#  pterodactyls: A Tool to Uniformly Search and Vet for Young Transiting
Planets In TESS Primary Mission Photometry

Rachel B. Fernandes Lunar and Planetary Laboratory, The University of Arizona,
Tucson, AZ 85721, USA  Alien Earths Team, NASA Nexus for Exoplanet System
Science, USA  Gijs D. Mulders Facultad de Ingeniería y Ciencias, Universidad
Adolfo Ibáñez, Av. Diagonal las Torres 2640, Peñalolén, Santiago, Chile
Millennium Institute for Astrophysics, Chile  Alien Earths Team, NASA Nexus
for Exoplanet System Science, USA  Ilaria Pascucci Lunar and Planetary
Laboratory, The University of Arizona, Tucson, AZ 85721, USA  Alien Earths
Team, NASA Nexus for Exoplanet System Science, USA  Galen J. Bergsten Lunar
and Planetary Laboratory, The University of Arizona, Tucson, AZ 85721, USA
Alien Earths Team, NASA Nexus for Exoplanet System Science, USA  Tommi T.
Koskinen Lunar and Planetary Laboratory, The University of Arizona, Tucson, AZ
85721, USA  Alien Earths Team, NASA Nexus for Exoplanet System Science, USA
Kevin K. Hardegree-Ullman Steward Observatory, The University of Arizona,
Tucson, AZ 85721, USA  Alien Earths Team, NASA Nexus for Exoplanet System
Science, USA  Kyle A. Pearson Jet Propulsion Laboratory, California Institute
of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA  Steven Giacalone
Department of Astronomy, University of California Berkeley, Berkeley, CA
94720-3411, USA  Jon Zink California Institute of Technology, Pasadena, CA,
USA  David R. Ciardi Caltech/IPAC-NASA Exoplanet Science Institute Pasadena,
CA, USA  Patrick O’Brien Lunar and Planetary Laboratory, The University of
Arizona, Tucson, AZ 85721, USA

(Accepted for publication in The Astronomical Journal; May 31st, 2022)

###### Abstract

_Kepler_ ’s short-period exoplanet population has revealed evolutionary
features such as the Radius Valley and the Hot Neptune desert that are likely
sculpted by atmospheric loss over time. These findings suggest that the
primordial planet population is different from the Gyr-old _Kepler_
population, and motivates exoplanet searches around young stars. Here, we
present pterodactyls, a data reduction pipeline specifically built to address
the challenges in discovering exoplanets around young stars and to work with
TESS Primary Mission 30-min cadence photometry, since most young stars were
not pre-selected TESS 2-min cadence targets. pterodactyls builds on publicly
available and tested tools in order to extract, detrend, search, and vet
transiting young planet candidates. We search five clusters with known
transiting planets: Tucana-Horologium Association, IC 2602, Upper Centaurus
Lupus, Ursa Major and Pisces Eridani. We show that pterodactyls recovers seven
out of the eight confirmed planets and one out of the two planet candidates,
most of which were initially detected in 2-min cadence data. For these
clusters, we conduct injection-recovery tests to characterize our detection
efficiency, and compute an intrinsic planet occurrence rate of 49$\pm$20% for
sub-Neptunes and Neptunes (1.8-6 $R_{\oplus}$) within 12.5 days, which is
higher than _Kepler_ ’s Gyr-old occurrence rates of 6.8$\pm$0.3%. This
potentially implies that these planets have shrunk with time due to
atmospheric mass loss. However, a proper assessment of the occurrence of
transiting young planets will require a larger sample unbiased to planets
already detected. As such, pterodactyls will be used in future work to search
and vet for planet candidates in nearby clusters and moving groups.

exoplanets — young transiting exoplanet, exoplanet evolution, young stellar
clusters/associations, moving groups

††software: NumPy (van der Walt et al., 2011), SciPy (Jones et al., 2001–),
Matplotlib (Hunter, 2007), eleanor (Feinstein et al., 2019), Wōtan (Hippke et
al., 2019), transitleastsquares (Hippke & Heller, 2019), vetting (Hedges,
2021), triceratops (Giacalone et al., 2021), EDI-Vetter Unplugged (Zink,
2019), EXOTIC (Zellem et al., 2020), epos (Mulders et al., 2018)

##  1 Introduction

The _Kepler_ mission was instrumental in the discovery of thousands of
exoplanets (Borucki et al., 2010; Borucki, 2017), most of which were found to
be closer to their star than Mercury is to our Sun. A closer look at this
population of short-period exoplanets revealed two prominent features: the Hot
Neptune Desert and the Radius Valley. The Hot Neptune Desert (3$-$10
$R_{\oplus}$; $<$4 days) is a region in the Gyr-old, period-radius plane with
a significant dearth of Neptune-sized planets (Beaugé & Nesvorný, 2013). As
Neptune-sized planets should be easier to find in short-period orbits, and
many sub-Neptunes have been discovered with longer orbital periods from
surveys such as CoRoT (Baglin et al., 2006) and Kepler, the Hot Neptune Desert
appears to not be an observational bias. The Radius Valley, a region with a
much lower frequency of planets with radii $\sim$1.8 $R_{\oplus}$ than at
$\sim$1.3 $R_{\oplus}$ (Super-Earths) or at $\sim$2.4 $R_{\oplus}$ (sub-
Neptunes), was discovered by Fulton et al. (2017) using accurate stellar, and
hence planetary, radii from the California-_Kepler_ survey (Petigura et al.,
2017; Johnson et al., 2017). More recently, the Radius Valley was also
detected in _K2_ data (Hardegree-Ullman et al., 2020).

Both the Hot Neptune Desert and the Radius valley are most likely caused by
atmospheric mass loss due to XUV photoevaporation (see, e.g. Owen & Wu 2013,
2017) and/or core-powered mass loss (see e.g., Ginzburg et al. 2016, 2018;
Gupta & Schlichting 2019, 2020). Given that these features are most likely to
be evolutionary, it is likely that the primordial population of short-period
planets was very different. Uncovering that population requires discovering
exoplanets around young stars which can be further used to test the theories
of atmopheric mass loss.

The _Kepler_ mission, however, was not able to detect any planets younger than
1 Gyr since there were only four open clusters (0.7-9 Gyr) in the _Kepler_
field (Meibom et al., 2011, 2013). On the other hand, the _K2_ mission (Howell
et al., 2014) discovered several young transiting planets while surveying the
Taurus, Hyades, Praesepe and Upper Scorpius (e.g., Mann et al. 2016a, b, 2017;
Ciardi et al. 2018; Rizzuto et al. 2017, 2018; Gaidos et al. 2017; Vanderburg
et al. 2018). Detailed studies of these planets have already begun to shed
light on how these planets differ from their Gyr-old counterparts. For
example, the planets in the 23 Myr-old V1298 Tau system, that currently occupy
gaps in the _Kepler_ distribution, is thought to be undergoing
photoevaporation and is predicted to “shrink” or lose their atmospheres with
time (David et al., 2019).

With the Transiting Exoplanet Sky Satellite (TESS) mission (Ricker et al.,
2014), we now have the unique opportunity to detect planets around stars in
more young clusters and associations than those observed with _K2_. During its
primary mission, TESS monitored each strip of the sky (also known as sectors)
for approximately 27 days, which means that it can detect planets with an
orbital period of $\sim$14 days (assuming two transits per candidate). Per
sector, there are about 200,000 bright nearby stars that were pre-selected for
the two year primary mission to be observed in a short 2-minute cadence mode
known as the Candidate Target List (CTL; Stassun et al. 2018). Moreover, TESS
obtained images of each sector at a 30-minute cadence which are also known as
Full-Frame Images (FFIs). Over a billion stars that were observed in this mode
are listed as part of the TESS Input Catalog (TIC), which contains a
relatively untapped reservoir of young planetary systems. In fact, while a
handful of young planets have already been detected using 2-min cadence data
within 200 pc (e.g.,Newton et al. 2019, 2021; Rizzuto et al. 2020; Mann et al.
2020), only two have been detected thus far using the FFIs (Nardiello et al.,
2020; Bouma et al., 2020).

Automating the detection of young transiting planets poses several challenges,
the biggest one primarily being the removal or modeling of instrumental
systematics and stellar variability $-$ the latter of which is more important
for young stars due to their high variability. Young stars also tend to have
stellar rotation rates that are comparable to the orbital periods of short-
period planets that can be detected by TESS (e.g., Rebull et al., 2016),
thereby making it hard to find transiting planets in their light curves. A
study led by Nardiello et al. (2020), PATHOS, used a PSF approach to extract
light curves from TESS Primary Mission FFIs and searched for planets in them.
However, most of their clusters were far away ($>$500 pc) and while they were
able to find 35 planets, only two of these were within 200 pc thereby making
precise radial velocity of these targets challenging. Additionally, TESS
QuickLook Pipeline111https://archive.stsci.edu/hlsp/qlp (Huang et al., 2020a,
b; Kunimoto et al., 2021) only considers stars brighter than T mag = 13.5 and
is not optimized for highly variable stars such as the ones found in these
clusters. To this effect, we have developed a dedicated pipeline to understand
the survey completeness and thus properly calculate the intrinsic planet
occurrence rates.

Here, we present pterodactyls222https://github.com/rachelbf/pterodactyls
(Python Tool for Exoplanets: Really Outstanding Detection and Assessment of
Close-in Transits around Young Local Stars), a pipeline that builds on
publicly available and tested tools in order to extract, detrend, search, and
vet young transiting planet candidates detected using TESS Primary Mission
30-minute cadence photometry. In Section 2, we discuss how we select the
clusters that have been included in this analysis and, Section 3 describes the
inner workings of pterodactyls. Finally, in Sections 5 & 6, we summarize our
main results and some preliminary occurrence rates calculations followed by a
discussion on our next steps (Section 7).

##  2 Sample of Young Stellar Clusters

Cluster | Distance (pc) | Age (Myr) | Obs/Total
---|---|---|---
THA | $46^{+8}_{-6}$ | 45$\pm$4 | 201/214
IC 2602 | 146$\pm$5 | $46^{+6}_{-5}$ | 502/504
UCL | 130$\pm$20 | 16$\pm$2 | 719/937
UMa |  $\sim$25 | 414$\pm$23 | 16/17
PiEri | 80$-$226 | 120 | 153/254
Table 1: Moving groups and clusters that have been homogeneously searched for
transiting planets in this paper. Distance, age, and membership are from Gagné
et al. (2018) and Babusiaux et al. (2018). The last column specifies how many
stars were observed during the TESS Primary mission vs. the total number of
stars in the cluster. Figure 1: Equatorial locations of stars in selected
clusters used in this study

In order to develop and test pterodactyls, we limited our search to only those
young clusters in which TESS, along with followup observations with the
_Spitzer_ space telescope (Werner et al., 2004), had already found transiting
planets during its primary mission: Tucana-Horologium Association (THA), IC
2602, Upper Centaurus Lupus (UCL), Ursa Major (UMa), and Pisces-Eridani
(PiEri). DS TUC A b (Newton et al., 2019), HIP 67522 b and c (Rizzuto et al.,
2020), TOI 1726 b and c (Mann et al., 2020), and TOI 451 b, c and d (Newton et
al., 2021) were discovered using TESS 2-min cadence data and also had
_Spitzer_ data. All of these are confirmed planets except for HIP 67522 c. In
contrast, the planets in IC 2602 were discovered using 30-min cadence data:
TOI 837 b which is a confirmed planet with mass measurements from radial
velocity (Bouma et al., 2020), and TIC 460950389 b (Nardiello et al., 2020)
which is a Community TESS Object of Interest
(CTOI)333https://exofop.ipac.caltech.edu/tess/view_ctoi.php.

In summary, a total of ten planets have been discovered so far in the selected
clusters: of them eight were discovered in TESS 2-min cadence data and two in
30-min cadence data. Followup observations have confirmed eight of these while
HIP 67522 c and TIC 460950389 b are only candidate exoplanets.

For the selected clusters and associations, we relied on the memberships
provided in the BANYAN $\Sigma$ (Gagné et al., 2018) and the Gaia DR2 open
cluster member lists (Gaia Collaboration, Babusiaux et al. 2018) which gives
us a total of 1940 stars out of which 1591 were observed during the TESS
Primary Mission. Based on parameters available in the TIC, these stars span a
large range in Gaia G magnitude (1.73-20.45) and stellar mass (0.11-3.2
$M_{\odot}$). Table 1 provides a breakdown of the main properties of the
moving groups and clusters that were included in this analysis while Figure 1
shows the relative positions of the clusters and their respective members that
were analyzed in this work.

##  3 Transit Detection Pipeline

Figure 2: Schematic of pterodactyls. ${}^{\text{*}}$Before passing to
triceratops, we conducted a centroid test whenever the Target Pixel File (TPF)
was available on MAST.

pterodactyls builds on publicly available and tested tools in order to extract
the light curves (Section 3.1), detrend them (Section 3.2), search for
transit-like signals (Section 3.3), and vet planet candidates (Section 3.4) in
these clusters. We further optimized the efficiency of the detrending, search
and vetting components of pterodactyls via injection-recovery tests. For the
latter, we injected $\sim$1000 transit signals with planets ranging in size
from 0.5-10 $R_{\oplus}$ and with orbital periods between 0.5-10 days into a
sample of our light curves using the Python-based
batman444https://www.cfa.harvard.edu/l̃kreidberg/batman/ package (Kreidberg,
2015). We then processed the light curves with pterodactyls and examined the
distribution of planets that were recovered. We used this planet distribution
as feedback in order to improve pterodactyls. The specifics of the extensive
testing using planet injection-recovery tests are summarized in the respective
sub-sections while the main steps of the pipeline are summarized in Figure 2.

###  3.1 Light Curve Extraction

Given that less than 10% of our targets were part of the pre-selected TESS
2-min cadence targets, we use the primary mission’s 30-min cadence photometry
extracted from TESS FFIs. Here, we employed
eleanor555http://adina.feinste.in/eleanor/, an open-source tool developed by
Feinstein et al. (2019). eleanor carries out background subtraction, and
removal of spacecraft systematics such as jitter and pointing drift. eleanor
provides four different types of light curves: raw light curves, corrected
light curves, light curves with systematics removed using Principle Component
Analysis (PCA), and Point Spread Function (PSF) modeled light curves.

In this work, we used PSF-modeled light curves since they better enable the
recovery of small signals and minimize the effects of scattered light from the
Earth and Moon (Feinstein et al., 2019). eleanor creates these PSF light
curves by modeling the shape of the PSF as a multi-variate Gaussian (major
axis, minor axis, and a rotation) for each star at each cadence. Then, eleanor
integrates that Gaussian function to calculate the flux of the target star at
each cadence. The quality flags assigned to the FFI data by the TESS team are
implemented during the extraction of the light curves by eleanor (see Table 32
in the TESS Science Data Products Description
Document666https://archive.stsci.edu/files/live/sites/mast/files/home/missions-
and-data/active-missions/tess/_documents/EXP-TESS-ARC-ICD-TM-0014-Rev-F.pdf).
By default, we only keep the data with the bit value 0 i.e., the highest
quality data. Once we download the light curves for each sector for a
particular target, we ‘stitch’ them together and run the search on all
available Primary Mission data for the target.

####  3.1.1 Accounting for Systematics

Any instrumental systematics that affect the shape of the PSF, such as the
temperature of the instrument, are well-captured by the PSF model and the flux
is conserved across it. However, there were several instrumental effects in
these light curves that were not captured during the PSF modeling and remain
in the light curve such as mid-sector flux drops caused by data downlink, and
offsets in the light curves caused by errors in the uploaded Guidestar tables
(see TESS’ Data Release Notes777https://archive.stsci.edu/tess/tess_drn.html
for a more detailed description of these issues). Since these instrumental
effects would generate spikes in the light curve that affect pterodactyls’
ability to detrend and search for planets, we further optimized these light
curves by masking the mid-sector flux drops and re-scaling any offsets. In
some cases, eleanor could not properly fit the PSF flux of the target star
possibly due to the target being faint, nearby bright stars, etc. We removed
148 such light curves from our sample.

We also masked a number of cadences in sectors 3, 10, 11, and 12 (see Figure
3) because we noticed that they triggered an anomalous number of transit-like
detections in the search, indicating an issue with the light curves in those
regions. We used a test similar to the “Skye” metric used by Thompson et al.
(2018) that was also adopted for _K2_ data by Zink et al. (2020). The test
measures the number of transit-like signals at each cadence and if the number
of signals is $>$3$\sigma$, we masked those cadences before re-running the
search.

Figure 3: Skye Excess Metric for Sectors 3, 10, 11 and 12 respectively. Red
dashed line depicts the 3$\sigma$ threshold.

###  3.2 Light Curve Detrending

In order to detrend the light curves of these young stars, we explored several
options presented in Wōtan, an open-source Python package on
GitHub888https://github.com/hippke/wotan/ developed by Hippke et al. (2019).
In their study, Hippke et al. (2019) used injection recovery tests and found
that, in the presence of significant stellar variation, spline-based methods
(where adjacent functional pieces join each other at fixed knots) maximized
the fraction of injected planets that were recovered. Following up on this
result, we tested the following three different spline techniques (see
Appendix A for an example): i) a robust spline with iterative sigma clipping,
ii) a Huber estimator spline (Huber, 1981) and, iii) a penalized spline with
iterative sigma clipping (Eilers & Marx, 1996). We also tested the commonly
used Savitzky-Golay filter (Savitzky & Golay, 1964) and found that it often
over-fits for the transit thereby causing an inaccurate transit depth
measurement, as pointed out in Hippke et al. (2019).

We evaluated the detrending based on the low noise or the root mean square
(hereafter, RMS) of the light curve, and recovery fraction from the injection-
recovery tests. We found that the penalized spline with iterative sigma
clipping works best for our sample of young stars as it gives the lowest RMS
measured on a 7-hour window and had the highest recovery fraction ($\sim$92%).
We found that, in agreement with Nardiello et al. (2020), the brighter stars
contribute more flux and have low RMS. We also see a lot of scatter in the
faint star region where there is more flux contamination. Furthermore, the
ratio of the recovered planetary radii to the injected radii was close to
unity, thereby suggesting that we did not over-detrend our light curves.

In carrying out these tests, we also noticed that the edges of light curves
are often challenging to detrend due to the lack of data on one side and would
often trigger a search. As such, we decided not to consider 0.5 days worth of
data on either edge. We also noticed that the penalized spline uses a cut of
2$\sigma$ i.e., it uses sigma clipping in estimating the trend and does not
consider any data that is more than 2$\sigma$ away. While this works well for
almost the entire sample, it does not do a good job for light curves with high
amplitude ($>$2-3%) rotational signals where it clips out peaks which leaves
periodic residuals that are picked up by the search. We manually identified 20
such light curves and applied a 3$\sigma$ cut to them in order to achieve a
better detrending.

####  3.2.1 Optimization Based on Stellar Rotation Rates

A penalized spline is essentially a piecewise polynomial fit in which the
routine tries all numbers of splines up to a set maximum, and uses a penalty
function to evaluate if a better fit outweighs the added degrees of freedom.
The penalized spline provides additional flexibility: unlike other spline
methods where the exact number of knots must be chosen manually, the penalized
spline identifies the best number of knots by comparing it against the smaller
residuals from an improved fit starting from a given maximum number. This
feature turns out to be useful for our sample as some young stars are rapid
rotators ($<$1 day) with periodic signals on timescales similar to the orbital
period. Using injection-recovery tests, we found that the highest planet
detection efficiency could be achieved by limiting the maximum number of
splines based on the stellar rotation rate.

To this effect, we used a Lomb-Scargle periodogram (Lomb 1976; Scargle 1982;
implemented in astropy) to first calculate the stellar rotation rate and then
implement the following step function to determine the maximum number of
splines that should be used in order to best detrend any given light curve:

  * •

if $R_{\text{rot}}$$\leqslant$ 2 days: max splines = 200

  * •

if $R_{\text{rot}}$$>$ 2 days and $\leqslant$ 10 days: max splines =
200/$R_{\text{rot}}$

  * •

if $R_{\text{rot}}$$\geq$ 10 days: max splines = 25

If the periodogram was not able to find a period, it defaults to the length of
the segment (half a sector since there is a break in the middle). Since that
is $\sim$10 days, only a small number of splines (25) is used which is ideal
for a light curve of low variability. However, this is a maximum number of
splines which means that the detrending can still pick the right number of
splines even if the rotation period is estimated to be shorter than it really
is.

At this stage, we visually inspected all of the light curves and found 80 with
variablility trends that were difficult to detrend e.g., extremely fast
rotators with a rotational rate $<$0.5 days999Based on the stellar rotation
rate, we ideally would use $\sim$500 splines to detrend the light curve but we
realized that by doing so, we would likely be fitting noise.. Since we were
not able to properly detrend these light curves, we also would not have been
able to find planets in them. As such, we removed these light curves from our
sample and are left with $\sim$1359 light curves that we used to search for
planets.

###  3.3 Planet Candidate Search

We searched the detrended light curves for periodic, transit-like signals with
transitleastsquares (hereafter, TLS; Hippke & Heller 2019). TLS is optimized
for signal detection of small planets by taking into account the effects of
limb darkening to better model the ingress and egress shape (Manduca et al.,
1977; Mandel & Agol, 2002). TLS searches for these signals by phase-folding
the light curve over a range of epochs, transit durations and orbital periods
calculated using a function based on the mass and radius of the host star as
detailed in Ofir (2014). The period search grid is set by TLS by dividing the
length of the light curve by the minimum number of required transits which is
set to two.

For the purposes of our work, we defined a Threshhold Crossing Event (TCE) as
having a signal-to-noise ratio (SNR) of 7 and a signal detection efficiency
(SDE) of 7101010SDE is essentially the SNR of the signal in Fourier space. For
more details, see Kovács et al. (2002). Most transit survey studies choose an
SDE value between 6 and 10 (see e.g., Dressing & Charbonneau 2015; Livingston
et al. 2018; Siverd et al. 2012; Pope et al. 2016; Aigrain et al. 2016; Feliz
et al. 2021). While a lower SDE would mean higher completeness, a higher SDE
would reduce the number of false positives. Our chosen SNR and SDE cuts
reduced the number of false positives, which arose from detrending artifacts
caused by the significant ($\sim$20%) number of rapid rotators with periodic
signals comparable to stellar rotation rates. Additionally, an SNR and SDE cut
of 7 recovers eight out of the ten the previously detected planets (see
Section 5.1).

###  3.4 Candidate Vetting

Transiting surveys (like _Kepler_ , _K2_ and TESS) that target a large number
of stars face a major challenge while distinguishing false alarms (transit-
like events caused by instrumental artifacts) and astrophysical false
positives (transit-like events that are astrophysical in origin but are not
caused by planets). The process of sorting out false alarms and false
positives from real transit signals is known as vetting. In order to filter
out any instrumental false alarms that could be due to detrending artifacts,
we used criteria inspired by RoboVetter (_Kepler_ ; Thompson et al. 2018) and
EDI-Vetter (_K2_ ; Zink 2019; Zink et al. 2020) to create four checks in order
to address the issues unique to our sample. Only the TCEs that pass the
following tests are considered objects of interest:

  * •

At least two transits with data: We required two transit signals with in-
transit data points in a given light curve which allowed us to find planets
with orbital periods of up to 13.5 days around most of the stars (assuming
each star only had single sector data). If we required at least three unique
transits like _Kepler_ did, we would be limited to transit signals with
orbital periods less than 9 days.

  * •

Orbital period dissimilar to stellar rotation rate: While analysing the
results of the search, we often found residuals at orbital periods similar
($\sim$20%) to the stellar rotation rate (and some of these at half the
rotation rates), despite detrending. To combat this, we flag any such TCEs.

  * •

Consistency in individual transit depths: We found that, quite often, false
alarms have transit depths with larger variance than real planets. Similar to
_Kepler_ ’s Robovetter Single Event Statistic (SES), we flagged signals with
large variations in transit depth as likely false positives. We weed out these
signals based on the ratio of the standard deviations of the individual
transit depths to the average transit depth, which we set to be greater than
1.5 for a false positive. This cutoff was determined by preserving known
planets while keeping the number of false positives low.

  * •

Observed transit duration should be consistent with expected transit duration:
On visual inspection, we found that some TCEs had transit durations that were
inconsistent with those of planetary transits. For example, stellar
variability can lead to dips with a duration longer than a transit, and single
occurrence outliers can appear to have a shorter transit duration. In such
cases, it is beneficial to compare the observed transit duration to the
expected transit duration that is determined using the planetary parameters
calculated by TLS. If the observed transit duration is within 75% of the
expected transit duration, the TCE passes this test. This cut was also set to
preserve known planets and reduce the number of false positives.

In addition, we also used two checks from EDI-Vetter Unplugged (Zink et al.,
2020) that were initially designed to vet transits in _K2_ data but has now
been adapted to vet TESS light curves (for e.g., see Feliz et al. 2021).

  * •

Individual Transit Test: Derived from the Marshall test designed by Mullally
et al. (2016) for _Kepler_ , this test used transit models and those of common
non-transiting false positives and fit these to the individual transits. It
then used the Bayesian Information Criterion (BIC) to gauge the goodness of
these fits, thereby flagging the non-transiting signals that are often assumed
to belong to transiting planets.

  * •

Secondary Eclipse Test: This test looked for transit events between the 40-60%
phase range of the folded light curve, allowing for some mild eccentricity
variations. If a meaningful secondary eclipse was identified i.e., the
secondary eclipse has a transit depth $>$10% of the primary transit, this flag
was triggered and the transit was labeled a false positive. Secondary eclipses
with less than 10% depth can be associated with reflected light from hot
Jupiters.

Once we removed the clear false alarms and only have transit-like signals, we
were left with 21 pterodactyls Objects of Interest (hereafter POIs; see Tables
2 and 3) on which we conducted a centroid test (Hedges,
2021)111111https://pypi.org/project/vetting/ in order to determine whether the
transiting signal was indeed coming from the target star (see Appendix C).
This test compares the distributions of centroids for the data inside and
outside the transit. An offset would indicate that the transiting signal was
coming from a contaminating source such as a nearby or background star. We
chose a probability p of 5% for the Student t-test below which the centroids
positions inside and outside transits are not considered to come from the same
parent distribution.

All POIs were then passed on to triceratops
121212https://github.com/stevengiacalone/triceratops (Giacalone et al., 2021)
$-$ a vetting tool designed to distinguish bona fide planets from
astrophysical false positives in TESS data. triceratops calculated the
marginal likelihood of each transit-producing scenario using observational
constraints such as the transit depth and transit duration from TLS for each
potential host, positions and magnitude of nearby stars from Gaia dr2 (Gaia
Collaboration et al., 2018), priors on planet occurrence and stellar
multiplicity rates, and models of planetary transits and eclipsing binaries.
These scenarios include transiting planets and eclipsing binaries originating
from the target star, known nearby stars, and unknown unresolved stars located
near the target on the sky. Lastly, triceratops calculates the Bayes factor
between all scenarios involving a transiting planet around the target star and
all astrophysical false positive scenarios. Using this Bayes factor,
triceratops can place a statistically robust constraint on the reliability of
any given planet candidate detected by TESS. Here, we made a transiting planet
probability cut of 50% in order to preserve known planets.

##  4 Fitting for Planet Properties

Once the POIs have passed all of the vetting tests described in Section 3.4,
we fit the phase-folded light curve131313Since the PSF light curves from
eleanor do not currently have uncertainties, we use the RMS of the detrended
light curve as errors while fitting for planet parameters in order to derive a
more accurate planet radius. Since TLS only provided an initial fit to the
phase-folded light curve and did not provide uncertainties on the planet
radius, we used TLS’ outputs as priors for a more rigorous optimization in
order to derive uncertainties using EXOTIC (Zellem et al., 2020). Here, the
transit parameters are optimized using the multi-modal nested sampling
algorithm called UltraNest (Buchner, 2021) which is a Bayesian inference tool
that uses the Monte Carlo strategy of nested sampling to calculate the
Bayesian evidence allowing simultaneous parameter estimation and model
selection. A nested sampling algorithm is efficient at probing parameter
spaces which could potentially contain multiple modes and pronounced
degeneracies in high dimensions; a regime in which the convergence of
traditional Markov Chain Monte Carlo (MCMC) techniques becomes incredibly slow
(Skilling 2004; Feroz & Hobson 2008). This approach has been validated on
Kepler light curves, TESS data and ground-based measurements (Pearson et al.,
2018, 2019; Pearson, 2019).

##  5 Results

We processed $\sim$1359 young stellar light curves extracted from TESS FFIs
i.e., 30-min cadence data through pterodactyls (see Appendix D for the TIC IDs
processed in this work). As an illustration, Figure 4 shows the different
steps that were used in the recovery of the planet TOI 451 d. We detected 21
POIs that were then passed to triceratops where their phase-folded light
curves were vetted to separate transiting planet signals from astrophysical
false positives.

Figure 4: Left: Recovery of TOI 451 d. Upper panel: PSF flux (in dark gray)
and penalized spline trend (in blue). Lower panel: Detrended light curve (PSF
flux divided by the trend). The multi-transit signature (in red) can be
clearly seen. Right: Upper panel shows Phase-folded light curve of TOI 451 d
(gray data points) along with the best fit model using EXOTIC (in red). Lower
panel shows the residuals in parts per million.

###  5.1 Recovery of Known Exoplanets

Planet | Ref. | Cluster | Radius (pub; $R_{\oplus}$) | Period (pub; days) | Radius (rec; $R_{\oplus}$) | Period (rec; days) | TP prob %
---|---|---|---|---|---|---|---
DS Tuc A b∗ | a | THA | 5.70$\pm$0.17 | 8.138268$\pm$0.000011 | $5.349^{+0.464}_{-0.458}$ | 8.215$\pm$0.066 | 54.93
TIC 460950389 b | b | IC 2602 | 3.8$\pm$0.2 | 2.8622$\pm$0.0004 | $3.554^{+0.320}_{-0.304}$ | 2.861$\pm$0.005 | 99.69
TOI 837 b | b,c | IC 2602 |  $6.9^{+0.6}_{-0.4}$; $8.90^{+0.74}_{-0.71}$ | 8.3252$\pm$0.0006 | $7.224^{+0.410}_{-0.387}$ | 8.325$\pm$0.016 | 97.45
HIP 67522 b∗ | d | UCL | $9.72^{+0.48}_{-0.47}$ | 6.95993$\pm$0.00034 | $13.400^{+1.354}_{-1.328}$ | 6.893$\pm$0.019 | 86.06
HIP 67522 c∗ | d | UCL | $8.01^{+0.75}_{-0.71}$ | $54^{+70}_{-24}$ | xx | xx | xx
TOI 1726 b∗ | e | UMa | 2.15$\pm$0.10 | $7.10793^{+0.00046}_{-0.00034}$ | $2.134^{+0.214}_{-0.213}$ | 7.116$\pm$0.043 | 75.32
TOI 1726 c∗ | e | UMa | 2.67$\pm$0.12 | 20.5455$\pm$0.0011 | $2.225^{+0.264}_{-0.267}$ | 20.5234$\pm$0.1022 | 75.72
TOI 451 b∗ | f | PiEri | $1.94^{+0.15}_{-0.34}$ | $1.858701^{+0.000027}_{-0.000033}$ | xx | xx | xx
TOI 451 c∗ | f | PiEri | 3.07$\pm$0.14 | $9.192523^{+0.000064}_{-0.000084}$ | $2.604^{+0.308}_{-0.294}$ | 9.195$\pm$0.036 | 71.11
TOI 451 d∗ | f | PiEri | 4.03$\pm$0.15 | $16.364981^{+0.000047}_{-0.000049}$ | $3.678^{+0.306}_{-0.294}$ | 16.368$\pm$0.070 | 70.63
Table 2: Published and Recovered Properties of planets detected in young
clusters. References: a) Newton et al. (2019); b) Nardiello et al. (2020); c)
Bouma et al. (2020); d) Rizzuto et al. (2020); e) Mann et al. (2020); f)
Newton et al. (2021) ∗Planet originally detected in 2-min cadence data.

In the five clusters that were searched in this work, there are eight
confirmed planets and two planet candidates. More specifically, three were
single planet systems (DS Tuc A b, TIC 460950389 b, and TOI 837 b; the latter
two discovered in 30min-cadence data) and seven were part of three multi-
planet systems (HIP 67522 b and c, TOI 1726 b and c, and TOI 451 b, c and d),
all discovered in 2-min cadence data (see Section 2). As pterodactyls, which
is automated, is built to search for just one planet per star, the discovery
of additional planets in a system is carried out after finding a first planet
and masking it out.

Among the 21 POIs detected by pterodactyls in the first automated run, we find
six of the confirmed exoplanets that were previously detected by various teams
using TESS (summarized in Table 2; for light curves, see Appendix B).
pterodactyls was able to recover the values for the orbital periods and radii
for three of these planets that were consistent (within uncertainties) with
the literature. This includes two single planets (TIC 460950389 b, and TOI 837
b) that were initially discovered in 30-min cadence data, and one multi-planet
system (TOI 451 b, c and d) that was initially discovered in 2-min cadence
data. We first recovered TOI 451 d (4.1 $R_{\oplus}$) at an orbital period of
16.36 days. After masking this transit, we were also able to recover TOI 451 c
(3.1 $R_{\oplus}$) at 9.19 days (see Figures 4 and 16). However, pterodactyls
was not able to recover TOI 451 b (1.9 $R_{\oplus}$) since it has a low SNR
($\sim$5). We find that all of the confirmed planet and planet candidates that
pterodactyls recovers pass the centroid test.

Two out of the other three recovered transiting systems (out of a total of six
as stated above) suffered from sparse cadence (few in-transit data points): DS
Tuc A b and HIP 67522 b. For these, pterodactyls was able to accurately
recover the orbital periods but not the same radii as in the literature. In
the case of DS Tuc A b, at first we considerably underestimated the planet’s
radius value. On further inspection, we noticed that this was caused by very
few in-transit data points that was due to the removal of “bad” data that was
flagged using the TESS team’s quality flags. In this specific case, we found
that inclusion of certain quality flags lead to a better estimation of the
planetary radius i.e 5.35 $R_{\oplus}$(see Figure 11) which is within errors
of the value of 5.70 $R_{\oplus}$that was measured using TESS’ 2-min cadence
and _Spitzer_ data (see Table 2). In the case of HIP 67522 b, the
overestimation of the planet radius was severe: we recovered a radius of 13.4
$R_{\oplus}$while the planet’s observed radius is 9.72 $R_{\oplus}$. This
could be due to several factors. First, as can be seen in Figure 5, the middle
transit was not recovered (but predicted by TLS) due to the default edge
cutoff for all stars being 0.5 days. However, the severe overestimation of the
radius could also be due to the planet being discovered in the more abundant
2-min cadence data. We tested this by processing the publicly available 2-min
cadence light curve through pterodactyls (see Figure 6) and found that with
the increased number of in-transit data points (along with higher RMS compared
to 30-min cadence data), we were able to recover a planet radius of 9.8
$R_{\oplus}$which is close to the literature value of 9.72 $R_{\oplus}$. We
were not able to recover HIP 67522 c due to it being a single transit event
and hence, beyond the scope of pterodactyls since it requires a minimum of two
transits.

Finally, for the TOI 1726 system in UMa, we recovered a transit signal from a
2.48$R_{\oplus}$ planet with an orbital period of 11.32 days. However, the
TOI-1726 system has two small planets (b and c) of radii 2.15 $R_{\oplus}$and
2.67 $R_{\oplus}$, with orbital periods of 7.11 and 20.55 days respectively
(Mann et al., 2020). Given that the planet sizes (and hence, transit depths)
are similar, the signals were initially detected by pterodactyls as coming
from one planet. Upon further inspection, we realized that TLS set the maximum
orbital period in the grid based on the minimum number of transits. So, for
single sector data ($\sim$27 days) with the minimum number of transits set to
2, the maximum orbital period would be $\sim$13.5 days which is shorter than
the orbital period of TOI 1726 c. With this in mind, for this case alone, we
set the minimum number of transits to one and were able to recover TOI 1726 c
(see Figure 14). We then masked this transit and re-processed it through
pterodactyls and recovered TOI 1726 b as well (see Figure 15).

After implementing the aforementioned fixes, we find that all of the recovered
orbital periods are the same as those reported in the discovery papers while
for the radii, four are the same within 1$\sigma$ and three within 2$\sigma$
(Figure 7). The recovery of these planets demonstrates the usefulness of
pterodactyls in discovering young planets in 30-min cadence data.

Figure 5: Left: Recovery of HIP 67522 b. Upper panel: PSF flux (in dark gray)
and penalized spline trend (in blue). Lower panel: Detrended light curve (PSF
flux divided by the trend). The multi-transit signature (in red) can be
clearly seen. Right: Upper panel shows Phase-folded light curve of HIP 67522 b
(gray data points) along with the best fit model using EXOTIC (in red). Lower
panel shows the residuals in parts per million.

Figure 6: Left: Comparison of phase-folded light curve of HIP 67522 b using
2-min cadence data (orange) and 30-min cadence data (black). Right: Upper
panel shows Phase-folded light curve of HIP 67522 b using 2-min cadence (dark
gray points) along with the best fit model using EXOTIC (in red). Lower panel
shows the residuals in parts per million.

Figure 7: Left: Comparison of planetary radii recovered using pterodactyls
(fitted with EXOTIC) vs. known planet radii for the eight recovered known
planets. As can be seen, despite being recovered from 30-min cadence data, the
radii are often consistent with those published. In two cases, TOI 1726 c and
TOI 451 c, we slightly underestimate the planet’s radius. We also overestimate
the radius of the planet for HIP 6752 b. Right: Comparison of orbital periods
recovered using pterodactyls vs. known orbital periods for the eight recovered
planets to depict consistency between the results of our work and those from
the discovery papers. Note: Orbital period errors are extremely small and
hence cannot be seen in the plot.

###  5.2 Astrophysical False Positives Vetting

Apart from the six confirmed planets, pterodactyls also detected 15 other POIs
(see Table 3), including two eclipsing binary signals around two stars in UCL
i.e., TIC 129116176 and TIC 148158540. We weren’t able to conduct centroid
tests on all of these targets since the Target Pixel File on the MAST server
(which is used for the centroid test) were only available for three of the
candidates (all of the ones in UCL) in Table 3 but not for the 12 other
candidates (IC2602). As such, we conducted the centroid test whenever the data
was available. For the targets, where we could not conduct the centroid test,
we visually inspected the eleanor pixel by pixel light curves. While
determining the probability of a transiting signal being due an astrophysical
false positive or a transiting planet, triceratops (by default) takes into
account planet occurrence rates priors that are based on the Gyr-old exoplanet
population (e.g., Howard et al. 2012; Dong & Zhu 2013; Petigura et al. 2013;
Dressing & Charbonneau 2015; Mulders et al. 2015, 2018). However, if the
planet population around young stars is different from that around Gyr-old
stars, for example because young planets are larger in size, the probability
that triceratops would calculate is likely to be biased. In order to test the
effect of priors on the probabilities of the different scenarios investigated
by triceratops, we also calculated the astrophysical false positive
probability using non-informative (flat) priors that were recently implemented
in triceratops.

Out of our remaining 15 POIs, we found that 11 were not affected by the choice
of priors and had the same probability of being an astrophysical false
positive in both cases. In two out of the remaining four, we detected a
transiting signal in each each of them (TIC 466579089 and TIC 466035035; see
Table 3) that had passed all our vetting tests. Using Gyr-old priors,
triceratops calculated the most likely scenario to be a nearby eclipsing
binary (NEB). However, when using flat priors, the most likely probability was
calculated to be a transiting planet. Given that IC 2602 is an extremely
crowded cluster ($\sim$5 stars per TESS pixel), we used eleanor’s pixel level
light curves to investigate whether these transits were indeed around our
target stars. In doing this, we found that the signal was coming from giant
stars (TIC 466579123 and TIC 466035000, respectively) a couple of pixels away
and actually contributed more flux to the pixel than our target star. With
this information in hand, we ran pterodactyls on those stars and were able to
detect the same signal in the light curve but, this time, triceratops found
that the most likely scenario was that the signal was due to an eclipsing
binary around TIC 466579123 and TIC 466035000.

When the false positive probability was calculated using flat priors, the
remaining two POIs that were initially calculated to be nearby eclipsing
binaries with Gyr-old priors, showed a $>$25% chance that the signal was
either a nearby eclipsing binary or a nearby transiting planet. These POIs
have large transits depths that could either be attributed to small stars,
brown dwarfs or giant planets since the two populations have comparable radius
distributions (Chen & Kipping, 2017). This, along with the fact that
identifying shallow secondary transits can be arduous, makes it harder for
statistical validation tools such as triceratops to properly distinguish
between these scenarios (Shporer et al., 2017). In cases such as these, masses
obtained via radial velocity follow-up are necessary to differentiate between
these scenarios. This illustrates the need to properly take into account flux
contamination in young clusters while vetting planet candidates.

TIC ID | Cluster | Period (d) | Most likely (Gyr-old priors) | Most likely (Flat priors) | Potential Host Star(s)
---|---|---|---|---|---
390758843 | IC 2602 | 0.890 | 25% NEB | 25% NEB | TIC 390758947
376731139 | IC 2602 | 12.769 | 50% NEBx2P | 49% NEBx2P | TIC 376731097
911870867 | IC 2602 | 20.018 | 42% NEB | 40% NTP; 27% NEB | TIC 390843430
911870847 | IC 2602 | 20.018 | 50% NEB | 37%NEB; 30% NTP | TIC 390843430
315312718 | IC 2602 | 2.203 | 28% NEB | 30% NEB | TIC 315312721; TIC 315312651
466035035 | IC 2602 | 1.522 | 99% EB | 92% TPx | TIC 466035000
466579089 | IC 2602 | 15.910 | 91% NEB | 44% NEB; 44% TPx | TIC 466579123
913701079 | IC 2602 | 2.900 | 88% NEBx2P | 84% NEBx2P | TIC 465306570
465306494 | IC 2602 | 2.899 | 86% NEBx2P | 85% NEBx2P | TIC 465306570
378611172 | IC 2602 | 7.542 | 89% NEBx2P | 87% NEBx2P | TIC 378611218
466422383 | IC 2602 | 33.247 | 99% NEBx2P | 99% NEBx2P | TIC 466422466
390757974 | IC 2602 | 1.705 | 54% NEB | 54% NEB | TIC 390758017
177631209 | UCL | 2.144 | 32% EB | 21% PEB; 21% NEB | TIC 177631209; TIC 1167076020
129116176 | UCL | 4.032 | 74% EBx2P | 91% EBx2P | -
148158540 | UCL | 3.700 | 65% EBx2P | 64% EBx2P | -
Table 3: List of POIs/Potential Binaries detected by pterodactyls and vetted
using triceratops in both Gyr-old and flat prior mode. Key: TP = Transiting
Planet around Target Star; EB = Eclipsing Binary around Target Star; EBx2P =
Eclipsing Binary around Target Star with twice the orbital period compared to
what was detected by TLS; NTP = Nearby Transiting Planet; NEB = Nearby
Eclipsing Binary; NEBx2P = Nearby Eclipsing Binary with twice the orbital
period compared to what was detected by TLS; PEB: Eclipsing Binary around
Primary Star with Unresolved Bound Companion. xSee discussion in Section 5.2
Note: The signals found in TIC 911870867 & TIC 911870847 as well as TIC
913701079 & TIC 465306494 have similar orbital periods with the same potential
host star suggesting that they might be blended or part of the same multiple
system.

##  6 Planet Occurrence Rates in investigated clusters

###  6.1 Detection Efficiency

An advantage of having an automated planet detection pipeline is that it
enables the measurement of the survey detection efficiency which is necessary
to compute intrinsic occurrence rates. The detection efficiency of our survey
was calculated using injection-recovery tests on a 3$\times$4 grid in
$\frac{R_{\text{p}}}{R_{\star}}$ from 0.01 to 0.3 and in orbital period from
0.5 to 27 days , equally spaced in both $\frac{R_{\text{p}}}{R_{\star}}$and
orbital period. The injections are carried out in the
$\frac{R_{\text{p}}}{R_{\star}}$ space because most stars in our clusters
currently lack stellar properties. We injected a transit signal in each bin in
each light curve in our sample while taking into account the flux contribution
of each star as calculated by triceratops. We then passed these injections
through pterodactyls and calculated the fraction that were recovered as
planets to produce a detection efficiency map per cluster as well as an
average map for the entire sample. The average detection efficiency map is
presented in Figure 8 and shows that the overall detection efficiency does not
exceed 50% for any bin below 0.1 $\frac{R_{\text{p}}}{R_{\star}}$(i.e., a
Jupiter-sized planet assuming it orbits a Sun-like star). Interestingly, all
the previously known recovered planets (denoted using blue stars in Figure 8)
are in bins with fairly low values ($<$20%). This might be due to the
intrinsic occurrence of smaller vs. larger planets being higher (Mulders et
al., 2015; Petigura et al., 2018; Mulders et al., 2018).

We also investigated how the detection efficiencies of each cluster
contributed to the overall detection efficiency. Figure 9 illustrates that the
detection efficiency of a cluster can be quite different from the average. For
example, Pisces-Eridani (top panel) has a significantly larger detection
efficiency. IC 2602 (middle panel), on the other hand, has an extremely low
detection efficiency. These differences might be due to age (IC 2602 is
younger, hence its stars might be more variable) and/or to flux contamination
due to stellar crowding, which is significantly more pronounced in IC 2602.

We further investigated the effects of flux contamination on IC 2602’s
detection efficiency by re-running the injection recovery tests without
accounting for flux contamination. In other words, signals are injected into
the light curve assuming that all of the flux comes from the target star and
hence, there is no transit depth dilution. The detection efficiency map is
given in the bottom panel of Figure 9 and it is similar to that of Pisces
Eridani within 10 days and above 0.06$\frac{R_{\text{p}}}{R_{\star}}$. This
test demonstrates that flux contamination significantly reduces the
detectability of all planets but stellar variability in the youngest
associations still plays a role for the smaller planets.

Figure 8: Overall detection efficiency of pterodactyls while taking into
account flux contamination. The confirmed planets are depicted using blue
stars, except for TOI 1726 b whose recovery required changing pterodactyls.
Darker bins represent regions of higher detection efficiency. ${n_{\star}}$ is
the total number of stars in our sample while n is the total number of
injections done. Black box denotes the bin over which the intrinsic occurrence
rates were calculated i.e., sub-Neptunes and Neptunes (0.017-0.055
$\frac{R_{\text{p}}}{R_{\star}}$ or 1.8-6 $R_{\oplus}$, assuming a solar
radius) within 12.5 days (about half a TESS sector).

Figure 9: A comparison of extreme detection efficiencies to highlight the
effect of flux contamination: Top: Detection efficiency of Pisces-Eridani, a
moving group with members that are spread out so flux contamination is
minimal. Middle: Detection efficiency of IC 2602, a crowded cluster, while
taking into account flux contamination while injecting planets. Bottom:
Detection efficiency of IC 2602 while assuming no flux contamination while
injecting planets.

###  6.2 Preliminary Calculation of Occurrence Rates

The intrinsic occurrence rate of planets ($\eta$) can be calculated from the
fraction of stars with detected planets in a survey and the survey
completeness. Here, we used the inverse detection efficiency method as
follows:

$\eta=\frac{{n_{\text{p}}}}{n_{\star}}*\frac{1}{comp_{\text{bin}}}$ (1)

where $comp_{\text{bin}}$ is the survey completeness evaluated in the defined
bin, $n_{p}$ is the number of detected planets in the bin and $n_{\star}$ is
the number of surveyed stars. The survey completeness is computed by combining
the detection efficiency and the geometric transit probability, which is given
by

$f_{\text{geo}}=\frac{R_{\star}}{a}$ (2)

Here, $R_{\star}$ is the stellar radius, and $a$ is the average semi-major
axis which is calculated using _Kepler_ ’s third law. The uncertainty on the
occurrence rate was calculated from the square root of the number of detected
planets in the bin, assuming Poissonian statistics.

In our analysis, we only considered sub-Neptunes and Neptunes (0.017-0.055
$\frac{R_{\text{p}}}{R_{\star}}$ or 1.8-6 $R_{\oplus}$, assuming a solar
radius) within 12.5 days (about half a TESS sector)141414Here, we use the
$\frac{R_{\text{p}}}{R_{\star}}$fit by TLS and not the values from EXOTIC
since EXOTIC is not part of pterodactyls and is only used to fit for the
planetary parameters once the POI is vetted by triceratops. because we wanted
to understand the primordial population of sub-Neptunes and Neptunes before
being stripped off of their atmospheres. With an average detection efficiency
of 9% and a $f_{\text{geo}}$ of 0.1 (at a geometric mean orbital period of 3.5
days and assuming a Solar-type star), we compute an occurrence rate of
49$\pm$20% for our sample of young clusters.

We then use epos (Mulders et al., 2018) to calculate the _Kepler_ Gyr-old FGK
(Sun-like) occurrence in the same bin. epos is a well documented and tested
Python code developed by our team151515http://eos-nexus.org/epos/, it is
available on GitHub161616https://github.com/GijsMulders/epos, and has already
been used in several publications to compute occurrence rates as well as to
compare planet formation models to the _Kepler_ exoplanetary systems (e.g.,
Kopparapu et al., 2018; Pascucci et al., 2018; Fernandes et al., 2019; Mulders
et al., 2019; Pascucci et al., 2019; Mulders et al., 2020). Here, we computed
an occurrence rate value of 6.8$\pm$0.3%, which is much lower than our
computed value for young clusters. This could be attributed to several
reasons, the major one being that our sample is heavily biased towards
clusters with known planets. For example, if we increased the sample of young
stars to search by a factor of six, which is about all nearby young stars
within $\sim$200 pc and assumed the same detection efficiency with no new
planets, the occurrence would drop to $\sim$8% which is the same as the
_Kepler_ value. Furthermore, since most of the stars in the sample do not have
stellar radii, masses or effective temperatures, it is very likely that we are
considering non-FGK stars, most likely lower mass stars (Henry et al., 2006;
Winters et al., 2014), while calculating the occurrence rate which would make
the comparison to _Kepler_ inaccurate, where the sample is mostly Sun-like
stars. Therefore, in order to better estimate the occurrence rates of planets
in young clusters, we will need to expand our search to all nearby clusters,
measure the stellar parameters for those stars, and only compute the
occurrence for FGK stars in our sample. However, if we continue to see this
increased occurrence after we expand our sample to include all nearby clusters
and moving groups, it could imply that there is an excess of larger planets at
young ages possibly because their atmospheres have not yet been stripped due
to photoevaporation and/or core-powered mass loss.

##  7 Summary and Future Work

In this paper, we present pterodactyls $-$ a Python-based pipeline that is
built using publicly available codes, and is specifically designed to extract,
detrend, search for, and vet transiting exoplanets in young clusters using
TESS’ Primary Mission 30-min cadence FFIs. Here, we only consider 5 specific
young clusters and moving groups: Tucana-Horologium Association, IC 2602,
Upper Centaurus Lupus, Ursa Major, and Pisces Eridani. These clusters were
chosen solely due to the presence of eight confirmed planets and two
candidates which were used to validate pterodactyls. Using pterodactyls,

  * •

We were able to recover eight out of ten known transiting planets/candidates.
For the two that we were not able to recover (both initially discovered using
2-min cadence data), one planet was too small to detect (PiEri; TOI 451 b) and
the other is a long period, single transit planet (UCL; HIP 67522 c), which is
beyond the capabilities of the pipeline.

  * •

We also detected 15 transiting signals, all of which were found to be either
eclipsing binaries or nearby eclipsing binaries when their phase-folded light
curves were vetted by triceratops.

  * •

While taking into account the stellar flux contribution, we conducted
injection-recovery tests in order to measure the detection efficiency of the
pterodactyls. We found that the overall detection efficiency does not exceed
50% for any bin below 0.1 $\frac{R_{\text{p}}}{R_{\star}}$(i.e., a Jupiter-
sized planet orbiting a Sun-like star) and that all the recovered planets are
in bins with fairly low values ($<$20%), hinting that even in young clusters
smaller planets are more frequent than giant planets.

  * •

For our biased sample, we computed a planet occurrence rate of 49$\pm$20%
which is significantly higher than _Kepler_ ’s Gyr-old occurrence rates of
6.8$\pm$0.3% for sub-Neptunes and Neptunes (0.017-0.055
$\frac{R_{\text{p}}}{R_{\star}}$ or 1.8-6 $R_{\oplus}$, assuming a Solar
radius) within 12.5 days (about half a TESS sector).

Since most of these planets were initially detected in 2-min cadence data, our
work shows that 30-min cadence data can be used to detect young transiting
planets and thus has the potential for more planet discoveries. The planet
occurrence rate we calculated for our sample is higher than that for _Kepler_
’s Gyr old stars. However, we realize that this value is heavily biased since
we only consider clusters with confirmed/candidate planets and can be further
improved upon by using pterodactyls to search for young ($<1$ Gyr) transiting
planets in a larger sample of nearby clusters and moving groups ($<$200 pc)
using TESS Primary and Extended Mission FFIs. We also plan on uniformly
characterizing all the stars in our sample, so as to only consider FGK stars
in future studies. With this young population of transiting, short-period
planets, we hope to establish how the radius distribution of transiting
exoplanets evolved over time, and therefore provide observational constraints
on the mass loss mechanisms of planetary atmospheres.

##  8 Acknowledgements

R.B.F. would like to thank the following individuals for their expertise,
assistance and, invaluable insights throughout the testing of pterodactyls:
Adina D. Feinstein and Benjamin T. Montet (eleanor), Michael Hippke (Wōtan and
TLS), Robert T. Zellem (EXOTIC), Christina Hedges (vetting, centroid test),
and the Scaling _K2_ team i.e., Jessie L. Christiansen, Sakhee Bhure and Britt
Duffy Adkins. G.D.M. acknowledges support from ANID — Millennium Science
Initiative — ICN12_009. This paper includes data collected by the TESS
mission. Funding for the TESS mission is provided by the NASA’s Science
Mission Directorate. This material is based upon work supported by the
National Aeronautics and Space Administration (NASA) under Agreement No.
NNX15AD94G for the program Earths in Other Solar Systems, under Agreement No.
80NSSC21K0593 for the program “Alien Earths”, and Grant No. 80NSSC20K0446
issued through the Astrophysics Data Analysis Program (ADAP). The results
reported herein benefited from collaborations and/or information exchange
within NASA’s Nexus for Exoplanet System Science (NExSS) research coordination
network sponsored by NASA’s Science Mission Directorate. This publication
makes use of data products from Exoplanet Watch, a citizen science project
managed by NASA’s Jet Propulsion Laboratory on behalf of NASA’s Universe of
Learning. This work is supported by NASA under award number NNX16AC65A to the
Space Telescope Science Institute.

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##  Appendix A Comparison of Spline-Based Detrending

In order to find the best detrending routine for our sample, we followed
Hippke et al. (2019) which used injection-recovery tests and found that for
highly variable stars, such as those found in young cluster, spline-based
methods maximized the fraction of recovered injected planets. We specifically
tested the following three splines available via Wōtan: robust spline with
iterative sigma clipping, Huber estimator spline Huber (1981), and a penalized
spline with iterative sigma clipping Eilers & Marx (1996). Here, we
demonstrate how each of these splines detrend the light curve of HIP 67522
which is in UCL and also has two planets around it. As can be seen below, the
penalized spline does the best job of detrending the light curve and has the
lowest RMS.

Figure 10: A demonstration of how different splines detrend the light curve of
HIP 67522. As can be seen by the low RMS, the penalized spline does a superior
job of matching the stellar variability trend and detrending the light curve.

##  Appendix B Recovery of Known Planets

The following plots depict the recovery of the known young transiting planets
using pterodactyls:

Figure 11: Left: Progression of the DS Tuc A light curve through pterodactyls.
Upper panel: PSF flux (in dark gray) and penalized spline trend (in blue).
Lower panel: Detrended light curve (PSF flux divided by the trend). The multi-
transit signature (in red) can be clearly seen. Right:  Upper panel shows
Phase-folded light curve of DS Tuc A b (gray data points) along with the best
fit model using EXOTIC (in red). Lower panel shows the residuals in parts per
million.

Figure 12: Left: Recovery of TIC 460205581 b. Upper panel: PSF flux (in dark
gray) and penalized spline trend (in blue). Lower panel: Detrended light curve
(PSF flux divided by the trend). The multi-transit signature (in red) can be
clearly seen. Right: Upper panel shows Phase-folded light curve of TIC
460205581 b (gray data points) along with the best fit model using EXOTIC (in
red). Lower panel shows the residuals in parts per million.

Figure 13: Left: Recovery of TOI 837 b. Upper panel: PSF flux (in dark gray)
and penalized spline trend (in blue). Lower panel: Detrended light curve (PSF
flux divided by the trend). The multi-transit signature (in red) can be
clearly seen. Right: Upper panel shows Phase-folded light curve of TOI 837 b
(gray data points) along with the best fit model using EXOTIC (in red). Lower
panel shows the residuals in parts per million.

Figure 14: Left: Recovery of TOI 1726 c. Upper panel: PSF flux (in dark gray)
and penalized spline trend (in blue). Lower panel: Detrended light curve (PSF
flux divided by the trend). The multi-transit signature (in red) can be
clearly seen. Right: Upper panel shows Phase-folded light curve of TOI 1726 c
(gray data points) along with the best fit model using EXOTIC (in red). Lower
panel shows the residuals in parts per million.

Figure 15: Left: Recovery of TOI 1726 b. Upper panel: PSF flux (in dark gray)
and penalized spline trend (in blue). Lower panel: Detrended light curve (PSF
flux divided by the trend). The multi-transit signature (in red) can be
clearly seen. Right: Upper panel shows Phase-folded light curve of TOI 1726 b
(gray data points) along with the best fit model using EXOTIC (in red). Lower
panel shows the residuals in parts per million.

Figure 16: Left: Recovery of TOI 451 c. Upper panel: PSF flux (in dark gray)
and penalized spline trend (in blue). Lower panel: Detrended light curve (PSF
flux divided by the trend). The multi-transit signature (in red) can be
clearly seen. Right: Upper panel shows Phase-folded light curve of TOI 451 c
(gray data points) along with the best fit model using EXOTIC (in red). Lower
panel shows the residuals in parts per million.

##  Appendix C Centroid Test

###  C.1 Recovered Known Transiting Planets

The following plots show the results of the centroid tests for the recovered,
known, young transiting planets using pterodactyls. We find that, in all
cases, no significant offset was detected i.e., the transiting signal was
indeed coming from the target star.

Figure 17: Centroid tests for single planet systems

Figure 18: Centroid tests for multi-planet systems

###  C.2 POIs/Potential Binaries

Hedges (2021) uses the TESS Target Pixel File (TPF; and the aperture
information therein) in order to conduct the centroid test. However, TPFs were
only available for three of the potential binaries (all of the ones in UCL;
shown below) in Table 3 but not for the 12 other candidates (IC2602). As such,
we were only able to use this test when the TPF was available. As can be seen
below in two of the cases, we see no significant offsets. However, in the case
of TIC 177631209, an offset is detected which is consistent with triceratops’
Flat prior prediction i.e., the transiting signal is actually coming from a
nearby/background star.

Figure 19: Centroid tests for POIs/Potential Binaries in UCL

##  Appendix D TESS Input Catalog (TIC) IDs of Cluster Members Searched in
this work

###  D.1 Tucana Horologium Association (THA)

290496318, 266997586, 355766445, 425934574, 281461138, 231867117, 231907973,
231910539, 231914259, 271503441, 234495456, 394210384, 234506344, 234506911,
237880881, 237883772, 237885807, 237910557, 232073492, 234333175, 234338669,
238876720, 274017928, 220523369, 394355443, 238194430, 238196350, 25118964,
33864387, 33881250, 294754396, 319289907, 179315999, 149351776, 141423634,
270623499, 350712873, 150068381, 280865190, 410421717, 79403675, 259845346,
316854083, 406277015, 139984208, 238815210, 327667965, 71274771, 403237836,
234284556, 317016534, 273416539, 197960398, 261560580, 293507177, 229807000,
229807051, 410213494, 410214984, 410214986, 350215424, 325220989, 234290432,
201226029, 325525541, 650381163, 2054867096, 120462356, 12509218, 116157661,
156002545, 117874958, 117874959, 281670243, 206592394, 41862041, 158595208,
206623351, 230982053, 231005004, 229142539, 231020924, 231020638, 219993473,
219998026, 231064749, 231064750, 201753428, 201795667, 201861769, 166787846,
166852312, 166852313, 201898220, 201919099, 201938513, 207138379, 339607562,
381949410, 175298549, 149838027, 224276435, 40059734, 67630561, 140460192,
266746662, 77111651, 152970890, 200790343, 200790342, 401913214, 79566479,
219229275, 219257563, 259542669, 220437346, 381003375, 318785502, 318841562,
141306513, 165184400, 49906916, 176852917, 160008866, 308305105, 93122097,
144653213, 321100028, 44793998, 44794000, 152505948, 170673573, 77339881,
259573397, 161576005, 235056185, 685945639, 632601393, 70596114, 178857861,
117748478, 178969585, 178969584, 406498177, 188969241, 188969240, 77959676,
220622233, 738102496, 397231463, 317325489, 369862028, 451535889, 276967501,
401820403, 401820823, 411956826, 339397736, 466265409, 219953459, 360912453,
265332355, 372106647

###  D.2 IC 2602

269788982, 270294307, 373886624, 374507880, 374434502, 376150973, 376248958,
376731139, 377487978, 463722209, 463914418, 280562557, 281404104, 295146126,
296056755, 303021887, 303938254, 315312718, 315556844, 316108752, 316657304,
338027557, 338153421, 338155185, 344331260, 344500353, 344748662, 371442380,
372091372, 372598349, 372810731, 374748039, 375211992, 375586505, 375590099,
376026697, 376346464, 376802322, 376802477, 377369998, 377370859, 377954373,
378030265, 378229702, 378229708, 378412167, 378421253, 378503608, 378611172,
378968986, 378971350, 389925947, 389927730, 389987955, 389989102, 389989103,
389992758, 389994091, 390287165, 390297263, 390297906, 390356253, 390358373,
390358936, 390359665, 390359863, 390362683, 390362687, 390364291, 390365611,
390366165, 390366768, 390369742, 390370044, 390440616, 390442052, 390442224,
390442286, 390442621, 390443919, 390444472, 390446082, 390756608, 390757974,
390759555, 390759810, 390759889, 390760156, 390760423, 390840249, 390840539,
390841015, 390842457, 390847186, 390849159, 390850870, 390852244, 390853511,
390853705, 390953365, 390953417, 390954082, 390954865, 390955053, 390965584,
390966887, 390967697, 391166737, 391169363, 391247092, 391248084, 391251375,
391252554, 391333587, 391333777, 391334152, 391336297, 391336489, 391341577,
391345891, 391420878, 391421013, 391421894, 391422697, 391423247, 391423941,
391426350, 391426355, 391426724, 391742621, 391742931, 391798710, 391800466,
397179567, 397256049, 397451050, 397607720, 397608769, 397735761, 397781652,
397786354, 398002694, 398003321, 398007252, 398007510, 398009616, 398497171,
398859114, 398913671, 398919018, 398919062, 400066956, 400326671, 401066440,
401885249, 402190411, 402197704, 453950110, 460019760, 460042206, 460042668,
460044249, 460052791, 460053781, 460071039, 460169886, 460179837, 460205515,
460205581, 460205610, 460205613, 460209001, 460228276, 460230188, 460235527,
460297171, 460335450, 460336403, 460337200, 460338822, 460364093, 460366104,
460451570, 460473652, 460474388, 460493086, 460496906, 460500756, 460500920,
460501099, 460502873, 460526824, 460527147, 460613215, 460623602, 460625223,
460648865, 460649476, 460651700, 460651946, 460652126, 460765494, 460771098,
460772349, 460774571, 460774855, 460793411, 460793464, 460795626, 460796730,
460797477, 460797491, 460803319, 460823191, 460823505, 460825967, 460826876,
460827760, 460835832, 460910972, 460950389, 460950671, 460951259, 460953778,
460957968, 460958645, 460982124, 460982877, 460985868, 461080220, 461117076,
461120837, 461121683, 461123552, 461124617, 461125055, 461125245, 461125565,
461129500, 464897777, 464898410, 464900625, 464901555, 464902649, 464903262,
464905819, 464907721, 464907793, 464925976, 464925998, 464928326, 464928360,
464930364, 464934793, 464935013, 464935253, 464935435, 464936128, 464936356,
464936632, 464937455, 464937480, 464938239, 464969661, 465051041, 465069629,
465071629, 465075473, 465100077, 465104773, 465107223, 465107251, 465107412,
465107540, 465107704, 465109422, 465131523, 465132340, 465250214, 465261021,
465263287, 465264828, 465268721, 465268826, 465271210, 465272595, 465273919,
465275413, 465296988, 465297405, 465302289, 465306494, 465451355, 465456282,
465458552, 465459529, 465461596, 465462490, 465466499, 465466759, 465466991,
465470619, 465470793, 465472920, 465512275, 465593684, 465621749, 465661670,
465663582, 465801421, 465801835, 465803266, 465823847, 465828067, 465828262,
465831049, 465865592, 465902398, 465998642, 466002083, 466003005, 466010610,
466030199, 466032289, 466034300, 466035035, 466181275, 466183196, 466186713,
466194095, 466208965, 466209622, 466215841, 466218647, 466368276, 466370148,
466422383, 466568973, 466573354, 466576983, 466577068, 466579089, 466593335,
466617413, 466617428, 466630156, 466705111, 466736533, 466794262, 466831513,
466953672, 466982490, 467136716, 467138305, 467162035, 467170455, 467232072,
467342418, 467349410, 467351743, 467557909, 467739360, 467953288, 467976475,
467980197, 468093585, 468172174, 468205592, 844245965, 844522717, 847701323,
847769574, 848933728, 849260294, 850363872, 850582149, 850582150, 911292786,
911713906, 911870847, 911870867, 911872987, 911894290, 911920053, 911976941,
912047875, 912047923, 912058973, 913701079, 913996012, 914038861, 915086533,
923545851, 374517370, 374930544, 375679671, 376420337

###  D.3 Upper Centaurus Lupus (UCL)

410464477, 231813631, 436248798, 157209108, 284422031, 60024614, 53369126,
140295287, 45688827, 280207697, 446764692, 188084200, 48781344, 49046625,
448474635, 178659732, 29982064, 333734230, 437266963, 847323329, 872689258,
73650567, 73710370, 103625477, 124286087, 124512998, 124515557, 134976179,
142391542, 144609763, 144678969, 144921815, 152484504, 152484511, 162093865,
162208214, 178759525, 181229149, 248078069, 301219220, 323245745, 333832656,
390009811, 451452509, 452419080, 461125552, 911963409, 940640910, 998337743,
998337745, 388237166, 454856551, 273349137, 361818250, 258588387, 442062521,
287670422, 245298317, 339301537, 245430125, 363781484, 275705109, 438586540,
438692318, 243164696, 243237647, 165729961, 165775281, 243321910, 165823257,
243330489, 243344284, 243341756, 101940827, 243389982, 243390044, 243393076,
243396962, 243412695, 243427058, 243430178, 243477650, 243496587, 243511069,
241511379, 241511375, 30067072, 241570607, 241573601, 243618821, 207786920,
166447153, 243642384, 243647020, 241640242, 166577188, 241677723, 276004385,
241685708, 111947267, 307143242, 241739877, 113350106, 113277027, 166843863,
420522238, 359830202, 178931743, 359762838, 112176566, 178936965, 261389834,
261389883, 242119768, 326467176, 326742300, 242149069, 179099805, 179130687,
312420298, 312512588, 179220045, 396137563, 328700272, 179291515, 328811406,
242267549, 330123048, 329299765, 179367009, 179413040, 179413905, 179538968,
329815628, 210806853, 242336470, 242367242, 179623765, 179623744, 323269451,
242391843, 179743858, 339413946, 330987798, 331335557, 339530484, 179878718,
413285274, 331523868, 179905128, 332012383, 242548962, 179964001, 242557720,
332213483, 414138813, 125757999, 242583230, 242583644, 167480388, 242595135,
242612195, 242610390, 167546864, 420582698, 167596713, 332888505, 167670025,
90800382, 127024985, 167704195, 241827885, 241825308, 127089264, 333544395,
127203998, 264137167, 127249954, 127311608, 127246209, 211517703, 127315102,
290932786, 457557304, 241883618, 127664368, 83863971, 127731749, 392788625,
291909020, 158809330, 127794299, 127861722, 127791732, 392838495, 128079374,
158979332, 128119540, 159043143, 159195919, 289425666, 430829746, 369971171,
128453434, 128622430, 379593781, 460844584, 159376787, 159372538, 159421340,
159428617, 159428519, 383492888, 383582909, 159496289, 129116176, 129117325,
129060941, 159537293, 188212197, 188991120, 159752939, 383632304, 159754676,
47752102, 129419398, 47828022, 81003, 47884213, 250091359, 129623324,
366011440, 366011855, 250123846, 160089427, 48064387, 129774131, 129948345,
455309397, 160444470, 160404487, 160444291, 455375884, 455410480, 48364505,
160502580, 160504689, 48437482, 309456404, 164844, 160695823, 307425592,
333651699, 440863421, 276130740, 276219648, 121094784, 121102482, 461663855,
35001854, 440880146, 121240521, 121196226, 334129050, 121250827, 334425144,
334424163, 334417833, 121407551, 75543709, 75540884, 334648804, 75616091,
334835256, 75642561, 75648725, 335146096, 335139519, 75735567, 370476997,
121779963, 121779961, 121726626, 335454137, 121839093, 75869475, 335643748,
121982262, 121981993, 75873633, 75931110, 121983359, 121979152, 75933042,
75970186, 75971901, 61012630, 61079477, 160417350, 160417246, 160549804,
76050403, 122083452, 122162363, 76057224, 160633268, 160701354, 160704414,
122244909, 160632970, 160703925, 122250596, 160703933, 121850125, 122288890,
122397232, 122394390, 122397233, 76322064, 76397021, 276293815, 371122327,
276300910, 76435066, 276452267, 276491524, 276503464, 76580025, 141662588,
76587359, 307526685, 307533179, 61530691, 76652075, 142513032, 143414073,
76706808, 76706801, 272341056, 148087359, 148158374, 148158540, 272397344,
272395377, 148158169, 48630780, 272396062, 148261121, 272456799, 272462967,
460329848, 460323913, 225797367, 148480904, 148494823, 225957292, 148495018,
89026796, 148772375, 54172975, 54175032, 54175033, 148904033, 292265209,
292364079, 148904850, 148904891, 54245747, 54449487, 185053184, 54667962,
54810190, 54811378, 1037289516, 976426321, 128116539, 1052698599, 1174609023,
127871423, 42974961, 133010063, 132241629, 149640056, 141045993, 413145172,
461728725, 413693742, 413693728, 414077635, 152377452, 153079294, 149437620,
153781478, 154438290, 155430355, 170986304, 289877522, 172608950, 172608996,
189421351, 172615355, 173560788, 173560502, 173871956, 254322223, 254365686,
254406143, 254387071, 190372855, 176463845, 254451455, 98761335, 98909539,
177342508, 177336303, 177631209, 254597659, 99039745, 99039926, 178201756,
99041233, 99039843, 266271836, 99039842, 99046173, 99046104, 362351038,
254628801, 99205053, 178456568, 269155561, 269155560, 179051609, 179051461,
270107026, 99324522, 179622269, 272977820, 254740868, 254771390, 442611273,
295901750, 295905052, 295899674, 254844960, 295911223, 277674241, 296039638,
442642949, 254930869, 254901458, 296483317, 296700769, 255092900, 58413338,
442813719, 301036163, 301087756, 301048970, 255134616, 442828160, 58583881,
364200069, 364200072, 364200513, 255263576, 255236579, 58751944, 255246336,
292566342, 386943436, 58752825, 58749494, 386980599, 58832313, 294993587,
281164246, 281164807, 279883855, 255403319, 279819212, 279821618, 255407474,
59017926, 59095543, 59095516, 59183599, 59232730, 255464386, 59334299,
93457683, 93456758, 275018323, 255475779, 59403154, 59336031, 59504074,
59500324, 93610654, 93700013, 93779101, 93778206, 69283667, 69377602,
69178294, 256902444, 69420071, 93932740, 214870481, 93985722, 69514028,
69609942, 94159843, 161786522, 161873315, 70041394, 374542527, 374648559,
94491270, 374823554, 374812449, 374719920, 215392772, 374732772, 94731904,
94683443, 457995946, 457993297, 67978974, 382643945, 163141448, 382799779,
382794993, 382870216, 382800509, 382800518, 462044648, 462077825, 462083149,
462147302, 462148256, 462146157, 462147898, 462146834, 68256179, 164029492,
95468062, 382549695, 303188383, 164707310, 303188775, 68416596, 164707361,
318027415, 318030913, 317906231, 318035342, 68565222, 3084844, 410857373,
364368528, 364523302, 96552404, 318141346, 318141352, 96631952, 210541258,
210577071, 221355243, 3926262, 4061225, 222835418, 210908741, 210908710,
222940415, 392328254, 350869718, 210975114, 2743109, 211086449, 224004929,
351521484, 211143017, 211237627, 211237621, 225109252, 352162554, 211459804,
323187268, 211609345, 211681133, 291866634, 280474618, 292925229, 280828479,
280822724, 212201942, 382951562, 205461071, 83687552, 310053760, 458058639,
94972416, 233981889, 397712527, 234869424, 78981730, 79358659, 245927009,
245934292, 337243296, 338104678, 338105219, 246664608, 338495232, 34404183,
339989392, 247348620, 343976519, 212461524, 377523286, 378094374, 381441805,
381441323, 44207349, 193169513, 194744695, 160689461, 17509396, 1232119536,
1233589158, 1336147896, 1343250594, 1160500678, 1247277024, 504761559,
1170473308, 1172055696, 1255305471, 446547327, 469811127, 148910632, 97044158,
285117481, 393808105

###  D.4 Ursa Major (UMa)

11895653, 224288693, 224292240, 316331312, 224305606, 99381773, 229534764,
1001230963, 157272202, 159190005, 159191044, 141821609, 150387644, 142277151,
159189482, 416538839

###  D.5 Pisces-Eridani (PiEri)

80363380, 41858251, 262531383, 12787754, 399570739, 240720758, 4579839,
188627184, 311085703, 8938429, 66437682, 66471572, 89526411, 228383334,
89547213, 89547209, 114749459, 37763129, 212963433, 382306185, 28077586,
28092085, 248349830, 67643537, 248384545, 248952247, 70490059, 257434109,
29848163, 404467056, 164777021, 33625968, 423750380, 423750384, 257483561,
257484419, 72729895, 139526229, 120888774, 175491080, 144110354, 630138333,
332714671, 332740776, 270432631, 1028816, 332825272, 332862003, 332864335,
420000810, 1122408, 251064437, 251081955, 64008790, 251088243, 4741056,
65346691, 425095257, 35745429, 35841788, 204613238, 204613241, 141287580,
98855268, 365332374, 23193695, 9805084, 274037216, 441515106, 92250588,
279068672, 55893164, 9967295, 423442532, 12546422, 382326499, 12631414,
121006547, 166741952, 325707772, 156460685, 165219666, 279403260, 44647574,
461713170, 178286446, 257605131, 152590946, 170674625, 651901104, 457161840,
38613715, 55406666, 55441489, 34086013, 34147414, 9161614, 34238114, 34267639,
269724428, 332661361, 250133028, 37816550, 37860207, 248613540, 37903382,
37948770, 71089681, 71091056, 248655215, 38049622, 38049612, 38128400,
55935823, 117735557, 117745508, 56000236, 56127663, 146804027, 167485031,
246896530, 316915529, 152439649, 169396430, 169451121, 169529956, 231303250,
188968885, 188987821, 24607967, 442926120, 442926121, 24719594, 442965496,
143353370, 408233707, 437759888, 385141581