11institutetext:  School of Physics and Astronomy, Raymond and Beverly Sackler
Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 6997801, Israel
22institutetext: Porter School of the Environment and Earth Sciences, Raymond
and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv
6997801, Israel 33institutetext: Center for Astrophysics, Harvard &
Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 44institutetext:
Department of Astronomy, University of Geneva, Chemin Pegasi 51, 1290 Versoix,
Switzerland 55institutetext: Institute of Astronomy, University of Cambridge,
Madingley Road, Cambridge CB3 0HA, UK

# Gaia–TESS synergy:
Improving the identification of transit candidates

Aviad Panahi 11 Tsevi Mazeh 11 Shay Zucker 22 David W. Latham 33 Karen A.
Collins 33 Lorenzo Rimoldini 44 Dafydd Wyn Evans 55 Laurent Eyer 44

(Received x x, x; accepted x x, x)

###### Abstract

Context. The TESS team periodically issues a new list of transiting exoplanet
candidates based on the analysis of the accumulating light curves obtained by
the satellite. The list includes the estimated epochs, periods, and durations
of the potential transits. As the point spread function (PSF) of TESS is
relatively wide, follow-up photometric observations at higher spatial
resolution are required in order to exclude apparent transits that are
actually blended background eclipsing binaries (BEBs).

Aims. The Gaia space mission, with its growing database of epoch photometry
and high angular resolution, enables the production of distinct light curves
for all sources included in the TESS PSF, up to the limiting magnitude of
Gaia. This paper reports the results of an ongoing Gaia-TESS collaboration
that uses the Gaia photometry to facilitate the identification of BEB
candidates and even to confirm on-target candidates in some cases.

Methods. We inspected the Gaia photometry of the individual sources included
in the TESS PSF, searching for periodic dimming events compatible with their
ephemerides and uncertainties, as published by TESS. The performance of the
search depends mainly on the number of Gaia measurements during transit and
their precision.

Results. Since February 2021, the collaboration has been able to confirm $126$
on-target candidates and exclude $124$ as BEBs. Since June 2021, when our
search methodology matured, we have been able to identify on the order of
$5\%$ as on-target candidates and another $5\%$ as BEBs.

Conclusions. This synergistic approach is combining the complementary
capabilities of two of the astronomical space missions of NASA and ESA. It
serves to optimize the process of detecting new planets by making better use
of the resources of the astronomical community.

###### Key Words.:

Methods: data analysis – Methods: statistical – Techniques: photometric –
Planets and satellites: detection – Binaries: eclipsing

##  1 Introduction

The Transiting Exoplanet Survey Satellite (TESS; Ricker et al., 2015) is
systematically scanning the sky in search of transiting exoplanets, producing
hundreds of thousands of photometric light curves. TESS collects its data
using four wide-field cameras with a relatively wide point spread function
(PSF), namely on the order of $1\,\mathrm{arcmin}$ for bright stars (Sullivan
et al., 2015). Faint unknown background eclipsing binary stars (BEBs) residing
within the PSF of the TESS target star might therefore cause photometric
modulations that would appear as planetary transits (e.g., Brown, 2003;
Cameron, 2012). For this reason, photometric follow-up observations with high
spatial resolution are required for the TESS objects of interest (TOIs) and
their nearby stars to determine the actual source of the transit-like signal
(e.g., Astudillo-Defru et al., 2020; Waalkes et al., 2021; Gan et al., 2021).
This is usually done by ground-based seeing-limited photometric observations
that can be used to differentiate between true and false-positive detections
(e.g., Deeg et al., 2009; Collins et al., 2018; Lendl et al., 2020).

To identify the source of the modulations seen by TESS, one can also use the
Gaia photometric data that have been accumulating since the launch of the
European space mission in 2013 (Gaia Collaboration et al., 2016). Although the
main objective of the Gaia mission is high-accuracy astrometry of more than a
billion objects (Gaia Collaboration et al., 2021), Gaia also produces
photometric measurements in its wide $G$ band, which mostly covers the visible
wavelength range (Jordi et al., 2010).

By itself, Gaia photometry is not optimized for detecting transiting planets,
as the satellite scans the sky in an irregular low-cadence fashion, with
typically a dozen observations per year (Gaia Collaboration et al., 2016). On
the other hand, TESS (during its prime mission) has been continuously
monitoring the sky for about $27.5$ days per sector, with a high cadence of 2
minutes for bright stars and 30 minutes for faint ones (Ricker et al., 2015).
Nevertheless, thanks to the large number of stars sampled by Gaia and the
photometric precision that can be on the order of a few millimagnitudes (mmag)
or less (Gaia Collaboration et al., 2021), two new transiting hot-Jupiters
have already been discovered using Gaia photometry and validated via radial
velocities (Panahi et al., 2022). More candidates were published in Gaia DR3
(Eyer et al., 2022).

The high angular resolution of Gaia currently enables it to safely resolve
sources with a separation above $\sim 0.7\,\mathrm{arcsec}$, and it is
expected to even improve in future data releases (Fabricius et al., 2021). In
the case where a BEB is the origin of an apparent transit detected by TESS,
Gaia may have already observed the eclipse photometrically. In this case, as
Gaia is observing the undiluted and deeper transit, it can identify this star
as the culprit of the TESS false positive. However, this is only possible if
Gaia photometry has indeed sampled the eclipse events of the background
binary. Short-period binaries might also display an ellipsoidal variability
(e.g., Morris & Naftilan, 1993; Faigler & Mazeh, 2011) that can be detected by
Gaia if the companion is sufficiently massive. If the secondary is
sufficiently luminous, we might also see a secondary eclipse. On the other
hand, the object eclipsing the background star might actually be a planet,
shifting the planet-host candidacy to the nearby star. In case where the
observed transit is due to the brightest star within the PSF, and the transit
is deep enough to be discerned in the Gaia photometry, we can confirm the
authenticity of the TOI as a transiting planet candidate (”on-target
confirmation”).

Assessing the source of the transit signal has a time-sensitive nature, as
successful identifications can save valuable observational resources. Joining
the forces of the two space missions became imperative. We therefore initiated
a collaboration between Gaia Data Processing and Analysis Consortium (DPAC;
Gaia Collaboration et al., 2016) and SubGroup 1 of the TESS Follow-up
Observing Program Working Group (SG1; Collins, 2019), liaised by the Tel Aviv
University (TAU) group (which is part of DPAC), whose goal is to examine the
TESS candidates with the help of the accumulating Gaia data. The TAU group
examines the unpublished Gaia photometry to identify genuine and false
candidates and shares those identifications with SG1 shortly after the release
of the candidates. This collaboration started in February 2021, around the
time TESS announced TOI-$2400$. The detection capability of the search
gradually improved until June 2021, when TESS released TOI-$3504$.

This paper presents the details of the Gaia-TESS collaboration. We present the
search methodology and list $124$ BEBs, $124$ on-target confirmations, and two
planets in wide binary systems. Section 2 describes the search method for
cases in which Gaia had measured dimming events in the TOIs or their
neighboring stars and the initial assessment of whether these cases were on
target. Section 3 presents the current results of the collaboration, including
examples of on-target confirmations and identified BEBs. Section 4 presents an
early assessment of the performance of the procedure and Sect. 5 discusses the
significance of this collaboration and its future.

##  2 Search procedure

For each TOI, the procedure starts by retrieving the Gaia $G$-band photometry
of each source within $1\,\mathrm{arcmin}$ of the position reported for the
TOI; such sources are referred to as PSF neighbors hereafter. This radius was
chosen in order to roughly accommodate the angular size of 3 TESS pixels, or
an aperture area of $\pi\cdot 3^{2}\approx 30$ pixels, which should include
most of the accumulated light (see discussion below and Fig. 13 in Sullivan et
al. (2015)). In each light curve, we remove points that are brighter than the
median magnitude by more than three times the median absolute deviation (MAD)
of the photometric time series. After removing these points, only sources that
have a minimum number of Gaia measurements are considered. Our most limiting
criterion is the minimum number of in-transit points. We chose this number to
be two, because one point is insufficient to constrain the periodicity and
three would be too strict considering the sparsity of the Gaia photometry. We
chose the minimum total number of points to be $14$, somewhat arbitrarily, in
an attempt to avoid dealing with small number statistics for the out-of-
transit points.

Next, we explore the parameter space allowed by the uncertainties of the TESS
parameters by applying a modified version of the box-fitting least square
algorithm (BLS; Kovács et al., 2002) to the Gaia data, scanning a small region
in the two-dimensional space around the TOI nominal period
($P_{\scaleto{\mathrm{TOI}}{4pt}}$) and transit duration
($d_{\scaleto{\mathrm{TOI}}{4pt}}$), as reported by the TOI alert. The goal is
to find the parameter values that produce the highest BLS signal residue
($\mathcal{SR}$)111The $\mathcal{SR}$ is related to the sum of squared
residuals in the least-squares fit of the attempted box-shaped model.
statistic (Kovács et al., 2002), while having at least two measurements in-
transit. The search is restricted to a range of $\pm 3\Delta$ of the period
and duration, where $\Delta$ is the respective uncertainty as reported by
TESS.

We do not restrict the mid-transit time $T$ at this stage and scan the whole
range of phases in steps of one-tenth of the nominal transit duration. To
incorporate the prior knowledge of the transit events, we apply Gaussian
priors for the transit period, mid-transit time, and duration, resulting in a
modified signal residue ($\mathcal{MSR}$),

$\mathcal{MSR}=\mathcal{SR}-\left(\dfrac{P-P_{\scaleto{\mathrm{TOI}}{4pt}}}{\Delta
P_{\scaleto{\mathrm{TOI}}{4pt}}}\right)^{2}-\left(\dfrac{T-T_{\scaleto{\mathrm{TOI}}{4pt}}}{\Delta
T_{\scaleto{\mathrm{extended}}{4pt}}}\right)^{2}-\left(\dfrac{d-d_{\scaleto{\mathrm{TOI}}{4pt}}}{\Delta
d_{\scaleto{\mathrm{TOI}}{4pt}}}\right)^{2}\,.$ (1)

The prior for $T$ includes an extended uncertainty —taking into account the
reported uncertainty for $T_{\scaleto{\mathrm{TOI}}{4pt}}$ and the accumulated
uncertainty of the period— due to the number of cycles between the Gaia and
TESS measurements:

$\Delta T_{\scaleto{\mathrm{extended}}{4pt}}=\sqrt{\left(\Delta
T_{\scaleto{\mathrm{TOI}}{4pt}}\right)^{2}+\left(\dfrac{\tilde{t}_{\scaleto{\mathrm{TESS}}{4pt}}-\tilde{t}_{\scaleto{\mathrm{Gaia}}{4pt}}}{P_{\scaleto{\mathrm{TOI}}{4pt}}}\Delta
P_{\scaleto{\mathrm{TOI}}{4pt}}\right)^{2}}\,,$ (2)

where $\tilde{t}$ is the average observation time of the candidate, for each
of the two space missions. Using the extended uncertainty for $T$ lowers the
weight of the mid-transit time prior, thus allowing the phase to shift and
appear as a variation in the transit time.

The algorithm then selects the light curve that yields the highest
$\mathcal{MSR}$, using the best-fitting parameters to derive the transit depth
$\delta$, as seen by Gaia, and a merit function defined as the transit signal-
to-noise ratio:

$\mathcal{S/N}_{\mathrm{T}}=\dfrac{\delta}{\sigma_{\scaleto{\mathrm{OOT}}{4pt}}}\sqrt{N_{\scaleto{\mathrm{IT}}{4pt}}}\,.$
(3)

Here $\sigma_{\scaleto{\mathrm{OOT}}{4pt}}$ is the standard deviation of the
out-of-transit (OOT) measurements (as a proxy to the inherent variability of
the light curve, ignoring the transits) and $N_{\scaleto{\mathrm{IT}}{4pt}}$
is the number of in-transit (IT) Gaia measurements. We found most stars with
$\mathcal{S/N}_{\mathrm{T}}>7$ to be good candidates either for confirming or
refuting the TOI candidacy and only very few with
$\mathcal{S/N}_{\mathrm{T}}<7$.

We proceed to inspect the candidates individually and group them into on-
target and BEB candidates based on their angular distance from the TOI
location. For on-target candidates, we make sure that the star is the
brightest or one of the brightest stars in the TESS PSF, and that the transit
depths of Gaia and TESS are similar. For BEB candidates, we check that the
observed depth in the Gaia light curve is compatible with the depth reported
by TESS, after correcting for dilution, and make sure the Gaia light curve of
the target star shows no significant variability. We then proceed to visually
examine the candidates to finally identify the BEB and on-target cases.

##  3 Results

###  3.1 Overview

The collaboration has so far gone through two phases. In the first preliminary
phase (henceforth Phase I), during February-May 2021, the search procedure was
still evolving, while producing partial results: $52$ BEBs, $29$ on-target
confirmations, and one planet in a wide binary system. Since the second phase
(Phase II) started in June 2021, a regular search has been performed. After
examining $1600$ TOIs in Phase II ($3504$ – $5103$), the search yielded $72$
BEBs, $95$ on-target confirmations, and one planet in a binary system. As
mentioned in Sect. 2, we included in our analysis only Gaia light curves with
a minimum number of $14$ measurements, after removing outliers.

We list the results of the two phases in Tables LABEL:tab:rest_params_conf,
LABEL:tab:rest_params_bebs, LABEL:tab:group_params_conf, and
LABEL:tab:group_params_bebs. The tables include the period and depth of the
released TOIs, the number of measurements in the Gaia light curve, $N$, the
number of in-transit measurements, $N_{\mathrm{IT}}$, and the derived depth of
the Gaia transit (or eclipse in case of a BEB). All transit depths are given
in parts per thousand (ppt). The depths in the Gaia photometry are calculated
based on the box-shaped model of the BLS algorithm. The small number of points
and the precision available do not allow us to fit a more accurate shape to
the transit, which includes the limb-darkening effect (e.g., Mandel & Agol,
2002; Hippke & Heller, 2019).

In total, since February 2021, the search has yielded $124$ BEBs, $124$ on-
target confirmations, and two planets in wide binary systems. We were also
able to confirm a few dozen cases of known planets, but for conciseness we
chose to exclude them from the present discussion.

###  3.2 Examples

We present the details of five specific cases that demonstrate the various
types of discoveries made by the collaboration: two on-target cases confirmed
by Gaia, for which the transits reported by TESS originate from the TOI target
stars themselves, two BEBs, and one on-target transit in a wide binary system.

We obtained the TESS full-frame-image (FFI) photometry using the Python
libraries Lightkurve (Lightkurve Collaboration et al., 2018), Eleanor
(Feinstein et al., 2019), and TESScut.MAST (Brasseur et al., 2019). We used
the flatten() method of the Lightkurve library to detrend the data. In the
following figures, the Gaia and TESS light curves are phase-folded with the
period and mid-transit time obtained by our analysis.

####  3.2.1 On-target confirmations

Figures 1 and 2 show two on-target confirmations, with little or no dilution
in the TESS light curves. We note that even two or three Gaia measurements in
transit can be sufficient to confirm the transit events.

Figure 1: On-target confirmation of TOI-$4034$. Top: Gaia and TESS light
curves of TOI-$4034$, phase folded with a period of $P=1.80209590$ days.
Middle: Zoomed-in view of the transit. Bottom: Unfolded Gaia light curve. The
Gaia light curves are marked by red circles, the TESS light curves are marked
by light-gray squares, and the bins by blue squares. The duration of the
transit, as reported by TESS, is marked by two vertical green dashed lines.
Figure 2: On-target confirmation of TOI-$4293$. Top: Gaia and TESS light
curves of TOI-$4293$, phase folded with a period of $P=1.62421090$ days.
Middle: Zoomed-in view of the transit. Bottom: Unfolded Gaia light curve. See
Fig. 1 for details of the lines and symbols.

####  3.2.2 Background eclipsing binaries

Figures 3 and 4 show two BEBs identified by Gaia photometry, both found less
than $1\,\mathrm{arcmin}$ away from the position reported for their TOI. In
both cases, the periodicity of the BEB star is consistent with the parameters
of the TESS transit. The Gaia depths are larger, because the angular
resolution of Gaia enables it to see the undiluted eclipse. The Gaia light
curve of the TESS target star showed no significant variability. Figure 3
displays an ellipsoidal modulation, and Fig. 4 shows a secondary eclipse, both
features point to the stellar nature of the companion.

Figure 3: BEB found near TOI-$4216$. Top: TESS light curve of TOI-$4216$,
phase folded with a period of $P=2.18168090$ days, together with the Gaia
light curve of its BEB PSF neighbor. We note the clear ellipsoidal effect
often seen in close-by binaries (see text). Bottom: Unfolded Gaia light curve.
See Fig. 1 for details of the lines and symbols. Figure 4: BEB found near
TOI-$4346$. Top: TESS light curve of TOI-$4346$, phase folded with a period of
$P=3.907574060$ days, together with the Gaia light curve of its BEB PSF
neighbor. We note the clear secondary eclipse of the BEB centered at phase
$0.5$, indicating a circular orbit. The TESS light curve does not show the
transit due to the vertical scale, determined by the deep eclipse. Bottom:
Unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols.

####  3.2.3 Planet in a binary system

Figure 5 shows the transit of TOI-$3722$, suggesting an on-target
identification. However, the significantly deeper transit observed by Gaia
indicates a nearby star unresolved by TESS. Indeed, Gaia EDR3 lists two stars
separated by $\sim 1.2\,\mathrm{arcsec}$ at the TOI location:
490902499803340800 (A), exhibiting the transit in Gaia data, and
490902465447630976 (B) which does not exhibit any transit-like features. Based
on the proximity between their locations on the sky, their parallax, and
proper motion (Table 1), we propose that the two stars, with a projected
separation of $830\pm 10$ AU, form a wide binary. Using the criteria listed by
El-Badry et al. (2021), the spatial parameters of the two stars are consistent
with a bound binary system, although El-Badry et al. do not include the pair
in their final catalog.

Figure 5: On-target confirmation of a planet in a binary system, TOI-$3722$. Top: Gaia and TESS light curves of TOI-$3722$, phase folded with a period of $P=1.078945850$ days. The transit in the TESS light curve is diluted by the light of a neighboring star, which is suspected to form a binary system with the host star. Bottom: Unfolded Gaia light curve. See Fig. 1 for details of the lines and symbols. Table 1: TOI-$3722$: Gaia EDR3 parameters of the two stars suspected to be in a binary system. Star |  $\alpha$ (J2016.0) |  $\delta$ (J2016.0) | $\mu_{\alpha\ast}$ | $\mu_{\delta}$ | $\varpi$ | $G$ | $G_{\mathrm{BP}}-G_{\mathrm{RP}}$
---|---|---|---|---|---|---|---
| h:m:s | d:m:s | $\mathrm{mas}\leavevmode\nobreak\ \mathrm{yr}^{-1}$ | $\mathrm{mas}\leavevmode\nobreak\ \mathrm{yr}^{-1}$ | $\mathrm{mas}$ | mag | mag
A | 3:21:18.05 | +63:43:56.75 | $3.361\pm 0.021$ | $-3.038\pm 0.029$ | $1.403\pm 0.030$ | $14.6773\pm 0.0028$ | $1.204\pm 0.062$
B | 3:21:17.89 | +63:43:57.37 | $3.602\pm 0.018$ | $-2.542\pm 0.022$ | $1.449\pm 0.026$ | $14.6342\pm 0.0028$ | $1.164\pm 0.027$

##  4 Performance

###  4.1 Discovery rate

As explained above, we consider on-target confirmations or BEB detections only
if there are at least two points in transit. Therefore, when estimating the
expected rate of confirmations or detections, it is important to consider how
many Gaia measurements per star were available at the time of the search. We
chose to use the sample of $1600$ Phase II TESS candidates (TOIs $3504$ –
$5103$) for this purpose. In the Gaia database, we find $89\,460$ PSF
neighbors of the $1600$ TOIs, $77\,049$ of them having at least $14$ Gaia
measurements, which is the lower limit we chose for our current analysis (Fig.
6). There are about $200$ measurements for one cluster of sources, which is
due to stars in the ecliptic poles, which Gaia sampled extensively during the
first $28$ days of its operation (Gaia Collaboration et al., 2016).

Figure 6: Phase II: Number of Gaia measurements per star for all $89\,460$
objects around the $1600$ TOIs in Phase II. We note the cluster of stars with
more than $200$ measurements, which is due to the scanning law of Gaia at the
beginning of the mission (see text).

For a given star, the expected number of in-transit measurements,
$\mathcal{N}_{\scaleto{\mathrm{IT}}{4pt}}$, can be estimated by multiplying
the number of its Gaia measurements, $N$, by the fractional duration of the
transit (duration divided by the period):

$\mathcal{N}_{\scaleto{\mathrm{IT}}{4pt}}=N\frac{d_{\scaleto{\mathrm{TOI}}{4pt}}}{P_{\scaleto{\mathrm{TOI}}{4pt}}}\,.$
(4)

When considering the discovery rate of on-target confirmations, it is
important to note that the published transit depths of TOIs can be quite
small. As the photometric precision of Gaia depends on the target brightness
in a complicated manner (Riello et al., 2021), we consider only cases that are
detectable by Gaia in terms of their expected $\mathcal{S/N}_{\mathrm{T}}$. We
therefore only consider cases for which $\mathcal{S/N}_{\mathrm{T}}>5$. This
leaves $148$ cases out of the $1600$ from Phase II, of which only $85$ had at
least two measurements expected in transit.222The expected number of in-
transit measurements is rounded to the nearest integer, and therefore the
actual criterion we used in the estimate is
$\mathcal{N}_{\scaleto{\mathrm{IT}}{4pt}}>1.5$.

BEBs on the other hand are expected to display substantially deeper eclipses,
easily detectable by Gaia. However, the number of measurements of the star,
$N$, for BEBs can only be estimated, because the identity of the eclipsing
binary is not known in advance. We therefore use $\tilde{\mathcal{N}}$
instead, which is the median number of Gaia measurements of the PSF neighbors
of each TOI, and the corresponding expected number of measurements in transit,
$\tilde{\mathcal{N}}_{\scaleto{\mathrm{IT}}{4pt}}$.

Within the sample of $1600$ TOIs in Phase II, there are $562$ TOIs with
$\tilde{\mathcal{N}}_{\scaleto{\mathrm{IT}}{4pt}}\geq 1.5$. According to
Sullivan et al. (2015, their Fig. 2), the estimated fraction of BEB false
positive TOIs is $f_{\mathrm{BEB}}=0.15\pm 0.08$, corresponding to $250\pm
125$ BEBs in the Phase II sample and $87\pm 43$ in the restricted sample of
$562$ TOIs.

For on-target detections, the fraction given by Sullivan et al. is
$f_{\mathrm{on-target}}=0.84\pm 0.12$, corresponding to $1350\pm 190$ in the
Phase II sample and $73\pm 10$ in the restricted sample of $85$ TOIs.
Comparing these estimates with the $72$ detected BEBs (vs. $87$ estimated) and
$87$ on-target confirmations with $\mathcal{S/N}_{\mathrm{T}}>5$ (vs. $73$
estimated), we suggest that the search for both BEBs and on-target
confirmations is performing as expected, with a detection rate of $\sim 5\%$
for each case. The main limiting factor is the number of Gaia measurements.

###  4.2 Transit depths

Figure 7 presents a histogram of the differences between the transit depths as
originally reported by TESS and the depths derived from the Gaia photometry,
for the $95$ on-target confirmations found in Phase II. The scatter is
$\sigma_{\mathrm{d}}=6.5$ mmag, and therefore we adopt this value as the Gaia
transit depth uncertainty for the on-target confirmations (Tables
LABEL:tab:rest_params_conf and LABEL:tab:group_params_conf).

Figure 7: Phase II: Distribution of the differences between the Gaia and TESS
transit depths for the $95$ on-target confirmations in Phase II. The mean and
standard deviation of these differences are
$(\mu,\sigma)=(1.3,6.5)\,\mathrm{mmag}$.

Figure 8 presents the dependence of the ratio between the Gaia and TESS depths
on the angular distances between the identified Gaia sources and the
corresponding TOI target stars. Naturally, the depth seen by Gaia is
substantially larger for BEBs. As expected, the angular distance is small for
on-target confirmations and large for BEBs, further delineating the separation
between the two sets. Three out of the four BEB cases that had the smallest
depth ratios were marked by the SG1 team as potential nearby planetary
candidates (TOI-4211, TOI-4236 and TOI-4292). The BEB with the smallest depth
ratio (TOI-3580) remained a BEB, as the stellar radius of the nearby host star
is large enough to suggest a stellar eclipsing companion.

Figure 8: Phase II: Transit depth ratios versus angular distance between the
TOI targets and the Gaia detections, either BEBs or on-target confirmations.
We omitted the transit-depth uncertainties for the on-target confirmations.
For most of the BEBs, the uncertainties are smaller than the square sizes.

##  5 Discussion

This is an interim report on a collaborative effort of the TESS and Gaia teams
to identify TOIs whose observed transit-like modulations are caused by faint
neighboring BEBs and to confirm the TOI candidacy in some cases. The
collaboration uses the growing database of Gaia epoch photometry and takes
advantage of its high angular resolution and photometric precision, and has so
far been able to confirm $\sim 5\%$ of the TESS candidates as on-target and
dismiss another $\sim 5\%$ as BEBs.

As the BEB modulations are large and their eclipses are deep, the eclipses are
easily seen in the Gaia photometry, as demonstrated by Figs. 3 and 4. In a few
cases where the eclipse was found to occur in a neighboring star, the depth of
the undiluted eclipse seen in the Gaia data was shallow enough to still be
caused by a planet orbiting the nearby star. In these cases the candidacy was
shifted from the target star of the TOI.

The main limiting factor for identifying BEBs is the number of Gaia
photometric measurements during transits, which was too small for most BEBs to
allow a safe identification. In the sample of $1600$ TOIs, one could expect to
have about 250 BEBs, while the search identified only $72$, simply because of
the small number of Gaia photometric measurements.

Figure 9 displays the angular distances of the detected BEBs in Phase II. One
can see that most of them were found within $40\,\mathrm{arcsec}$ of their
TOIs. Only $5$ out of $72$ BEBs are found in the range of
$40$–$60\,\mathrm{arcsec}$, indicating that the contamination drops
substantially beyond $40\,\mathrm{arcsec}$, equivalent to an area of
approximately ten TESS pixels. We note that this is probably in accordance
with (Sullivan et al., 2015, see their Fig. 14), who suggested an optimal
collecting area of about ten pixels for a star of 10 mag. Furthermore, SG1
members privately reported that no BEBs further than $1\,\mathrm{arcmin}$ have
been found so far, probably because these cases were mostly rejected early on
by the TESS team via the centroid analysis method. However, the
$60\,\mathrm{arcsec}$ radius might be too restrictive for a thorough search,
and we will slightly enlarge this radius in the next Gaia–TESS phase.

Figure 9: Phase II: Angular distances of BEBs from their TOIs.

Figure 10 shows the distribution of orbital periods for our detections of on-
target confirmations and BEBs relative to all TOIs in Phase II, up to a period
of $30$ days. Given the sparsity of the Gaia photometry, we expected to mostly
detect cases with short orbital periods, as the fractional duration of a
transit (duty cycle) declines with larger periods as $d/P\propto P^{-2/3}$
(Sackett, 1999).

Figure 10: Phase II: Normalized distribution of orbital periods for all TOIs
up to a period of $30$ days (gray) and detected on-target confirmations (lined
green) and BEBs (dotted red).

The Gaia data available to the collaboration consist of the first $34$ months
of operation. In the near future, the available photometry is expected to
contain $66$ months of data, greatly increasing the capability and discovery
rate of the present method, and possibly even allowing us to refine the
ephemerides of some candidates. When more Gaia measurements are available, we
will be able to exclude more BEB alternatives. This will serve as a new way of
confirming the on-target candidacy, allowing us to rule out all possible BEBs
in neighboring stars and thus confirm the candidacy simply by elimination.

In the future, we plan to use the unpublished Gaia photometry, combined with
the TESS photometry, to refine the TESS ephemerides, and to extend the BLS
method to look for signs of transit-timing variations (TTV).

PLATO, the next transiting planet detection space mission, is expected to have
a PSF of similar size to that of TESS (Rauer et al., 2016). By the time PLATO
is operational, Gaia photometry will have already become public, allowing the
community to perform similar checks that will allow quick identification of
genuine transit candidates and save valuable resources required for ground-
based follow-up observations.

###### Acknowledgements.

We deeply thank the referee, Alexandre Santerne, for reviewing this paper and
for the enlightening and helpful comments that greatly helped us improve the
manuscript. This work has made use of data from the European Space Agency
(ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia
Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, some of which participate in the Gaia
Multilateral Agreement. T.M. acknowledges support of the United States-Israel
Binational Science Foundation (BSF), grant No. 2016069. S.Z. acknowledges
support by the Ministry of Science and Technology, Israel (grant 3-18143), and
a grant from the Tel Aviv University Center for AI and Data Science (TAD). We
have used the following Python code libraries: Matplotlib (Hunter, 2007),
NumPy (Harris et al., 2020), AstroPy (Astropy Collaboration et al., 2013),
Lightkurve (Lightkurve Collaboration et al., 2018), TESScut.MAST (Brasseur et
al., 2019), Eleanor (Feinstein et al., 2019) and Pandas (Reback et al., 2021).

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##  Appendix A Analysis results for Phase I and Phase II.

Table 2: On-target confirmations in Phase I search.a TESS | Gaia
---|---
| TOI | TIC | Orbital Period | Transit Duration | Transit Depth | $N$ | $N_{\scaleto{\mathrm{IT}}{4pt}}$ | $\mathcal{S/N}_{\mathrm{T}}$ | Transit Depth
|  |  | [day] | [day] | [ppt] |  |  |  | [ppt]
1 | 2378.01 | 231063955 | $3.49728\pm 0.00037$ | $0.0903\pm 0.0045$ | $17.35\pm 0.63$ | 64 | 3 | 9.5 | 21.1
2 | 2487.01 | 394346745 | $3.40249\pm 0.00010$ | $0.1373\pm 0.0026$ | $14.15\pm 0.22$ | 40 | 4 | 17.1 | 12.9
3 | 2580.01 | 102713734 | $3.39786\pm 0.00019$ | $0.1876\pm 0.0052$ | $9.96000\pm 0.00093$ | 82 | 6 | 9.3 | 9.0
4 | 2724.01 | 119290630 | $1.48750550\pm 5.0\cdot 10^{-7}$ | $0.07808\pm 0.00071$ | $44.40000\pm 0.00056$ | 40 | 3 | 13.1 | 36.5
5 | 2757.01 | 147125706 | $3.4813976\pm 3.5\cdot 10^{-6}$ | $0.1122\pm 0.0045$ | $21.8000\pm 0.0054$ | 35 | 2 | 10.2 | 21.2
6 | 2799.01 | 156887426 | $1.43679140\pm 9.0\cdot 10^{-7}$ | $0.0908\pm 0.0029$ | $23.1800\pm 0.0025$ | 39 | 5 | 14.0 | 22.2
7 | 2818.01 | 151483286 | $4.0397189\pm 3.1\cdot 10^{-6}$ | $0.1523\pm 0.0025$ | $15.11000\pm 0.00090$ | 55 | 2 | 7.6 | 12.7
8 | 2847.01 | 175604949 | $2.6488450\pm 2.1\cdot 10^{-6}$ | $0.0888\pm 0.0084$ | $16.7700\pm 0.0071$ | 44 | 2 | 7.9 | 12.8
9 | 2916.01 | 76663549 | $3.9216762\pm 6.4\cdot 10^{-6}$ | $0.0865\pm 0.0034$ | $17.4000\pm 0.0069$ | 45 | 4 | 7.7 | 22.5
10 | 3073.01 | 448744179 | $3.14199\pm 0.00053$ | $0.082\pm 0.013$ | $13.310\pm 0.018$ | 58 | 3 | 13.2 | 10.5
11 | 3172.01 | 398502253 | $3.00293\pm 0.00096$ | $0.119\pm 0.023$ | $5.080\pm 0.022$ | 44 | 4 | 10.0 | 8.7
12 | 3183.01 | 370385007 | $4.2162\pm 0.0020$ | $0.160\pm 0.016$ | $6.330\pm 0.013$ | 46 | 2 | 9.4 | 13.9
13 | 3237.01 | 242389810 | $3.02703\pm 0.00045$ | $0.1581\pm 0.0077$ | $21.5800\pm 0.0088$ | 26 | 4 | 14.4 | 20.6
14 | 3264.01 | 468055102 | $3.313349\pm 2.0\cdot 10^{-5}$ | $0.1617\pm 0.0062$ | $8.9000\pm 0.0026$ | 21 | 2 | 10.2 | 14.1
15 | 3274.01 | 360822008 | $2.907508\pm 2.3\cdot 10^{-5}$ | $0.1217\pm 0.0093$ | $10.0200\pm 0.0087$ | 33 | 4 | 16.7 | 12.7
16 | 3295.01 | 456574511 | $3.4380\pm 0.0010$ | $0.161\pm 0.013$ | $8.370\pm 0.010$ | 42 | 6 | 9.6 | 11.8
17 | 3297.01 | 451538240 | $3.93479\pm 0.00033$ | $0.185\pm 0.014$ | $8.1800\pm 0.0044$ | 39 | 3 | 8.8 | 7.7
18 | 3404.01 | 18795429 | $2.5087868\pm 4.2\cdot 10^{-6}$ | $0.1054\pm 0.0048$ | $15.7500\pm 0.0046$ | 68 | 3 | 13.4 | 16.2
19 | 3406.01 | 410159011 | $2.6233540\pm 7.9\cdot 10^{-6}$ | $0.119\pm 0.014$ | $8.7900\pm 0.0053$ | 40 | 3 | 7.0 | 8.2
20 | 3416.01 | 145910571 | $2.3626917\pm 8.2\cdot 10^{-6}$ | $0.1224\pm 0.0070$ | $7.2800\pm 0.0044$ | 54 | 5 | 8.0 | 12.1
21 | 3441.01 | 393196631 | $4.25899\pm 0.00051$ | $0.142\pm 0.014$ | $5.8900\pm 0.0067$ | 48 | 3 | 9.0 | 7.4
22 | 3444.01 | 161299119 | $2.71943\pm 0.00039$ | $0.095\pm 0.021$ | $13.570\pm 0.022$ | 67 | 2 | 7.0 | 14.5
23 | 3458.01 | 340228388 | $3.17305\pm 0.00011$ | $0.090\pm 0.015$ | $17.510\pm 0.027$ | 50 | 2 | 13.6 | 9.4
24 | 3473.01 | 406861922 | $4.03676\pm 0.00086$ | $0.120\pm 0.014$ | $11.250\pm 0.013$ | 44 | 3 | 14.4 | 16.2
25 | 3474.01 | 274367763 | $3.87893\pm 0.00071$ | $0.156\pm 0.011$ | $12.1200\pm 0.0063$ | 37 | 3 | 8.4 | 13.4
26 | 3477.01 | 402391147 | $3.3614\pm 0.0023$ | $0.157\pm 0.024$ | $10.780\pm 0.047$ | 72 | 3 | 16.5 | 14.7
27 | 3479.01 | 402219289 | $2.1968\pm 0.0012$ | $0.127\pm 0.016$ | $6.040\pm 0.017$ | 46 | 4 | 8.8 | 6.9
28 | 3484.01 | 221882319 | $5.1905\pm 0.0012$ | $0.216\pm 0.013$ | $7.5700\pm 0.0031$ | 38 | 2 | 7.8 | 13.3
29 | 3491.01 | 208719443 | $2.40389\pm 0.00022$ | $0.1515\pm 0.0061$ | $31.360\pm 0.012$ | 42 | 5 | 20.7 | 41.1
Transit confirmations in binary systems
1 | 3277.01 | 319568619 | $1.5265889\pm 1.8\cdot 10^{-6}$ | $0.0703\pm 0.0025$ | $23.6300\pm 0.0031$ | 43 | 3 | 11.2 | 29.8

a As described in Sect. 4.2, we adopt a uniform value of
$\sigma_{\mathrm{d}}=6.5$ mmag for the Gaia transit depth uncertainty of on-
target confirmations.

Table 3: BEBs in Phase I search. TESS | Gaia
---|---
| TOI | TIC | Orbital Period | Transit Duration | Transit Depth | $N$ | $N_{\scaleto{\mathrm{IT}}{4pt}}$ | $\mathcal{S/N}_{\mathrm{T}}$ | Transit Depth
|  |  | [day] | [day] | [ppt] |  |  |  | [ppt]
1 | 607.01 | 153651591 | $2.14563\pm 0.00030$ | $0.090\pm 0.013$ | $1.44\pm 0.10$ | 67 | 5 | 56.8 | $82.3\pm 1.6$
2 | 644.01 | 63303499 | $1.92713\pm 0.00021$ | $0.190\pm 0.016$ | $0.586\pm 0.035$ | 60 | 7 | 27.9 | $278\pm 12$
3 | 1323.01 | 256886630 | $2.0390\pm 0.0012$ | $0.094\pm 0.040$ | $0.430\pm 0.011$ | 72 | 2 | 24.9 | $569\pm 34$
4 | 1354.01 | 365683032 | $1.42904\pm 0.00048$ | $0.137\pm 0.019$ | $1.21\pm 0.16$ | 41 | 8 | 28.0 | $109.9\pm 4.6$
5 | 1374.01 | 190430205 | $1.06884\pm 0.00034$ | $0.105\pm 0.020$ | $0.4700\pm 0.0017$ | 52 | 6 | 23.7 | $177.3\pm 8.7$
6 | 1380.01 | 274170255 | $1.41072\pm 0.00028$ | $0.109\pm 0.017$ | $0.5000\pm 0.0011$ | 46 | 6 | 29.4 | $149.5\pm 5.9$
7 | 1395.01 | 468472950 | $0.98736\pm 0.00017$ | $0.061\pm 0.010$ | $0.3700\pm 0.0012$ | 51 | 2 | 14.4 | $83.8\pm 6.2$
8 | 1503.01 | 428065977 | $1.65445\pm 0.00067$ | $0.133\pm 0.028$ | $0.6100\pm 0.0020$ | 51 | 3 | 22.3 | $309\pm 17$
9 | 1510.01 | 377739433 | $1.23852\pm 0.00023$ | $0.131\pm 0.016$ | $0.44000\pm 0.00095$ | 41 | 4 | 22.0 | $334\pm 19$
10 | 1514.01 | 270238522 | $1.36991\pm 0.00028$ | $0.173\pm 0.012$ | $1.1700\pm 0.0012$ | 47 | 15 | 38.8 | $84.3\pm 2.8$
11 | 1557.01 | 320506985 | $1.08697\pm 0.00021$ | $0.082\pm 0.015$ | $0.8600\pm 0.0031$ | 76 | 5 | 9.2 | $38.6\pm 4.4$
12 | 1583.01 | 403256331 | $3.77188\pm 0.00076$ | $0.122\pm 0.019$ | $0.4500\pm 0.0010$ | 59 | 3 | 59.5 | $141.4\pm 2.6$
13 | 1950.01 | 327663613 | $1.41144\pm 0.00052$ | $0.105\pm 0.021$ | $0.4144\pm 0.0013$ | 47 | 3 | 36.4 | $363\pm 13$
14 | 1998.01 | 429295277 | $1.10833\pm 0.00032$ | $0.095\pm 0.014$ | $1.0600\pm 0.0018$ | 45 | 4 | 35.4 | $471\pm 19$
15 | 2004.01 | 439610306 | $1.79988\pm 0.00056$ | $0.147\pm 0.023$ | $0.18000\pm 0.00045$ | 52 | 2 | 11.6 | $79.0\pm 7.2$
16 | 2115.01 | 54464870 | $3.69443\pm 0.00019$ | $0.194\pm 0.023$ | $0.21000\pm 0.00040$ | 66 | 5 | 28.5 | $70.9\pm 2.7$
17 | 2517.01 | 48178229 | $2.678825\pm 2.8\cdot 10^{-5}$ | $0.104\pm 0.016$ | $0.35000\pm 0.00079$ | 72 | 6 | 39.4 | $194.1\pm 5.7$
18 | 2732.01 | 34466256 | $0.7029205\pm 1.9\cdot 10^{-6}$ | $0.0552\pm 0.0085$ | $2.4800\pm 0.0034$ | 35 | 2 | 17.3 | $384\pm 28$
19 | 2754.01 | 148233571 | $0.9422588\pm 6.0\cdot 10^{-6}$ | $0.061\pm 0.011$ | $1.0600\pm 0.0036$ | 34 | 2 | 14.0 | $195\pm 16$
20 | 2759.01 | 134315574 | $1.5971584\pm 9.2\cdot 10^{-6}$ | $0.143\pm 0.017$ | $5.07\pm 0.30$ | 31 | 2 | 30.1 | $173.5\pm 6.5$
21 | 2767.01 | 48806546 | $0.9340570\pm 5.2\cdot 10^{-6}$ | $0.055\pm 0.014$ | $0.6200\pm 0.0026$ | 84 | 3 | 32.9 | $388\pm 15$
22 | 2789.01 | 251209368 | $3.007150\pm 3.9\cdot 10^{-5}$ | $0.186\pm 0.023$ | $3.3100\pm 0.0079$ | 36 | 2 | 10.4 | $27.1\pm 2.7$
23 | 2805.01 | 5024743 | $12.45086\pm 0.00025$ | $0.239\pm 0.028$ | $1.540\pm 0.029$ | 58 | 2 | 23.8 | $94.9\pm 4.3$
24 | 2811.01 | 78775584 | $5.555378\pm 3.5\cdot 10^{-5}$ | $0.094\pm 0.014$ | $1.0500\pm 0.0025$ | 48 | 3 | 50.0 | $230.5\pm 5.4$
25 | 2812.01 | 105801221 | $3.075073\pm 3.3\cdot 10^{-5}$ | $0.092\pm 0.017$ | $0.5100\pm 0.0019$ | 61 | 2 | 45.3 | $333.8\pm 9.1$
26 | 2829.01 | 114103134 | $1.1469027\pm 2.7\cdot 10^{-6}$ | $0.0643\pm 0.0049$ | $3.7\pm 1.4$ | 49 | 2 | 29.3 | $175.4\pm 6.7$
27 | 2838.01 | 81231810 | $5.452107\pm 3.4\cdot 10^{-5}$ | $0.196\pm 0.031$ | $8.170\pm 0.011$ | 52 | 3 | 8.9 | $74.4\pm 8.9$
28 | 2878.01 | 4999813 | $2.084952\pm 2.2\cdot 10^{-5}$ | $0.129\pm 0.031$ | $2.380\pm 0.011$ | 25 | 2 | 14.6 | $42.1\pm 3.1$
29 | 2936.01 | 22020459 | $1.332804\pm 1.0\cdot 10^{-5}$ | $0.115\pm 0.012$ | $1.9600\pm 0.0026$ | 48 | 4 | 10.0 | $54.1\pm 5.8$
30 | 2998.01 | 34737413 | $1.529712\pm 1.5\cdot 10^{-5}$ | $0.096\pm 0.018$ | $2.4100\pm 0.0061$ | 49 | 5 | 96.2 | $278.4\pm 3.6$
31 | 3008.01 | 383666033 | $3.967814\pm 4.3\cdot 10^{-5}$ | $0.177\pm 0.025$ | $0.7600\pm 0.0016$ | 59 | 2 | 10.6 | $39.1\pm 3.8$
32 | 3018.01 | 45684223 | $6.583202\pm 3.0\cdot 10^{-5}$ | $0.131\pm 0.011$ | $5.2800\pm 0.0040$ | 53 | 2 | 28.2 | $133.8\pm 5.2$
33 | 3064.01 | 463070290 | $0.6771705\pm 2.0\cdot 10^{-6}$ | $0.0594\pm 0.0096$ | $1.1400\pm 0.0015$ | 36 | 2 | 16.7 | $118.0\pm 7.7$
34 | 3258.01 | 369789627 | $1.22785\pm 0.00010$ | $0.071\pm 0.014$ | $2.0700\pm 0.0056$ | 38 | 4 | 12.2 | $189\pm 18$
35 | 3347.01 | 131581531 | $3.059164\pm 2.8\cdot 10^{-5}$ | $0.177\pm 0.025$ | $2.1100\pm 0.0035$ | 52 | 3 | 12.6 | $51.5\pm 4.3$
36 | 3357.01 | 412259468 | $2.65358\pm 0.00038$ | $0.088\pm 0.015$ | $1.45\pm 0.11$ | 52 | 2 | 15.7 | $141.0\pm 9.8$
37 | 3369.01 | 190981760 | $3.546358\pm 2.0\cdot 10^{-5}$ | $0.174\pm 0.026$ | $6.0200\pm 0.0084$ | 56 | 3 | 64.6 | $122.8\pm 2.1$
38 | 3375.01 | 185482513 | $1.236832\pm 1.0\cdot 10^{-5}$ | $0.089\pm 0.020$ | $1.9300\pm 0.0069$ | 55 | 2 | 13.1 | $43.4\pm 3.4$
39 | 3377.01 | 184670625 | $0.5241284\pm 2.1\cdot 10^{-6}$ | $0.0424\pm 0.0073$ | $2.4\pm 1.2$ | 43 | 2 | 23.1 | $267\pm 14$
40 | 3385.01 | 175079720 | $2.262326\pm 1.1\cdot 10^{-5}$ | $0.127\pm 0.025$ | $2.9400\pm 0.0060$ | 41 | 2 | 14.0 | $51.7\pm 3.9$
41 | 3388.01 | 173860688 | $0.84566\pm 0.00026$ | $0.076\pm 0.016$ | $0.3900\pm 0.0020$ | 36 | 3 | 28.7 | $380\pm 17$
42 | 3392.01 | 80174172 | $1.1104301\pm 6.0\cdot 10^{-6}$ | $0.067\pm 0.014$ | $4.870\pm 0.015$ | 38 | 4 | 23.4 | $282\pm 15$
43 | 3399.01 | 153197346 | $2.64245\pm 0.00071$ | $0.182\pm 0.022$ | $4.700\pm 0.011$ | 55 | 3 | 8.0 | $23.5\pm 3.0$
44 | 3402.01 | 152685831 | $3.471417\pm 2.8\cdot 10^{-5}$ | $0.125\pm 0.038$ | $3.580\pm 0.017$ | 46 | 3 | 16.6 | $140.5\pm 9.4$
45 | 3420.01 | 293978434 | $1.59714\pm 0.00042$ | $0.138\pm 0.019$ | $2.1500\pm 0.0045$ | 55 | 4 | 20.8 | $234\pm 13$
46 | 3423.01 | 144970275 | $2.531342\pm 1.0\cdot 10^{-5}$ | $0.0936\pm 0.0095$ | $5.8300\pm 0.0075$ | 50 | 4 | 31.6 | $219.5\pm 8.1$
47 | 3424.01 | 283702603 | $0.6691882\pm 2.0\cdot 10^{-6}$ | $0.056\pm 0.012$ | $2.8500\pm 0.0078$ | 74 | 5 | 26.1 | $266\pm 12$
48 | 3436.01 | 132320310 | $1.3955317\pm 7.7\cdot 10^{-6}$ | $0.109\pm 0.016$ | $0.9600\pm 0.0018$ | 37 | 2 | 16.4 | $219\pm 15$
49 | 3440.01 | 208030798 | $1.7168\pm 0.0013$ | $0.085\pm 0.015$ | $13.620\pm 0.055$ | 59 | 3 | 22.3 | $475\pm 29$
50 | 3466.01 | 284254253 | $1.8629\pm 0.0020$ | $0.190\pm 0.016$ | $3.4\pm 1.4$ | 61 | 8 | 22.4 | $49.1\pm 2.4$
51 | 3467.01 | 453289469 | $0.779919\pm 5.3\cdot 10^{-5}$ | $0.0643\pm 0.0082$ | $1.9200\pm 0.0035$ | 40 | 2 | 9.2 | $182\pm 22$
52 | 3472.01 | 275562670 | $1.58106\pm 0.00035$ | $0.1015\pm 0.0082$ | $33.340\pm 0.038$ | 44 | 2 | 21.9 | $197\pm 10$
Table 4: On-target confirmations in Phase II.b TESS | Gaia
---|---
| TOI | TIC | Orbital Period | Transit Duration | Transit Depth | $N$ | $N_{\scaleto{\mathrm{IT}}{4pt}}$ | $\mathcal{S/N}_{\mathrm{T}}$ | Transit Depth
|  |  | [day] | [day] | [ppt] |  |  |  | [ppt]
1 | 3510.01 | 57753734 | $2.8729\pm 0.0011$ | $0.111\pm 0.014$ | $11.760\pm 0.023$ | 50 | 3 | 17.4 | 14.2
2 | 3528.01 | 67247610 | $1.97480\pm 0.00037$ | $0.065\pm 0.016$ | $11.780\pm 0.054$ | 42 | 4 | 8.5 | 20.2
3 | 3531.01 | 316038054 | $3.80974\pm 0.00029$ | $0.181\pm 0.015$ | $13.4800\pm 0.0034$ | 50 | 7 | 18.6 | 12.3
4 | 3558.01 | 195750008 | $2.5678\pm 0.0014$ | $0.085\pm 0.016$ | $12.080\pm 0.042$ | 51 | 3 | 9.3 | 9.4
5 | 3582.01 | 290308758 | $4.41685\pm 0.00026$ | $0.160\pm 0.011$ | $10.6200\pm 0.0076$ | 43 | 2 | 9.2 | 10.2
6 | 3599.01 | 194461202 | $3.25231\pm 0.00066$ | $0.113\pm 0.011$ | $11.410\pm 0.011$ | 70 | 2 | 7.3 | 8.1
7 | 3602.01 | 331146317 | $2.38761\pm 0.00016$ | $0.1098\pm 0.0060$ | $14.7000\pm 0.0073$ | 52 | 2 | 13.7 | 14.0
8 | 3622.01 | 432761635 | $3.21300\pm 0.00092$ | $0.140\pm 0.014$ | $10.330\pm 0.013$ | 46 | 4 | 9.9 | 13.1
9 | 3635.01 | 428003305 | $1.80427\pm 0.00027$ | $0.1722\pm 0.0098$ | $4.3000\pm 0.0035$ | 64 | 4 | 9.5 | 7.3
10 | 3646.01 | 445407434 | $2.17959\pm 0.00013$ | $0.1089\pm 0.0050$ | $19.4600\pm 0.0069$ | 84 | 3 | 15.3 | 28.0
11 | 3664.01 | 348437470 | $3.2963\pm 0.0011$ | $0.093\pm 0.013$ | $13.000\pm 0.035$ | 39 | 2 | 8.2 | 9.2
12 | 3673.01 | 452964680 | $2.23910\pm 0.00015$ | $0.1224\pm 0.0077$ | $15.1200\pm 0.0074$ | 76 | 3 | 12.5 | 20.3
13 | 3685.01 | 252118701 | $4.97848\pm 0.00067$ | $0.117\pm 0.010$ | $10.540\pm 0.014$ | 81 | 2 | 8.2 | 16.7
14 | 3699.01 | 266401846 | $3.04416\pm 0.00057$ | $0.121\pm 0.013$ | $11.1800\pm 0.0098$ | 45 | 4 | 15.1 | 11.6
15 | 3703.01 | 260962960 | $3.8881\pm 0.0014$ | $0.166\pm 0.019$ | $8.5600\pm 0.0063$ | 39 | 2 | 6.9 | 9.3
16 | 3706.01 | 252430813 | $4.3721\pm 0.0011$ | $0.1631\pm 0.0085$ | $13.800\pm 0.010$ | 53 | 3 | 10.4 | 11.4
17 | 3714.01 | 155867025 | $2.15483\pm 0.00015$ | $0.0645\pm 0.0028$ | $45.880\pm 0.014$ | 59 | 2 | 9.7 | 49.5
18 | 3719.01 | 150074121 | $1.22203\pm 0.00018$ | $0.0685\pm 0.0083$ | $8.730\pm 0.011$ | 73 | 5 | 7.7 | 7.4
19 | 3749.01 | 284174392 | $1.87541\pm 0.00036$ | $0.1241\pm 0.0083$ | $9.41\pm 0.49$ | 30 | 2 | 8.6 | 12.8
20 | 3751.01 | 284173938 | $2.91544\pm 0.00043$ | $0.1479\pm 0.0058$ | $21.31\pm 0.68$ | 29 | 3 | 10.2 | 10.4
21 | 3758.01 | 280254984 | $3.41769\pm 0.00017$ | $0.1443\pm 0.0061$ | $10.4700\pm 0.0032$ | 53 | 4 | 7.9 | 10.7
22 | 3780.01 | 468832904 | $1.4005325\pm 2.7\cdot 10^{-6}$ | $0.0863\pm 0.0030$ | $21.9700\pm 0.0098$ | 61 | 7 | 19.6 | 23.4
23 | 3787.01 | 457104362 | $4.81500\pm 0.00081$ | $0.153\pm 0.011$ | $15.4000\pm 0.0080$ | 52 | 2 | 10.1 | 11.1
24 | 3791.01 | 400432230 | $3.1833866\pm 2.5\cdot 10^{-6}$ | $0.0841\pm 0.0032$ | $9.720\pm 0.012$ | 43 | 2 | 10.3 | 10.7
25 | 3814.01 | 155873992 | $4.951310\pm 1.4\cdot 10^{-5}$ | $0.1622\pm 0.0081$ | $8.7800\pm 0.0038$ | 67 | 4 | 6.7 | 10.1
26 | 3842.01 | 165985431 | $3.65662\pm 0.00027$ | $0.1065\pm 0.0048$ | $21.7300\pm 0.0084$ | 52 | 3 | 16.8 | 13.8
27 | 3901.01 | 357373216 | $9.54685\pm 0.00011$ | $0.097\pm 0.018$ | $19.050\pm 0.029$ | 48 | 2 | 16.8 | 16.0
28 | 3915.01 | 81247877 | $2.201376\pm 9.4\cdot 10^{-5}$ | $0.0932\pm 0.0043$ | $25.6300\pm 0.0043$ | 64 | 4 | 8.9 | 27.1
29 | 3946.01 | 336399144 | $5.703341\pm 3.8\cdot 10^{-5}$ | $0.1266\pm 0.0087$ | $14.7300\pm 0.0065$ | 41 | 3 | 9.2 | 12.3
30 | 3947.01 | 336092760 | $6.77151\pm 0.00029$ | $0.264\pm 0.028$ | $3.4000\pm 0.0049$ | 38 | 5 | 8.9 | 6.2
31 | 3952.01 | 321861405 | $2.989774\pm 1.4\cdot 10^{-5}$ | $0.1347\pm 0.0055$ | $13.9000\pm 0.0024$ | 42 | 2 | 8.8 | 11.8
32 | 3955.01 | 314375831 | $3.127759\pm 2.0\cdot 10^{-5}$ | $0.0936\pm 0.0066$ | $13.5100\pm 0.0051$ | 49 | 3 | 7.2 | 13.3
33 | 3965.01 | 269043098 | $4.72540\pm 0.00012$ | $0.209\pm 0.014$ | $6.3200\pm 0.0036$ | 44 | 3 | 10.1 | 9.1
34 | 3974.01 | 156007004 | $1.792224\pm 5.6\cdot 10^{-5}$ | $0.0701\pm 0.0040$ | $18.2700\pm 0.0054$ | 46 | 3 | 8.7 | 23.2
35 | 3978.01 | 468329664 | $3.547237\pm 9.3\cdot 10^{-5}$ | $0.187\pm 0.014$ | $6.5800\pm 0.0039$ | 41 | 4 | 8.9 | 6.2
36 | 4000.01 | 283015592 | $3.702766\pm 5.2\cdot 10^{-5}$ | $0.1483\pm 0.0080$ | $11.2200\pm 0.0052$ | 50 | 2 | 8.3 | 12.5
37 | 4003.01 | 399346877 | $3.960696\pm 8.0\cdot 10^{-5}$ | $0.140\pm 0.011$ | $5.8800\pm 0.0046$ | 64 | 2 | 9.1 | 9.7
38 | 4007.01 | 389910188 | $4.543204\pm 4.8\cdot 10^{-5}$ | $0.1555\pm 0.0059$ | $12.3100\pm 0.0043$ | 64 | 3 | 6.5 | 13.9
39 | 4012.01 | 280315875 | $1.825438\pm 1.1\cdot 10^{-5}$ | $0.0738\pm 0.0040$ | $21.270\pm 0.011$ | 77 | 4 | 7.9 | 31.0
40 | 4034.01 | 375654303 | $1.802096\pm 1.0\cdot 10^{-5}$ | $0.1254\pm 0.0065$ | $8.7400\pm 0.0021$ | 41 | 7 | 10.3 | 8.6
41 | 4069.01 | 143009290 | $2.72342\pm 0.00056$ | $0.073\pm 0.015$ | $13.090\pm 0.032$ | 49 | 4 | 14.0 | 12.4
42 | 4077.01 | 57159675 | $5.56878\pm 0.00042$ | $0.0849\pm 0.0069$ | $12.330\pm 0.010$ | 51 | 3 | 8.7 | 8.9
43 | 4080.01 | 428892437 | $3.751998\pm 1.3\cdot 10^{-5}$ | $0.126\pm 0.014$ | $18.200\pm 0.019$ | 44 | 3 | 13.3 | 12.0
44 | 4104.01 | 235664497 | $2.37636\pm 0.00065$ | $0.1411\pm 0.0094$ | $7.2700\pm 0.0085$ | 74 | 4 | 5.6 | 7.6
45 | 4115.01 | 199610140 | $2.985597\pm 1.5\cdot 10^{-5}$ | $0.0517\pm 0.0059$ | $9.720\pm 0.099$ | 37 | 2 | 9.0 | 10.2
46 | 4147.01 | 138329479 | $2.374539\pm 2.2\cdot 10^{-5}$ | $0.1351\pm 0.0069$ | $10.2600\pm 0.0040$ | 51 | 4 | 8.8 | 9.3
47 | 4160.01 | 441580526 | $4.442746\pm 2.6\cdot 10^{-5}$ | $0.1353\pm 0.0053$ | $13.2900\pm 0.0030$ | 61 | 3 | 8.0 | 15.2
48 | 4181.01 | 426017070 | $0.5992462\pm 4.1\cdot 10^{-6}$ | $0.0923\pm 0.0046$ | $23.3\pm 1.2$ | 34 | 4 | 8.6 | 27.9
49 | 4209.01 | 200090347 | $0.86317\pm 0.00020$ | $0.0511\pm 0.0092$ | $6.330\pm 0.025$ | 68 | 4 | 8.8 | 6.0
50 | 4218.01 | 142628514 | $2.62695\pm 0.00045$ | $0.1460\pm 0.0063$ | $12.0100\pm 0.0045$ | 72 | 2 | 5.9 | 13.1
51 | 4262.01 | 53365065 | $5.997789\pm 1.2\cdot 10^{-5}$ | $0.1801\pm 0.0066$ | $7.7500\pm 0.0010$ | 37 | 3 | 8.0 | 7.5
52 | 4274.01 | 290388627 | $0.445962\pm 3.1\cdot 10^{-5}$ | $0.0566\pm 0.0083$ | $11.500\pm 0.024$ | 49 | 5 | 7.4 | 9.1
53 | 4280.01 | 387193925 | $3.518972\pm 1.8\cdot 10^{-5}$ | $0.1338\pm 0.0086$ | $13.8200\pm 0.0063$ | 32 | 2 | 9.5 | 13.0
54 | 4282.01 | 374348168 | $13.509804\pm 3.6\cdot 10^{-5}$ | $0.1123\pm 0.0070$ | $24.500\pm 0.032$ | 67 | 2 | 6.5 | 16.5
55 | 4283.01 | 343952976 | $3.013092\pm 4.4\cdot 10^{-5}$ | $0.0976\pm 0.0072$ | $14.1500\pm 0.0036$ | 45 | 2 | 12.8 | 14.8
56 | 4285.01 | 310105752 | $1.170544\pm 9.5\cdot 10^{-5}$ | $0.057\pm 0.010$ | $4.890\pm 0.013$ | 49 | 5 | 6.6 | 4.6
57 | 4289.01 | 278540265 | $2.9757432\pm 9.6\cdot 10^{-6}$ | $0.1864\pm 0.0077$ | $6.98000\pm 0.00057$ | 38 | 5 | 7.8 | 11.4
58 | 4293.01 | 101696403 | $1.6242109\pm 4.1\cdot 10^{-6}$ | $0.0947\pm 0.0025$ | $17.7400\pm 0.0019$ | 45 | 3 | 14.0 | 19.0
59 | 4329.01 | 256722647 | $2.922470\pm 3.0\cdot 10^{-5}$ | $0.2100\pm 0.0087$ | $4.18000\pm 0.00081$ | 43 | 5 | 7.7 | 7.2
60 | 4381.01 | 305767364 | $1.497422\pm 2.1\cdot 10^{-5}$ | $0.09266\pm 0.00066$ | $39.32\pm 0.31$ | 52 | 4 | 5.3 | 34.1
61 | 4439.01 | 267545252 | $3.37921\pm 0.00042$ | $0.1230\pm 0.0063$ | $18.14\pm 0.66$ | 31 | 2 | 20.6 | 17.5
62 | 4442.01 | 446158352 | $4.04318\pm 0.00084$ | $0.1627\pm 0.0094$ | $10.97\pm 0.56$ | 39 | 2 | 7.4 | 9.4
63 | 4463.01 | 8599009 | $2.8807180\pm 4.3\cdot 10^{-6}$ | $0.0647\pm 0.0089$ | $11.1600\pm 0.0097$ | 40 | 3 | 8.5 | 6.6
64 | 4468.01 | 441763252 | $2.77090\pm 0.00017$ | $0.0959\pm 0.0032$ | $20.70\pm 0.45$ | 35 | 3 | 19.4 | 20.5
65 | 4497.01 | 436166416 | $3.600219\pm 1.2\cdot 10^{-5}$ | $0.148\pm 0.013$ | $8.15\pm 0.22$ | 72 | 2 | 5.6 | 7.5
66 | 4666.01 | 165202476 | $2.90939\pm 0.00019$ | $0.0865\pm 0.0042$ | $45.160\pm 0.016$ | 50 | 2 | 4.6 | 37.8
67 | 4674.01 | 89062142 | $4.243063\pm 2.2\cdot 10^{-5}$ | $0.149\pm 0.012$ | $7.2700\pm 0.0059$ | 60 | 3 | 2.9 | 2.8
68 | 4678.01 | 206717400 | $4.774317\pm 2.4\cdot 10^{-5}$ | $0.124\pm 0.014$ | $10.690\pm 0.011$ | 27 | 2 | 6.6 | 7.7
69 | 4680.01 | 31258738 | $17.43140\pm 0.00015$ | $0.169\pm 0.013$ | $8.1800\pm 0.0089$ | 55 | 2 | 6.4 | 10.5
70 | 4720.01 | 124322274 | $3.781083\pm 2.4\cdot 10^{-5}$ | $0.128\pm 0.013$ | $8.030\pm 0.012$ | 27 | 2 | 4.8 | 9.0
71 | 4754.01 | 61344769 | $3.630728\pm 1.2\cdot 10^{-5}$ | $0.133\pm 0.015$ | $10.5500\pm 0.0081$ | 33 | 4 | 14.3 | 9.8
72 | 4761.01 | 440849210 | $3.786305\pm 4.6\cdot 10^{-5}$ | $0.199\pm 0.021$ | $2.1400\pm 0.0036$ | 23 | 2 | 4.5 | 5.7
73 | 4777.01 | 170368805 | $2.958876\pm 1.1\cdot 10^{-5}$ | $0.112\pm 0.027$ | $12.90\pm 0.17$ | 56 | 5 | 13.6 | 13.0
74 | 4778.01 | 145163386 | $3.807421\pm 2.2\cdot 10^{-5}$ | $0.166\pm 0.016$ | $7.6700\pm 0.0069$ | 43 | 8 | 13.3 | 6.4
75 | 4793.01 | 65949719 | $3.465863\pm 2.3\cdot 10^{-5}$ | $0.138\pm 0.012$ | $9.580\pm 0.011$ | 45 | 4 | 5.9 | 10.0
76 | 4797.01 | 265011923 | $2.9922495\pm 8.5\cdot 10^{-6}$ | $0.0664\pm 0.0076$ | $10.895\pm 0.018$ | 32 | 2 | 2.7 | 9.2
77 | 4799.01 | 65805840 | $4.023463\pm 2.5\cdot 10^{-5}$ | $0.134\pm 0.013$ | $7.5600\pm 0.0098$ | 59 | 7 | 10.8 | 8.3
78 | 4825.01 | 53047383 | $2.81847\pm 0.00025$ | $0.1572\pm 0.0094$ | $1.72000\pm 0.00093$ | 45 | 4 | 6.4 | 8.2
79 | 4867.01 | 74484423 | $2.835273\pm 2.1\cdot 10^{-5}$ | $0.177\pm 0.037$ | $3.3700\pm 0.0053$ | 52 | 5 | 8.9 | 4.6
80 | 4877.01 | 447054140 | $5.222053\pm 1.7\cdot 10^{-5}$ | $0.1768\pm 0.0090$ | $4.8500\pm 0.0014$ | 58 | 4 | 6.6 | 8.5
81 | 4885.01 | 72504752 | $6.939285\pm 3.6\cdot 10^{-5}$ | $0.244\pm 0.011$ | $14.5900\pm 0.0066$ | 51 | 3 | 8.0 | 35.7
82 | 4936.01 | 68030406 | $4.775018\pm 2.0\cdot 10^{-5}$ | $0.1517\pm 0.0079$ | $9.4700\pm 0.0054$ | 84 | 4 | 9.4 | 13.3
83 | 4953.01 | 405571798 | $2.959018\pm 1.8\cdot 10^{-5}$ | $0.1180\pm 0.0086$ | $12.520\pm 0.016$ | 64 | 5 | 15.4 | 14.0
84 | 4968.01 | 253961767 | $2.23481\pm 0.00048$ | $0.1385\pm 0.0051$ | $7.2600\pm 0.0055$ | 78 | 6 | 9.9 | 12.8
85 | 4969.01 | 406106335 | $3.077366\pm 2.2\cdot 10^{-5}$ | $0.1491\pm 0.0071$ | $5.1400\pm 0.0048$ | 64 | 3 | 5.1 | 10.5
86 | 4991.01 | 247180220 | $0.77021\pm 0.00020$ | $0.036\pm 0.011$ | $29.13\pm 0.52$ | 44 | 2 | 8.7 | 69.0
87 | 4992.01 | 362111691 | $4.880747\pm 2.0\cdot 10^{-5}$ | $0.1312\pm 0.0098$ | $11.4400\pm 0.0088$ | 71 | 2 | 11.4 | 17.2
88 | 4996.01 | 384709136 | $4.813141\pm 2.4\cdot 10^{-5}$ | $0.206\pm 0.012$ | $5.0300\pm 0.0024$ | 52 | 4 | 4.6 | 4.7
89 | 5002.01 | 418471116 | $3.731882\pm 1.3\cdot 10^{-5}$ | $0.1346\pm 0.0073$ | $10.8500\pm 0.0039$ | 41 | 4 | 5.9 | 13.2
90 | 5021.01 | 403405969 | $12.97506\pm 0.00018$ | $0.255\pm 0.030$ | $6.210\pm 0.012$ | 46 | 2 | 4.7 | 6.7
91 | 5050.01 | 282701278 | $2.306457\pm 1.1\cdot 10^{-5}$ | $0.0863\pm 0.0082$ | $5.6500\pm 0.0075$ | 45 | 3 | 4.0 | 6.3
92 | 5052.01 | 208151094 | $4.06681\pm 0.00077$ | $0.1245\pm 0.0074$ | $19.690\pm 0.010$ | 50 | 2 | 10.8 | 20.0
93 | 5054.01 | 401704685 | $4.210006\pm 2.6\cdot 10^{-5}$ | $0.111\pm 0.014$ | $7.9900\pm 0.0041$ | 46 | 2 | 6.2 | 9.8
94 | 5061.01 | 214218272 | $3.364535\pm 2.3\cdot 10^{-5}$ | $0.131\pm 0.013$ | $7.010\pm 0.010$ | 49 | 3 | 10.4 | 12.0
95 | 5073.01 | 458686969 | $3.1393697\pm 2.8\cdot 10^{-6}$ | $0.1656\pm 0.0018$ | $9.09000\pm 0.00031$ | 63 | 2 | 8.5 | 10.8
Transit confirmations in binary systems
1 | 3722.01 | 346015394 | $1.078948\pm 6.2\cdot 10^{-5}$ | $0.0770\pm 0.0053$ | $13.4100\pm 0.0070$ | 60 | 6 | 11.9 | 30.7

b As described in Sect. 4.2, we adopt a uniform value of
$\sigma_{\mathrm{d}}=6.5$ mmag for the Gaia transit depth uncertainty of on-
target confirmations.

Table 5: BEBs in Phase II. TESS | Gaia
---|---
| TOI | TIC | Orbital Period | Transit Duration | Transit Depth | $N$ | $N_{\scaleto{\mathrm{IT}}{4pt}}$ | $\mathcal{S/N}_{\mathrm{T}}$ | Transit Depth
|  |  | [day] | [day] | [ppt] |  |  |  | [ppt]
1 | 3507.01 | 86451883 | $1.7561\pm 0.0010$ | $0.119\pm 0.022$ | $11.010\pm 0.048$ | 50 | 4 | 17.4 | $114.4\pm 7.3$
2 | 3508.01 | 278968371 | $1.29978\pm 0.00034$ | $0.098\pm 0.011$ | $7.140\pm 0.012$ | 55 | 5 | 31.1 | $101.7\pm 3.6$
3 | 3525.01 | 373576942 | $0.89122\pm 0.00031$ | $0.077\pm 0.013$ | $9.160\pm 0.024$ | 60 | 4 | 20.4 | $172.3\pm 9.5$
4 | 3526.01 | 89876424 | $1.53807\pm 0.00034$ | $0.093\pm 0.013$ | $8.770\pm 0.025$ | 43 | 2 | 11.6 | $198\pm 19$
5 | 3541.01 | 291147951 | $2.53195\pm 0.00041$ | $0.107\pm 0.015$ | $8.850\pm 0.018$ | 41 | 3 | 13.1 | $43.3\pm 3.5$
6 | 3548.01 | 271167979 | $0.309395\pm 1.0\cdot 10^{-5}$ | $0.0184\pm 0.0035$ | $7.7\pm 4.0$ | 36 | 2 | 15.1 | $210\pm 16$
7 | 3562.01 | 193708920 | $1.32985\pm 0.00030$ | $0.1253\pm 0.0058$ | $2.19\pm 0.80$ | 39 | 7 | 23.0 | $113.0\pm 5.8$
8 | 3566.01 | 169187982 | $1.76444\pm 0.00019$ | $0.090\pm 0.020$ | $20.55\pm 0.43$ | 44 | 2 | 24.0 | $225\pm 11$
9 | 3578.01 | 358186451 | $1.31707\pm 0.00029$ | $0.073\pm 0.016$ | $0.6400\pm 0.0028$ | 45 | 3 | 15.7 | $63.4\pm 4.3$
10 | 3579.01 | 316606244 | $3.3106\pm 0.0014$ | $0.162\pm 0.034$ | $0.5900\pm 0.0026$ | 61 | 3 | 18.2 | $82.1\pm 4.8$
11 | 3580.01 | 305478010 | $3.12134\pm 0.00019$ | $0.1805\pm 0.0072$ | $26.3000\pm 0.0066$ | 74 | 2 | 13.3 | $32.9\pm 2.6$
12 | 3581.01 | 295413003 | $3.03730\pm 0.00036$ | $0.194\pm 0.026$ | $6.29\pm 0.57$ | 40 | 2 | 26.5 | $119.1\pm 4.9$
13 | 3608.01 | 267867517 | $2.68163\pm 0.00072$ | $0.112\pm 0.025$ | $3.100\pm 0.017$ | 47 | 2 | 15.0 | $132.9\pm 9.7$
14 | 3627.01 | 1979500576 | $2.63427\pm 0.00049$ | $0.167\pm 0.022$ | $3.19\pm 0.57$ | 49 | 4 | 26.3 | $198.5\pm 8.7$
15 | 3659.01 | 374778982 | $2.3878\pm 0.0021$ | $0.108\pm 0.026$ | $6.800\pm 0.045$ | 76 | 3 | 9.0 | $38.3\pm 4.4$
16 | 3672.01 | 50943163 | $2.4254\pm 0.0013$ | $0.138\pm 0.022$ | $1.9100\pm 0.0051$ | 57 | 4 | 56.1 | $137.6\pm 2.7$
17 | 3745.01 | 666567477 | $1.68831\pm 0.00079$ | $0.111\pm 0.015$ | $7.400\pm 0.017$ | 34 | 3 | 6.8 | $42.2\pm 6.6$
18 | 3746.01 | 284747017 | $1.80127\pm 0.00093$ | $0.133\pm 0.018$ | $1.8000\pm 0.0036$ | 47 | 3 | 14.1 | $117.1\pm 9.1$
19 | 3781.01 | 470974162 | $3.25885\pm 0.00084$ | $0.094\pm 0.027$ | $4.580\pm 0.022$ | 35 | 2 | 12.1 | $62.0\pm 5.4$
20 | 3924.01 | 456042145 | $2.047483\pm 6.4\cdot 10^{-5}$ | $0.132\pm 0.012$ | $6.8\pm 2.4$ | 44 | 7 | 52.4 | $205.0\pm 4.8$
21 | 3925.01 | 435167167 | $3.03309\pm 0.00018$ | $0.168\pm 0.027$ | $1.2800\pm 0.0036$ | 38 | 2 | 12.2 | $155\pm 14$
22 | 3979.01 | 444523623 | $2.04166\pm 0.00012$ | $0.147\pm 0.040$ | $3.230\pm 0.017$ | 60 | 3 | 25.3 | $179.1\pm 8.0$
23 | 3981.01 | 312548415 | $2.24375\pm 0.00014$ | $0.159\pm 0.027$ | $2.8800\pm 0.0087$ | 67 | 5 | 15.0 | $49.2\pm 3.5$
24 | 3985.01 | 604863428 | $3.23585\pm 0.00017$ | $0.157\pm 0.025$ | $5.460\pm 0.016$ | 56 | 2 | 9.9 | $33.6\pm 3.5$
25 | 3990.01 | 420446142 | $5.84236\pm 0.00022$ | $0.101\pm 0.017$ | $2.2800\pm 0.0070$ | 55 | 2 | 41.2 | $144.0\pm 3.8$
26 | 3991.01 | 418133917 | $2.27748\pm 0.00012$ | $0.156\pm 0.025$ | $1.5200\pm 0.0040$ | 53 | 4 | 17.2 | $34.1\pm 2.1$
27 | 3994.01 | 372505528 | $3.897414\pm 7.8\cdot 10^{-5}$ | $0.086\pm 0.016$ | $1.9900\pm 0.0032$ | 49 | 3 | 8.9 | $30.2\pm 3.6$
28 | 4005.01 | 395773226 | $3.84717\pm 0.00011$ | $0.092\pm 0.018$ | $1.7700\pm 0.0064$ | 42 | 2 | 22.6 | $206\pm 10$
29 | 4036.01 | 367913453 | $2.77616\pm 0.00013$ | $0.089\pm 0.021$ | $1.3400\pm 0.0068$ | 44 | 3 | 16.2 | $44.8\pm 2.9$
30 | 4048.01 | 279605855 | $1.972401\pm 3.0\cdot 10^{-5}$ | $0.101\pm 0.026$ | $7.460\pm 0.020$ | 42 | 2 | 22.0 | $332\pm 19$
31 | 4052.01 | 236775063 | $0.7409429\pm 7.0\cdot 10^{-6}$ | $0.045\pm 0.010$ | $2.4600\pm 0.0070$ | 38 | 3 | 32.3 | $390\pm 16$
32 | 4068.01 | 159334269 | $1.1578392\pm 7.2\cdot 10^{-6}$ | $0.057\pm 0.014$ | $9.660\pm 0.024$ | 33 | 2 | 14.6 | $157\pm 12$
33 | 4083.01 | 399444057 | $2.071480\pm 5.6\cdot 10^{-5}$ | $0.130\pm 0.019$ | $1.6600\pm 0.0023$ | 60 | 5 | 56.0 | $149.6\pm 3.0$
34 | 4126.01 | 141616639 | $3.24287\pm 0.00015$ | $0.101\pm 0.021$ | $1.4700\pm 0.0066$ | 49 | 2 | 17.1 | $95.5\pm 6.0$
35 | 4130.01 | 71396541 | $6.26972\pm 0.00027$ | $0.154\pm 0.032$ | $1.2400\pm 0.0033$ | 75 | 3 | 24.0 | $40.1\pm 1.7$
36 | 4134.01 | 420803693 | $0.913597\pm 2.4\cdot 10^{-5}$ | $0.052\pm 0.014$ | $0.5400\pm 0.0032$ | 47 | 2 | 7.0 | $133\pm 21$
37 | 4135.01 | 288471040 | $2.513920\pm 3.3\cdot 10^{-5}$ | $0.0994\pm 0.0082$ | $0.59000\pm 0.00043$ | 33 | 4 | 13.4 | $14.2\pm 1.1$
38 | 4139.01 | 408729765 | $4.62008\pm 0.00011$ | $0.090\pm 0.015$ | $3.4800\pm 0.0090$ | 48 | 3 | 38.5 | $209.1\pm 6.3$
39 | 4143.01 | 371711170 | $9.84822\pm 0.00073$ | $0.177\pm 0.034$ | $1.6700\pm 0.0062$ | 48 | 2 | 18.4 | $100.0\pm 5.8$
40 | 4164.01 | 420108587 | $3.52313\pm 0.00012$ | $0.110\pm 0.018$ | $0.8200\pm 0.0022$ | 29 | 5 | 11.6 | $12.9\pm 1.2$
41 | 4211.01 | 385654601 | $2.2715616\pm 8.4\cdot 10^{-6}$ | $0.114\pm 0.010$ | $8.1900\pm 0.0066$ | 35 | 4 | 7.2 | $19.0\pm 2.9$
42 | 4216.01 | 187861378 | $2.181681\pm 1.4\cdot 10^{-5}$ | $0.160\pm 0.020$ | $1.2800\pm 0.0017$ | 56 | 3 | 15.2 | $45.5\pm 3.1$
43 | 4225.01 | 141405814 | $1.1355486\pm 8.4\cdot 10^{-6}$ | $0.110\pm 0.014$ | $0.39000\pm 0.00074$ | 43 | 3 | 44.5 | $163.1\pm 4.1$
44 | 4229.01 | 319282294 | $1.13857\pm 0.00046$ | $0.079\pm 0.014$ | $6.220\pm 0.024$ | 50 | 4 | 29.7 | $205.2\pm 8.0$
45 | 4232.01 | 126357909 | $1.22480\pm 0.00053$ | $0.069\pm 0.014$ | $7.640\pm 0.037$ | 53 | 5 | 17.8 | $123.4\pm 7.8$
46 | 4236.01 | 36227841 | $0.4021282\pm 1.9\cdot 10^{-6}$ | $0.034\pm 0.012$ | $2.4\pm 1.0$ | 58 | 6 | 10.0 | $6.64\pm 0.71$
47 | 4243.01 | 400683848 | $1.0883300\pm 8.6\cdot 10^{-6}$ | $0.101\pm 0.020$ | $0.5400\pm 0.0016$ | 48 | 6 | 10.0 | $61.3\pm 6.8$
48 | 4256.01 | 77102895 | $1.0962372\pm 6.5\cdot 10^{-6}$ | $0.097\pm 0.017$ | $2.4600\pm 0.0042$ | 48 | 4 | 30.0 | $189.4\pm 7.3$
49 | 4258.01 | 74484886 | $3.850566\pm 2.7\cdot 10^{-5}$ | $0.104\pm 0.014$ | $6.070\pm 0.012$ | 46 | 4 | 48.5 | $211.4\pm 5.1$
50 | 4292.01 | 255918903 | $1.72035\pm 0.00018$ | $0.1086\pm 0.0087$ | $7.4900\pm 0.0064$ | 72 | 7 | 8.8 | $20.7\pm 2.5$
51 | 4300.01 | 266843799 | $0.8062768\pm 2.8\cdot 10^{-6}$ | $0.0818\pm 0.0095$ | $0.66000\pm 0.00082$ | 55 | 2 | 19.5 | $286\pm 18$
52 | 4335.01 | 443658196 | $4.4990\pm 0.0024$ | $0.257\pm 0.021$ | $4.08\pm 0.30$ | 51 | 2 | 40.7 | $225.3\pm 6.4$
53 | 4346.01 | 389371332 | $3.907712\pm 4.6\cdot 10^{-5}$ | $0.397\pm 0.032$ | $0.600\pm 0.048$ | 201 | 14 | 44.4 | $465\pm 15$
54 | 4396.01 | 379723086 | $7.439891\pm 4.4\cdot 10^{-5}$ | $0.120\pm 0.012$ | $1.0100\pm 0.0014$ | 75 | 3 | 27.7 | $148.2\pm 5.9$
55 | 4397.01 | 107728509 | $2.6646\pm 0.0028$ | $0.172\pm 0.032$ | $0.8400\pm 0.0032$ | 36 | 5 | 22.5 | $264\pm 15$
56 | 4423.01 | 344600402 | $1.3875331\pm 9.7\cdot 10^{-6}$ | $0.099\pm 0.017$ | $1.1400\pm 0.0021$ | 41 | 3 | 24.9 | $322\pm 16$
57 | 4498.01 | 305943739 | $5.30735\pm 0.00011$ | $0.155\pm 0.029$ | $0.20000\pm 0.00057$ | 93 | 3 | 15.0 | $117.8\pm 8.4$
58 | 4502.01 | 239372503 | $1.71043\pm 0.00076$ | $0.053\pm 0.029$ | $0.2500\pm 0.0050$ | 47 | 5 | 14.0 | $67.6\pm 5.3$
59 | 4808.01 | 126772538 | $1.470060\pm 1.0\cdot 10^{-5}$ | $0.091\pm 0.017$ | $4.760\pm 0.015$ | 58 | 4 | 19.6 | $190\pm 11$
60 | 4812.01 | 81744640 | $3.313845\pm 4.0\cdot 10^{-5}$ | $0.161\pm 0.032$ | $3.5500\pm 0.0097$ | 71 | 2 | 10.4 | $30.8\pm 3.1$
61 | 4829.01 | 268439377 | $0.9855374\pm 3.8\cdot 10^{-6}$ | $0.0492\pm 0.0070$ | $3.2900\pm 0.0074$ | 33 | 3 | 23.0 | $354\pm 20$
62 | 4840.01 | 80029842 | $2.399288\pm 2.6\cdot 10^{-5}$ | $0.106\pm 0.017$ | $1.1800\pm 0.0040$ | 37 | 2 | 13.8 | $118.4\pm 9.4$
63 | 4846.01 | 418971787 | $1.0638184\pm 7.1\cdot 10^{-6}$ | $0.133\pm 0.016$ | $3.2200\pm 0.0048$ | 46 | 3 | 18.1 | $208\pm 13$
64 | 4870.01 | 446135868 | $1.811917\pm 1.6\cdot 10^{-5}$ | $0.109\pm 0.024$ | $5.510\pm 0.020$ | 56 | 6 | 19.0 | $64.0\pm 3.7$
65 | 4874.01 | 463754499 | $2.286686\pm 2.3\cdot 10^{-5}$ | $0.120\pm 0.016$ | $3.7200\pm 0.0083$ | 42 | 3 | 16.9 | $37.6\pm 2.3$
66 | 4876.01 | 458300989 | $4.13795\pm 0.00016$ | $0.197\pm 0.032$ | $2.610\pm 0.010$ | 45 | 6 | 14.3 | $76.7\pm 6.0$
67 | 4894.01 | 469333534 | $3.561122\pm 4.8\cdot 10^{-5}$ | $0.114\pm 0.024$ | $5.240\pm 0.023$ | 47 | 2 | 9.1 | $48.1\pm 5.5$
68 | 4902.01 | 358072664 | $4.193494\pm 3.5\cdot 10^{-5}$ | $0.078\pm 0.014$ | $2.7100\pm 0.0091$ | 52 | 4 | 20.2 | $186\pm 11$
69 | 4946.01 | 319783554 | $1.819376\pm 2.9\cdot 10^{-5}$ | $0.124\pm 0.042$ | $5.240\pm 0.081$ | 60 | 6 | 23.8 | $94.5\pm 4.4$
70 | 4964.01 | 406443564 | $1.1167145\pm 4.3\cdot 10^{-6}$ | $0.0757\pm 0.0054$ | $12.81\pm 0.74$ | 67 | 3 | 32.5 | $246.0\pm 8.8$
71 | 5006.01 | 449107129 | $4.254955\pm 2.8\cdot 10^{-5}$ | $0.176\pm 0.038$ | $2.3700\pm 0.0031$ | 43 | 4 | 10.9 | $21.7\pm 2.1$
72 | 5075.01 | 23113034 | $0.856742\pm 5.7\cdot 10^{-5}$ | $0.0522\pm 0.0078$ | $0.34000\pm 0.00070$ | 48 | 3 | 64.1 | $315.4\pm 6.1$