported by the National Science Foundation under grants AST-0807690,
AST-1109468, AST-1004488 (Alan T. Waterman Award), and AST- 1616624, and upon
work supported by the National Aeronautics and Space Administration under
Grant No. 80NSSC18K0476 issued through the XRP Program. This work is made
possible by a grant from the John Templeton Foundation. The opinions expressed
in this publication are those of the authors and do not necessarily reflect
the views of the John Templeton Foundation. 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. Funding for the TESS
mission is provided by NASA’s Science Mission directorate. We acknowledge the
use of public TESS Alert data from pipelines at the TESS Science Office and at
the TESS Science Processing Operations Center. This research has made use of
the Exoplanet Follow-up Observation Program website, which is operated by the
California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.
This paper includes data collected by the TESS mission, which are publicly
available from the Mikulski Archive for Space Telescopes (MAST). Resources
supporting this work were provided by the NASA High-End Computing (HEC)
Program through the NASA Advanced Supercomputing (NAS) Division at Ames
Research Center for the production of the SPOC data products. This work makes
use of data from the Mount Wilson HK-Project. The HK_Project_v1995_NSO data
derive from the Mount Wilson Observatory HK Project, which was supported by
both public and private funds through the Carnegie Observatories, the Mount
Wilson Institute, and the Harvard-Smithsonian Center for Astrophysics starting
in 1966 and continuing for over 36 years. These data are the result of the
dedicated work of O. Wilson, A. Vaughan, G. Preston, D. Duncan, S. Baliunas,
and many others. This work makes use of observations from the LCOGT network.
Some of the observations in the paper made use of the High-Resolution Imaging
instrument(s) ‘Alopeke (and/or Zorro). ‘Alopeke (and/or Zorro) was funded by
the NASA Exoplanet Exploration Program and built at the NASA Ames Research
Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley.
‘Alopeke (and/or Zorro) was mounted on the Gemini North (and/or South)
telescope of the international Gemini Observatory, a program of NOIRLab, which
is managed by the Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foundation. on behalf
of the Gemini partnership: the National Science Foundation (United States),
National Research Council (Canada), Agencia Nacional de Investigación y
Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación
(Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações
(Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).
FLWO 1.5 m, CHIRON, TESS, LCOGT, MEarth, Gemini, Subaru

## References

  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123
  * Bailer-Jones et al. (2018) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantelet, G., & Andrae, R. 2018, AJ, 156, 58
  * Baliunas et al. (1995) Baliunas, S. L., Donahue, R. A., Soon, W. H., et al. 1995, ApJ, 438, 269
  * Barentsen et al. (2019) Barentsen, G., Hedges, C., Vinícius, Z., & Saunders, N. e. a. 2019, KeplerGO/lightkurve: Lightkurve v1.0b29 (Version v1.0b29)., Zenodo, doi:10.5281/zenodo.2565212
  * Barnes (2007) Barnes, S. A. 2007, ApJ, 669, 1167
  * Bell et al. (2017) Bell, C. P. M., Murphy, S. J., & Mamajek, E. E. 2017, MNRAS, 468, 1198
  * Berta et al. (2012) Berta, Z. K., Irwin, J., Charbonneau, D., Burke, C. J., & Falco, E. E. 2012, AJ, 144, 145
  * Bianchi et al. (2017) Bianchi, L., Shiao, B., & Thilker, D. 2017, ApJS, 230, 24
  * Bouma et al. (2019) Bouma, L. G., Hartman, J. D., Bhatti, W., Winn, J. N., & Bakos, G. . 2019, ApJS, 245, 13
  * Brasseur et al. (2019) Brasseur, C. E., Phillip, C., Fleming, S. W., Mullally, S. E., & White, R. L. 2019, Astrocut: Tools for creating cutouts of TESS images, ascl:1905.007
  * Brown et al. (2013) Brown, T. M., Baliber, N., Bianco, F. B., et al. 2013, PASP, 125, 1031
  * Buchhave et al. (2010) Buchhave, L. A., Bakos, G. Á., Hartman, J. D., et al. 2010, ApJ, 720, 1118
  * Buchhave et al. (2012) Buchhave, L. A., Latham, D. W., Johansen, A., et al. 2012, Nature, 486, 375
  * Cantat-Gaudin et al. (2018) Cantat-Gaudin, T., Jordi, C., Vallenari, A., et al. 2018, å, 618, A93
  * Cantat-Gaudin et al. (2019) Cantat-Gaudin, T., Jordi, C., Wright, N. J., et al. 2019, å, 626, A17
  * Castelli & Kurucz (2004) Castelli, F., & Kurucz, R. L. 2004, ArXiv Astrophysics e-prints, astro-ph/0405087
  * Ciardi et al. (2018) Ciardi, D. R., Crossfield, I. J. M., Feinstein, A. D., et al. 2018, AJ, 155, 10
  * Claret (2017) Claret, A. 2017, A&A, 600, A30
  * Claret & Bloemen (2011) Claret, A., & Bloemen, S. 2011, A&A, 529, A75
  * Collier Cameron et al. (2010) Collier Cameron, A., Guenther, E., Smalley, B., et al. 2010, MNRAS, 407, 507
  * Collins et al. (2017a) Collins, K. A., Kielkopf, J. F., Stassun, K. G., & Hessman, F. V. 2017a, AJ, 153, 77
  * Collins et al. (2017b) —. 2017b, AJ, 153, 77
  * Cutri & et al. (2013) Cutri, R. M., & et al. 2013, VizieR Online Data Catalog, II/328
  * Czesla et al. (2019) Czesla, S., Schröter, S., Schneider, C. P., et al. 2019, PyA: Python astronomy-related packages, ascl:1906.010
  * Damiani et al. (2019) Damiani, F., Prisinzano, L., Pillitteri, I., Micela, G., & Sciortino, S. 2019, A&A, 623, A112
  * David et al. (2019a) David, T. J., Petigura, E. A., Luger, R., et al. 2019a, ApJ, 885, L12
  * David et al. (2016) David, T. J., Hillenbrand, L. A., Petigura, E. A., et al. 2016, Nature, 534, 658
  * David et al. (2018a) David, T. J., Mamajek, E. E., Vanderburg, A., et al. 2018a, AJ, 156, 302
  * David et al. (2018b) David, T. J., Crossfield, I. J. M., Benneke, B., et al. 2018b, AJ, 155, 222
  * David et al. (2019b) David, T. J., Cody, A. M., Hedges, C. L., et al. 2019b, AJ, 158, 79
  * Dias et al. (2014) Dias, W. S., Monteiro, H., Caetano, T. C., et al. 2014, å, 564, A79
  * Donati et al. (1997) Donati, J.-F., Semel, M., Carter, B. D., Rees, D. E., & Collier Cameron, A. 1997, MNRAS, 291, 658
  * Dotter (2016) Dotter, A. 2016, ApJS, 222, 8
  * Douglas et al. (2016) Douglas, S. T., Agüeros, M. A., Covey, K. R., et al. 2016, ApJ, 822, 47
  * Duncan et al. (1991) Duncan, D. K., Vaughan, A. H., Wilson, O. C., et al. 1991, ApJS, 76, 383
  * Fűrész (2008) Fűrész, G. 2008, PhD thesis, Univ. of Szeged, Hungary
  * Findeisen et al. (2011) Findeisen, K., Hillenbrand, L., & Soderblom, D. 2011, AJ, 142, 23
  * Fleming et al. (1995) Fleming, T. A., Schmitt, J. H. M. M., & Giampapa, M. S. 1995, ApJ, 450, 401
  * Foreman-Mackey et al. (2017) Foreman-Mackey, D., Agol, E., Angus, R., & Ambikasaran, S. 2017, ArXiv
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306
  * Fulton et al. (2017) Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, AJ, 154, 109
  * Gagné & Faherty (2018) Gagné, J., & Faherty, J. K. 2018, ApJ, 862, 138
  * Gagné et al. (2018a) Gagné, J., Roy-Loubier, O., Faherty, J. K., Doyon, R., & Malo, L. 2018a, ApJ, 860, 43
  * Gagné et al. (2018b) Gagné, J., Mamajek, E. E., Malo, L., et al. 2018b, ApJ, 856, 23
  * Gaia Collaboration et al. (2018a) Gaia Collaboration, Babusiaux, C., van Leeuwen, F., et al. 2018a, å, 616, A10
  * Gaia Collaboration et al. (2018b) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018b, A&A, 616, A1
  * Gray (2005) Gray, D. F. 2005, The Observation and Analysis of Stellar Photospheres
  * Green (2018) Green, G. 2018, The Journal of Open Source Software, 3, 695
  * Green et al. (2019) Green, G. M., Schlafly, E., Zucker, C., Speagle, J. S., & Finkbeiner, D. 2019, ApJ, 887, 93
  * Høg et al. (2000) Høg, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A, 355, L27
  * Howell et al. (2016) Howell, S. B., Everett, M. E., Horch, E. P., et al. 2016, ApJ, 829, L2
  * Howell et al. (2011) Howell, S. B., Everett, M. E., Sherry, W., Horch, E., & Ciardi, D. R. 2011, AJ, 142, 19
  * Huang et al. (2019) Huang, X., Burt, J., Vanderburg, A., et al. 2019, in American Astronomical Society Meeting Abstracts, Vol. 233, American Astronomical Society Meeting Abstracts #233, 209.08
  * Irwin et al. (2007) Irwin, J., Irwin, M., Aigrain, S., et al. 2007, MNRAS, 375, 1449
  * Irwin et al. (2015) Irwin, J. M., Berta-Thompson, Z. K., Charbonneau, D., et al. 2015, in Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, Vol. 18, 18th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, 767–772
  * Jenkins et al. (2016) Jenkins, J. M., Twicken, J. D., McCauliff, S., et al. 2016, in Proc. SPIE, Vol. 9913, Software and Cyberinfrastructure for Astronomy IV, 99133E
  * Jensen (2013) Jensen, E. 2013, Tapir: A web interface for transit/eclipse observability, Astrophysics Source Code Library, ascl:1306.007
  * Kharchenko et al. (2013) Kharchenko, N. V., Piskunov, A. E., Schilbach, E., Röser, S., & Scholz, R.-D. 2013, å, 558, A53
  * Kounkel & Covey (2019) Kounkel, M., & Covey, K. 2019, arXiv:1907.07709 [astro-ph], arXiv: 1907.07709
  * Kovács et al. (2002) Kovács, G., Zucker, S., & Mazeh, T. 2002, A&A, 391, 369
  * Kraus et al. (2014) Kraus, A. L., Shkolnik, E. L., Allers, K. N., & Liu, M. C. 2014, AJ, 147, 146
  * Kreidberg (2015) Kreidberg, L. 2015, PASP, 127, 1161
  * Krumholz et al. (2019) Krumholz, M. R., McKee, C. F., & Bland -Hawthorn, J. 2019, ARA&A, 57, 227
  * Li et al. (2019) Li, J., Tenenbaum, P., Twicken, J. D., et al. 2019, PASP, 131, 024506
  * Livingston et al. (2018) Livingston, J. H., Dai, F., Hirano, T., et al. 2018, AJ, 155, 115
  * Livingston et al. (2019) —. 2019, MNRAS, 484, 8
  * Lodieu et al. (2019) Lodieu, N., Pérez-Garrido, A., Smart, R. L., & Silvotti, R. 2019, A&A, 628, A66
  * Lopez et al. (2012) Lopez, E. D., Fortney, J. J., & Miller, N. 2012, ApJ, 761, 59
  * Mamajek (2009) Mamajek, E. E. 2009, in American Institute of Physics Conference Series, Vol. 1158, American Institute of Physics Conference Series, ed. T. Usuda, M. Tamura, & M. Ishii, 3–10
  * Mamajek & Hillenbrand (2008) Mamajek, E. E., & Hillenbrand, L. A. 2008, ApJ, 687, 1264
  * Mann et al. (2016a) Mann, A. W., Gaidos, E., Mace, G. N., et al. 2016a, ApJ, 818, 46
  * Mann et al. (2016b) Mann, A. W., Newton, E. R., Rizzuto, A. C., et al. 2016b, AJ, 152, 61
  * Mann et al. (2017) Mann, A. W., Gaidos, E., Vanderburg, A., et al. 2017, AJ, 153, 64
  * Mann et al. (2018) Mann, A. W., Vanderburg, A., Rizzuto, A. C., et al. 2018, AJ, 155, 4
  * Mann et al. (2020) Mann, A. W., Johnson, M. C., Vanderburg, A., et al. 2020, arXiv e-prints, arXiv:2005.00047
  * Masuda & Winn (2020) Masuda, K., & Winn, J. N. 2020, AJ, 159, 81
  * Mazeh & Faigler (2010) Mazeh, T., & Faigler, S. 2010, A&A, 521, L59
  * McCully et al. (2018) McCully, C., Volgenau, N. H., Harbeck, D.-R., et al. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10707, Proc. SPIE, 107070K
  * McLaughlin (1924) McLaughlin, D. B. 1924, ApJ, 60, 22
  * Montet et al. (2020) Montet, B. T., Feinstein, A. D., Luger, R., et al. 2020, AJ, 159, 112
  * Moraux et al. (2013) Moraux, E., Artemenko, S., Bouvier, J., et al. 2013, A&A, 560, A13
  * Morris et al. (2020) Morris, R. L., Twicken, J. D., Smith, J. C., et al. 2020, Kepler Data Processing Handbook: Photometric Analysis, Kepler Data Processing Handbook (KSCI-19081-003)
  * Newton et al. (2019) Newton, E. R., Mann, A. W., Tofflemire, B. M., et al. 2019, ApJ, 880, L17
  * Noyes et al. (1984) Noyes, R. W., Hartmann, L. W., Baliunas, S. L., Duncan, D. K., & Vaughan, A. H. 1984, ApJ, 279, 763
  * Obermeier et al. (2016) Obermeier, C., Henning, T., Schlieder, J. E., et al. 2016, AJ, 152, 223
  * Oh et al. (2017) Oh, S., Price-Whelan, A. M., Hogg, D. W., Morton, T. D., & Spergel, D. N. 2017, AJ, 153, 257
  * Owen & Lai (2018) Owen, J. E., & Lai, D. 2018, MNRAS, 479, 5012
  * Owen & Wu (2013) Owen, J. E., & Wu, Y. 2013, ApJ, 775, 105
  * Owen & Wu (2017) —. 2017, ApJ, 847, 29
  * Perryman et al. (1997) Perryman, M. A. C., Lindegren, L., Kovalevsky, J., et al. 1997, A&A, 500, 501
  * Pollacco et al. (2006) Pollacco, D. L., Skillen, I., Collier Cameron, A., et al. 2006, PASP, 118, 1407
  * Quinn et al. (2012) Quinn, S. N., White, R. J., Latham, D. W., et al. 2012, ApJ, 756, L33
  * Quinn et al. (2014) —. 2014, ApJ, 787, 27
  * Randich et al. (1997) Randich, S., Aharpour, N., Pallavicini, R., Prosser, C. F., & Stauffer, J. R. 1997, A&A, 323, 86
  * Randich et al. (2001) Randich, S., Pallavicini, R., Meola, G., Stauffer, J. R., & Balachandran, S. C. 2001, A&A, 372, 862
  * Rebull et al. (2017) Rebull, L. M., Stauffer, J. R., Hillenbrand, L. A., et al. 2017, ApJ, 839, 92
  * Rebull et al. (2016) Rebull, L. M., Stauffer, J. R., Bouvier, J., et al. 2016, AJ, 152, 113
  * Ricker et al. (2016) Ricker, G. R., Vanderspek, R., Winn, J., et al. 2016, in Proc. SPIE, Vol. 9904, Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, 99042B
  * Rizzuto et al. (2011) Rizzuto, A. C., Ireland, M. J., & Robertson, J. G. 2011, MNRAS, 416, 3108
  * Rizzuto et al. (2017) Rizzuto, A. C., Mann, A. W., Vanderburg, A., Kraus, A. L., & Covey, K. R. 2017, AJ, 154, 224
  * Rizzuto et al. (2018) Rizzuto, A. C., Vanderburg, A., Mann, A. W., et al. 2018, AJ, 156, 195
  * Rizzuto et al. (2020) Rizzuto, A. C., Newton, E. R., Mann, A. W., et al. 2020, arXiv e-prints, arXiv:2005.00013
  * Rosat (2000) Rosat, C. 2000, VizieR Online Data Catalog, IX/30
  * Röser et al. (2011) Röser, S., Schilbach, E., Piskunov, A. E., Kharchenko, N. V., & Scholz, R.-D. 2011, A deep all-sky census of the Hyades, doi:10.1051/0004-6361/201116948
  * Rossiter (1924) Rossiter, R. A. 1924, ApJ, 60, 15
  * Sanchis-Ojeda et al. (2013) Sanchis-Ojeda, R., Winn, J. N., Marcy, G. W., et al. 2013, ApJ, 775, 54
  * Seager & Mallén-Ornelas (2003) Seager, S., & Mallén-Ornelas, G. 2003, ApJ, 585, 1038
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  * Stassun et al. (2018) Stassun, K. G., Oelkers, R. J., Pepper, J., et al. 2018, AJ, 156, 102
  * Stauffer et al. (2018) Stauffer, J., Rebull, L. M., Cody, A. M., et al. 2018, AJ, 156, 275
  * Sullivan et al. (2015) Sullivan, P. W., Winn, J. N., Berta-Thompson, Z. K., et al. 2015, ApJ, 809, 77
  * Tokovinin (2018) Tokovinin, A. 2018, PASP, 130, 035002
  * Tokovinin et al. (2013) Tokovinin, A., Fischer, D. A., Bonati, M., et al. 2013, PASP, 125, 1336
  * Triaud (2017) Triaud, A. H. M. J. 2017, The Rossiter-McLaughlin Effect in Exoplanet Research, 2
  * Twicken et al. (2010) Twicken, J. D., Clarke, B. D., Bryson, S. T., et al. 2010, in Proc. SPIE, Vol. 7740, Software and Cyberinfrastructure for Astronomy, 774023
  * Twicken et al. (2018) Twicken, J. D., Catanzarite, J. H., Clarke, B. D., et al. 2018, PASP, 130, 064502
  * Vanderburg et al. (2018) Vanderburg, A., Mann, A. W., Rizzuto, A., et al. 2018, AJ, 156, 46
  * Vanderburg et al. (2019) Vanderburg, A., Huang, C. X., Rodriguez, J. E., et al. 2019, ApJ, 881, L19
  * Vaughan et al. (1978) Vaughan, A. H., Preston, G. W., & Wilson, O. C. 1978, PASP, 90, 267
  * Voges et al. (2000) Voges, W., Aschenbach, B., Boller, T., et al. 2000, VizieR Online Data Catalog, IX/29
  * Žerjal et al. (2013) Žerjal, M., Zwitter, T., Matijevič, G., et al. 2013, ApJ, 776, 127
  * Žerjal et al. (2017) —. 2017, ApJ, 835, 61
  * Žerjal et al. (2019) Žerjal, M., Ireland, M. J., Nordlander, T., et al. 2019, MNRAS, 484, 4591
  * Williams & Cieza (2011) Williams, J. P., & Cieza, L. A. 2011, ARA&A, 49, 67
  * Wilson (1978) Wilson, O. C. 1978, ApJ, 226, 379
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
  * Zari et al. (2018) Zari, E., Hashemi, H., Brown, A. G. A., Jardine, K., & de Zeeuw, P. T. 2018, å, 620, A172
  * Zhou et al. (2018) Zhou, G., Rodriguez, J. E., Vanderburg, A., et al. 2018, AJ, 156, 93
  * Zhou et al. (2020) Zhou, G., Winn, J. N., Newton, E. R., et al. 2020, ApJ, 892, L21
  * Ziegler et al. (2020) Ziegler, C., Tokovinin, A., Briceño, C., et al. 2020, AJ, 159, 19