# The SHERLOCK pipeline: new exoplanet candidates in the WASP-16, HAT-P-27,
HAT-P-26, and TOI-2411 systems

Martín Dévora-Pajares,1,2 Francisco J. Pozuelos,3 Antoine Thuillier,5,6
Mathilde Timmermans,4 Valérie Van Grootel,5 Victoria Bonidie,7,8 Luis Cerdeño
Mota,x Juan C. Suárez,1

1Dpto. Física Teórica y del Cosmos. Universidad de Granada. 18071. Granada,
Spain
2Avature Machine Learning, Spain
3Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía
s/n, 18008 Granada
4Astrobiology Research Unit, Université de Liège, Allée du 6 Août 19C, B-4000
Liège, Belgium
5Space Sciences, Technologies and Astrophysics Research (STAR) Institute,
Université de Liège, Allée du 6 Août 19C, B-4000 Liège, Belgium
6Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles
(ULB), CP 226 1050 Bruxelles, Belgium
7Department of Physics and Astronomy, University of Pittsburgh, 3941 O’Hara
Street, Pittsburgh, PA 15260, USA
8Pittsburgh Particle Physics, Astrophysics, and Cosmology Center (PITT PACC),
University of Pittsburgh, Pittsburgh, PA 15260, USA E-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The launches of NASA _Kepler_ and _TESS_ missions have significantly enhanced
the interest in the exoplanet field during the last 15 years, providing a vast
amount of public data that is being exploited by the community thanks to the
continuous development of new analysis tools. However, using these tools is
not straightforward, and users must dive into different codes, input-output
formats, and methodologies, hindering an efficient and robust exploration of
the available data. We present the SHERLOCK pipeline, an end-to-end public
software that allows the users to easily explore observations from space-based
missions such as _TESS_ or _Kepler_ to recover known planets and candidates
issued by the official pipelines and search for new planetary candidates that
remained unnoticed. The pipeline incorporates all the steps to search for
transit-like features, vet potential candidates, provide statistical
validation, conduct a Bayesian fitting, and compute observational windows from
ground-based observatories. Its performance is tested against a catalog of
known and confirmed planets from the _TESS_ mission, trying to recover the
official TESS Objects of Interest (TOIs), explore the existence of companions
that have been missed, and release them as new planetary candidates. SHERLOCK
demonstrated an excellent performance, recovering 98% of the TOIs and
confirmed planets in our test sample and finding new candidates. Specifically,
we release four new planetary candidates around the systems WASP-16 (with
P$\sim$10.46 d and R$\sim$2.20 $R_{\oplus}$), HAT-P-27 (with P$\sim$1.20 d and
R$\sim$4.33 $R_{\oplus}$), HAT-P-26 (with P$\sim$6.59 d and R$\sim$1.97
$R_{\oplus}$), and TOI-2411 (with P$\sim$18.75 d and R$\sim$2.88
$R_{\oplus}$).

###### keywords:

data analysis – photometry – planetary systems – detection

††pubyear: 2024††pagerange: The SHERLOCK pipeline: new exoplanet candidates in
the WASP-16, HAT-P-27, HAT-P-26, and TOI-2411 systems–14

##  1 Introduction

The search for exoplanets has experienced one the most significant
developments in modern astronomy, where space missions such as _Kepler_
(Borucki et al., 2010) and _TESS_ (Ricker et al., 2016) have emerged as
beacons of discovery confirming thousands of new worlds and providing with
thousands of planetary candidates waiting to be confirmed. In addition, these
missions’ public nature has produced hundreds of thousands of light curves,
allowing the community to conduct alternative data exploration. To explore and
exploit this vast amount of data, many software packages emerged; some
designed for the analysis of light curves, including data loading and
visualization tools such as lightkurve (Lightkurve Collaboration et al., 2018)
and eleanor (Feinstein et al., 2019), some others to conduct data detrending
using a variety of functions and algorithms to remove instrumental systematics
that produce photometric variability such as everest (Luger et al., 2016,
2018), _K2_ ssf (Vanderburg & Johnson, 2014) and wötan (Hippke et al., 2019),
others to conduct a transit search such as the Box Least Squares (BLS; Kovács
et al., 2002), the quasiperiodic automated transit search (QATS; Carter &
Agol, 2013), and the Transit Least Squares (TLS; Hippke & Heller, 2019),
others to perform results vetting such as vetter (Zink et al., 2020) and
robovetter (Coughlin et al., 2016), others dedicated to validate planetary
candidates by determining whether a transit-like signal is statistically
likely to be caused by a planet or a background eclipsing binary such as vespa
(Morton, 2012), pastis (Díaz et al., 2014) and triceratops (Giacalone et al.,
2021), others to conduct a Bayesian fitting of the data to refine the planet
parameters such as allesfitter (Günther & Daylan, 2021), juliet (Espinoza et
al., 2019) and exoplanet (Foreman-Mackey et al., 2021), and others to compute
observational windows such as tapir (Jensen, 2013), to name a few.

While most of these packages are open-source, their different methodologies
and input-output formats hinder their correct usage and implementation,
relegating them to independent uses in most cases instead of an efficient
workflow where all the procedures are connected. The lack of connection
between these packages drives the community to rely mostly on the alerts
issued by the official pipelines such as Science Processing Operations Center
(SPOC; Jenkins et al., 2016) and the Quick Look Pipeline (QLP; Huang et al.,
2020), that is, the so-called _Kepler_ objects of interest (KOIs) and _TESS_
objects of interest (TOIs). However, many planets remain unnoticed due to the
detection thresholds of these pipelines, the lack of data exploration, or the
poor photometric quality. A proof of that is the number of alternatives
catalogs providing hundreds of new planetary candidates using _Kepler_ data
(see, e.g., Ofir & Dreizler, 2013; Coughlin et al., 2016), _K2_ data (see,
e.g., Mayo et al., 2018; Barros et al., 2016; Kruse et al., 2019) and _TESS_
data (Feliz et al., 2021; Cloutier, 2019; Montalto et al., 2020; Montalto,
2023), highlighting the importance of the parallel analyses of the data
provided by the space-based missions by multiple teams. A brief review of some
of these alternative catalogs can be found in Melton et al. (2023), where the
authors presented their own catalog using _TESS_ data from cycle 1.
Nonetheless, the pipelines producing these extra candidates are mostly non-
public; only a few are open-source, such as dave (Kostov et al., 2019a), which
is designed to search and vet planetary candidates using _K2_ data. Then, the
community is restricted to solely focus on those alerts, impeding the freedom
to concentrate on specific scientific cases designed by independent groups.
This paper presents the SHERLOCK (Searching for Hints of Exoplanets fRom Light
curves Of spaCe-based seeKers) pipeline. This public Python package allows the
users to conduct their own planetary searches, examining robustly the data
from space-based missions. The tool was first introduced at its initial
development stages with its core search functionality in Pozuelos et al.
(2020) and Demory et al. (2020), and has been used in a number of studies. The
iterative development has led SHERLOCK to become an end-to-end pipeline where
a special effort has been made to reduce user intervention and sorting all the
steps in an efficient workflow. With only a few command lines, the users can
explore the existing data, conduct the transit search, vet the most promising
signals, compute a statistical validation, conduct a Bayesian fitting to
refine planetary parameters and ephemerides, and trigger a follow-up camping
using ground-based facilities. With the implementation of its six modules,
SHERLOCK can be used in any imaginable exoplanetary survey that relies on
space-based data. For example, SHERLOCK is being used in the SPECULOOS project
(Gillon, 2018; Sebastian et al., 2021), which aims at finding transiting
planets orbiting nearby ultracool dwarfs using a network of six 1-m ground-
based telescopes located in different observatories such as ESO Paranal
Observatory (Atacama Desert, Chile) (Burdanov et al., 2018; Delrez et al.,
2018), Teide Observatory (Canary Islands, Spain) (Burdanov et al., 2022) and
National Astronomical Observatory of Mexico (San Pedro Mártir, Mexico) (Demory
et al., 2020). Due to the small sizes of these stars, transiting planets
orbiting them are prime targets for atmospheric characterization using, for
example, the _James Webb Space Telescope_ (Gillon et al., 2017, 2020). In this
context, SHERLOCK is exploring those stars in the SPECULOOS target list that
have been observed by _TESS_ , searching for transit-like features that might
be attributable to planets. While the SPECULOOS telescopes have better
photometric precision than _TESS_ for these stars (see, e.g., Delrez et al.,
2022), a robust inspection of the _TESS_ data can help to speed up the process
of planetary searching, saving telescope time. In addition, SHERLOCK is the
main pipeline of the FATE project (Van Grootel et al., 2021), which aims at
finding the first observational evidence of transiting planets orbiting hot
subdwarf stars, which are direct post-RGB objects that have lost most of their
envelopes. In particular, the project objective is to shed light on
understanding what happens to planetary systems once their host stars leave
the main sequence and engulf close-in planets, presumably perturbing the
dynamical architecture of the system. In this context, SHERLOCK systematically
searches for transiting-like features in the _Kepler_ , _K2_ , and _TESS_ data
(Thuillier et al., 2022).

Hence, the idea behind SHERLOCK is not producing a vast amount of new
planetary candidates as other existing pipelines do, but empowering
independent researchers to carry on their own designed surveys. The paper is
organized in the following way: Section 2 presents the key concepts and the
workflow behind SHERLOCK ; in Section 3, we use SHERLOCK to recover the
planets of some known _TESS_ systems, evaluate the pipeline performance while
also presenting the detection of four new candidates within those systems. In
Section 4, we present a new project in which SHERLOCK will be used to search
for extra planets that remain unnoticed. Finally, Section 5 presents our
discussions, conclusions, and prospects.

##  2 The SHERLOCK pipeline

SHERLOCK is an end-to-end pipeline that allows the users to explore the data
from space-based missions to search for planetary candidates. It can be used
to recover alerted candidates by the automatic pipelines such as Science
Processing Operations Center (SPOC; Jenkins et al., 2016) and the Quick Look
Pipeline (QLP; Huang et al., 2020), the so-called _Kepler_ objects of interest
(KOIs) and _TESS_ objects of interest (TOIs), and to search for candidates
that remain unnoticed due to detection thresholds, lack of data exploration or
poor photometric quality. To this end, SHERLOCK has seven different modules to
(1) acquire and prepare the light curves from their repositories, (2) search
for planetary candidates, (3) vet the interesting signals, (4) perform a
statistical validation, (5) carry out planetary system stability tests, (6)
model the signals to refine their ephemeris, and (7) compute the observational
windows from ground-based observatories to trigger a follow-up campaign. To
execute all these modules, the user only needs to fill in an initial yaml file
with some basic information such as the star ID, the cadence to be used, etc.,
and use sequentially one command line to pass from one step to the next.
Alternatively, the user may provide SHERLOCK with the light curve in a csv
file, where the time, the normalized flux, and the flux error need to be
given. In the following subsections, we describe in detail each of these
steps. The complete list of parameters that can be used in the yaml file,
along with a description of each one, can be found in GitHub’s SHERLOCK
repository111https://github.com/franpoz/SHERLOCK/blob/master/sherlockpipe/properties.yaml
keeping in mind that future implementations and releases might require new
parameters; hence we suggest regularly checking the list.

###  2.1 Light curve acquisition and preparation

SHERLOCK makes use of the lightkurve package (Lightkurve Collaboration et al.,
2018) to obtain the data of the space-based missions _Kepler_ , __K2__ and
__TESS__ , from NASA Mikulski Archive for Space Telescope (MAST). In most
cases, the user only needs to provide the star’s KIC, EPIC, or TIC
identification number and the cadence to be used, that is, 20, 120, 200, 600
or 1800 s for _TESS_ and 120 or 1800 s for _Kepler_ /_K2_. In the case of the
600 and 1800 s for _TESS_ , that is, the full-frame images (FFIs), the data
can also be retrieved via the eleanor package (Feinstein et al., 2019). By
default, the Pre-search Data Conditioning Simple APerture (PDC-SAP) is used,
which has some level of processing with long-term trends removed using co-
trending basis vectors. However, the PDC-SAP light curves are often affected
by some other trends or systematics that need to be corrected before starting
any planetary search. For example, some light curves present noisy regions
with a high level of data dispersion, some others are affected by strong
variability due to a fast rotation or stellar pulsations, and some others
present short-term trends induced by the instrumentation. To efficiently deal
with all these scenarios SHERLOCK accounts with different semi-automatic
tools.

####  2.1.1 Masking noisy regions

The light curves often show regions with high data dispersion where the
photometric quality is significantly reduced, strongly affecting the
performance of the search algorithm. These noisy regions are sometimes related
to the spacecraft’s motion, light scattering produced by the Earth, background
moving objects, or other unidentified sources. Hence, to clean the light curve
of such nuisance data, SHERLOCK can automatically compute the root-mean-square
(RMS) of the dataset by four-hour binning. Afterwards, all the light curve
time gaps longer than three days are identified to split the data into
segments. The mean RMS of each data segment is then computed, and each data
point that falls into an RMS bin above 2$\times$ the mean RMS of its
respective data segment is removed (see Fig. 1). The threshold of 2 is applied
by default, but the user can adjust it if needed in the yaml file. As shown in
Fig. 1, SHERLOCK also plots three RMS threshold suggestions (1.25, 1.5, and
1.75 $\times$ the RMS) alongside the user selection to provide insight into
the typical values used for this mask. In this figure, some potential transit
signals from TOI-144 appear to be masked when low RMS threshold values are
used, whereas a threshold of $1.75\times$ RMS seems to be optimal for masking
the entire noisy region without affecting the transits. In cases where the
automatic high-RMS-masking algorithm is not precise enough due to the
complexity of the noisy features, the user can freely enter a set of time
ranges to be masked.

Figure 1: Output from SHERLOCK high-RMS masked regions for the _TESS_ light
curve corresponding to TIC 261136679, observed during the Sector 1. The first
panel shows the binned RMS values and the computed thresholds: red, the user-
selected value (2 $\times$ RMS); purple, 1.75 $\times$ RMS; pink, 1.5 $\times$
RMS; orange, 1.25 $\times$ RMS. The bottom panels show the curve flux values
masked by each of the shown thresholds in the top panel.

####  2.1.2 Stationary stellar pulsations extraction (SSPE )

For quasi-stationary pulsations, we identified many cases (thanks to injection
and recovery tests) where short-period transits might be confused with them,
and then our targets would be removed using the automatic RMS-based noise
removal algorithm. For such targets where these types of pulsations are
identified, we developed a custom variation of the Barceló Forteza et al.
(2015) steps to reduce their effect on the light curve:

  1. 1.

Clear transits masking: An initial batch of searches with tls is done to mask
transits with low residuals, which are typically appreciable in the light
curve periodogram and might significantly alter the results of the next steps.
That would happen because the sub-harmonics of the main transit period get
narrower, and their shape in the periodogram might get close to the ones
offered by the stationary pulsations that we would like to reduce.

  2. 2.

Computation of highest-peak signal-to-noise (S/N): Once the highest peak is
identified in the periodogram, its S/N is computed by dividing its power by
the median of powers of its surrounding periods within a window of 4 hours. We
used the median instead of the mean as it is typically a more robust
statistical estimator of baseline values, which is what we try to extract
here.

  3. 3.

Model the stationary signal: In case the S/N is higher than a given threshold
(defaults to 4), the signal is modeled with a non-linear least squares
algorithm with an initial estimation of the amplitude and frequency through a
fit of a cosine wave.

  4. 4.

Check model validity: If the model shows an amplitude uncertainty lower than
20% and a phase uncertainty lower than 0.2 radians, it will be extracted from
the current light curve flux. If the resulting signal shows lower RMS, it will
be accepted, and the resulting flux will be stored. We return to step 2 and
apply the algorithm iteratively whenever a model is accepted.

To test the capabilities of the SSPE algorithm, we selected the TIC 169285097,
cataloged as a hot subdwarf pulsating in p and g modes by Sahoo et al. (2020).
These targets are complex hosts to search for small planets producing
transits. Indeed, the strong RMS induced by the several pulsation modes would
make such planets undetectable, increasing their residuals and reducing their
S/N. Also, the typical transit detection algorithms often fail when searching
for transits around these targets because they usually match sine-shaped
pulsations to transit models, and their noise can be strongly correlated. As
we are trying to diminish these effects, we tried our algorithm on the
selected target to inspect the results that could be achieved on one of the
available sectors from the TESS mission. We display the resulting flux in Fig.
2, which was obtained after subtracting 44 pulsation frequencies. The most
powerful frequencies are shown in Fig. 10, where their corresponding models
are overplotted to the phase-folded light curves. To properly investigate the
capabilities of the algorithm in terms of transiting exoplanet signals
recovery and to ensure that the procedure does not remove transit features, we
tried our implementation on a public tool that we also developed in-house and
published in a public repository under a free usage license: The MATRIX
ToolKit222https://github.com/PlanetHunters/tkmatrix. Built on top of the same
code base as SHERLOCK , it contains the same algorithmic capabilities as the
former and is conceived as an injection and recovery engine that includes a
stage to generate a grid of periods, radii, and epochs to be injected in the
original target’s light curve. Those synthetic curves are later used in a
recovery stage to search for the known injected transits. matrix will store a
csv file to keep track of which models were found and which were not,
generating at the end a heat map showing the matches for each period, radius,
and epoch from the grid.

Figure 2: Results of applying the SSPE algorithm to the TIC 169285097 PDCSAP
flux data obtained from TESS sector 2. The original light curve is depicted in
orange, while the corrected light curve, following the removal of pulsations
by our algorithm, is shown in red

To assess properly the improvement brought by our SSPE algorithm, we firstly
tried the injection and recovery scenario for a simple search without using
it. Later, we tried the same scenario with the inclusion of the algorithm. The
results can be appreciated in the Fig. 3, where we can see that the first
algorithm could add for this target an increment in the detectability of $1$
R⊕ for the best cases. Altogether this study case leads us to an outstanding
improvement in our detection rates for our current transit surveys like the
one started in Van Grootel et al. (2021) and upcoming ones in the near future.

Figure 3: Injection and recovery results for the hybrid pulsator TIC 169285097
without and with the usage of SSPE . Above, the injection and recovery
execution with a standard biweight detrend and search. Below, the same
scenario execution including a previous SSPE run to reduce the quasi-
stationary periodic pulsations effect on the light curve.

An improved version of this iterative algorithm would include the entire set
of already selected signals on each iteration to improve the model-fitted
parameters as it is done with felix in Charpinet et al. (2010) and Zong et al.
(2016). However, this is not included in the SHERLOCK SSPE procedure yet.

####  2.1.3 Removing short trends

SHERLOCK uses a multi-detrend approach to deal with short trends caused, for
example, by instrumental drifts and intrinsic stellar variability. This
strategy is implemented via the wötan package (Hippke et al., 2019). By
default, SHERLOCK detrends the flux using the bi-weight method. This choice is
based on its good speed-performance ratio compared with other methods, such as
the Gaussian process, which is also available. The bi-weight method is a time-
windowed slider, where short windows can efficiently remove short trends, but
there is an associated risk of removing any actual transit signal. Hence, to
prevent this issue, the pipeline explores, by default, ten cases with
different window sizes. The minimum value of the window size is obtained by
computing the transit duration (T14) of a hypothetical Earth-size planet with
an orbital period of 10 d. A minimum window size of 3$\times T_{14}$ is set to
protect such a transit. On the other hand, the maximum value explored is
20$\times T_{14}$, which is enough to remove the variability in most of the
cases. However, if preferred, the user may set the number of detrends to be
applied and the minimum and maximum values of the window size in the yaml
file. Hence, from the original PDC-SAP flux, SHERLOCK generates a new set of
detrended light curves, each differing only in the window size used for
detrending.

The transit search, described later in Section 2.2, is then conducted over all
the detrended light curves jointly with the original PDC-SAP light curve. If a
signal is detected in only one (or very few) of the light curves, it is
considered "detrend-dependent", suggesting it may be an artifact produced by
the detrending algorithm. Conversely, if a signal is consistently found in
multiple (or all) light curves, it is considered "detrend-independent", thus
increasing its credibility. By comparing the S/N and Signal Detection
Efficiency (SDE) of each detection across these light curves, we can determine
the most appropriate window size for detrending. This method enhances the
reliability of our planet detections by minimizing the risk of false positives
due to the detrending process, ensuring that any promising signals found are
not artifacts of a specific detrending configuration.

####  2.1.4 Correcting strong variability

Many stars suffer significant changes in brightness, which might be caused,
for example, by stellar spots or intrinsic stellar variability. In such cases,
the PDC-SAP light curves show intense sinusoidal trends of high amplitudes. To
deal with these scenarios, SHERLOCK computes the Lomb-Scargle periodogram
(LSP) and extracts the value of the strongest peak using the lightkurve
package (Lightkurve Collaboration et al., 2018). By default, a factor of this
value is used to remove the sinusoidal trend by fitting a sum of sines and
cosines employing the cosine function provided by the wötan package (Hippke et
al., 2019). Our calibration experiments showed that the most appropriate value
for such a factor is 0.25. However, the user may adjust it to any other value
if wanted in the yaml file. There are some limitations in this procedure; for
example, the presence of a hot Jupiter may induce a strong peak in the LSP
that can be confused by a sinusoidal trend. Hence, a visual inspection is
always desirable before applying this correction.

###  2.2 Search for planetary candidates

By default, SHERLOCK performs the transit search by using a modified version
of the tls package (tls ; Hippke & Heller, 2019). Since tls uses an analytical
transit model taking into account the stellar parameters, it offers a better
S/N and SDE than classical algorithms based on bls (bls ; Kovács et al.,
2002). This stellar-model optimization allows the detection of shallow
periodic transits, which are more challenging to find. However, if desired,
the user may set the bls algorithm in the yaml file.

The procedure followed by SHERLOCK is to search for transits in all the
detrended light curves jointly with the original one (PDC-SAP flux). Then, the
results obtained for each individual light curve are stored; that is, the
orbital period ($P$) and its error in days, mid-transit time for the first
identified transit (T0) in TBJD or BJD, the transit depth in ppt, the transit
duration ($D$) in min, the number of transits, the S/N, the SDE, and the
false-alarm probability (FAP). Once all the light curves are analyzed, the
results are combined to select the best transiting signal. To this end,
SHERLOCK provides first a border-correction algorithm. This algorithm computes
a synthetic SDE value for each signal, penalizing the transits that are found
in the border of the data set, which often corresponds to regions where there
are more uncorrected systematics, as follow:

$\displaystyle SDE_{synthetic}=SDE\left(1-\frac{N_{tb}}{N_{t}}\right)$

Where $N_{tb}$ is the number of transits close to borders and $N_{t}$ is the
total number of transits. Secondly, the signal selection is performed by a
quorum algorithm, where signals found in more light curves are favored in a
voting process over those found on less light curves. Once a signal is
selected as the best candidate, SHERLOCK masks it in the PDC-SAP light curve
using its $P$, T0 and 3$\times D$, and starts a new searching run. The user
can set how many times this process is repeated in the yaml file; however, our
experience points out that results found beyond five runs are less reliable.
This issue is coming due to the accumulated gaps in a given light curve after
many mask-and-run iterations. Hence, by default, this process is repeated five
times. In addition, SHERLOCK establishes minimum thresholds for the S/N and
the SDE of a selected signal to pass from one run to the next. By default,
both S/N and SDE are set to five, but the user may change these minimum
thresholds in the yaml file.

Besides the quorum algorithm, SHERLOCK has two other more simple alternative
selection methods. These two methods are based on the selection of the signal
with larger S/N and the larger S/Nsynthetic, respectively. Moreover, SHERLOCK
provides a flexible module to use any other user-defined selection algorithm.

Once the searching stage is finished, SHERLOCK produces as many folders as the
number of runs executed, containing plots showing for each light curve
(original PDC-SAP flux and detrended light curves) the best signal found.
Moreover, SHERLOCK provides two log files: (1) report.log , where the user can
find all the information about the searching process, and (2) candidates.log ,
where is listed a summary of the main signals found. Moreover, the user will
have access to extra folders named /fov , /detrends , /rms and /sa . In /fov
(from field-of-view) is stored the target pixel file (TPF) with the aperture
used to extract the photometry over-plotted along with the nearby stars from
Gaia DR2 catalog, obtained via the tpfplotter package (Aller et al., 2020),
and the TPF with the light curves corresponding to each individual pixel using
the lightkurve package (Lightkurve Collaboration et al., 2018). In /detrends ,
the user can visually inspect all the detrends applied to the original PDC-SAP
light curve as described in Section 2.1.3. In /rms , a collection of plots
shows the regions of the light curve that are masked due to their high RMS
values, if any, as explained in Section 2.1.1. In case the SSPE module is
activated (Section 2.1.2), the extracted sinusoidal trends are plotted into
the /sa directory. Finally, the LSP and the value of the strongest peak are
displayed as described in Section 2.1.4. Combining these outputs, SHERLOCK
gives the user the information needed to evaluate the results’ reliability and
the signals listed as promising.

####  2.2.1 TLS metrics fine-tuning

The original tls algorithm presented by Hippke & Heller (2019) reported some
inconsistencies with the SDE and S/N in some scenarios. Hippke & Heller (2019)
compute the transit duration by using a custom factor called ‘curve stretch‘,
supposedly taking into account the time gaps within the curve. Despite, this
does not seem to be working properly and the error created in the transit
duration propagates to the S/N calculation, which is based on this value. The
S/N is especially hindered in curves with long time gaps, which are a typical
case in the _TESS_ mission. That is why we decided to rewrite the transit
duration calculation by only taking the best model fit provided by tls ,
measuring the period fraction where it falls below 1. This fix to the
algorithm seemed to repair the S/N computations and the package began to
return very stable S/N and some compared outputs can be explored in Table 1.

Table 1: S/N for three known transiting planets with long time gaps given by SHERLOCK searches with the standard tls version and with our modified version. Planet | Sectors | S/NTLS | S/NTLS-Modified
---|---|---|---
LHS 1140 b | 3,30 | 18.065 | 41.962
TOI 178 d | 2,29 | 11.723 | 35.317
TOI 736 c | 9,36 | 13.940 | 43.312

In addition, the SDE is a measurement that is expected to remain at scale
among use cases and, hence, be comparable. We remind the reader that SDE is a
metric indicating the statistical significance of a given period compared to
the other periods tested in the transit search. In particular, an SDE value of
$x$ for any given period $P$ means that the statistical significance of this
period is $x\times\sigma$ compared to the mean significance of all other
periods (we refer the reader to Hippke & Heller (2019) and references therein
for further details). Then, this metric allows us to evaluate and compare the
prominence of detected signals across different periods. However, the
computation of SDE by tls implies the calculation of the residuals, which in
some edge cases are set to a default baseline that can lead to an
overestimation of the SDE. Specifically, when many residuals are set to the
baseline value, the few significant spikes can cause abnormally high SDE
values, for example, when a given light curve contains many gaps. To mitigate
this, we rescale each final SDE value based on the proportion of local
residuals that are above the baseline. This adjustment ensures that the SDE
values more accurately reflect the true statistical significance of the
detected signals. As an example, Fig. 4 shows the difference between an
original SDE spectrum with many baseline values and its re-scaled counterpart.
The last problem that we observed affecting the SDE is the difficulty of
establishing fixed thresholds based on False Alarm Probabilities (FAP). The
original tls implementation calibrated a bijective relationship between SDE
and FAP values. However, this calibration was carried out only for scenarios
with timespans up to 28 days (the _TESS_ typical length for one sector data)
and does not provide good FAP values for longer data contexts, where SDEs tend
to be higher on average even for false positives.

Figure 4: SDE periodogram for TIC 10837041 (TOI-2411) obtained during the
third run, that is, the transits corresponding to TOI-2411 b and another
candidate found during the searching process (Sec. 3) have been removed from
the light curve. Due to the short orbital period of TOI-2411 b, which is only
0.78 days, the resulting light curve used in the third run contains many gaps
after removing the transits. These numerous gaps impact the computation of the
SDE conducted by tls , leading to overestimated values, as seen in the top
panel. The bottom panel displays the proposed correction by SHERLOCK , where
the SDE periodogram now displays more reliable values, indicating the very low
detection significance of the found signals (see text for details).

####  2.2.2 The Savitsky-Golay digital filter

SHERLOCK allows applying the Savitsky-Golay digital filter (Savitzky & Golay,
1964) to the original PDC-SAP flux before any detrend and starting the transit
search. This filter is implemented by using the scipy package (Jones et al.,
2001), which performs a data convolution by fitting sub-sets of adjacent data
points with a low-degree polynomial using the linear least square method.
Hence, the filter correlates nearby points in the data reducing their local
white-noise without distorting the signal trend, leading to half the initial
RMS value in the light curves. The Savitsky-Golay digital filter is handy when
dealing with threshold-crossing events with low S/N. While the usage of this
filter has the potential to find signals buried in the noise, it also has the
associated risk of obtaining more false-positive detections that the user
needs to vet carefully. In Table 2 we show the S/N and SDE values for TOI-270
(Günther et al., 2019) and TOI-736 (Crossfield et al., 2019; Peterson et al.,
2023) using a pure-TLS search and applying first the Savitsky-Golay digital
filter. As can be noticed, the S/N reported by TLS is improved by a factor of
2 and the SDE is sometimes improved and sometimes worsened without a
noticeable impact in the search. The S/N and SDE reported by SHERLOCK are
extracted directly from the tls algorithm, calculated with a naive estimation
that can not be compared with values from the SPOC pipeline. Therefore, these
values are only used internally to compare the goodness of selected candidates
and choose the clearest one. A recent application of this filter was used to
recover the low S/N candidate TOI-4306.01 by Delrez et al. (2022), for which
the pure-TLS search found the candidate with S/N below the typical detection
threshold of S/N$\geq$5.

Table 2: Transit parameters for TOI-270 and TOI 736 known planets given by SHERLOCK searches without and with Savitzky-Golay filter. Planet | P | D | Depth | S/N | S/N | SDE | SDE
---|---|---|---|---|---|---|---
(d) | (min) | (ppt) |  | (SG) |  | (SG)
TOI-270 b | 3.36 | 75.3 | 0.8 | 14.3 | 31.6 | 61.1 | 40.4
TOI-270 c | 5.66 | 94.7 | 2.9 | 49.1 | 112.4 | 39.8 | 46.6
TOI-270 d | 11.38 | 115.9 | 2.0 | 28.1 | 70.2 | 44.7 | 44.0
TOI-736 b | 0.95 | 35.8 | 3.8 | 8.9 | 17.4 | 18.5 | 18.7
TOI-736 c | 4.99 | 59.1 | 14.4 | 17.7 | 41.2 | 24.4 | 25.0
TOI-736 d | 2.75 | 49.2 | 2.15 | 5.192 | 12.2 | 6.6 | 6.6

###  2.3 Semi-automatic vetting

As described in Section 2.2, once the searching step is done, SHERLOCK
provides several outputs that allow the user to perform a preliminary vetting.
However, many other effects might be causing the detected signals that need
careful inspection.

The finished _Kepler_ mission (Borucki et al., 2003) provided more than 30,000
Threshold Crossing Events (TCES; Thompson et al., 2018), which are candidate
signals that were found by the SPOC main search pipeline. However, different
sources could generate these signals or even be instrumental artifacts induced
into a target’s light curve. To rule out these scenarios, the SPOC implemented
the Data Validation Reports (DVR) (Twicken et al., 2018), which are documents
showing different metrics to qualify or discard an analyzed candidate. These
scenarios are 1) transit shape model fit, 2) odd-even transits checks, 3)
centroids shifts, 4) optical ghost effects, 4) transit source offsets, 5)
rolling band contamination, 6) secondary depth significance, and some
additional numerical tests. Based on these tests SHERLOCK implements a vetting
procedure which are explained in the next sub-sections.

While these tests may offer a good vetting for promising signals, there are
some limitations, mainly when dealing with shallow transits with very low S/N,
where the results of the vetting might be inconclusive. SHERLOCK uses the
vetting stage by importing the WATSON package, which we also developed and
published as an independent open-source
tool333https://github.com/PlanetHunters/watson, offered in the official python
repositories444https://pypi.org/project/dearwatson/ with its own
documentation555https://dearwatson.readthedocs.io/en/latest/.

####  2.3.1 Single transit inspection

For each vetted candidate, SHERLOCK computes the light curve with the official
pipeline aperture and a smaller one and displays them together for each single
transit. The official pipeline aperture’s centroids, motion, and background
flux data are also displayed. In addition, the TPF is folded and plotted
focused on each single transit. No metrics are computed from this data, but
the visual inspection of these plots is very useful for finding differences or
problematic features in single transits.

####  2.3.2 Cadence-based curves signal reliability

By using the period, epoch, and duration of a promising signal found in the
transit search module, SHERLOCK computes the S/N for a box-shaped transit for
each available cadence. If the transit is not significant enough (S/N$\geq$5)
in any of the cadences or the S/N is substantially different from the nominal
cadence, SHERLOCK will warn about it in the report.

####  2.3.3 Odd-even and secondary events

The transit-like signals might be originated by astrophysical sources that
might not be planets. This is the case of Eclipsing Binaries (EB) or Nearby
Eclipsing Binaries (NEB), which typically show secondary eclipses with
different transit signatures to the primary one. SHERLOCK computes the S/N for
odd and even transits depths and also for secondary eclipses. A red flag is
reported when secondary eclipses are detected with S/N$\geq$3 or in case
either odd or even transits show S/N$\leq$5.

####  2.3.4 Transit source offset: images

The difference imaging method proposed in Bryson et al. (2017) was the
selected approach by the SPOC to accept or reject signals based on the offset
found on the computed transit source from pixel images. The method consists of
computing the center of mass of the subtraction of the flux measured within
the TPF for in-transit and out-of-transit per-pixel data. This way the most
probable source of the transit events can be estimated. We have implemented a
simplified version of this test in SHERLOCK . In addition, we have also
included a second method to compute this metric by running a per-pixel bls
search with a fixed period on the folded TPFs. We then compute the so-called
center of mass from each of the per-pixel bls residuals and, finally, average
the output of both methods to get the final transit source position.

####  2.3.5 Transit source offset: centroids shift

An alternative method to estimate scenarios where the transit signal might
have originated outside the target is the centroids diagnosis, also presented
by Bryson et al. (2017). In our case, we subtract the mission-computed motion
values (polynomials relating the sky and the focal plane for each cadence) to
the mission-computed centroid data (target position on the TPF given by the
Pixel Response Function obtained from the out-of-transit control image (Bryson
et al., 2013)). This method measures the deviation of the target position
variations on the TPF against the focal plane alignment variations to the sky.
If these values report an S/N > 3, SHERLOCK will be placing a red flag for the
analyzed signals.

####  2.3.6 Optical ghost diagnostic

Sometimes the transit-like signals are caused by artificial sources. That is
the case of optical ghosts, which can be created by light reflections from
high-intensity sources between the optical system and the CCD as shown by
Caldwell et al. (2010). To find false positives caused by optical ghosts, the
_Kepler_ (DVR performs a test that measures the correlation between core (mean
flux from all pixels within the target aperture) and halo (mean flux from all
the pixels around the target aperture) fluxes and the transit signal. When the
signal is affected by a ghost, the halo flux will be more correlated than the
core one.

SHERLOCK implements a similar test. In our case, we compute and subtract the
core and halo fluxes. In case the result still shows a transit signal with an
S/N > 3, SHERLOCK will reject the candidate.

###  2.4 System stability

In some cases, several promising signals are selected during the transit
search, but their orbital periods are very close to each other. In other
cases, the selected signal is very close to a known confirmed planet. The
system’s architecture might be unstable in these scenarios, revealing that the
candidates found are likely false positives.

To shed light on these scenarios, SHERLOCK incorporates a module to assess the
system dynamics stability. This analysis can be conducted at two points:
during the initial vetting of a signal to assess whether there are possible
system configurations for our candidates and as part of the validation
scenario to get stability indicators for realistic or known configurations.
That is, SHERLOCK can run a stability analysis in two modes. The first
consists of giving user inputs, which create a linear grid of possible orbital
parameters for each candidate. The second one loads the results from the
Bayesian fit (see Section 2.6) for the selected signal, allowing the addition
of some constraints to the most likely system configuration.

To compute the system stability, SHERLOCK evaluates the fast chaos index Mean
Exponential Growth factor for Nearby Orbits (MEGNO; Cincotta & Simó, 1999,
2000; Cincotta et al., 2003), which is widely used in this context (see, e.g.,
Jenkins et al., 2019; Delrez et al., 2022; Pozuelos et al., 2023). SHERLOCK
uses the N-body numerical package rebound (Rein & Liu, 2012), which provides a
MEGNO implementation by employing the Wisdom-Holman WHfast code (Rein &
Tamayo, 2015). The MEGNO mean value over time, denoted as $\langle
Y(t)\rangle$, enhances stochastic fluctuations. This characteristic
facilitates the differentiation of trajectories into quasi-periodic, that is
to say, stable orbits, where $\langle Y(t\rightarrow\infty)\rangle$ approaches
2, and chaotic orbits, where $\langle Y(t\rightarrow\infty)\rangle$ tends
towards infinity for an infinitive integration time or diverging from 2 for
finite integration times.

This highly flexible module allows users to investigate as many parameters as
desired to test the system’s stability. Indeed, the user can explore the
system’s stability by varying the stellar mass, the planetary period,
eccentricity, mass, argument of periastron, and inclination. Since we are
dealing with transiting planets, not always the planetary masses are known;
then, for these cases, SHERLOCK obtains the planetary mass relying on mass-
radius relationships from Chen & Kipping (2017), which provides
differentiation between small and large planets in a similar way than Weiss et
al. (2013) and Bashi et al. (2017). In all the cases, for each parameter
SHERLOCK uses uniform distributions, where the user needs to provide the
nominal value, the associate uncertainty, and the number of bins that want to
explore within that range. The results are then stored in csv files that the
user can employ to construct stability maps. It is important to notice that
while SHERLOCK offers the possibility of exploring a number of the parameters,
not all of them equally affect the system stability. Indeed, as stated in
Cranmer et al. (2021), the planetary semi-major axes (or the orbital periods),
the masses, and the eccentricities are the parameters that most affect the
stability of a given system. Out of these three parameters, usually are the
masses and the eccentricities the most unconstrained and, hence, the ones used
to explore system architecture (see, e.g., Demory et al., 2020; Murgas et al.,
2023).

To correctly sample the planetary positions over their orbits, the scenarios
are integrated using a time-step of 5% of the shortest orbital period in the
system. Finally, running the integration for a time of $10^{5}$ to $10^{6}$
times the largest planetary orbital period in the system is recommended to
start getting convergent and reliable results. In any case, this analysis does
not intend to replace a more robust dynamical study of a given system but a
preliminary view of the credibility of planetary candidates and the potential
system architecture.

###  2.5 Statistical validation

_Kepler_ /_K2_ and _TESS_ found many candidates that, due to the faint nature
of their host stars and/or the shallowness of their transits, can not be
confirmed from ground-based observatories as true planets. To mitigate this
situation were developed the first statistical-validation tools during the
_Kepler_ -era (see, e.g., Torres et al., 2011; Morton, 2012; Morton et al.,
2016), which allow to calculate the false positive probability of a given
detection to validate it statistically.

This procedure is nowadays widespread to support the planetary interpretation
of a given signal even when the candidate can be reached from ground-based
observatories (see, e.g., Kostov et al., 2019b; Quinn et al., 2019). SHERLOCK
allows the user to perform a statistical validation automatically connecting
the results with the triceratops
666https://github.com/stevengiacalone/triceratops package (Giacalone et al.,
2021, 2022). Originally, triceratops was designed to vet and validate _TESS_
candidates only; however, we have contributed to developing this open-source
package to manage also _Kepler_ /_K2_ candidates. In short, triceratops
computes the probabilities of a wide range of transiting-producing
astrophysical scenarios such as a transiting planet and eclipsing binary (in
many different configurations) using the primary transit of the candidate, the
prior knowledge of the host and nearby stars, and the current understanding of
planet occurrence and stellar multiplicity. Hence, triceratops computes the
location of a given candidate in the false-positive probability (FPP) – nearby
false-positive probability (NFPP) plane, where the candidate will be
classified as a validated planet if FPP$<$0.015 and NFPP$<10^{3}$, as likely
planet if FPP$<0.5$ and NFPP$<10^{-3}$, and as likely false positive if
NFPP$>10^{-1}$. Due to the probabilistic nature of the procedure to calculate
the values of FPP and NFPP by triceratops , SHERLOCK performs five
computations and then averages the results to provide the final values. In
addition, SHERLOCK uses the results from Lissauer et al. (2012), which
estimated the fraction of planet candidates that are false positives when in
systems with multiple planet candidates based on _Kepler_ data. Then, this
prior probability is multiplied by the FPP and NFPP previously computed (see,
e.g., Demory et al., 2020).

###  2.6 Bayesian model to refine the ephemeris

Once a candidate has been vetted and validated, it can be desirable to trigger
a follow-up campaign to firmly confirm the planet in the target star using
ground-based observatories. However, the results from the searching stage via
tls are not optimal for scheduling an observation due to the large uncertainty
associated with the found orbital period ($\Delta P$), whose value directly
depends on the period grid density. Indeed, the transit time ($T$) and its
uncertainty ($\Delta T$) of future observational windows are given by (see,
e.g., Mallonn et al., 2019):

$\displaystyle T=T_{0}+n\cdot P$ $\displaystyle\Delta T=\sqrt{\Delta
T_{0}^{2}+(n\cdot\Delta P)^{2}}$

With T0 and $P$ previously defined in Section 2.2, and $n$ the number of
cycles since T0. Hence, error propagation is strongly dominated by the term
$n\cdot\Delta P$, which may produce $\Delta T$ of the order of several hours
if the detection is performed in _Kepler_ /_K2_ data or early _TESS_ sectors.
This situation might hinder any ground-based confirmation.

In this context, SHERLOCK allows the user to refine the ephemeris by
performing a Bayesian fit using the allesfitter
777https://github.com/MNGuenther/allesfitter package (Günther & Daylan, 2019).
allesfitter is an open-source code that performs a Bayesian fit to infer the
star and exoplanet properties given a set of photometric and/or radial
velocity data. Then, SHERLOCK automatically injects the results from the
searching stage and the stellar parameters in allesfitter as priors and
implements two steps fitting: 1) The candidate signals are masked, and the
out-of-transit correlated noise estimation is performed using a Gaussian
Process (GP) with a 3/2 Matérn kernel with a MCMC fit on the PDCSAP-flux light
curve, which can describe smooth long-term trends and short-term stochastic
variations by its two hyper-parameters: the amplitude scale ($\sigma$) and
length scale ($\rho$). 2) The candidate signals priors are fit taking into
account the previously derived GP parameters using normal priors, modeling the
radius ratio of the planet to host, $R_{p}/R_{\star}$, the sum of the stellar
and companion radii divided by the semimajor axis, $(R_{\star}+R_{p})/a_{b}$,
the cosine of the orbital inclination, $\cos i_{p}$, the epoch/transit midtime
in days, $T_{0}$, the orbital period of the planet in days, $P_{p}$, the
transformed limb-darkening coefficients following a quadratic law,
$q_{1}$–$q_{2}$, and the natural logarithm of the white noise,
log$\sigma_{w}$. By default, the Bayesian model used by SHERLOCK is the Nested
Sampling, but the user might switch to MCMC if desired in the yaml file. All
the posterior distributions and the derived parameters are stored in a new
folder named /fit . At the end of this stage, the user obtains a robust
inference of the planetary parameters. In particular, the $\Delta P$ is
reduced considerably, and the new values can be used to schedule ground-based
observations with much more accurate predictions.

###  2.7 Ground-based observational windows

Once the planetary properties are optimal from Section 2.6, the user may
safely plan a follow-up campaign from ground-based observatories to confirm
the planetary nature of a given candidate. This step is particularly critical
for results obtained using _TESS_ data. Indeed, the pixel scale of _TESS_ , of
21", is remarkably larger than _Kepler_ ’s, of 4", moreover the _TESS_ ’
point-spread function (PSF) might be as large as 1’. Hence, due to dilution
effects, the pixel scale, and the large PSF, the probability of contamination
by nearby eclipsing binaries, whose deep eclipses might mimic shallow transits
detected in the target star, is not null and, ideally, has to be checked from
ground-based facilities. This ground-based confirmation is the primary goal of
the seeing-limited photometry working group of _TESS_ (see, e.g., Kostov et
al., 2019b). To schedule these observations, the community typically uses the
_TESS_ Transit Finder tool, which is a customized version of the tapir package
(Jensen, 2013).

In this context, SHERLOCK automatically loads the Bayesian fit results and a
list of observatories provided by the user from where the transit windows will
be computed. The observational windows from each observatory will consider
some user-defined constraints, such as the minimum altitude of the object,
distance from the moon in relationship with its illumination phase, and the
minimum transit coverage. Then, SHERLOCK displays the observational windows in
csv and pdf files, including the ingress, mid-transit, and egress times in UT
for each event and plots with the airmass and altitudes of the host star
during the entire event. This module was built by using the astropy package
(Astropy Collaboration et al., 2013, 2018) and was tested against the _TESS_
Transit Finder tool to verify its good performance.

##  3 SHERLOCK performance

Previously, we have outlined several projects leveraging the SHERLOCK
pipeline, such as SPECULOOS and FATE. Moreover, many other studies employed
this pipeline to retrieve alerts from the TESS mission and known planets, as
well as to identify new planetary candidates (see e.g., Wells et al., 2021;
Schanche et al., 2022; Murgas et al., 2023; Dransfield et al., 2023; Dreizler
et al., 2024; Gillon et al., 2024). In this section, our focus shifts to
demonstrating the performance of the SHERLOCK pipeline through a specifically
designed experiment to provide a level of reliability.

In particular, we built a catalog of 100 stars that fulfill the following
conditions in the ExoFOP
list888https://exofop.ipac.caltech.edu/tess/view_toi.php; retrieved in October
2023: (1) the targets should, at least, contain one previously known planet or
a TOI confirmed planet, (2) one of these planets should have orbital periods
shorter than ten days, (3) the maximum number of sectors should be two, and
(4) the produced list with previous conditions is sorted by descending
brightness and limited to the first 100 stars. Filters (1), (2), and (3) are
applied to reduce the computational cost of this experiment. Appendix B lists
the catalog obtained following these criteria providing the TIC-IDs. The main
goal of this test is to run SHERLOCK over this catalog and record the
successful recovery and non-recovery of planets and TOIs. Hence, to easily
illustrate the performance, we introduce the recall parameter defined as
$TP/(TP+FN)$, where $TP$ are the true positives, that is, the number of
correct planets or TOIs found, and $FN$ are the false negatives, that is, the
number of known planets or TOIs that we do not recover. Then, the performance
of the code is optimal when this parameter approaches 1, indicating that
SHERLOCK successfully identifies the expected planets without omissions.

From the 100 stars composing our catalog, there were 104 TOIs that might
correspond to previously confirmed planets, that is, known planets for which
TESS also provided an official TOI, or new planetary candidate alerts released
by TESS that the scientific community has confirmed as planets. The number of
multi-alert stars was very reduced because of the filters used to build the
target list. Indeed, our filters favored targets with large planets in short
orbital periods, such as hot Jupiters (periods up to 10 days and radius from 6
$R_{\oplus}$). Population studies suggested that nearby planetary companions
rarely accompany these planets. However, thanks to the extreme photometric
precision of space-based missions and dedicated radial velocity surveys,
nearby planetary companions to hot Jupiters have emerged in recent years (Wu
et al., 2023). These recent discoveries suggest that the formation of hot
Jupiters via quiescent mechanisms is more efficient than previously thought,
when the main formation channel invoked was the dynamical high-eccentricity
migration (Dawson & Johnson, 2018). Hence, in this context, our target list
not only serves to compute the recall factor and establish the goodness of the
SHERLOCK pipeline but also offers an interesting scientific case searching for
low S/N signals that might hint at the existence of planetary companions to
these hot Jupiters in our list, supporting this new emergence of planets.

Once our target list was well established, we ran SHERLOCK over it. In
general, after the execution of the first module, that is, the exploration of
the available data for a given candidate (see Section 2.1), we triggered a
standard search with no initial fine-tuning. However, we had to refine the
search parameters for some targets due to several factors, such as poor
photometric quality and lack of data from the official pipelines. We provide a
brief explanation for these particular cases:

  * •

TIC 146520535 and TIC 464646604: In our multi-detrend procedure, the window
size ranges from 0.2 to 1.2 days by default, which we found optimal for most
cases. However, due to the strong short-term variability of these light
curves, we had to adapt the minimum and maximum window sizes to lower values
from 0.25 to 0.75 days.

  * •

TIC 189380158, TIC 281408474, and TIC 33595516: The data for these targets
were not available in MAST, impeding us from gathering them using lightkurve ,
which is the default route to get the data. Hence, we switch to eleanor long-
cadence data by specifying the author in the yaml file.

SHERLOCK recovered 102 out of 104 transiting planets in the catalog, making a
count of two false negatives. These two were Kepler-89 e (TOI 4581.02), which
was present in the TESS data as a single transit and hence, SHERLOCK
mismatched it with a different period, and K2-285 c (TOI 4538.01), which was
entirely missed in favor of a different non-promising signal. With this data,
the final recall made up a value of 0.98 for our catalog. However, SHERLOCK
was also able to recover two other known planets that were not alerted with a
TOI: the TOI-942 c and Kepler-89 c. For the TOI-942 system, TESS alerted one
candidate with an orbital period of 4.3 d, (TOI-942 b), and the follow-up of
the system conducted by Carleo et al. (2021) found an outermost transiting
planet with an orbital period of 10.16 d (TOI-942 c), which corresponds to our
detection. In the case of the Kepler-89 system (Marcy et al., 2014), TESS
alerted one candidate that corresponded to Kepler-89 d with an orbital period
of 22.34 d, and a single transit that belonged to Kepler-89 e. In our
experiment, SHERLOCK also found a planetary candidate with an orbital period
of 10.42 d, which corresponded to Kepler-89 c.

On top of this, SHERLOCK spotted four interesting signals that could be
attributable to planets and for which there is not any previous information.
These new candidates were found in the systems WASP-16, HAT-P-27, HAT-P-26,
and TOI-2411. We followed all the steps to verify their planetary nature by
using the modules available in SHERLOCK as described in Section 2. In the
following subsections, we describe these new candidates and the confirmation
steps that we conducted to claim them as planetary candidates with high
probabilities of being genuine planets. Table 3 shows the summary of these new
candidates, and the planetary systems architectures are presented in Fig. 5.
We release these candidates as Community TESS Objects of Interest (CTOI), and
will be listed in the ExoFOP CTOIs
list999https://exofop.ipac.caltech.edu/tess/view_ctoi.php.

Hence, despite the small size of our sample, these results allow us to confirm
the high performance of SHERLOCK as a planetary search engine that can be used
to explore space-based data efficiently, not only to recover known planets but
also to search for new ones that remained unnoticed by the community.

Table 3: New planetary candidates found during the performance survey System | CTOI-ID | Period (d) | T0 \- 2457000 (BJDTDB) | Duration (h) | Depth (ppt) | Radius ($R_{\oplus}$) | Teq (K)
---|---|---|---|---|---|---|---
WASP-16 | 46096489.02 | $10.457_{-0.028}^{+0.018}$ | $1618.725_{-0.014}^{+0.012}$ | $3.67_{-0.45}^{+0.32}$ | $0.54\pm 0.1$ | $2.20\pm 0.23$ | $810\pm 36$
HAT-P-27 | 461239485.02 | $1.1994\pm 0.0002$ | $2705.510_{-0.001}^{+0.002}$ | $1.27_{-0.10}^{+0.11}$ | $2.13\pm 0.20$ | $4.33\pm 0.44$ | $1426\pm 87$
HAT-P-26 | 420779000.02 | $6.594_{-0.007}^{+0.009}$ | $2683.160_{-0.010}^{+0.014}$ | $2.71_{-0.41}^{+0.19}$ | $0.59\pm 0.11$ | $1.97\pm 0.20$ | $785\pm 15$
TOI-2411 | 10837041.02 | $18.750\pm 0.004$ | $2141.315_{-0.003}^{+0.004}$ | $3.56_{-0.08}^{+0.10}$ | $1.77\pm 0.12$ | $2.88\pm 0.15$ | $430\pm 15$
Figure 5: The planetary architectures of the systems WASP-16, HAT-P-27,
HAT-P-26, and TOI-2411 are shown from top to bottom. The sizes of the elements
in this figure scale with the sizes of the represented stars and planets. The
sizes of the stars are scaled relative to each other, and the planets are
scaled relative to each other, but the relative scales between stars and
planets are not accurate, with planets oversized for clearer visualization.
Known planets in the systems are displayed in solid colors, while the
candidates found in this study are highlighted with a gray halo and
transparency, whose properties are listed in Table 3.

###  3.1 WASP-16

WASP-16 is a Sun-like star with $T_{\textrm{eff}}=5700\pm 150\,K$ ,
$R_{\star}=0.946\pm 0.054\,R_{\odot}$ and $M_{\star}=1.022\pm 0.101M_{\odot}$
observed by the WASP project (Pollacco et al., 2006), in particular using
WASP-South, between 2006 and 2008. These observations hinted at the presence
of a giant planet that was later confirmed using spectroscopic observations
with the CORALIE spectrograph in 2008 and 2009. The results confirmed the
planetary nature of this signal, yielding $R=1.008\,R_{Jup}$,
$M=0.855\,M_{Jup}$ and with an orbital period of 3.12 d. This planet is the
hot Jupiter WASP-16 b (Lister et al., 2009).

WASP-16 was observed by the TESS mission in Sector 11 between April and May of
2019, using the 120 and 1800 sec cadences (TIC-46096489). The search performed
with SHERLOCK was conducted using the standard parameters, and we recovered in
the first run the signal corresponding to WASP-16 b, with S/N=97.9 and
SDE=18.6 in the 11 light curves (see Section 2.1.3). During the second run,
SHERLOCK did not spot any promising signal, but events that happened close to
the borders of the light curves, which clearly hinted at a systematic origin.
During the third run, we found a weak signal with S/N=4.7 and SDE=13 with a
period of 10.44 d. While this signal is just below our default detection
threshold of S/N$\geq$5, it was found in all the 11 light curves processed,
which reveals a non-detrend dependence. Hence, we vetted the signal and
excluded the possibility of it being produced by any systematics (see Section
2.3). Then, we conducted the statistical validation (see Section 2.5), and we
got FPP=0.26 and NFPP=0.0036 values, slightly above the likely planet area
defined by Giacalone et al. (2021). Subsequently, we conducted the Bayesian
fitting (see Section 2.6) and compared the Bayes Factor ($\Delta\ln Z$) of two
models: 1) only with the WASP-16 b planet, that is, the null hypothesis, and
2) including the second potential planet found by SHERLOCK , that is, a more
complex scenario with two planets. Then, we got $\Delta\ln Z=\Delta\ln
Z_{2planet}-\Delta\ln Z_{1planet}\sim 6.7$, what favours the 2-planet scenario
(Kass & Raftery, 1995). Considering the global results of these analyses, we
concluded that the signal found with a 10.44 d is a strong planetary candidate
named CTOI-46096489.02, which would correspond to a mini-Neptune of $\sim$2.2
R⊕. Its main parameters from the fitting can be consulted in Table 3. However,
it is important to notice that the Bayes Factor is suggestive but not
decisive; hence, extra observations using high-precision photometry would be
needed to firmly confirm the planetary nature of the CTOI-46096489.02
candidate. Due to the shallowness of its transit of $\sim$0.54 ppt, ground-
based instrumentation is inadequate for detecting such a subtle eclipse.
Indeed, the limited sensitivity and atmospheric interference associated with
terrestrial telescopes prevent accurate measurement of these weak signals.
Therefore, to obtain precise and reliable data that allow us to confirm the
planet, it is essential to utilize space-based instrumentation, such as CHEOPS
(Benz et al., 2021), which can bypass atmospheric distortions and provide the
necessary sensitivity to observe these shallow transits effectively (see,
e.g., Delrez et al., 2021). Unfortunately, since the last observational data
available comes from TESS Sector 11, the current uncertainty in the transit
time, $\Delta T$ (see Section 2.6), is $\sim$100 h, which makes any time-
critical observation impracticable. Another TESS-like campaign would be needed
to mitigate this lack of accuracy in the current transit times. According to
the TESS-point web tool101010https://heasarc.gsfc.nasa.gov/wsgi-
scripts/TESS/TESS-point_Web_Tool/TESS-point_Web_Tool/wtv_v2.0.py/, WASP-16
will be re-observed in April 2025, what will offer the opportunity to recover
this candidate and trigger an accurate follow-up campaign that will allow us
to confirm or refute its planetary nature.

The two-planet model is displayed in Fig. 8, the posterior distribution is
provided in Appendix C, Table 4, and the convergence of the model is
visualized in Fig. 11.

###  3.2 HAT-P-27

HAT-P-27 is a G8-dwarf star with a $T_{eff}=5250\pm 100\,K$,
$R_{\star}=0.90\pm 0.05\,R_{\odot}$ and $M_{\star}=0.94\pm 0.04\,M_{\odot}$
monitored on a nightly basis by The Hungarian-made Automated Telescope Network
(HATNet; Bakos et al., 2011) from January to August 2009. These photometric
observations were combined with nine spectroscopic measurements using the
HIRES instrument on the Keck I Telescope from December 2009 to June 2010. The
results were presented in Béky et al. (2011), reporting the discovery of
HAT-P-27 b, a hot Jupiter with a size of 1.038 RJup, a mass of 0.66 MJup and
an orbital period of 3.04 d.

HAT-P-27 was observed by the TESS mission in Sector 51 in May 2022, using the
120 and 600 sec cadences (TIC-461239485). We used the 120 s data in our search
with SHERLOCK , allowing us to recover in all the light curvers a transiting
signal corresponding to the HAT-P-27 b planet with S/N=37.3 and SDE=12.6.
During the second run, SHERLOCK spotted a transit-like feature with a period
of 1.20 d, with S/N=10.3 and SDE=29.8, also detected in all the light curves.
We executed the vetting module for this signal, which allowed us to rule out
its systematic origin. We noticed that SPOC identified a threshold crossing
event (TCE) for a candidate with an orbital period of 2.40 d, that is, the
first harmonic of the signal that SHERLOCK spotted. Hence, during the vetting
stage, we carefully examined the depths of the odd/even eclipses and transit
shapes in short and long cadences and found no remarkable difference among
them. Moreover, the candidate did not show any problematic metric either on
the transit source or the optical ghost checks, reinforcing our findings with
a period of 1.20 d as the more plausible solution. The TCE found by SPOC did
not become a TOI due to its low S/N ($<$10) and slightly centroids offset.
Next, we launched the statistical validation module, yielding values of
FPP=0.18 and NFPP=0.00054, which fall on the likely planet area.

Following the same procedure as in the case of the WASP-16 system, we
conducted the Bayesian fitting and compared the Bayes Factor between two
models: 1) only with the HAT-P-27 b planet (null hypothesis) and 2) including
the second potential planet found by SHERLOCK . We got $\Delta\ln Z=\Delta\ln
Z_{2planet}-\Delta\ln Z_{1planet}\sim 64.6$, which strongly favors the
2-planet scenario over the simplest with a single planet. This candidate is
then the CTOI-461239485.02, which corresponds to a hot Neptune-size planet of
$\sim$4.3 R⊕. Its parameters from the fitting can be consulted in Table 3. The
transit depth found for this candidate is $\sim$2.1 ppt, which is deep enough
for small- and medium-sized ground-based telescopes. Moreover, its orbital
period is 1.20 d, which eases scheduling and follow-up efforts due to the
large number of possible observable events. However, the uncertainty in the
transit time is $\Delta T\sim$ 3.3 h, which is challenging to conduct time-
critical observations from the ground but still possible. An alternative
approach would be to conduct long observations from space-based telescopes
such as CHEOPS, allowing for scanning up to 3$\sigma$ the predicted time
without the day-night cycles, making a putative detection easier. All these
considerations make CTOI-461239485.02 an excellent candidate to be confirmed
or refuted with relatively low effort.

The two-planet model is displayed in Fig. 8, the posterior distribution is
provided in Appendix C, Table 4, and the convergence of the model is
visualized in Fig. 12.

Figure 6: Stability map of the system HAT-P-27 composed of the two planets:
HAT-P-27 b and the planetary candidate CTOI-461239485.02. The map contains
40$\times$40 pixels, exploring the $e_{p}-M_{p}$ parameter space for the
candidate. The stability of each scenario is evaluated using the MEGNO
parameter, where $\langle Y(t)\rangle\rightarrow 2$ (purple shaded regions)
represents quasi-periodic orbits and chaotic systems when $\langle
Y(t)\rangle\rightarrow 5$ (yellow shaded regions).

Despite the vetting and validation tests passed by CTOI-461239485.02, the
resulting planetary configuration with a hot Jupiter at 3.04 d and an
innermost candidate at 1.20 d might be questionable due to stability concerns.
For this reason, we executed the stability test (see Section 2.4) assuming the
nominal values for the star and HAT-P-27 b planet as reported by Béky et al.
(2011), and for the new candidate using a grid of 40 eccentricities from 0 to
0.6 and 40 planetary masses from 9.5 to 32 $M_{\oplus}$ derived from the
radius using a mass-radius relationship (17${}^{+13.8}_{-8.1}\,M_{\oplus}$;
Chen & Kipping, 2017). This configuration allowed us to build a stability map
exploring 1600 scenarios in the $e_{p}-M_{p}$ parameter space. Then, the MEGNO
value is computed six times in each scenario by modifying randomly the orbital
parameters. Hence, in total, the stability map explored 9600 scenarios. Each
scenario was integrated over $\sim 10^{7}$ orbits of the outermost planet. The
stability map in Fig. 6 shows that the HAT-P-27 system can be stable for
eccentricities up to 0.19 for the full range of masses explored for the
planetary candidate. For larger eccentricities, the system becomes unstable
for any of the masses within our explored grid. This analysis allowed us to
conclude that despite the unusual architecture of the two-planet solution
proposed here, consisting of a hot Jupiter and an inner hot Neptune, the
system has ample room for stable configurations, resembling the WASP-84
system, where recently, an inner mini-Neptune has been found accompanying the
previously known hot Jupiter WASP-84 b (Maciejewski et al., 2023).

###  3.3 HAT-P-26

HAT-P-26 is a K1 star with a $T_{eff}=5079\pm 88\,K$,
$R_{\star}=0.79_{-0.04}^{+0.10}\,R_{\odot}$ and $M_{\star}=0.82\pm
0.03\,M_{\odot}$ observed nightly by the HAT-5 and HAT-6 telescopes of the
HATNet project between January and August 2009, that hinted at the presence of
a transiting planet with an orbital period of 4.23 d. The planetary origin of
this signal was later confirmed using the HIRES spectrograph on the Keck I
Telescope from December 2009 to June 2010. All these observations together
allowed the confirmation of the low-density Neptune-mass planet HAT-P-26 b
(Hartman et al., 2011) with a size of 0.565 RJup, a mass of 0.059 MJup and an
orbital period of 4.23 d.

This star was observed by the TESS mission in Sector 50 in May 2022, using the
120 and 600 sec cadences (TIC-420779000). During our search with SHERLOCK , we
fully recovered the signal corresponding to HAT-P-26 b with S/N=42.2 and
SDE=15.6 in the first run. During the second run, SHERLOCK spotted an
interesting signal with a period of 6.59 d. While this signal was slightly
below our detection threshold, with S/N=4.9 and SDE=7.4, it was confidently
found in all the light curves. This motivated us to run the vetting module,
where we did not find any solid potential systematic origin that explained
this signal; however, it is important to note that due to its very low S/N,
some of the tests were not conclusive. Still, we decided to conduct the
statistical validation, which yielded FPP=0.24 and NFPP=0.0075, falling in the
likely planet area.

We then executed the fitting module to refine the planet parameters and
compare the Bayes factor of the two models as for the other candidates. We
found $\Delta\ln Z=\Delta\ln Z_{2planet}-\Delta\ln Z_{1planet}\sim 4.7$, which
slightly favors the 2-planet scenario over the single-planet model. The
candidate, named CTOI-420779000.02, would correspond to a mini-Neptune of
$\sim$2.0 R⊕ (see planet parameters in Table 3), producing shallow transits of
only $\sim$0.6 ppt, which hinders any confirmation using ground-based
telescopes. However, its confirmation would be feasible, as stated for the
CTOI-46096489.02 in the WASP-16 system, by employing space-based telescopes
such as CHEOPS. The uncertainty in the transit time is $\Delta T\sim$ 22.7 h,
which is too large for time-critical observations, and unfortunately,
according to the TESS-point web tool, this star will not be revisited in
future cycles, preventing us from reducing this uncertainty using upcoming
TESS data. However, the orbital period of this candidate of only 6.59 d would
favor a filler follow-up camping to recover the planet by accumulating
observations. This strategy is also applied in the FATE project using CHEOPS
observations (Van Grootel et al., 2021) to find unknown transiting planets
with orbital periods shorter than 10 d. Following this strategy, it would be
possible to confirm or refute the existence of this planet.

The two-planet model is displayed in Fig. 8, the posterior distribution is
provided in Appendix C, Table 4, and the convergence of the model is
visualized in Fig. 13.

As for HAT-P-27, the candidate’s orbital period was close to the known planet
HAT-P-26 b. That architecture might be physically impossible and discarded by
exploring the system stability. We, hence, followed the same strategy as for
the HAT-P-27 system, building a stability map to explore 1600 scenarios in the
$e_{p}-M_{p}$ parameter space, displayed in Fig. 7. In this analysis, the
candidate’s eccentricity must be lower than 0.05 to ensure the system’s
stability for all the planetary masses explored, while the scenarios with the
candidate’s mass below 6$\,M_{\oplus}$ show stable solutions for
eccentricities up to 0.09 in most scenarios.

A particularly interesting point of the HAT-P-26 system is that von Essen et
al. (2019) reported the detection of a drift in the spectroscopic data
alongside a weak curvature in the timing residuals in the photometric data.
The authors conducted a follow-up of the planet and obtained a $\sim$4 min
amplitude of transit timing variation (TTVs). While the authors prudently did
not attribute these TTVs to a planetary companion, they gathered enough
information to rule out the spot-induced origin of such TTVs. In a more recent
study, A-thano et al. (2023) revisited the transit timings of HAT-P-26 b over
seven years, reporting a TTV amplitude of $\sim$2 min, which might be
attributable to the presence of an additional planet in the system of $\sim
6.36\,M_{\oplus}$ with an orbital period of 8.47 d, that is, in a first-order
mean-motion resonance 2:1. However, there is not any hint of a transiting
planet under this scenario. On the contrary, our solution points to the
transiting nature of a potential planetary candidate of $\sim$1.96
$R_{\oplus}$ (predicted mass from mass-radius relationships of
4.8${}^{+3.5}_{-2.0}\,M_{\oplus}$) with an orbital period of 6.59 d, that is,
within $\sim$6$\%$ of the first-order resonance 3:2. The findings presented
here can significantly encourage the scientific community to continue
monitoring the HAT-P-26 system, to ultimately unravel its planetary
architecture.

Figure 7: A stability map similar to the one displayed in Fig. 6 but for the
system HAT-P-26 composed of the two planets: HAT-P-26 b and the planetary
candidate CTOI-420779000.02.

###  3.4 TOI-2411

TOI-2411 (TIC-10837041) is a K7-dwarf star with $T_{eff}=4099\pm 123\,K$,
$R_{\star}=0.68\pm 0.02\,R_{\odot}$ and $M_{\star}=0.65\pm 0.02\,M_{\odot}$.
This star was monitored by the TESS mission in Sector 3 (October 2018) using
1800 s cadence and in Sector 30 (October 2020) using 120 and 600 s cadences.
Orbiting TOI-2411 was alerted in November 2020 a planetary candidate, which
was validated by (Giacalone et al., 2022) by combining high-resolution images
collected using the SOAR/HRCam, Palomar/PHARO, and Keck/NIRC2 instruments,
ground-based multi-band photometry (i’ and r’) taken employing the 1 m
Sinistro telescope at Las Cumbres Observatory and the 0.7 m CDK telescope at
the Mt. Kent Observatory, and statistical arguments. The planet, TOI-2411 b,
is a super-Earth of $1.68\pm 0.11\,R_{\oplus}$ in an ultra-short period orbit
of 0.78 d.

During our SHERLOCK search, we found in the first run a signal of 18.75 d with
a S/N=14.9 and SDE=14.1 in 9 of the 11 light curves processed. In the second
run, we found a signal corresponding to TOI-2411 b with S/N=8.4 and SDE=16.7
in all the light curves. We executed the vetting module for the 18.75 d signal
and found one red flag that might indicate a false positive: a momentum dump
near the first transit. Momentum dumps might originate flux dimmings that can
confuse the search algorithm; however, their shapes do not necessarily
resemble transit-like features. We carefully visually inspected the two events
in the 120 s data, and they both look similar in shape, duration, and depth.
Moreover, during the vetting, was also inspected the 600 s cadence, and the
signal corresponding to the 18.75 d was also found. Hence, we concluded that
the momentum dump, or any other systematic, was not the origin of the transit-
like feature detected by SHERLOCK . Next, we conducted the statistical
validation, which yielded values of FPP=0.022 and NFPP=0.0, falling in the
likely planet area.

We then performed the fitting analysis and compared the two models as
described for the previous candidates. We found $\Delta\ln Z=\Delta\ln
Z_{2planet}-\Delta\ln Z_{1planet}\sim 66.1$, which highly supports the two-
planet model. The candidate, CTOI-10837041.02, is found to be a mini-Neptune
of 2.88 $R_{\oplus}$, whose transit depth is estimated to be $\sim$1.77 ppt
(see Table 3), which can be detected using small- and medium size telescopes.
However, its moderately long orbital period of 18.75 d and estimated
uncertainty in the transit time of $\Delta T\sim$ 6.7 h make very challenging
to confirm its planetary nature utilizing ground-based facilities.
Unfortunately, TESS will not revisit this star, and hence, as in the case of
CTOI-420779000.02 (HAT-P-26 system), a filler program using CHEOPS would be a
potential solution to recover and confirm the candidate as a genuine planet.

The two-planet model is displayed in Fig. 8, the posterior distribution is
provided in Appendix C, Table 4, and the convergence of the model is
visualized in Fig. 14.

Figure 8: Detrended TESS photometry phase-folded to the periods of the known
planets (left column) and planetary candidates (right columns), along with the
best-fit transit models (solid black line). The unbinned data points are
depicted in grey, while the colored circles with error bars correspond to
binned data adapted in each case to ease the visualization. From top to
bottom, the WASP-16, the HAT-P-27, the HAT-P-26, and the TOI-2411 systems. The
posterior distributions of these fits are provided in the Appendix C and the
corner plots in Figs. 11,12, 13, and 14, respectively.

##  4 The Hidden Gems project

Nearby and low-mass stars ($M<0.6\,M_{\odot}$) represent the best opportunity
nowadays to study in great detail small transiting planets (Rp $<4$R⊕).
Indeed, these stars ease the characterization of small exoplanets, not only in
terms of radius and mass but also in terms of internal structure and
atmospheric properties, which encodes information about physical and chemical
properties, in turn providing insights into planets’ formation and
evolutionary history (see, e.g., Pudritz et al., 2018; Triaud, 2021).

Summarizing, there are three critical points that support this reasoning: 1)
their small sizes and lower masses compared to solar-like stars produce larger
transit depths and induce larger radial velocities for a given planet,
allowing for an accurate determination of planetary bulk properties, such as
the radius and mass, with precisions better than $\sim$4$\%$ and $\sim$25$\%$,
respectively. This allows us to derive the mean density and give a rough
estimation of the bulk composition and internal structure (Otegi et al.,
2020). This advantage has been the driver of many transit and Doppler surveys
such as MEarth (Nutzman & Charbonneau, 2008), SPECULOOS (Sebastian et al.,
2021), CARMENES (Quirrenbach et al., 2014), and SPIRou (Artigau et al., 2014),
to name a few. 2) Atmospheres of planets orbiting these small stars can be
explored using transit spectroscopy, which relies on the chromatic signature
of the chemical species present in the atmosphere, detectable with current and
future space-based observatories such as JWST and Ariel. Transit spectroscopy
allows three configurations to study planetary atmospheres: Transmission
spectroscopy, emission spectroscopy, and phase curves (Madhusudhan, 2019). The
possibility of atmospheric characterization of small planets with any of these
three techniques has been the drive behind the detection of new planets around
such stars, notably thanks to the TESS and Kepler/K2 missions. It has even now
become one of the main science goals of the community, with its importance
recognized at the highest level with a recommendation by the JWST Exoplanet
Working Group to dedicate over 500 hours of Director’s Discretionary Time to
this
end111111https://www.stsci.edu/files/live/sites/www/files/home/hst/about/space-
telescope-users-committee/presentations-and-
documentation/_documents/2023_nov/exoplanets-DDWG.pdf. 3) Low-mass stars are
the most common in the solar neighborhood (Winters et al., 2015), representing
up to 70$\%$ of the stellar content of our Galaxy. Moreover, they have a lower
binary fraction than solar-like stars. In addition, computational simulations,
as well as Doppler and transit surveys, have concluded that the fraction of
stars hosting small planets increases with decreasing mass (see, e.g., Alibert
& Benz, 2017; Bonfils et al., 2013; Dressing & Charbonneau, 2015). By
combining the high frequency of low-mass stars with the occurrence rate of
small planets orbiting them, there might exist $\sim$10$\times$ more small
planets orbiting these stars than around Solar analogs. Hence, planets
discovered orbiting low-mass stars are more representative of planet formation
processes than planets orbiting single Sun-like stars (Triaud, 2021).

Of particular interest are these systems hosted by a low-mass star where more
than one transiting planet exists. In these cases, by studying different
planets that were born in the same protoplanetary disc, we can get information
not only about the planets but also about the formation and evolution of the
whole planetary system. By aggregating information gleaned from the analysis
of numerous multiplanetary systems, we will be able to formulate a robust
planetary formation model that can resolve existing degeneracies and overcome
the limitations currently constraining our understanding (see, e.g., Raymond &
Morbidelli, 2022). This comprehensive model will eventually enable us to
systematically decipher the underlying processes that govern planetary
formation and evolution across different environments, unifying disparate
observations and refining our predictions regarding the distribution and
characteristics of exoplanets.

The full sample of transiting exoplanets around low-mass stars keeps on
growing and now exceeds 1400121212NASA Exoplanet Archive (20 Feb 2024)
https://exoplanetarchive.ipac.caltech.edu/ planets with 85$\%$ of them being
smaller than Neptune. As the race to detect new small planets amenable for
detailed studies is still ongoing, we present the Hidden Gems project, which
relies on the capabilities of SHERLOCK to discover extra planets in low-mass
star systems hosting at least one transiting planet.

Our target list is constructed by filtering stars with
T${}_{\mathrm{eff}}<5300$ K to include K- and M-dwarf stars and select a
volume-limited sample within a distance of 50 pc, which totals 167 transiting
planets in 107 unique systems at the time of writing. However, this catalog
will be updated with the upcoming releases of newly discovered planetary
systems. Occurrence rate studies show that M dwarfs host at least 2 planets on
average (e.g. Dressing & Charbonneau, 2015; Tuomi et al., 2019), this
corresponds to twice the number reported by Kunimoto & Matthews (2020) for K
dwarfs. It implies, on a statistical level, that there could still be
additional planets in these systems. Moreover, a transiting system has a
favorable orbital inclination that enhances the likelihood of finding extra
planet candidates. TESS offers an exquisite opportunity, thanks to its long
baselines of observations, to search for concealed low S/N signals that might
have been unnoticed. The search will be conducted on each system’s available
TESS sectors and will be updated as soon as new data becomes public. This
strategy increases the S/N of the putative detections, reaching smaller
planetary radii and longer period candidates, as shown in Fig. 9.

By developing this project, we will eventually be able to pinpoint the
presence of small transiting planets in the habitable zones of their stars
within the solar neighborhood, setting the stage for detailed studies. Hence,
the ultimate objective of this project is to compile an accurate census of
nearby transiting potential habitable planets.

Figure 9: Improvements between the injection and recovery scenarios for a
simple search on GJ 806 using different number of sectors. Above, results of
injection and recovery scenarios only using sector 41. Bottom, same retrieval
scenarios using sectors 41, 55 and 56.

##  5 Conclusions

Providing open-sourced software packages is a valuable contribution to the
scientific community, especially in cases where the documentation is abundant,
detailed, and focused on hands-on examples. With SHERLOCK , we are not only
doing that but also releasing a mature pipeline standardizing scientific
procedures that increase the scientist’s productivity, help the
reproducibility of the end-to-end processes, and empower individual teams to
conduct their own planetary searches relying on space-based missions.

SHERLOCK represents an advanced exoplanetary search pipeline that leverages a
suite of robust and community-validated astrophysical packages including
lightkurve , eleanor , tls , triceratops , and allesfitter . These are
complemented by bespoke modules tailored to create a streamlined and
integrated workflow. Initially, SHERLOCK systematically acquires and
preprocesses available data, setting the stage for effective exoplanet
detection. Subsequent phases involve rigorous vetting of candidates to
identify and eliminate potential false positives through comprehensive
analysis and statistical validation techniques. The pipeline further refines
estimates of planetary characteristics through sophisticated data modeling,
enhancing the precision of the derived orbital and physical parameters.
SHERLOCK concludes the analyses by determining the best observational windows,
crucial for planning ground-based confirmatory follow-ups. Each phase is
encapsulated within dedicated modules, optimizing the accuracy and efficiency
of the whole process of finding reliable planetary candidates. Still, we
highlight that SHERLOCK may need manual fine-tuning to operate to its fullest
potential, making it not an entire automated search pipeline, requiring visual
inspection of detected signals before passing through all the modules.

Our performance test showed that SHERLOCK has an excellent recall of 0.98 when
recovering SPOC official alerts confirmed as planets, which makes it a very
reliable pipeline for the community. During this test, we not only recovered
98$\%$ of the planets but also found some candidates that were confirmed
planets but did not have any associated alerts, such as TOI-942 c and
Kepler-89 c, strengthening the conclusion of being a reliable planetary
searching tool. On top of that, we found four new planetary candidates
unnoticed until now that fulfilled all our tests, only lacking ground-based
observation to confirm their planetary nature fully. These four candidates
were found to be in the planetary systems WASP-16 (CTOI-46096489.02), HAT-P-27
(CTOI-461239485.02), HAT-P-26 (CTOI-420779000.02) and TOI-2411
(CTOI-10837041.02).

The vetting implemented by SHERLOCK , based on the robust tests conducted by
the SPOC pipeline, reports a variety of metrics that are marked as red flags
whenever they are found to be above specific thresholds. However, low data
quality sometimes produces inconclusive results for these metrics, especially
on the centroids and optical ghost diagnoses. Hence, in these cases, the red
flags have to be taken as warning bells instead of a robust indication of a
false positive, which needs further exploration by the user. SHERLOCK ’s
vetting will be further developed in coming releases towards a more robust
data exploration, producing a more reliable set of metrics even for very low
S/N signals. In particular, we are currently exploring implementing a deep
learning neural network similar to ExoMiner (Valizadegan et al., 2022),
allowing us to discern genuine planets from false positives unbiasedly.

## Acknowledgements

We thank the anonymous referee for the helpful comments. F.J.P. acknowledges
financial support from the Severo Ochoa grant CEX2021-001131-S funded by
MCIN/AEI/10.13039/501100011033 and through the project PID2022-137241NB-C43.
We acknowledge support from the Spanish Ministry of Science through the
project PID2019-107061GB-C64/SRA (State Research
Agency/10.13039/501100011033). Funding for open access charge: Universidad de
Granada / CBUA. This publication benefits from the support of the French
Community of Belgium in the context of the FRIA Doctoral Grant awarded to M.T.
V.V.G. is an F.R.S.-FNRS Research Associate.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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##  Appendix A TIC 169285097 SSPE fit signals

Figure 10: Output from SHERLOCK SSPE algorithm for Sector 2 data of TIC
169285097. From top-left to bottom-right, the first nine pulsations fits are
represented after the previous ones have already been subtracted. The blue
dots show the phased flux, and the orange lines show the best sinusoidal fit.

##  Appendix B Performance survey catalog: TIC ids

100566492, 102264230, 10837041, 111991770, 112099249, 120247528, 12862099,
136916387, 139375960, 142937186, 144700903, 146520535, 147797743, 157230659,
165297570, 168281028, 172598832, 175772482, 181949561, 188876052, 189380158,
189625051, 20096620, 201186294, 201604954, 206284139, 207077681, 21113347,
229047362, 237320326, 243921117, 245392284, 248853232, 250707118, 257567854,
262715204, 263179590, 269217040, 27039476, 273231214, 281408474, 283419843,
288246496, 291685334, 291751373, 292152376, 305048087, 32487566, 33595516,
336732616, 339522221, 347430350, 354619337, 368739874, 368805700, 369455629,
372172128, 374530847, 375942197, 37718056, 381856447, 391958006, 392476080,
398895470, 39926974, 399402994, 401604346, 420779000, 420814525, 425817867,
429302040, 431701493, 434226736, 436478932, 437704321, 441420236, 452808876,
453064665, 459730973, 460396820, 46096489, 461239485, 464646604, 466382581,
466390120, 467971286, 49043968, 51637609, 53728859, 54002556, 57984377,
6663331, 7088246, 90850770, 91051152, 9155187, 92449173, 9385460, 9443323,
97409519

##  Appendix C Posterior distributions from the fits

Table 4: Posterior distributions for WASP-16, HAT-P-27, HAT-P-26 and TOI-2411 systems Parameter | Unit | WASP-16 b | CTOI-46096489.02
---|---|---|---
$R_{p}/R_{\star}$ |  | $0.1150_{-0.0019}^{+0.0022}$ | $0.0215_{-0.0022}^{+0.0017}$
$(R_{\star}+R_{p})/a_{p}$ |  | $0.1266_{-0.0040}^{+0.0036}$ | $0.0493_{-0.0031}^{+0.0040}$
$\cos{i_{p}}$ |  | $0.0921_{-0.0051}^{+0.0046}$ | $0.016_{-0.010}^{+0.013}$
Mid-transit time, $T_{0;p}$ | $\mathrm{BJD}_{TDB}-2457000$ | $1613.66548\pm 0.00020$ | $1618.725_{-0.014}^{+0.012}$
Orbital Period, $P_{p}$ | $\mathrm{days}$ | $3.118531\pm 0.000073$ | $10.457_{-0.028}^{+0.018}$
$q_{1}$ |  | $0.60_{-0.20}^{+0.23}$
$q_{2}$ |  | $0.35_{-0.21}^{+0.28}$
$\log{\sigma_{w}}$ | $\log{\mathrm{rel.flux.}}$ | $-6.5560\pm 0.0055$
$\mathrm{GP:\ln{\sigma}}$ |  | $-8.69_{-0.15}^{+0.16}$
$\mathrm{GP:\ln{\rho}}$ |  | $-0.75_{-0.31}^{+0.34}$
Parameter | Unit | HAT-P-27 b | CTOI-461239485.02
$R_{p}/R_{\star}$ |  | $0.1209_{-0.0045}^{+0.0050}$ | $0.0457_{-0.0040}^{+0.0042}$
$(R_{\star}+R_{p})/a_{p}$ |  | $0.1069_{-0.0063}^{+0.0059}$ | $0.188_{-0.017}^{+0.025}$
$\cos{i_{p}}$ |  | $0.0767\pm 0.0076$ | $0.0130_{-0.031}^{+0.033}$
Mid-transit time, $T_{0;p}$ | $\mathrm{BJD}_{TDB}-2457000$ | $2705.8727\pm 0.0004$ | $2705.5090_{-0.0015}^{+0.0014}$
Orbital Period, $P_{p}$ | $\mathrm{days}$ | $3.03908\pm 0.000019$ | $1.19949_{-0.00022}^{+0.00021}$
$q_{1}$ |  | $0.75_{-0.22}^{+0.16}$
$q_{2}$ |  | $0.67_{-0.33}^{+0.21}$
$\log{\sigma_{w}}$ | $\log{\mathrm{rel.flux.}}$ | $-6.0260\pm 0.0073$
$\mathrm{GP:\ln{\sigma}}$ |  | $-6.83_{-0.24}^{+0.28}$
$\mathrm{GP:\ln{\rho}}$ |  | $0.52\pm 0.31$
Parameter | Unit | HAT-P-26 b | CTOI-420779000.02
$R_{p}/R_{\star}$ |  | $0.0722_{-0.0016}^{+0.0015}$ | $0.0230\pm 0.0024$
$(R_{\star}+R_{p})/a_{p}$ |  | $0.0821_{-0.0013}^{+0.0014}$ | $0.0584\pm 0.0010$
$\cos{i_{p}}$ |  | $0.0331_{-0.0049}^{+0.0042}$ | $0.022\pm 0.014$
Mid-transit time, $T_{0;p}$ | $\mathrm{BJD}_{TDB}-2457000$ | $2678.8923\pm 0.0005$ | $2683.1598_{-0.0014}^{+0.0010}$
Orbital Period, $P_{p}$ | $\mathrm{days}$ | $4.23440\pm 0.00031$ | $6.5938_{-0.0069}^{+0.0087}$
$q_{1}$ |  | $0.44_{-0.23}^{+0.34}$
$q_{2}$ |  | $0.26_{-0.16}^{+0.31}$
$\log{\sigma_{w}}$ | $\log{\mathrm{rel.flux.}}$ | $-6.3901\pm 0.0064$
$\mathrm{GP:\ln{\sigma}}$ |  | $-8.78_{-0.23}^{+0.19}$
$\mathrm{GP:\ln{\rho}}$ |  | $-1.92_{-0.75}^{+1.3}$
Parameter | Unit | TOI-2411 b | CTOI-10837041.02
$R_{p}/R_{\star}$ |  | $0.021\pm 0.001$ | $0.0390_{-0.0018}^{+0.0016}$
$(R_{\star}+R_{p})/a_{p}$ |  | $0.2230_{-0.0055}^{+0.0060}$ | $0.02741_{-0.00081}^{+0.00094}$
$\cos{i_{p}}$ |  | $0.0334_{-0.020}^{+0.017}$ | $0.0115_{-0.0030}^{+0.0024}$
Mid-transit time, $T_{0;p}$ | $\mathrm{BJD}_{TDB}-2457000$ | $2129.3198_{-0.0016}^{+0.0012}$ | $2141.3147_{-0.0034}^{+0.0034}$
Orbital Period, $P_{p}$ | $\mathrm{days}$ | $0.78289_{-0.00018}^{+0.00014}$ | $18.7496_{-0.0041}^{+0.0047}$
$q_{1}$ |  | $0.41_{-0.23}^{+0.34}$
$q_{2}$ |  | $0.41_{-0.25}^{+0.32}$
$\log{\sigma_{w}}$ | $\log{\mathrm{rel.flux.}}$ | $-6.6475\pm 0.0045$
$\mathrm{GP:\ln{\sigma}}$ |  | $-8.961\pm 0.089$
$\mathrm{GP:\ln{\rho}}$ |  | $-1.49_{-0.35}^{+0.40}$
Figure 11: Posterior probability distributions for the fitting parameters used
to model the planetary system WASP-16 as described in Section 2.6 considering
the two-planet scenario from Section 3.1. The vertical dashed lines represent
the median and the 68$\%$ credible interval. The figure highlights the
correlation (or absence thereof) between all the parameters. The values of
each parameter can be consulted in Table 4. Figure 12: Similar to Fig. 11, but
for the HAT-P-27 system. Figure 13: Similar to Fig. 11, but for the HAT-P-26
system. Figure 14: Similar to Fig. 11, but for the TOI-2441 system.