# Searching the SN 1987A SETI Ellipsoid with TESS

Bárbara Cabrales Berkeley SETI Research Center, University of California,
Berkeley, CA 94720, USA  SETI Institute, 339 N Bernardo Ave Suite 200,
Mountain View, CA 94043  James R. A. Davenport Astronomy Department,
University of Washington, Box 951580, Seattle, WA 98195, USA  Sofia Sheikh
Department of Astronomy, University of California Berkeley, Berkeley CA 94720,
USA  SETI Institute, 339 N Bernardo Ave Suite 200, Mountain View, CA 94043
Steve Croft Berkeley SETI Research Center, University of California, Berkeley,
CA 94720, USA  Department of Astronomy, University of California Berkeley,
Berkeley CA 94720, USA  Andrew P. V. Siemion  Berkeley SETI Research Center,
University of California, Berkeley, CA 94720, USA  Department of Astronomy,
University of California Berkeley, Berkeley CA 94720, USA  SETI Institute, 339
N Bernardo Ave Suite 200, Mountain View, CA 94043  Daniel Giles  SETI
Institute, 339 N Bernardo Ave Suite 200, Mountain View, CA 94043  Ann Marie
Cody  SETI Institute, 339 N Bernardo Ave Suite 200, Mountain View, CA 94043

###### Abstract

The SETI Ellipsoid is a strategy for technosignature candidate selection which
assumes that extraterrestrial civilizations who have observed a galactic-scale
event — such as supernova 1987A — may use it as a Schelling point to broadcast
synchronized signals indicating their presence. Continuous wide-field surveys
of the sky offer a powerful new opportunity to look for these signals,
compensating for the uncertainty in their estimated time-of-arrival. We
explore sources in the TESS continuous viewing zone, which corresponds to 5%
of all TESS data, observed during the first three years of the mission. Using
improved 3D locations for stars from Gaia Early Data Release 3, we identified
32 SN 1987A SETI Ellipsoid targets in the TESS continuous viewing zone with
uncertainties better than 0.5 ly. We examined the TESS light curves of these
stars during the Ellipsoid crossing event and found no anomalous signatures.
We discuss ways to expand this methodology to other surveys, more targets, and
different potential signal types.

††software:  Python, IPython (Pérez & Granger, 2007), NumPy (Oliphant, 2007),
Matplotlib (Hunter, 2007), SciPy (Jones et al., 2001–), Pandas (Wes McKinney,
2010), Astropy (Astropy Collaboration et al., 2013, 2018, 2022) Scikit-Learn
(Pedregosa et al., 2011)

##  1 Introduction

Technosignatures are any measurable property which may provide evidence of
extraterrestrial technology (Tarter, 2007). The search for extraterrestrial
intelligence (SETI) is a branch of astrobiology which focuses on finding
technosignatures, as their detection would provide evidence for intelligent
life beyond Earth. Traditionally, targeted radio surveys have been the
mainstay of SETI research (Tarter, 2001), and many SETI projects currently
underway still take place in the radio band (e.g., Sheikh et al., 2023; Ma et
al., 2023; Margot et al., 2023). However, searches in other wavelengths, such
as the optical, are increasingly common (Zuckerman et al., 2023). New
instruments in development, such as the PANOSETI project (targeting all-sky,
all-the-time laser searches; Wright et al. 2019), promise to survey these
underexplored territories in SETI, and expand to search strategies that are
not exclusive to narrow radio frequencies. Additionally, while dedicated
searches have a important place in the SETI field versus commensal and/or
archival work with other astronomical projects (Wright, 2021), piggybacking
from larger surveys remains relevant to the SETI field in the era of big data,
e.g., the COSMIC project on the Very Large
Array111https://science.nrao.edu/facilities/vla/observing/cosmic-seti.

Modern sky surveys gather a rapidly-growing amount of information, which
provides more opportunities to find technosignatures (Djorgovski, 2000;
Davenport, 2019; Lazio et al., 2023). However, the development of cutting-edge
instruments, such as the Vera Rubin Observatory’s Large Synoptic Survey
Telescope (LSST), expected to produce 15 TB of raw data each night (Ivezić et
al., 2019), introduces the need for prioritization strategies which will help
optimize our searches. With such a large volume of data producing a wealth of
anomalies and interesting signals, we must use approaches to decide which of
them are interesting in the context of SETI. One possibility is to use a
Schelling point (Schelling, 1958), a strategy where two agents coordinate
their efforts towards a common goal without communicating, using a conspicuous
point of reference instead of searching randomly, which increases their odds
at succeeding; these have often been applied to SETI, e.g., as magic
frequencies (Wright, 2020). Another potential Schelling Point in SETI is the
“SETI Ellipsoid”.

The SETI Ellipsoid is a geometric method of target prioritization for
technosignature searches, which assumes an intentional attempt at
communication from an extraterrestrial agent (ETA), as opposed to the search
for signs of technology not intended for our discovery (Wright, 2020). In this
model, the ETA might use a sufficiently rare and outstanding galactic-scale
event, such as a nearby supernova, to synchronize a beacon indicating their
presence (Lemarchand, 1994) hoping to catch the attention of other astronomers
(i.e., us) who may be interested in studying such an event (Davenport et al.,
2022). The SETI Ellipsoid therefore helps select outliers or signals that are
interesting and require further analysis or follow-up from a technosignature
standpoint. This method can be used in conjunction with a variety of proposed
technosignatures including brightening or dimming in a stellar light curve,
narrowband radio transmissions or laser beacons. A detailed diagram and review
of the SETI Ellipsoid are provided in Section 2 of Davenport et al. (2022).

This particular work is a proof-of-concept paper, designed to develop the idea
of the SETI Ellipsoid in the context of modern instrumentation and data. In
addition, we have performed a search for particular technosignatures in state-
of-the-art data from the Transiting Exoplanet Survey Satellite (TESS; Ricker
et al., 2015) by looking for light curve anomalies. Many types of
technosignatures could produce apparent dimming or brightening behavior in a
star’s light curve, by emitting either broad or narrow wavelength signals, or
blocking the star’s natural photons. One example could be unusual or anomalous
transits in the light curve (e.g. Zuckerman et al., 2024), which could occur
in conjunction with the Ellipsoid crossing time. Another possible signal could
be an outburst that mimics the supernova profile in the light curve (Nilipour
et al., 2023), which would be distinct from e.g. normal stellar flares (Tovar
Mendoza et al., 2022).

Our distance estimates to stars have historically been too imprecise for a
geometric search of this kind, and have presented the greatest obstacle to the
SETI Ellipsoid technique (Makovetskii, 1977). However, the Gaia mission
produced improved distance uncertainties by calculating parallaxes with a
precision $\sim 100\times$ better than its predecessor Hipparcos (Gaia
Collaboration et al., 2016). It is now possible to apply the SETI Ellipsoid
technique as a method of target prioritization. For example, there were 134
SETI Ellipsoid candidates from the Gaia Catalog of Nearby Stars (GCNS) alone
within 0.1 ly of the SN 1987A Ellipsoid in 2022 (Davenport et al., 2022).

Gaia observations are sporadic and sparse over years (Hodgkin et al., 2021),
which makes their light curves suboptimal for short timescale technosignature
monitoring (Nilipour et al., 2023). Additionally, distance uncertainties
propagate into uncertainties in the expected arrival time for a potential
technosignature. Optimal windows of observation are proportional to the
distance uncertainties of stars — which work out to about a couple of months
for nearby targets. Thus the Gaia mission can be used to identify interesting
targets and times for observation, but on its own, it can only provide sparse
light curves with which to search for the hypothesized synchronous
technosignature. Here, we work around this shortcoming by combining Gaia
distance estimates from Early Data Release 3 (EDR3) and continuous
observations from TESS, to search for anomalies in light curves which span
longer periods of time.

Unlike its forerunner, Kepler, the TESS survey covers almost the whole sky,
surveying one near-full hemisphere a year by shifting its field of view to 13
different sectors in that time. Furthermore, these 13 fields overlap at the
ecliptic poles, providing yearlong coverage to targets located in this area,
referred to as the continuous viewing zone (CVZ). Searching for CVZ targets on
the SETI Ellipsoid will ensure access to one year’s worth of uninterrupted
light curve data for each source. This will provide enough information to
establish a target’s baseline behavior for anomaly detection strategies, and
enough leeway to account for the uncertainty of a hypothetical signal’s time-
of-arrival.

In this work, we show the advantages of using a continuous wide-field survey,
such as TESS, to monitor targets on the SETI Ellipsoid. In Section 2, we
describe our procedure for retrieving the 3D coordinates of the CVZ sources.
In section 3, we discuss the parameters we used to filter our initial data
sample and describe the Ellipsoid algorithm for SN 1987A, allowing us to
select the final targets which we analyze in Section 4, focusing especially on
the targets’ TESS light curves and their features. Finally, we summarize our
findings and consider future work in 5.

##  2 Data Selection: TESS and Gaia

Jointly, TESS and Gaia are well-suited surveys to carry out the SETI Ellipsoid
technique due to the complementary features of the missions; TESS offers
densely sampled light curves over long time periods, and Gaia provides the
most precise distances to stars ever computed. Additionally, their combined
focus on nearby sources — which have smaller distance uncertainties — reduces
the average time range that we need to monitor for, since the error on the
arrival time of a synchronized signal from a star is directly impacted by the
star’s distance uncertainty. Given that the maximum timescale for TESS’s
continuous photometric coverage is one year, nearby stars with timing
uncertainties that fit within this timescale are particularly good targets.

Figure 1: TESS data obtained during Cycle 1 (left), Cycle 2 (center), and
Cycle 3 (right) on the celestial plane. Common RA and Dec labels are displayed
for the entire Figure. Sources are color-coded by sector, highlighting the
geometry of the TESS field of view and the overlap of all 13 sectors — per
cycle — at the ecliptic poles (the CVZ). The circular area (bright orange)
near the pole on each plot is composed of the targets observed in at least 11
overlapping sectors during that cycle, and shows the data sample from which
SETI Ellipsoid targets were selected.

###  2.1 TESS and the CVZ

The TESS mission succeeded Kepler in the search for exoplanets, focusing on
stars 100$\times$ brighter and 10$\times$ closer to Earth — on average — than
the earlier mission. As a result, TESS’s coverage is mostly constrained to
stars that lie within 200–300 lyr of Earth as opposed to Kepler’s average of
$\sim$3000 lyr (Jenkins et al., 2016). Moreover, while the Kepler prime
mission field of view surveyed a fixed 100 deg2 area near the constellation
Cygnus, the TESS field of view shifts every 27.4 days, allowing it to complete
an all-sky survey in 2 years. (Koch et al., 2010; Ricker et al., 2015).

One 27-day continuous coverage of TESS’s 24∘ $\times$96∘ field of view is
known as an observing sector. One year of coverage — hereafter referred to as
a Cycle — contains 13 sectors and observes most of one hemisphere (Ricker et
al., 2015). In this work, we use the 2-minute cadence data from the first
three cycles, completed during 2018 through 2021. As shown in Figure 1, Cycles
1 and 3 — which ran during 2018–2019 and 2020–2021 respectively — provided
coverage of the southern hemisphere sky, whereas Cycle 2 — active during
2019–2020 — surveyed the northern hemisphere.

During these three cycles, 329,176 unique stars were observed, but most of
these sources were only present in one sector per cycle. This is apparent in
Figure 1. We are mainly interested in targets that appear in multiple sectors,
and therefore have long spans of continuous photometric coverage, since this
helps us account for the uncertainties in the expected arrival time of a
presumed signal, and provides multiple month-long, high-cadence light curves
to use for anomaly detection. Consequently, we focused our search on stars
which were present in at least 11 sectors in a given cycle, such that there
are between 300 and 356 days worth of data for each target. This criterion
shrinks our sample by 96%, resulting in 14,614 stars to select SETI Ellipsoid
targets from, and guarantees that we search the entire CVZ, as well as nearby
fields with very good coverage. The distribution of the reduced data sample on
the celestial plane is shown in bright orange in Figure 1; we will refer to
this sample simply as the “CVZ” in the following text.

Since Cycles 1 and 3 surveyed the same hemisphere, 48,744 southern-sky sources
were observed during both time periods, two years apart; 2,493 of which were
in the CVZ. Note that, although roughly the same area was surveyed, only about
15% of targets overlap. This is because we are using the TESS 2-minute
targets. These targets were selected through proposals, which saw a 500%
increase in the first extension of the mission (Cycles 3 and 4).
222https://heasarc.gsfc.nasa.gov/docs/tess/extended.html The Full Frame Image
(FFI) data from TESS include far more targets than those considered in this
work. We further discuss FFIs in Section 5. As will be described in Section 3,
timing is essential for this technique; thus, a source that might be trivial
in 2019 could be a target of interest in 2021. Accordingly, we decided to
independently consider the 2,493 overlapping targets in both cycles,
increasing our database of CVZ targets to 17,107 rows.

###  2.2 Distances from Gaia EDR3

The SETI Ellipsoid technique of target selection can only be applied when the
distances to the surveyed stars are precise and accurate. Gaia’s EDR3 provides
a significant improvement in parallax measurement precision over the previous
Data Release 2 (DR2), leading to median parallax uncertainties of 0.02–0.03
mas for bright stars (G $\leq$ 14 mag), a 40% decrease from Gaia DR2, which
had median uncertainties of 0.04 mas for stars of the same magnitude (Gaia
Collaboration et al., 2021; Lindegren et al., 2018, 2021). With this
unprecedented parallax precision, Bailer-Jones et al. (2021) estimated
geometric and photogeometric distances for 1.5 billion stars. As shown by
Davenport et al. (2022), the catalog of Gaia EDR3 geometric-probabilistic
distances from Bailer-Jones et al. (2021) can be effectively used to make
precise estimates for the expected arrival time of a presupposed synchronized
signal using the SETI Ellipsoid method for a well-documented source event.
Here, we use the same procedure of target selection but for TESS objects,
focusing on the 14,614 CVZ targets chosen in 2.1. We did not limit these
targets by any particular parameter (e.g., stellar type, binarity, or
habitability). A system could be used for the SETI Ellipsoid technique
regardless of whether it is habitable — in fact, it might be preferable for
the ETA to place the signalling technology in a uninhabited system.

###  2.3 Crossmatching the CVZ targets with EDR3 distances

To assign each target its corresponding Gaia ERD3 probabilistic distances, we
used the cross-match service provided by CDS, Strasbourg (Pineau et al.,
2020).

We merged our TESS data with the Gaia EDR3 distances database using the
targets’ celestial coordinates within a radius of $1\arcsec$. During the
crossmatching process of the CVZ sample, 725 sources were dropped, likely due
to a disagreement greater than the $1\arcsec$ threshold between the TESS and
Gaia RA and Dec values. We did not attempt to recover these missing targets,
which correspond to 4% of the initial CVZ list. Thus, the final data sample
contained 16,382 rows of TESS CVZ sources with Gaia EDR3 distance estimates.

##  3 Selecting Targets on the SN1987A SETI Ellipsoid

The addition of Gaia distances to our sample enables us to compute the
distance to a SETI Ellipsoid for any given target at any given time. This
allows for the selection of targets which are optimally placed for a
communication attempt coordinated with astronomical phenomena according to the
SETI Ellipsoid framework.

###  3.1 The Mathematics of the SETI Ellipsoid

As noted in Section 1, the SETI Ellipsoid is a method of target selection that
works under the assumption that an extraterrestrial civilization or agent
would actively try to draw attention to themselves by broadcasting a signal
soon after first witnessing a notable astronomical event (Makovetskii, 1977;
Lemarchand, 1994).

The speed of light, $c$, constrains our targets of interest to a particular
region of space at a particular point in time. We consider stars located at
the precise distances from Earth that allow for an electromagnetic signal —
sent in coordination with the astronomical event — to reach Earth at any given
time, with the intent of aligning our monitoring efforts accordingly.

The region of interest is the ellipsoid whose foci are at the source event and
at Earth. The ellipsoid grows with time as new stars observe the event, and is
defined by:

$d_{1}+d_{2}=2\,\mathscr{A}=2\,\mathscr{C}+T$ (1)

where ($d_{1}$) is the distance from the Earth to a target laying on the
ellipsoid, ($d_{2}$) is the distance from the event to the target,
$\mathscr{A}$ is the semi-major axis of the ellipsoid, $\mathscr{C}$ is the
distance from each foci to the center of the ellipsoid, and $T=c\,t$ is the
time since Earth observed the event times the speed of light. Therefore given
a synchronizing event with a known distance, and a sample of field stars with
distances, we can compute their Ellipsoid crossing times as a function of time
using Equation 1.

###  3.2 SN 1987A as the synchronizing event

Ideal events for the Ellipsoid technique are fixed in space and time,
relatively uncommon in our galactic neighborhood, and bright enough to be used
as a synchronizing beacon on a galactic scale (Lemarchand, 1994).

Although other events are worthy of examination as well (e.g., galactic novae,
as explored by Davenport et al., 2022), supernova outbursts are particularly
good source events to place at one of the foci within the Ellipsoid framework,
and SN 1987A is an ideal Schelling point for our purposes. First, its distance
to Earth is very well-documented with a low uncertainty. We used the distance
estimate computed by Panagia (1999) of 51.4 $\pm$ 1.2 kpc, where the 1.2 kpc
uncertainty corresponds to a 2.3% error. Secondly, SN 1987A is the closest
supernova to Earth since SN 1604. Given that it is relatively nearby in space-
time, SN 1987A has a thin associated Ellipsoid which closely surrounds Earth,
ensuring that many targets of interest will lie within relatively short
distances and therefore have low distance uncertainties, resulting in low
timing uncertainties for the arrival time of a synchronized signal. Lastly,
the location of SN 1987A in the Large Magellanic Cloud (LMC) is optimal for
this work due to the cloud’s proximity to the south ecliptic pole, which is
the area surveyed by TESS’s CVZ in Cycles 1 and 3. The polar location, along
with the current thin shape of the ellipsoid, allows for the intersection of a
significant portion of SN 1987A’s ellipsoid with the southern TESS CVZ cone,
making it highly likely to find several targets of interest within our
previously selected data sample for two of the three cycles considered. In
contrast, we expect little to no Ellipsoid candidates on the northern
hemisphere. This can be appreciated in Figure 2.

Figure 2:  Galactocentric Y-Z plane for TESS stars, color coded to show the
location of the southern CVZ, and their designation within the SETI Ellipsoid
framework for SN 1987A. 214,995 stars have seen SN 1987A (dashed line) but are
outside of the ellipsoid (green points). 97,514 stars have not observed SN
1987A (gray points). 23,148 stars are inside the SN 1987A Ellipsoid (yellow
points), implying that any coordinated beacon has already passed the Earth.
736 stars are laying on the SN 1987A ellipsoid (orange points). The 7,850
southern CVZ stars are shown in pink. 37 targets are both on the ellipsoid and
in the southern CVZ (black stars) and are our targets of interest. The contour
of the SETI Ellipsoid in the YZ plane is shown as a solid line. The sun is
also plotted (blue cross).

###  3.3 The SN 1987A Ellipsoid

The list of TESS CVZ sources found in Section 2.1 contains 14,614 individual
objects and 17,107 rows of data due to sources which were observed in two
different cycles. After the cross-match with Gaia distances performed in 2.3,
we know both where these targets are located in space, and when they were
observed by TESS. Solving equation 1 for a desired time allows us to calculate
the distance of our CVZ targets to the Ellipsoid at that time.

The algorithm we developed uses the start and end dates of observation for
each target’s first and last sectors respectively, obtained from NASA’s TESS
observation times site333https://heasarc.gsfc.nasa.gov/docs/tess/sector.html.
The mid-time of observation is then calculated, and since most of the targets
in our sample were observed in all TESS sectors, this mid-time is the same for
every 13-sector target in each cycle as shown in Table 1.

Cycle | Mid-Time Date
---|---
1 | 2019 January 20
2 | 2020 January 10
3 | 2020 December 28
Table 1: Mid-times for 13-sector TESS observations taken during the three
cycles considered in this work.

We then use the right-hand side of equation 1 to find the length of the semi-
major axis of the ellipsoid, $\mathscr{A}$, at these times. According to
equation 1, a target is on the ellipsoid if

$d_{1}+d_{2}-2\,\mathscr{A}=0$ (2)

however, we have decided to select targets which are within reasonable
distance to the ellipsoid as opposed to exactly on it, given the uncertainties
involved in the process of finding a target strictly on an infinitely thin
surface. Other uncertainties might also play a role, such as the error in the
distances to the sources, explored in Section 3.4, or the potential delay in
the broadcast of a burst from an ETA, discussed in Section 5. We allowed for
some leeway in the ellipsoid distance by creating a tolerance parameter, etol,
a positive value in ly which determines the distance-to-the-ellipsoid
threshold for target selection. This adds thickness to the ellipsoid,
essentially turning it into an ellipsoidal shell defined by:

$|d_{1}+d_{2}-2\,\mathscr{A}|<\texttt{etol}$ (3)

The same steps were followed by Davenport et al. (2022), where the selected
tolerance was etol = 0.1 ly, to make use of Gaia’s highest timing precisions.
However, as Davenport et al. state, the value of this threshold can and should
be picked based on the specific monitoring campaign’s properties. For this
work, we have selected etol = 0.5 ly to match the approximate duration of one
TESS cycle (1 year). Choosing targets 0.5 ly away from the mid-cycle ellipsoid
helps account for targets which would have been on it at the beginning of said
cycle — 0.5 years before mid-time — or at the end — 0.5 years after mid-time.
This is not a perfectly precise threshold since the ellipsoid grows slightly
slower than the speed of light near the foci, resulting in a decreasing
eccentricity over time such that the ellipsoid becomes a spheroid at
$t=\infty$. This widening effect is illustrated in Figure 5 of Davenport et
al. (2022). Due to this ellipsoid rate of growth differential, a 0.5 ly
tolerance potentially includes targets near Earth or near SN 1987A that did
not intersect the Ellipsoid exactly during the TESS’s observing cycle. Note
that this widening effect occurs over centuries, and is likely negligible over
timescales of individual missions.

After running our algorithm for the 17,107-row list of CVZ sources, we
obtained 12 targets of interest laying within 0.5 ly of the SN 1987A ellipsoid
as of 2019 January 20 — mid-time of Cycle 1 — and 24 targets of interest as of
2020 December 28 — mid-time of Cycle 3, resulting in 36 selected TESS objects.
As expected per the discussion in Section 3.2 no targets of interest were
found in the northern hemisphere, surveyed during Cycle 2. Accordingly, we did
not extend our search to TESS’s Cycle 4, which also observed this region of
the sky.

###  3.4 Incorporating Positional Uncertainties

The selection of the 36 targets of interest from our list of 17,107 CVZ
sources described in Section 3.3 was computed considering only their 50%
probability geometric distances, known as $r_{med}$, obtained from Bailer-
Jones et al. (2021), as well as the reported distance to SN 1987A from Panagia
(1999), and the celestial coordinates from the TESS two-minute data, not
accounting for errors for any of these quantities. However, these errors
directly impact the uncertainties in the intersection time between the
Ellipsoid and any target of interest, which consequently, establishes a window
for the expected time-of-arrival of a synchronized signal.

Figure 3: Histogram of simulated distances of the Cycle 1 Ellipsoid candidates
(top) and the Cycle 3 Ellipsoid candidates (bottom) to the SN 1987A ellipsoid
using a Monte Carlo method of random draws in a Gaussian distribution
calculated from Gaia’s distance errors. Common Distance to the Ellipsoid and
Frequency labels are displayed for the entire Figure. Even when including all
sources of uncertainty, all 32 of these targets have a standard deviation
smaller than 0.5 ly. The peaks of these distributions are also within 0.5 ly,
as expected from the etol value chosen in Section 3.3.

We investigated how much the error of each of these quantities affects the
distance of our targets to the ellipsoid to a) assess which one of these
uncertainties will have the greatest impact on our calculations, b) to
eliminate targets with very large uncertainties, i.e. uncertainties larger
than TESS’s yearlong coverage and c) to find the previously mentioned “window
of interest” to monitor, which corresponds to the range of time where we
expect to see an anomaly in the light curves of our targets of interest
coordinated with their first detection of SN 1987A. To accomplish this, we
incorporated the RA, Dec, SN 1987A distance and target distance uncertainties
into our original selection algorithm by using a Monte Carlo simulation. We
recalculated the distance to the ellipsoid for each selected target by drawing
1000 random Gaussian-distributed samples using the standard deviations for the
parameters mentioned above. For the target distances, we used Bailer-Jones’
16% and 84% distance probabilities , $r_{lo}$ and $r_{hi}$ respectively, such
that $\sigma_{r}=(r_{hi}-r_{lo})/2$. For the SN 1987A distance, we used the
uncertainty from Panagia (1999), $\sigma_{SN}$ = 1.2kpc. For the celestial
coordinates, RA and Dec, we used the errors from Bailer-Jones et al. (2021),
and Astropy (Astropy Collaboration et al., 2022) to assign celestial
coordinates to each draw using the angle standard deviation444We note
$\sigma_{RA}$ has the typical spherical coordinate dependence on $\cos(Dec)$.
we defined as $\sigma_{\angle}=(\sigma_{RA}^{2}+\sigma_{Dec}^{2})^{1/2}$. We
first ran the Ellipsoid calculation including the uncertainty for each
parameter in isolation in order to determine which error has a greater effect
on the final results. We found that the average error that propagates from the
uncertainty of the celestial coordinates to the distance-to-the-ellipsoid
uncertainty corresponds to 0.073 ly, while the uncertainty in the distance to
SN 1987A only contributed 0.006 ly to the mean error. As expected, the
dominant contribution to the distance-to-the-ellipsoid uncertainties
propagates from the Bailer-Jones et al. (2021) error of the distance to the
targets, which works out to 0.193 ly in average. The final simulation did,
however, consider the error in all the evaluated parameters.

A histogram illustrating the results of the Monte Carlo simulation for our
ellipsoid targets per cycle is shown in Figure 3. We used the standard
deviation of these results to assign a distance-to-the-Ellipsoid uncertainty
to each target in light years, which is equivalent to finding their ellipsoid
timing uncertainty, $\sigma_{et}$, in years. This uncertainty will indicate
the length of the window of interest, defined earlier as the best time to look
for abnormalities in the light curves of a selected target.

All targets in Cycle 1 had timing uncertainties below 0.3 yr due to their
proximity to Earth. However, some targets in Cycle 3 happened to lay farther
along the Ellipsoid towards SN 1987A. The most distant targets in Cycle 3 had
uncertainties of up to 13 yr, and with TESS’s continuous coverage lasting
about one year, we decided to set an ellipsoid timing uncertainty threshold
and only consider targets below $\sigma_{et}$ = 0.5 yr, which matches the
tolerance parameter we established earlier and guarantees that most of the
window of interest for any given target will occur during TESS’s coverage,
even when considering a distance-to-the-ellipsoid value close to 0.5 ly. Only
4 targets were dropped using this criterion, reducing the number of ellipsoid
targets to 32. The histogram in Figure 3 shows the distribution of distances
to the ellipsoid for the final 32 targets. In Table 2 we list all 32 of our
final TESS targets, their coordinates, and the estimated SN 1987A Ellipsoid
crossing times.

##  4 SN 1987A SETI Ellipsoid Targets

In Figure 4 we present the Gaia color–magnitude diagram for the 32 star
systems we have identified as being within 0.5 ly of the SN 1987A Ellipsoid
during their TESS 2-minute cadence observations. For context, we also show the
entire sample of the 329,176 TESS sources surveyed at 2-minute cadence with
cross matches to Gaia DR3 in the first three cycles of the mission. As
expected, stars at a wide range of stellar evolutionary stage are found to
intersect the Ellipsoid, with multiple turn-off and giant branch stars
included, along with 3 solar-type main sequence stars, and several apparent
high-mass stars. The SETI Ellipsoid framework provides a useful method for
identifying all types of nearby stars for SETI monitoring from surveys like
TESS, which is important for exploring all possible types of technosignatures
(Lacki et al., 2020).

Figure 4:  Gaia ($G_{bp}-G_{rp}$, $M_{G}$) color-magnitude diagram (CMD) for
the 32 stars that we find intersect the SN 1987A Ellipsoid (black stars with
error bars). The entire sample of 329,176 TESS 2-minute targets is shown for
reference, with point colors indicating the Gaia colors. The theoretical
location of the Sun is also shown (orange star). Ellipsoid targets in TESS
Cycles 1–3 include main sequence, sub-giant, and giant branch stars. Three
stars are found with near-Solar locations in the CMD.

###  4.1 Finding the Ellipsoid Crossing Times

While using Equation 3 with etol = 0.5 ly is a computationally efficient
method of target selection and finding the value of $\sigma_{et}$ is
equivalent to calculating the length of the window of interest, we still need
to find exactly when this window occurs for each target. To do this, we set
out to compute the “Ellipsoid crossing times” for each selected source, that
is, the time when the Ellipsoid and a given target are expected to meet.

To do this, we used the following rearrangement of Equation 2,

$d_{1}+d_{2}-2\,\mathscr{A}=E_{dist}$ (4)

where the left hand side is now equal to $E_{dist}$, the distance of the
target to the Ellipsoid at a given time in pc. We used Gaia’s $r_{med}$
distance as our $d_{1}$, and the date of each candidate’s first TESS
observation to get $\mathscr{A}$. We then calculated the distance to the
ellipsoid 130 subsequent times in steps of 2.8 days for a total of 364 days,
the approximate duration of one TESS cycle. This process is illustrated in
Figure 5, where we find the Ellipsoid crossing time for each of the 32 targets
of interest. As previously mentioned, the uncertainty of this value is equal
to $\sigma_{et}$, calculated in Section 3.

Figure 5: Distance to the ellipsoid in time for targets on Cycle 1 (top) and 3
(bottom). The slope of these lines corresponds to 99.9% the speed of light.
The Ellipsoid crossing times are the zeroes in each line. Targets with lines
that start and end later than the rest belong to targets whose first
observation was not in Cycle 3’s first sector.

Additionally, in Section 3.3 we found that depending on the location of the
targets in space, while their crossing times might fall within the etol = 0.5
ly tolerance, the actual Ellipsoid crossing times may not be within the TESS
observing Cycle. As we can see in Figure 5, this was not an issue and all the
targets did intersect the ellipsoid within their respective TESS cycles.
Furthermore, the slopes of the lines (i.e. the Ellipsoid distance over time)
are $\sim 0.999c$, showing that, as expected, any apparent super-luminal
projection effects are negligible at the scale of $\sim 1$ year.

###  4.2 Light curves and search for anomalies

Using the lightkurve package (Lightkurve Collaboration et al., 2018), we
obtained all the 2-minute cadence PDCSAP (Pre-search Data Conditioning Simple
Aperture Photometry) TESS light curves for each candidate. PDCSAP fluxes are
produced in the TESS science pipeline by identifying and removing long-term
systematic trends from the SAP (Simple Aperture Photometry) flux, which is
generated by adding all pixel values in a predetermined aperture (Morris et
al., 2017). After retrieving the PDCSAP data, we normalized the flux in each
sector, subsequently stitching all the light curves together for each
candidate. This allowed us to properly characterize the year-long photometric
behavior of each target of interest to establish a benchmark from which to
search for deviations or anomalies. We then performed additional flux-outlier
removal using the built-in sigma-clipping function in the lightkurve package.

The previously-computed Ellipsoid crossing times allow us to identify the
range of time where we would expect to see a technosignature appear if an
extraterrestrial civilization had sent a signal immediately after observing SN
1987A. Consequently, we looked for anomalies in all the retrieved light
curves, prioritizing the window of interest given by the uncertainties in the
crossing times discussed in Section 3.4.

Figure 6: Normalized light curves for six selected SN 1987A Ellipsoid crossing
targets that exhibit interesting behavior related to stellar variability,
described in the text. Common Time and Flux labels are displayed for the
entire Figure. Each light curve is color-coded by TESS sector to aid in
viewing. The vertical red line in each plot indicates the crossing time with
the SN 1987A Ellipsoid. The vertical black lines show the uncertainty window
of the crossing time calculated in Section 3. None of these objects show any
change in their light curve behavior coincident with the Ellipsoid crossing
times.

We first visually inspected the light curves of all 32 candidates, from which
we report no unexplained anomalies. As in Nilipour et al. (2023), we looked
for changes in the stellar variability coincident with the Ellipsoid crossing
times as a possible sign of anomalous behavior. However, no changes in the
underlying stellar variability properties were apparent in the sample.

Changes that would have warranted further inspection include unusual
brightening or dimming signals in the wide TESS band light curves, which may
stand out due to amplitude or morphology. Assuming intentionality, we expect
magnitude changes of at least 2–10% in order to stand out from noise. This
would indicate either the presence of megastructures of sizes comparable to
several Jupiter radii, or very high energy emissions, which are possible for
lasers (Kipping & Teachey, 2016). However, it is key to consider these
amplitude changes in the context of the usual light curve behavior of the
source; a brightening event in a star that has flares is less likely to stand
out unless it exceeds the typical magnitude change due to stellar activity by
a significant amount or has an anomalous shape. This example is particularly
relevant, as a flare star is further discussed later in this section.

As for light curve changes in shape, a signal that mimics the light curve of
the supernova is one possible morphology to look for, as noted by Nilipour et
al. (2023). Unfortunately, the long timescale PDCSAP calibration of TESS
2-minute data is not currently reliable for recovering low amplitude slow
signals, though work is underway with the TESS FFI data (Hattori et al.,
2022). Therefore, we focus on shorter-term flares and dips in this work.

As expected from the range of stellar evolutionary stage of our sample shown
in Figure 4, the TESS light curves exhibit a variety of variability amplitudes
and timescales. This includes rotational modulation, pulsation, flares, and
eclipses. In Figure 6 we present a sample of six of our Ellipsoid crossing
candidates from Table 2 that demonstrate a range of stellar variability
behaviors. As noted earlier, all of these targets show no discernible change
in their normal variability patterns coincident with the Ellipsoid-crossing
times. TIC 279614617, also known as CPD-57 1131, is a RS CVn Variable with
high amplitude (9.5%) modulations from the 7.4 day rotational period (Martínez
et al., 2022). This system also exhibits several large flares throughout its
TESS light curve, one of which occurs during the Ellipsoid window of interest.
However, these instances are consistent with both the magnitude changes and
the “fast rise, slow fall” behavior of known stellar flares, which are typical
for these magnetically active binary systems (Tovar Mendoza et al., 2022). TIC
453100169 (HD 63669) is a MIII giant star with long period quasi-periodic
modulations. The shapes of these modulations are visually compelling, but stay
consistent throughout the yearlong TESS light curve with no detectable changes
during the window of interest. TIC 349972412 and TIC 350954265 are eclipsing
binary systems. We calculated the orbital periods of these systems using the
Box Least Squares (BLS) periodogram (Kovács et al., 2002), from which we
report a 84.5 day period and 3.3 day period, respectively. A detailed
characterization of these binary star systems — which show no contextual
anomalies — is beyond the scope of this work. TIC 260266066 (HD 43902) and TIC
382187278 are nearby giant stars (d$\sim$621 pc and 432 pc, respectively),
with apparent asteroseismic oscillations in their light curves. No unusual
behavior, coordinated with SN 1987A or otherwise, is detected.

We also used an outlier detection algorithm, conceptually based on DBSCAN
(Ester et al., 1996) and built with Scikit-Learn (Pedregosa et al., 2011),
that was developed specifically for detecting anomalous stellar light curves
(Giles & Walkowicz, 2019, 2020) and applied to TESS light curves derived from
the full frame images in Cycles 1 and 2 (Giles et al. in preparation). This
generated a “weirdness score” to each target in every sector of data. This
analysis was motivated by a search for unusual dimming patterns that could be
indicative of the transit of an artificial structure. While inspired by
systems like Boyajian’s star, this outlier detection method is signal-
agnostic, specifically with the purpose of avoiding assumptions related to
what a technosignature might look like. Therefore, both intentional and
unintentional technosignatures may be flagged as “anomalous” using this
classifier.

The outlier detection algorithm was run on the 12 Ellipsoid crossing targets
from Table 2 with crossing times in Cycle 1. None of these targets stood out
as candidates needing further investigation related to anomalous light curve
behaviors associated with possible technosignatures. The algorithm flagged TIC
279614617 as a target with strong sinusoidal flux over time, ranking it within
the top 2.3% most anomalous TESS objects for sectors 2-5 and 7-13. TIC
382187278 also stood out in Sectors 4 and 8 as being in the top 4.2% most
anomalous targets in these Sectors. No changes in the stellar variability
occurred across these data.

##  5 Discussion and Conclusions

We have demonstrated a practical application of the SETI Ellipsoid technique
to examine archival data in an attempt to identify light curve anomalies that
might be indicative of technosignatures synchronized with astronomical events.
Building from Gaia’s EDR3 highly precise distance estimates, we have showcased
the feasibility of cross matching these data to other time domain surveys,
such as TESS, to expand on the monitoring and anomaly detection aspect of this
kind of SETI search.

TESS’s continuous viewing zone provides yearlong light curves for targets near
the ecliptic poles. This is useful when considering the average ellipsoid
intersection timing uncertainty of nearby targets, which is close to a few
months. We showed that the distance to the target is the main factor in its
timing uncertainty, therefore longer time scale observations might be needed
for targets farther from Earth. Conversely, we might not need a full year’s
worth of data for targets closer to Earth to cover the entire window of
interest. Thus, future work might include targets with smaller uncertainties
that need less coverage (i.e. less than 11 sectors). To do this, an analytical
treatment of these uncertainties and their propagation is ideal, and a
relevant topic for future work, since it would allow for calculation of these
precisions in advance. We also recommend enforcing the continuity of these
sectors, to avoid gaps in light curves during their windows of interest.
Future work might also involve consideration of more targets which only have
data available in the TESS Full-Frame Images (FFIs).

Throughout this work, we assumed that the window of interest for a given
target would only be determined by the uncertainty in their crossing time with
the Ellipsoid. This implies that a signal sent in coordination with SN 1987A
would be broadcast immediately after the extraterrestrial civilization first
observed the event. It instead might be appropriate to offer some additional
margin after the signal’s expected time-of-arrival, assuming that there may be
some delay between event observation and signal transmission. The ideal
duration of this window of time is unknown, and any choice is bound to be
somewhat arbitrary, however, in the context of TESS, we recommend analyzing
one or two sectors beyond the upper bound given by the ellipsoid crossing time
uncertainty.

The SETI Ellipsoid framework provides no specific information related to the
kind of synchronized technosignature we expect to see. We suggest searching
for a signal that mimics the event’s shape in the light curve, which would be
detectable by TESS, while traditional SETI searches lean toward narrowband
radio frequencies that are outside of TESS’s detection capabilities. Further
insights related to what a synchronized beacon might look like — in the
optical band or otherwise — are still needed (Sheikh, 2020; Davenport et al.,
2022). A potential avenue for future work could be refining a machine learning
classifier such as the one used in Section 4.2 with a training set containing
specific light curve behaviors associated with the SETI Ellipsoid (e.g.,
mimicry of a supernova light curve). Using Full Frame Image data might also be
prefered in this instance since these data haven’t gone through long-term
systematic trend removal.

The SETI Ellipsoid method, jointly with Gaia distances, provides a
straightforward and flexible method for SETI searches that can be adapted to
fit different modern surveys and source events. It can be applied
retroactively to look for signals in archival data, as well as propagated
forward in time to select targets and schedule monitoring campaigns as
demonstrated by Davenport et al. (2023). In this work, we have presented an
approach that can be used with larger, upcoming time domain surveys such as
LSST.

The authors thank Andy Nilipour for helpful discussions related to the SETI
Ellipsoid method and its timing uncertainties. The authors acknowledge support
from the Breakthrough Listen initiative. Breakthrough Listen is managed by the
Breakthrough Initiatives, sponsored by the Breakthrough Prize Foundation. JRAD
acknowledges support from the DiRAC Institute in the Department of Astronomy
at the University of Washington. The DIRAC Institute is supported through
generous gifts from the Charles and Lisa Simonyi Fund for Arts and Sciences,
and the Washington Research Foundation. SC acknowledges support as the
Director of the Berkeley SETI Research Center Research Experience for
Undergraduates Site, supported by the National Science Foundation under Grant
AST 1950897. S.Z.S. acknowledges that this material is based upon work
supported by the National Science Foundation MPS-Ascend Postdoctoral Research
Fellowship under Grant No. 2138147. We acknowledge ESA Gaia, DPAC and the
Photometric Science Alerts Team (http://gsaweb.ast.cam.ac.uk/alerts). Funding
for the TESS mission is provided by NASA’s Science Mission directorate. This
research made use of the cross-match service provided by CDS, Strasbourg.
(Pineau et al., 2020; Boch et al., 2012) This research made use of Lightkurve,
a Python package for Kepler and TESS data analysis (Lightkurve Collaboration
et al., 2018).

TICID | $\mathbf{RA^{(\circ)}}$ | $\mathbf{Dec^{(\circ)}}$ | $\mathbf{d_{1}(pc)}$ | $\mathbf{t_{cross}(yr)}$
---|---|---|---|---
279055252 | 102.35 $\pm$ 0.02 | -57.57 $\pm$ 0.02 | 313.32${}_{-1.81}^{+1.47}$ | 2018.58 $\pm$ 0.18
382187278 | 81.26 $\pm$ 0.01 | -57.24 $\pm$ 0.01 | 431.33${}_{-2.13}^{+1.98}$ | 2018.60 $\pm$ 0.16
349374407 | 110.09 $\pm$ 0.01 | -61.65 $\pm$ 0.01 | 368.79${}_{-1.72}^{+1.66}$ | 2018.78 $\pm$ 0.15
350434130 | 85.04 $\pm$ 0.01 | -55.99 $\pm$ 0.01 | 359.73${}_{-1.69}^{+1.33}$ | 2018.78 $\pm$ 0.14
38711529 | 67.05 $\pm$ 0.01 | -60.36 $\pm$ 0.01 | 493.05${}_{-1.93}^{+2.64}$ | 2018.89 $\pm$ 0.15
350580827 | 86.89 $\pm$ 0.02 | -55.04 $\pm$ 0.02 | 313.21${}_{-1.91}^{+2.22}$ | 2018.98 $\pm$ 0.23
306672432 | 120.59 $\pm$ 0.02 | -67.79 $\pm$ 0.02 | 360.68${}_{-2.74}^{+2.62}$ | 2018.99 $\pm$ 0.25
260368525 | 95.24 $\pm$ 0.02 | -58.35 $\pm$ 0.02 | 445.65${}_{-3.35}^{+4.58}$ | 2019.03 $\pm$ 0.32
382067226 | 79.61 $\pm$ 0.01 | -55.79 $\pm$ 0.01 | 346.06${}_{-1.18}^{+1.09}$ | 2019.08 $\pm$ 0.11
279614617 | 106.30 $\pm$ 0.01 | -57.57 $\pm$ 0.01 | 277.66${}_{-0.88}^{+0.97}$ | 2019.14 $\pm$ 0.11
350711056 | 88.26 $\pm$ 0.01 | -57.73 $\pm$ 0.01 | 469.82${}_{-3.03}^{+2.62}$ | 2019.24 $\pm$ 0.22
381976956 | 77.55 $\pm$ 0.01 | -57.59 $\pm$ 0.01 | 446.51${}_{-2.93}^{+2.20}$ | 2019.28 $\pm$ 0.19
382028301 | 78.59 $\pm$ 0.01 | -56.03 $\pm$ 0.01 | 371.06${}_{-1.47}^{+1.45}$ | 2020.64 $\pm$ 0.14
260416034 | 95.65 $\pm$ 0.04 | -56.81 $\pm$ 0.04 | 368.27${}_{-4.47}^{+3.91}$ | 2020.65 $\pm$ 0.44
272316124 | 118.76 $\pm$ 0.01 | -74.05 $\pm$ 0.01 | 485.10${}_{-3.10}^{+3.32}$ | 2020.69 $\pm$ 0.24
382028819 | 78.50 $\pm$ 0.02 | -57.58 $\pm$ 0.02 | 472.45${}_{-3.24}^{+3.18}$ | 2020.75 $\pm$ 0.24
349681799 | 112.53 $\pm$ 0.02 | -61.23 $\pm$ 0.02 | 333.39${}_{-1.77}^{+2.19}$ | 2020.83 $\pm$ 0.21
220404759 | 69.86 $\pm$ 0.01 | -59.91 $\pm$ 0.01 | 550.05${}_{-3.26}^{+2.96}$ | 2020.87 $\pm$ 0.21
349571548 | 111.68 $\pm$ 0.01 | -62.16 $\pm$ 0.01 | 382.82${}_{-1.58}^{+1.70}$ | 2020.89 $\pm$ 0.15
260266066 | 93.75 $\pm$ 0.01 | -59.73 $\pm$ 0.01 | 620.03${}_{-5.94}^{+7.12}$ | 2020.95 $\pm$ 0.38
348900215 | 106.21 $\pm$ 0.02 | -60.52 $\pm$ 0.02 | 414.98${}_{-3.23}^{+3.46}$ | 2020.96 $\pm$ 0.29
350715741 | 88.41 $\pm$ 0.02 | -57.09 $\pm$ 0.02 | 444.37${}_{-2.65}^{+2.47}$ | 2021.01 $\pm$ 0.22
453100169 | 116.22 $\pm$ 0.02 | -68.76 $\pm$ 0.02 | 516.53${}_{-4.82}^{+5.34}$ | 2021.10 $\pm$ 0.35
260542038 | 96.99 $\pm$ 0.01 | -58.14 $\pm$ 0.01 | 437.02${}_{-2.25}^{+2.00}$ | 2021.17 $\pm$ 0.18
300869262 | 117.18 $\pm$ 0.01 | -70.14 $\pm$ 0.01 | 520.21${}_{-2.97}^{+2.90}$ | 2021.27 $\pm$ 0.21
150431816 | 97.36 $\pm$ 0.01 | -61.04 $\pm$ 0.01 | 686.37${}_{-4.98}^{+4.84}$ | 2021.29 $\pm$ 0.26
382159540 | 81.02 $\pm$ 0.01 | -56.50 $\pm$ 0.01 | 415.38${}_{-1.74}^{+2.31}$ | 2021.32 $\pm$ 0.18
278731442 | 99.56 $\pm$ 0.01 | -55.79 $\pm$ 0.01 | 297.63${}_{-1.11}^{+0.91}$ | 2021.37 $\pm$ 0.13
278684349 | 99.23 $\pm$ 0.01 | -57.01 $\pm$ 0.01 | 350.63${}_{-1.33}^{+1.32}$ | 2021.40 $\pm$ 0.14
220424430 | 72.28 $\pm$ 0.01 | -57.46 $\pm$ 0.01 | 415.09${}_{-2.21}^{+2.05}$ | 2021.42 $\pm$ 0.19
349972412 | 114.47 $\pm$ 0.01 | -62.08 $\pm$ 0.01 | 336.72${}_{-1.25}^{+1.39}$ | 2021.43 $\pm$ 0.15
350954265 | 90.81 $\pm$ 0.01 | -55.48 $\pm$ 0.01 | 344.91${}_{-1.00}^{+1.02}$ | 2021.50 $\pm$ 0.11
Table 2: All 32 targets of interest found within 0.5 ly of the SN 1987A
Ellipsoid at the mid-time of their TESS observing cycle, arranged
chronologically by crossing time with the Ellipsoid. The twelve targets on the
top section of the table were on the Ellipsoid in Cycle 1. The twenty targets
on the bottom section of the table belong to Cycle 3. The TICID column shows
the TESS ID for each object. $RA$ and $Dec$ values and uncertainties were
obtained from TESS and Gaia data. The distances, $d_{1}$, and their
uncertainties were retrieved from Bailer-Jones et al. (2021).The Ellipsoid
crossing times, $t_{cross}$, and their uncertainties were computed using the
methods described in Section 3. All values were rounded to the hundredth
decimal place for visual simplicity and consistency.

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