#  Unbound Close Stellar Encounters in the Solar Neighborhood

Bradley M. S. Hansen Mani. L. Bhaumik Institute for Theoretical Physics,
Department of Physics and Astronomy, University of California, Los Angeles,
CA, 90095<EMAIL_ADDRESS>
###### Abstract

We present a catalog of unbound stellar pairs, within 100 pc of the Sun, that
are undergoing close, hyperbolic, encounters. The data are drawn from the GAIA
EDR3 catalogue, and the limiting factors are errors in the radial distance and
unknown velocities along the line of sight. Such stellar pairs have been
suggested (Hansen & Zuckerman, 2021) to be possible events associated with the
migration of technological civilisations between stars. As such, this sample
may represent a finite set of targets for a SETI search based on this
hypothesis.

Our catalog contains a total of 132 close passage events, featuring stars from
across the entire main sequence, with 16 pairs featuring at least one main
sequence star of spectral type between K1 and F3. Many of these stars are also
in binaries, so that we isolate eight single stars as the most likely
candidates to search for an ongoing migration event – HD 87978, HD 92577, HD
50669, HD 44006, HD 80790, LSPM J2126+5338, LSPM J0646+1829 and HD 192486.
Amongst host stars of known planets, the stars GJ 433 and HR 858 are the best
candidates.

Technosignatures – Astrostatistics – Stellar kinematics

##  1 Introduction

The accelerating pace of discovery of planets around other stars, including
now the discovery of potentially habitable planets, has brought into clear
focus the question of how frequently intelligent, technologically advanced,
civilizations occur in the Galaxy. Searches for signatures of extraterrestrial
technology have a long history (Tarter, 2001), but suffer from an enormous
needle-in-the-haystack problem, in that our capacity to search stars at a deep
enough level is limited to a very small subset of the available stars (Tarter
et al., 2010; Wright et al., 2018a).

Recently, we (Hansen & Zuckerman, 2021) – hereafter HZ21 – discussed the
possibility that interstellar migration could be most efficiently pursued
during those brief episodes when unbound stars pass close to one another. The
energy costs of interstellar migration are prohibitive most of the time, but
can be substantially reduced during such encounters. Such considerations may
become particularly important for civilizations whose host stars are beginning
to leave the main sequence. Close encounters typically occur at intervals of a
few tens of million years (depending on exactly how close one wishes to get)
and remain optimal for a few thousand years. If a civilization were to avail
itself of such an opportunity, then the presence of two unbound stars in close
proximity might serve as a signpost for a substantial enhancement in
technological activity. A search for SETI signatures might then have greater
chance of success if directed towards such a sample.

The traditional approach of searching for extraterrestrial technology is to
search in the radio, optical or infrared bands for evidence of narrow-band
signals characteristic of technological sophistication. A fundamental issue in
searches of this kind is the one of target selection, as the parameter space
of potential sources is enormous (Wright et al., 2018b). Most searches are
either broad in terms of source selection, such as Howard et al. (2004);
Isaacson et al. (2017); Enriquez et al. (2017); Tellis & Marcy (2017); Maire
et al. (2019); Price et al. (2020), or focussed on systems known to host
exoplanets (Siemion et al., 2013; Margot et al., 2018; Harp et al., 2016). The
proposal in HZ21 is based on a specific hypothesis and thus defines a much
smaller, focussed, sample than other studies. A search for technosignatures in
these systems may also require some differences in search strategy, as
traditional SETI searches assume a source located on a planet, orbiting a
star. In the case of a large-scale migration, and with sufficient angular
resolution, sources may also be found to be localised between the stars in
question, and not solely in orbit around one star or the other.

Stellar interactions may also produce signals of astronomical interest even in
the absence of technological effects. The idea that close stellar passages
sculpt the Oort cloud was an integral part of the original model of this
population (Oort, 1950; Hills, 1981). Although the tidal field of the galaxy
is now held to be of greater importance in determining the properties of the
Oort cloud (Heisler & Tremaine, 1986), close stellar interactions are believed
to be responsible for temporary enhancements in the rate of influx of comets
into the Solar system, so-called ‘comet showers’ (Hut et al., 1987; Fernandez
& Ip, 1987; Weissman, 1996; Dybczyński, 2002).

In this paper we therefore seek to identify pairs of stars that meet the
criterion of being in close physical proximity, but which are gravitationally
unbound. These may serve as a possible target list for a SETI search – one
with the particular motivating hypothesis laid out in HZ21. To do this, we
draw on the results of the GAIA satellite, which has provided a detailed map
of parallaxes and proper motions for nearby stars. We search for pairs of
stars that have a finite probability of passing within $10^{4}$ AU of one
another – either in the recent past or near future. This threshold is chosen
to be such that these events are sufficiently uncommon (only $\sim 10^{-4}$ G
stars will be involved in such an encounter at any one time) to justify the
hypothesis in HZ21 that migration is limited to rare events. In section 2 we
describe the selection of a sample of stellar pairs that satisfy the above
criterion, and which lie within 100 pc of the Sun. The accuracy of our stellar
matches decreases with distances and we choose the threshold of 100 pc to be
large enough to yield a sample of reasonable size while mitigating the
uncertainties. In section 3 we discuss possible technological and
astrophysical signatures associated with these events.

##  2 Close but unbound pairs

The GAIA Early Data Release 3 – EDR3 –(Gaia Collaboration et al., 2016, 2021a;
Lindegren et al., 2020), provides parallaxes and proper motions for several
billion stars surrounding the Sun. With distances, relative angular
separations, and relative velocities, we may try to project the encounter
histories of pairs of stars into the near future and recent past, to estimate
how close they have/will come. Several studies have investigated the sample of
wide binaries identifiable in the GAIA data (Hartman & Lépine, 2020; Gaia
Collaboration et al., 2021c; El-Badry et al., 2021). Our interest is in the
systems these analyses reject, in that we wish to identify systems that are in
close physical proximity but which are not gravitationally bound to one
another.

Our first cut is to select all pairs of stars which have parallaxes whose
naive conversion to distance places the radial distances within 0.5 pc of one
another, and whose projected separations on the sky lie within $3\times
10^{4}$AU, where we use the closest of the two parallaxes to convert angular
separation into distance. This procedure is dictated by the fact that the
uncertainty in the radial distance is greater than the uncertainties in the
angular separation. We adopt this relatively loose cut to define a sample that
we will refine further below. We will also restrict our sample to those stars
within 100 pc of the Sun. This is also dictated by the increase in error in
the radial separation as the distance increases. Finally, we use the GAIA
astrometric error cut astrometric_sigma5d_max$<1$ to remove those sources with
potentially problematic astrometry. Additional cuts based on photometric
precision can produce cleaner stellar samples (e.g. Gaia Collaboration et al.
(2018)), but we want our initial selection to err on the side of inclusion,
because our final candidate sample will be subject to additional quantitative
vetting.

This first cut identifies stars that are currently in close physical
proximity. Many of these will be genuine bound binaries. The GAIA catalogue
also provides proper motions, which can be converted into velocities. At the
separations of interest, the orbital velocity of stellar mass binaries is much
less the expected magnitude of relative velocities of unbound disk stars, so
we expect that genuinely bound objects should exhibit common proper motions to
a level that distinguishes them from unbound pairs. The quantification of
proper motion errors has its own uncertainties, but these are small enough
that one can identify binary samples of high fidelity (El-Badry et al., 2021).

Figure 1 shows the how the relative velocity of stars varies with their
relative separation from their nearest neighbours on the sky. We plot relative
velocity versus separation on the sky for all pairs whose distances are within
0.5 pc of each other and whose projected sky-plane separations are $\Delta
r_{\perp}<2\times 10^{5}$ AU. As noted by prior authors, GAIA proper motions
effectively separate binaries (towards the lower left of the diagram) from the
unbound pairs (towards the upper right of the diagram). The three solid red
lines indicate the escape velocity from the corresponding orbital separation,
for binaries of total mass $0.1M_{\odot}$, $1M_{\odot}$ and $10M_{\odot}$,
from bottom to top. The projected separation shown here is less than, or equal
to, the true separation of the corresponding binary and so systems that lie
below these curves have relative velocities consistent with orbital motion of
bound pairs. The sample to the upper right represents the pairs of stars that
are moving too fast to be gravitationally bound to one another. This group has
a small tail to low projected separations, and it is in this group that we are
interested.

There is also a substantial population of stars that lie above the uppermost
red line. Although these appear to be contiguous to the bound sample, their
interpretation would require system masses well in excess of $10M_{\odot}$.
Although this is technically possible, their frequency is unrealistic within
our understanding of stellar demographics and lifetimes. We have thus
investigated this population in more detail. In particular, we determine that
the bulk of these pairs have relative motions that are contaminated by orbital
motions of an unresolved binary in at least one member of the pair. To support
this, we downloaded, for each star, the GAIA ruwe (renormalised unit weight
error) parameter, which measures the excess astrometric noise remaining after
the astrometric fit of the position and motion of the source in question. A
value of ruwe$>1.4$ is considered to be an indicator of unmodelled astrometric
noise and a signature of a partially resolved binary. For the sources that lie
between the dashed and dotted lines in Figure 1, we find that 56/67 (84%) of
these sources have ruwe$>1.4$. We conclude that the bulk of the points at the
upper edge of the bound sample are hierarchical triples (at least), in which
the orbital motion of an unresolved binary has resulted in a biased
measurement of the relative motion of the wider pair. We therefore adopt a
criterion given by the dotted line in Figure 1. Our initial sample includes
pairs where $\Delta r_{\perp}<3\times 10^{4}$ AU and $\Delta v>8$ km s-1, but
with a higher threshold of $\Delta v>10$ km s-1 interior to $\Delta
r_{\perp}<5\times 10^{3}$ AU. This is to exclude the two extreme systems
featuring HD 1917 and HD 214165, both of which have $\Delta V>8$ km s-1 but
ruwe$>1.4$. Ultimately this leaves us with an initial sample of 446 stellar
pairs.

Figure 1:  The points show all pairs of stars within 100 pc, whose projected
separations are less than $2\times 10^{5}$ AU. The solid red lines indicate
the escape velocity from an orbit of the stated $\Delta r_{\perp}$, for three
different total system masses – $0.1M_{\odot}$ (lowest curve), $1M_{\odot}$
and $10M_{\odot}$ (uppermost line). The dotted lines enclose the subset of 446
stellar pairs that we select for further study. The points between the dashed
line and the dotted lines show a very high incidence of unmodelled astrometric
noise and are likely to be hierarchical triples.  Figure 2:  The quantity
$\Delta D$ represents the difference in distance to two members of a close
pair, as calculated using the model of Bailer-Jones et al. (2021). The
quantity $\Delta D_{\pi}$ indicates the corresponding radial separation using
the simple conversion from parallax $D=1000pc/\pi$ and $\delta D_{\pi}$ is the
distance error based on the parallax measurement – averaged over the two
members of the binary. $\Delta\theta$ is the angular separation on the sky for
each pair. The size of each point scales as the square root of the parallax to
each source. This demonstrates that the change in radial separation is small
in many cases, but does become significant – relative to the nominal error –
in some cases.  Figure 3: The black points show the choices of relative radial
distance and relative radial velocities, for a Monte Carlo simulation of the
possible trajectories for two pairs in our sample. The distances are chosen
using the measured uncertainties from Bailer-Jones et al. (2021), and the
relative radial velocities are drawn from the distributions in the Galactic
model of Rybizki et al. (2020). The red points indicate those trajectories
that allow the two stars to pass within $10^{4}$ AU of each other. On the
left, we show the results for the pair in our sample that allows for the
closest possible passage, namely the pair 2MASS J07315294+0633251 and 2MASS
J07321651+0628319. On the right, we show the results for the pair that has the
greatest probability of having a passage within $10^{4}$AU, namely 2MASS
J05100438+3306067 and 2MASS J05100212+3303535. In neither of these two cases
do we know the radial velocities of the stars in question.

The third, radial, component of the separation is the one with the largest
error, even with the unprecedented accuracy of the GAIA parallaxes.
Furthermore, the systematic errors in the astrometry can vary depending on how
crowded the field is. The angular separations of the pairs considered here can
extend to $>20^{\prime}$, and so we adopt the corrected distances from Bailer-
Jones et al. (2021) to ensure a uniform treatment for our entire sample.
Bailer-Jones et al. (2021) provide improved distance estimates to GAIA sources
using two methods. The geometric method adopts a prior distribution based on
the Galactic distribution of stars in that direction, while the photogeometric
estimate includes information from the photometry of the stars in question,
and their expected position in the color-magnitude diagram. We therefore
calculate the probability distribution of true separations for our stellar
pairs using the photogeometric distance distributions from Bailer-Jones et al.
Figure 2 shows the difference between the revised distances and the naive,
parallax-based distance $D_{\pi}=1000AU/\pi$, where $\pi$ is the parallax in
units of milliarcseconds. While the difference is well within the errors for
many systems, there is also a notable fraction for which the correction is
important.

In order to determine the true distance of closest approach in each encounter,
we need to specify the one remaining component – the relative radial velocity.
While GAIA does provide radial velocities for a subset of stars, most of the
ones in question here are not part of that sample. To determine the radial
velocities, we sample the radial velocities contained in the Galactic model
used by Bailer-Jones et al. (2021) to determine the distance probabilities.
This model is described in Rybizki et al. (2020), and we query the resulting
mock catalog for each pair. For each object, we draw all radial velocities for
stars with $2^{\circ}$ of the position to determine the radial velocity
distribution. We also restrict our query to model stars within $\pm 5$
magnitudes of the object. If two members of a pair have significantly
different magnitudes, they may then have slightly different line-of-sight
velocity dispersions, but there are no cases with large discrepancies. For
each choice of radial velocity, we then project a straight-line trajectory
forwards and backwards in time and isolate the distance and time of closest
approach. The encounters we consider here are significantly hyperbolic and so
deviations from straight trajectories are negligible. For each pair, we
evaluate $10^{7}$ trajectories, sampling the relative distance and relative
velocity distributions determined above. Our interest is in those systems
which pass the closest, as these will be the ones that would facilitate
interstellar migration. To score the relative attractiveness of each system,
we use two metrics. In the first, we count the number of trajectories that
result in a passage closer than $10^{4}$ AU and quantify the fraction
$P_{\mu}$ of all resulting trajectories that pass within this distance. A
second metric is to use the average $\langle 1/r_{min}^{2}\rangle$, where
$r_{min}$ is the minimum approach distance for each trajectory, and the
average is performed over all trial trajectories. The rationale for this
metric is that we want to select those systems that require the least energy
expenditure per unit mass for a transfer between the stars. A smaller
$r_{min}$ will require a smaller velocity to cross it in a finite time, so
that we anticipate the energy will scale $\propto r_{min}^{2}$. To favor the
minimum energy, we therefore seek to maximize the average of $1/r_{min}^{2}$
over all our trajectories.

For inclusion in our sample, we require $P_{\mu}>0.01$ or $\langle
1/r_{min}^{2}\rangle>0.1$ (where $r_{min}$ is normalised to $10^{4}$AU). We
have 115 pairs which satisfy both criteria, 13 which satisfy the first only
and 9 which satisfy the latter only. Taking these together, our final sample
contains 137 of the original 446 pairs. We also find that 30 of these pairs
involve at least one star that has a possible bound companion in the GAIA
sample. In some cases we find that both members of the binary are counted
independently as having an encounter with the third star. After accounting for
these duplications, we find 132 independent encounters, 28 of which involve
multiple stars. Of these, four encounters feature pairs in which both members
have proper motion companions.

We have also examined the ruwe parameter for the 269 individual stars involved
in the systems of our final sample, and find that 38 of them exhibit a value
$>1.4$, suggesting that about 14% of our stellar sample contains partially
resolved binary stars. This is a representative value for the stellar
population as a whole, and reinforces our conclusion – in Figure 2 – that the
upper envelope of the bound population is composed primarily of hierarchical
triples, because of the much higher fraction with ruwe$>1.4$.

Figure 3 illustrates the process by which we estimate the metrics $P_{\mu}$
and $\langle 1/r_{min}^{2}\rangle$. We show two examples. On the left, we show
the case of the closest passage found in our sample – between the pair of
stars 2MASS J07315294+0633251 and 2MASS J07321651+0628319. The proper motions
and astrometric separations are also sampled with their assumed errors,
although their uncertainties have a small effect compared to the radial
distance uncertainty. The right panel shows the case where we find the largest
probability of an encounter within $10^{4}$AU, namely the pair 2MASS
J05100438+3306067 and 2MASS J05100212+3303535. The reason for the higher
probability can be seen from the dimensions of the x-axis – the estimated
distances for these two stars are much closer to one another than most of the
other stars in the sample (their mean distances are only 0.07 pc discrepant).

###  2.1 Encounters involving Sun-like Stars

We are particularly interested in close passages featuring Sun-like stars, as
the motivation for this sample is to identify cases where Earth-analogue
technological civilizations might attempt to migrate to another star.
Therefore, Table 1 collects the information for that subset of the full sample
of 132 encounters which feature at least one star with $M_{G}<6$, where
$M_{G}$ is the absolute magnitude in the broad GAIA passband G. The spectral
classifications (taken from the literature) for the resulting stars range from
K1–F3, and so these represent an approximately Sun-like sample. The color
$B-R$ represents the $G_{BP}-G_{RP}$ color obtained by integrating the GAIA
low resolution blue and red prism spectra. Distances are the photogeometric
distances from Bailer-Jones et al. (2021). The time of closest approach is
relative to today – positive values mean that the closest approach will occur
in the future, while negative values indicate it already occurred. Co-
ordinates for the brighter member of each pair are given in the finding charts
in the Appendix.

Table 1:  The sample of close, unbound pairs featuring Sun-like stars, ordered
in increasing minimum possible close approach distances.

Index | $\Delta r$ | $T_{min}$ | $P_{\mu}$ | $P_{\rm rv}$ | $\langle\left(\frac{10^{4}AU}{\Delta r}\right)^{2}\rangle$ | Name (Type) | $D$ | $M_{G}$ | $B-R$ | $V_{\rm rad}$ | Index | Name (Type) | $D$ | $M_{G}$ | $B-R$ | $V_{\rm rad}$ | Notes
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (AU) | (yrs) |  |  |  |  | (pc) |  |  | (km s-1) |  |  | (pc) |  |  | (km s-1) |
1 | 1367 | +1750 | 0.05 | 0.03 | 0.55 | HD 157393 (F8) | 59.43${}^{+0.17}_{-0.20}$ | 3.74(2) | 0.65 | -21.9(4) |  | LSPM J1722+1513 | 59.15${}^{+0.09}_{-0.09}$ | 10.73(1) | 2.70 |  | (1,4)
2 | 1413 | -153 | 0.02 | 0.02 | 0.20 | HD 159902 (G5V) | 49.55${}^{+0.22}_{-0.27}$ | 4.81(2) | 0.82 | +5.4(4) |  | CD-45 11747 | 49.11${}^{+0.03}_{-0.04}$ | 5.95(1) | 1.07 | -32.0(5) | (1,2,4)
3 | 2032 | -4194 | 0.14 | 0.02 | 1.07 | HD 187154 (G1V) | 44.98${}^{+0.05}_{-0.06}$ | 4.38(1) | 0.78 | -32.3(2) |  | HD 187084 (K1V) | 45.27${}^{+0.05}_{-0.05}$ | 5.64(1) | 1.01 | +9.5(2) | (1)
4 | 2957 | \+ 15250 | 0.15 | 0.20 | 0.63 | HD 87978 (G6IV) | 40.84${}^{+0.06}_{-0.05}$ | 4.92(1) | 0.84 | 28.7(2) |  | J10090601-1109290 | 40.60${}^{+0.6}_{-0.4}$ | 13.5(1) | 4.12 |  | (5)
5 | 3193 | +1600 | 0.01 | 0.03 | 0.08 | HD 92577 (F2V) | $94.66^{+0.32}_{-0.25}$ | 3.14(2) | 0.51 | -8.9(6) |  | J10411261-1418509 | $93.99^{+0.86}_{-0.73}$ | 12.09(4) | 3.06 |  |
6 | 3849 | +3000 | 0.12 | $<0.01$ | 0.55 | TYC 5786-123-1 | $87.93^{+0.11}_{-0.11}$ | 5.89(1) | 1.14 | +29.0(7) |  | J21335912-0746358 | $87.86^{+0.64}_{-0.52}$ | 12.59(3) | 3.36 |  | (4,6)
7 | 6341 | +10152 | 0.10 | 0.14 | 0.28 | HD 143332 (F5V) | 99.07${}^{+0.36}_{-0.40}$ | 2.88(2) | 0.70 | -29.8(2) |  | J16000455-0712125 | 99.95${}^{+0.79}_{-0.70}$ | 11.23(4) | 2.97 |  | (1)
8 | 6374 | +3994 | 0.10 | 0.09 | 0.28 | HD 26770 (G0V) | 64.11${}^{+0.12}_{-0.14}$ | 3.99(1) | 0.70 | +17.3(6) |  | J04132532-2830440 | 63.90${}^{+0.15}_{-0.13}$ | 11.96(1) | 3.12 |  | (2)
9 | 6402 | -151 | 0.06 | 0.07 | 0.19 | HD 50669 (G8IV) | 94.17${}^{+0.13}_{-0.13}$ | 3.87(1) | 0.86 | +73.0(4) |  | J06540919-0148118 | 93.86${}^{+0.37}_{-0.43}$ | 10.94(2) | 2.48 |  |
10 | 6739 | +2538 | 0.07 |  | 0.20 | HD 44006 (G0V) | $96.04^{+0.18}_{-0.17}$ | 3.93(1) | 0.69 |  |  | J06191745-0020445 | $95.91^{+0.71}_{-0.51}$ | 8.71(3) | 2.26 |  | (5)
11 | 7819 | -357 | 0.06 | 0.05 | 0.33 | HD 210974A/B (K0V) | 85.80${}^{+0.17}_{-0.20}$ | 5.90(1) | 1.01 | -52.3(3) |  | UCAC2 18317515 | 85.75${}^{+0.13}_{-0.10}$ | 7.47(1) | 1.72 | -13.7(4) | (2)
12 | 8774 | -6456 | 0.10 | 0.16 | 0.29 | HD 80790 (F6V) | 54.68${}^{+0.05}_{-0.06}$ | 3.25(1) | 0.69 | -19.4(2) |  | J09191695-5901597 | 54.92${}^{+0.22}_{-0.22}$ | 11.08(2) | 2.83 |  | (7)
13 | 8832 | +1195 | 0.07 | 0.05 | 0.37 | LSPM J2126+5338 | 53.48${}^{+0.03}_{-0.03}$ | 5.97(1) | 1.10 | -15.1(46) |  | J21265700+5343001 | 53.50${}^{+0.07}_{-0.10}$ | 11.28(1) | 3.01 |  | (3)
14 | 9831 | -649 | 0.006 | $<0.01$ | 0.14 | LSPM J0646+1829 | 86.05${}^{+0.10}_{-0.12}$ | 5.83(1) | 1.03 | +75.2(8) |  | J06464503+1828391 | 86.13${}^{+0.41}_{-0.36}$ | 11.37(2) | 2.88 |  |
15 | 13033 | +1250 | 0 | 0 | 0.37 | HD 29836 (GV) | 42.22${}^{+0.03}_{-0.04}$ | 3.84(1) | 0.83 | 13,3(1) |  | LP 415-358 | 42.04${}^{+0.09}_{-0.07}$ | 12.32(1) | 3.10 |  | (2)
16 | 26072 | +850 | 0 | 0 | 0.13 | HD 192486 (F2V) | 43.94${}^{+0.04}_{-0.05}$ | 3.24(1) | 0.53 | -8.9(2) |  | HD 192527(G5V) | 44.02${}^{+0.05}_{-0.04}$ | 5.07(1) | 0.86 | -8.8(2) |

Note. — (1) Proper motion anomaly between HIPPARCOS and GAIA DR2 suggests
binarity for the brighter member of this pair; (2) The brighter of the two
members of this encounter has a proper motion companion; (3) The fainter of
the two members of this encounter has a proper motion companion; (4) The
brighter of the two members of this encounter shows excess astrometric noise
(5) The fainter of the two members of this encounter shows excess astrometric
noise (6) Both members of this encounter have proper motion companions; (7)
Identified as a binary in the literature;

There are also radial velocities available for many of the brighter stars in
this sample, and these are listed in Table 1. Of the 16 pairs in Table 1, 15
have at least one radial velocity available, and four pairs have known radial
velocities for both members. The radial velocities are drawn from the GAIA
EDR3 data, except for those for HD 92577 and HD 26770, which are drawn from
Gontcharov (2006). In no case do we mix velocities from different references,
and so we do not have to consider the possibilities of differences in offsets
or definition. Using this additional information we have calculated a second
probability of encounter for these objects (Prv, as opposed to the probability
Pμ, which is based purely on the measured proper motion). In the cases where
both radial velocities are known, we do not need to assume any distribution
for line-of-sight velocities, but simply repeat our integration of
trajectories using the known relative velocity and sampling only within the
quoted errors. In cases where the radial velocity is known for only one
member, we sample the distribution of radial velocities for the other star,
using the mock catalog of Rybizki et al. (2020) as described earlier. In
general terms, the inclusion of this extra information lowers the
probabilities of close encounter. In fact, after including the radial
velocities, 2/16 of our systems drop below the 1 per cent probability
threshold. The product $\Pi_{i=1}^{16}(1-P_{\rm rv})_{i}=0.37$ indicates that
there is a 37 per cent chance that none of these 16 systems have a close
passage within $10^{4}$AU, or that there is a 63 per cent chance that at least
one system does. More detailed examination of the combinatorics indicates that
there is a 39 per cent chance of one system passing close enough, an 18 per
cent chance that two pass close enough, and a 6 per cent chance that more than
2 of these systems will pass within $10^{4}$ AU of each other.

Figure 4 shows the photometry for these 16 pairs in Table 1. The photometry
for the brighter (yellow) and fainter (red) members of these pairs are
compared to that of the field sample within 100 pc. As expected, the
encounters are primarily with lower mass stars, although there are a few pairs
featuring similar stars.

Figure 4:  The small black points represent the population of well measured
stars from GAIA within 100 pc of the Sun. In this context, well measured means
fractional parallax errors of less than 10%, 5$\sigma$ astrometric error
parameter $<$0.1 and photometric precision in G $<0.02$. The yellow points
represent the brighter members of pairs in which one of the stars has absolute
GAIA magnitude $M_{G}<6$. The red points represent the fainter members of
these pairs.

Another important element of the HZ21 argument is that close stellar
encounters represent the best chance for migration in the case of
technological civilizations that orbit single stars. If the planet orbits a
star in a multiple system, then the bound companions are much easier targets
and more likely to be long-lived, given the stellar demographics. To that end,
it is important to constrain the binarity of the bright stars in our sample.

Indeed, four of the systems in Table 1 feature a bright star which has a high
probability proper motion companion in the GAIA EDR3 database. In cases where
our search independently flagged encounters with different members of
binaries, we report only the encounter featuring the brightest star (so that
each overall encounter between bound systems is counted only once).
Furthermore, four stars also show a proper motion anomaly between the
measurements of HIPPARCOS and GAIA DR2 (Kervella et al., 2019), which is taken
to be a signature of binarity as well. Finally, one more system is identified
as a binary in the literature (Tokovinin, 2014). Six of the stars in this
sample also have ruwe $>1.4$, which may also indicate binarity. Overall, 8/16
of the bright stars in this sample show evidence for binarity. Furthermore,
this census is likely to undercount companions, as our constraints are
primarily for wide binary members and closer companions may still remain
undetected.

###  2.2 The lower mass sample

We have compiled the rest of the likely close encounters (those that feature
no stars with $M_{G}<6$) in Table 2. In this table we calculated only the
probability of encounter on the basis of proper motions (Pμ) as radial
velocities are not available for most of the stars in the lower mass sample.
This leaves us with 116 encounters, to go with the 16 in the bright star
sample.

With this sample we can also examine the overall demographics of the stars
involved in these close encounters. The mass distribution of the stellar
population from Tables 1 and 2 is shown in Figure 5. Stellar masses are based
on the position of each star in the GAIA magnitude system, and a comparison
with the MESA models (Choi et al., 2016). Seven of the pairs contain a white
dwarf member. The result, as expected, is strongly peaked between
$0.1$–0.2$M_{\odot}$, and appears quite consistent with a random sampling of
the field stellar mass function.

With the larger number of systems, here, the probability that none will pass
with $10^{4}$AU is negligibly small ($\sim 7\times 10^{-7}$). A perhaps more
practical logistics question is to explore how many of these systems need one
explore to have a realistic chance of seeing a passage within $10^{4}$ AU. If
we calculate probabilities in Table 2 starting from the first entry, we need
only go to the twentieth entry to have a 50% chance of two or more close
passages. This is consistent with the order of magnitude estimate that about 1
in 10 of the systems in Tables 1 and 2 are expected to actually pass within
$10^{4}$ AU of each other. How does this compare to our expectations? If we
adopt the local stellar encounter rate calculation in the Solar neighbourhood
as estimated in HZ21, using a local stellar density $n_{*}$ and assuming the
dispersion in relative velocities is $\sqrt{2}\sigma$, where $\sigma$ is the
local average velocity dispersion in the Galactic disk, we estimate the rate
of encounter, per star, is

$\Gamma=0.016\,{\rm Myr^{-1}}\left(\frac{n_{*}}{0.1\,{\rm
pc}^{-3}}\right)\left(\frac{R_{0}}{10^{4}{\rm
AU}}\right)^{2}\left(\frac{\sigma}{48\,\rm kms^{-1}}\right)$ (1)

If we estimate time of encounter to be $\sim 2R_{0}/V\sim 1400$ years, then we
estimate $\sim 9$ ongoing encounters within the volume of 100 pc of the Sun.
This suggests our sample contains a significant fraction of the close
encounters happening in this volume.

Figure 6 shows the distribution of distances from the Sun shown by the
cumulative sample in Tables 1 and 2. We see that the bulk of our targets lie
at distances farther than the samples (Isaacson et al., 2017) used by the
stellar surveys of Project Phoenix (65 pc) and Breakthrough Listen (5 pc
–complete, and 50 pc –representative). The distribution of the sample with
distance scales approximately with the enclosed volume out to our distance
limit of 100 pc. This is consistent with estimates of GAIA EDR3 completeness
(Fabricius et al., 2021; Gaia Collaboration et al., 2021b, d) , which suggest
that the survey is highly complete between the magnitude limits $20<G<3$,
albeit with some degredation in crowded regions of the sky. Our use of a
Galactic model to refine our distances helps to mitigate the dangers of
crowded regions and none of the stars in our sample are bright enough to
saturate the GAIA photometry. Furthermore, the separations of interest to us
are much larger than the angular scales at which GAIA blends the images of
neighbouring stars – see Figure 2.

Table 2:  The sample of close, unbound pairs featuring lower mass stars,
ordered in increasing minimum possible close approach distances. In cases
where the star is not included in the 2MASS database, identifiers are either
from SDSS (start with ”S”) or from the Gaia DR2 catalog (start with ”G”),
followed by an index. The names themselves, in these cases, are too long to
fit the column width and so are given in the notes at the end. Spectral types
are indicated in the notes with the notation [1/2], when known, and those
members of the encounter pair that are members of multiple systems are
indicated by (bin-i) in the notes section, where i indicates either the first
or second entry in the row.

Name (Type) | $D$ | MG | B-R | Name | $D$ | MG | B-R | $\Delta r$ | $T_{min}$ | Prob | $\langle\left(\frac{10^{4}AU}{\Delta r}\right)^{2}\rangle$ | Notes
---|---|---|---|---|---|---|---|---|---|---|---|---
2MASS | (pc) |  |  | 2MASS | (pc) |  |  | (AU) | (yrs) |  |  |
J07315294+0633251 | 56.46${}^{+0.05}_{-0.05}$ | 9.58(1) | 2.46 | J07321651+0628319 | 56.28${}^{+0.44}_{-0.47}$ | 11.74(4) | 3.29 | 22 | +10050 | 0.17 | 13.2 |
J22314220+0023112 | 96.06${}^{+0.34}_{-0.30}$ | 10.24(2) | 2.65 | J22313478+0027179 | 96.55${}^{+1.35}_{-1.73}$ | 12.97(9) | 3.18 | 118 | -3701 | 0.03 | 2.73 | [$\cdots$/M4V]
J01024057+1610560 | 93.38${}^{+0.37}_{-0.37}$ | 10.03(2) | 2.43 | J01023204+1612129 | 92.92${}^{+0.51}_{-0.53}$ | 10.76(3) | 2.72 | 171 | -4601 | 0.10 | 6.09 |
G1 | 55.29${}^{+0.58}_{-0.46}$ | 14.87(5) | 1.01 | TYC 1568-917-1 | 54.88${}^{+0.05}_{-0.05}$ | 7.62(1) | 1.65 | 381 | +2593 | 0.09 | 3.35 |
S1 | 45.54${}^{+0.28}_{-0.28}$ | 14.84(3) | 0.93 | J00352199+2006142 | 45.45${}^{+0.09}_{-0.07}$ | 11.88(1) | 3.04 | 398 | -2698 | 0.14 | 5.20 | (bin-1)
J19200086-2241531 | 94.27${}^{+0.46}_{-0.46}$ | 10.68(2) | -0.24 | J19195587-2242109 | 92.92${}^{+0.50}_{-0.53}$ | 11.42(3) | 2.91 | 451 | +950 | 0.09 | 3.11 | (bin-1)
J07084492+5544576 | 97.31${}^{+0.63}_{-0.77}$ | 10.26(4) | 2.48 | J07085805+5545261 | 96.95${}^{+1.33}_{-1.37}$ | 12.85(7) | 3.41 | 498 | -2950 | 0.04 | 1.22 |
GD 84 | 35.45${}^{+0.04}_{-0.04}$ | 12.41(1) | 0.103 | LP 162-1 | 35.33${}^{+0.02}_{-0.03}$ | 10.62(1) | 2.85 | 522 | +4034 | 0.20 | 5.76 | (1),[WD/M4]
J19545686-6724041 | 57.15${}^{+0.43}_{-0.39}$ | 9.06(4) | 2.29 | J19544917-6719559 | 56.91${}^{+0.28}_{-0.24}$ | 8.82(3) | 2.12 | 587 | +1148 | 0.04 | 0.95 | (2),(bin-1)
J06433851-6417204 | $93.19^{+1.38}_{-1.19}$ | 10.76(6) | 2.97 | J06434304-6417291 | $92.84^{+0.18}_{-0.13}$ | 9.85(1) | 2.47 | 637 | -845 | 0.04 | 1.00 |
J06363407+0806450 | 40.85${}^{+0.09}_{-0.08}$ | 13.08(1) | 3.50 | J06364675+0808373 | 40.60${}^{+0.04}_{-0.05}$ | 11.48(1) | 2.58 | 662 | -1897 | 0.12 | 2.72 |
J10520964-0548506 | 91.19${}^{+0.72}_{-0.62}$ | 11.91(4) | 3.11 | J10515946-0549049 | 90.87${}^{+0.48}_{-0.45}$ | 10.65(3) | 2.72 | 738 | +898 | 0.02 | 0.17 |
J09051507-2342573 | $88.57^{+0.32}_{-0.29}$ | 11.85(2) | 3.13 | J09051785-2341229 | $88.68^{+1.24}_{-1.09}$ | 8.41(6) | 1.97 | 810 | +744 | 0.03 | 0.49 |
J08245980-1745049 | 89.29${}^{+0.56}_{-0.59}$ | 12.18(3) | 2.52 | J08244862-1741209 | 88.65${}^{+0.73}_{-0.73}$ | 12.50(4) | 3.15 | 976 | -3892 | 0.04 | 0.60 | (bin-1)
J05295170-3006557 | 98.46${}^{+0.62}_{-0.500}$ | 12.07(3) | 3.24 | J05295196-3003595 | 98.31${}^{+0.58}_{-0.62}$ | 12.39(3) | 3.35 | 1048 | -2951 | 0.07 | 1.10 |
J04590411+3804240 | 77.42${}^{+0.94}_{-0.92}$ | 13.40(6) | 3.58 | J04592452+3801272 | 76.95${}^{+0.28}_{-0.21}$ | 11.17(2) | 2.65 | 1074 | +2902 | 0.05 | 0.66 | (bin-2)
J08483006-0745120 | 81.70${}^{+0.35}_{-0.33}$ | 11.64(2) | 3.10 | J08482010-0747371 | 81.65${}^{+0.16}_{-0.14}$ | 7.51(1) | 1.67 | 1110 | -5652 | 0.20 | 2.23 |
J05381466+3056067 | 75.01${}^{+0.52}_{-0.56}$ | 12.39(4) | 3.50 | J05380946+3055453 | 74.63${}^{+0.11}_{-0.10}$ | 8.65(1) | 2.02 | 1196 | -1298 | 0.12 | 1.57 |
J06300702+7343471 | 98.73${}^{+2.0}_{-1.65}$ | 13.9(1) | 3.60 | J06302012+7342514 | 97.79${}^{+0.47}_{-0.54}$ | 9.52(3) | 2.32 | 1215 | -4745 | 0.04 | 0.51 |
TYC 5133-940-1 | 94.13${}^{+0.14}_{-0.14}$ | 6.27(1) | 1.22 | J19134957-0217557 | 94.04${}^{+0.59}_{-0.51}$ | 11.89(3) | 3.24 | 1272 | +4398 | 0.20 | 0.38 | (bin-1)

Note. — (1) GD 84 is referenced in papers about low mass companions (2) These
sources are in a very confused region in DSS/2MASS. G1=Gaia DR2
4522020089271002496; S1=SDSS J003542.03+200938.4 This table shows the first
twenty entries. The full table is available in machine readable format online.

Figure 5:  The histogram shows masses estimated for the stars in Tables 1 and
2, based on the GAIA magnitudes and colours, and using stellar models and
colours from Choi et al. (2016). The bin at negative stellar mass represent
the white dwarfs in the sample. White dwarfs of all masses are counted in this
bin. We see that the sample is dominated by the lowest mass stars.  Figure 6:
The histogram shows the cumulative distribution of counts of stars versus
distance in our sample. The dotted line indicates the function
$P(D)=(D/100\,{\rm pc})^{3}$, which represents the expected distribution for a
volume complete sample of uniform density, out to 100 pc. The short dashed
line indicates the distance limit of the Project Phoenix search for
Technosignatures, while the two long dashed lines indicate the two sub-samples
of the original Breakthrough Listen project (Isaacson et al., 2017).

###  2.3 Notes on Individual Systems

The 132 encounters identified here involve a variety of stellar systems.
Figure 7 shows the GAIA bandpass colour-magnitude diagram for the complete
set. A few notable systems are

Figure 7:  This shows the stellar parameters of all the stars involved in
close, unbound, stellar encounters, from Tables 1 or 2. The red horizontal
dashed line indicates an approximate dividing line between true hydrogen
burning stars and brown dwarfs (although the exact location would be age and
metallicity dependant). The diagonal dotted line indicates the division
between white dwarfs and main sequence stars. A handful of noteworthy objects
are indicated, and discussed in the text.

  * •

HD87978 is classified as G6IV and so should be starting to leave the main
sequence, and therefore is the perfect archetype of the rationale in HZ21 for
a system in which a civilisation might be motivated to make an attempt at
interstellar migration. It is also the system in Table 1 with the highest
probability of an encounter within $10^{4}$ AU. One potentially complicating
factor is that the star with which it is having an encounter appears to show
evidence for astrometric noise and so may be a partially resolved binary. How
this influences its suitability as a migration destination will depend on the
actual parameters of the system.

  * •

The star HD50669 is classified as G8IV and does indeed lie slightly to the red
of the upper main sequence. This star is also starting to leave the main
sequence. This system also shows no sign of binarity. Unfortunately, given the
uncertainties in distances, it has only a 3 per cent chance of actually
passing within $10^{4}$ AU.

  * •

A comparison of the sample in Table 1 with the NASA Exoplanet Archive (Akeson
et al., 2013) shows no known exoplanets around these stars. One star –
HD143332 – is included in the Lick-Carnegie Radial velocity sample (Butler et
al., 2017), but has no reported planet. It does show a non-zero acceleration
term, however. None of the sample is recorded in the archives of the HARPS
survey (Trifonov et al., 2020) or the California Legacy Survey (Rosenthal et
al., 2021). This paucity is not entirely surprising, as the radial velocity
searches are strongly weighted towards nearby stars, and most of the stars in
this sample are too distant to be well represented.

  * •

On the lower main sequence, the star G45-11 lies above the main sequence, but
is also a known spectroscopic binary and certainly lies in the correct
location for a binary unresolved by the GAIA photometry. As the lower mass
member of an encounter featuring a K4V star (HIP 53175) this may still be a
viable candidate for a migration event, if a planetary system formed around
the higher mass star. Four stars lie above the lower main sequence in Figure 7
– three are suspected binaries. The fourth (2MASS J13344645-5959405) lies in a
region of the sky where source confusion is a significant concern.

  * •

The stars to the left of the diagonal dotted line in Figure 7 are likely to be
white dwarfs. These are less likely to be viable candidates for a migration
because they do not offer a long-term stable habitable environment. However,
none of the white dwarfs identified here are in encounters with G stars in
Table 1. They are all undergoing encounters with M stars, so could potentially
be the starting points for migration from civilisations that have survived the
ravages of stellar evolution.

  * •

One white dwarf system of note is that of GD-84, identified as a candidate
wide binary system by Farihi et al. (2005) but only tentatively, because the
proper motion measurement was compromised by confusion with a background star.
The GAIA proper motion is now able to rule this out as a bound companion.
However, the original candidate companion is not the other star in this
candidate encounter. We show a finding chart for this field in the Appendix.

  * •

The horizontal dashed line in Figure 7 indicates the approximate location of
the base of the Hydrogen burning sequence (this shows the $M_{G}$ for a solar
metallicity $0.1M_{\odot}$ star of age 4 Gyr). Objects fainter than this are
candidate brown dwarfs and also not the optimal targets for migration because
of their slowly decreasing luminosities. None of the encounters with Sun-like
stars (Table 1) feature brown dwarf candidates. Some of these candidates (and
a couple of white dwarf candidates) have uncertain $M_{G}$ because the
photogeometric distance estimates of Bailer-Jones et al. (2021) have
significant tails to large values for these objects.

  * •

The closest system to the Sun in this sample is the encounter between two M
dwarfs, HD331161B and G125-30, which are at $\sim 14$ pc. The star HD331161B
is part of a binary.

  * •

The encounter with the closest minimum distance is between another pair of M
dwarfs, 2MASS J07315294+0633251 and 2MASS J07321651+062839, which has a
minimum encounter distance of 22 AU. This is also the system with the highest
score in the metric $\langle 1/r_{min}^{2}\rangle$.

  * •

The encounter with the highest probability of passage within $10^{4}$ AU is
the pair 2MASS J05100438+3306067 and 2MASS J05100212+3303535, which has a
probability of 37 per cent. The high probability here is driven by the very
close agreement in the distances to these stars.

###  2.4 Planet Hosting Stars

Our close encounter sample defined above does not contain any stars known to
host planets. Indeed, it contains very few stars that have even been searched
for evidence of planets. Therefore, let us examine the sample of stars that
are known to host planets, and estimate how close of an encounter is likely to
occur amongst this subsample.

To address this, we have repeated the GAIA search described above, but used,
as the source population for the comparison, the stars within 100 pc of the
Sun that are known to host planets. We draw this sample from the NASA
Exoplanet Database (Akeson et al., 2013), as of July 9, 2021. Figure 8 shows
the relative motions on the sky of all pairs whose parallaxes are consistent,
and with projected separations $50\rm AU<\Delta R_{\perp}<10^{5}\rm AU$. The
lower limit is chosen to exclude matches between the same star, since the NASA
database uses GAIA DR2 positions and we are using GAIA EDR3 positions, which
sometimes give small offsets. This leaves us with 129 pairs.

Figure 8:  The solid points show matches between known planet-hosting stars
and nearby companions on the sky. The horizontal dotted line represents our
nominal division between bound (lower left) and unbound (upper right) pairs.
The region between this criterion and the diagonal dashed line is suspected to
contain mostly hierarchical triples whose relative velocities are contaminated
by partially resolved orbital motion in one or both components. The vertical
dotted line indicates $\Delta R_{\perp}=3\times 10^{4}$ AU. The dotted circles
indicate pairs which are not noted as binaries in the exoplanet database, but
which appear to exhibit the necessary common motion. All other points below
the dashed line and to the left of the dotted line are known binary systems.

Figure 8 once again shows the division into bound and unbound pairs, as in
Figure 1. There are quite a few planetary hosts in binary systems, as is well
known. The vertical dotted line indicates the cut we used for further
consideration in our original sample. The two unbound pairs from this sample
that satisfy this criterion feature the stars GJ 433 and HR 858. These are the
only two planet hosts that make it into our initial sample of 446 encounters.

  * •

The star GJ 433 is an M2 dwarf ($\sim 0.5M_{\odot}$) hosting three planets,
whose periods are 7.37, 36.06 and 5094 days (Bonfils et al., 2013; Tuomi et
al., 2014; Feng et al., 2020). About 2000 years ago, it may have come to
within $\sim 9\times 10^{4}$ AU of the K0V dwarf HD 100623, which is actually
a binary containing a white dwarf companion. Both of these stars have measured
radial velocities as well, so this is a reasonably well determined measurement
(the biggest uncertainty being the respective radial distances). This star
does not make it into our sample because, without the radial velocity
information, the chance of the close encounter coming within $10^{4}$ AU is
less than 1 per cent, and $\langle 1/r_{min}^{2}\rangle=0.01$. However, when
we include the known radial velocities, $\langle 1/r_{min}^{2}\rangle$
increases to 0.16, although $P_{rv}$ is still $<0.01$.

  * •

The star HR 858/HD 17926 is a 1.2 $M_{\odot}$ F star at a distance of 32 pc,
also with three planets – periods 3.59, 5.97 and 11.23 days (Vanderburg et
al., 2019). This star also has a low mass binary companion. In $\sim 9000$
years, it will also come within $\sim 8\times 10^{4}$ AU of another binary
pair, dominated by the star TYC 7012-885-1. Once again, this encounter is well
characterised because both members have measured radial velocities. As in the
case of GJ 433, this pair also has a less than 1 per cent chance of coming
within $10^{4}$ AU, and $\langle 1/r_{min}^{2}\rangle=0.06$ in this case, even
with radial velocities included.

There is one other pair in Figure 8 that doesn’t match well with the bound
pairs – that containing the planet hosting star GJ 685 (Pinamonti et al.,
2019). This falls within the intermediate range we identified in § 2 as likely
contaminated by hierarchical triples. Indeed, this star is projected to
undergo an encounter with the spectroscopic binary HD 160269. The fact that
both stars share the same radial velocity suggests that this is truly a bound
pair, and the larger-than-expected differential proper motion may be affected
by the orbital motion of the binary. There are several planet-hosting stars,
designated with dotted circles in Figure 8, which are listed as single in the
Exoplanet database but seem to have wide companions, based on their positions
in this diagram. These possible binaries are GJ 685, HD 238090, HD 10647, HIP
38594, HD 39855, HD 8326, HD 221420, HD 23472, HD 24085, HD 31253 and WASP-29.
Also circled in Figure 8 are the systems HD 124330 and AU Mic, which appear to
lie between the elliptic and hyperbolic populations. In the case of AU Mic,
this may be a consequence of its youth and membership in the $\beta$ Pictoris
moving group.

##  3 Signatures of Interaction

We have identified a set of stars undergoing close, but unbound, stellar
encounters. HZ21 noted that the energy burden of transfer between stars is
considerably eased during such encounters and postulated that most
interstellar migration will occur during such episodes. If such migrations are
accompanied by an increase in construction of spaceships and communication
within a migrating population, then they might prove to be fruitful targets
for observations. To that end, we review here the possibility of infrared
excesses in this sample. We also present, in the Appendix, finding charts for
the 16 systems in Table 1.

###  3.1 Infrared Excess

One possible source of observable signals is the large-scale construction of
spaceships to transport material and individuals from one star to the next.
The most energy efficient way of doing this would be to utilise a population
of asteroids, and so we might search for an infra-red excess resulting from
dust released during the construction process.

In order to search for infrared excesses we cross-correlated the positions of
the stars in Table 1 with point sources detected in the 2MASS (Skrutskie et
al., 2006) and ALLWISE (Wright et al., 2010) catalogs. Figure 9 shows the
resulting set of J-W2 versus W1-W3 colors for sources detected at 12$\mu$m and
shorter wavelengths. There is no evidence of any sort of infrared excess
around any of the stars – either the putative origin systems or the
destinations.

Figure 9:  The solid points show the J-W2 and W1-W3 colors for the brighter
members of the 16 systems in Table 1. The open points are for the fainter star
in each encounter. The stars represent the white dwarfs in Table 2 and the
crosses are those stars undergoing close encounters with white dwarfs. Many of
these stars are not detected in the W4 bandpass, but those that do have a non-
zero detection in that bandpass are plotted in red, while the rest are plotted
in black. The dashed line indicates the black-body trend in these colours, as
a function of effective temperature.

In Figure 9 we also show the colours for the pairs featuring white dwarfs.
Most white dwarfs derive from stars originally in the same mass range as those
in Figure 1, and so may provide another source for migration if civilisations
survived the evolution of their host stars. Most of the white dwarfs are so
faint in the infra-red that they are not detected in WISE, but most of the
other members of the encounter pair are detected. The only source with
potentially interesting colours is GD 84, which has a large W1-W3 colour.
However, the source is still faint at WISE wavelengths and the uncertainty in
the W3 magnitude may be underestimated because of the uncertainty in the
background level in this image.

We have also examined the 2MASS and WISE magnitudes for the sample of lower
mass stars in Table 2. These stars are mostly much fainter and, although there
are a handful that show anomalous WISE colours, all excesses can be explained
by either source confusion or uncertainties in the background levels at W3 and
W4 wavelengths.

To assess what sort of limit these observations place on the presence of dust,
Figure 10 shows the spectral energy distributions for two stars – GD 84 (the
one star with a marginal detection of an excess) and HD 87978 (our best case
target in the sense that it is a slightly evolved G star and so best
corresponds to the scenario outlined in HZ21). In each case, we have taken the
WISE and 2MASS data, combined it with optical photometry from the literature,
and fit with a black body of appropriate temperature. We have then added, to
the GD 84 data, a black body at temperature 300 K. This is based on the
assumption that any technological activity would occur at approximately
habitable temperatures.

Figure 10: The solid points represent the available photometry (from B to W4)
for the star HD 87978 and the dashed line is a blackbody spectrum. The
excellent fit indicates no evidence for any significant infrared excess at
long wavelengths. The open circles indicate the available photometry for the
white dwarf GD 84. In this case, there does appear to be an excess at 12$\mu$m
(W3 band) and we can explain this with a population of dust at a temperature
of 300 K (as indicated by the second dotted line). However, inspection of the
WISE images suggests that the background levels are quite uncertain at this
magnitude and so this detection should be considered very tentative.

The measured flux can tell us the surface area that a population of optically
thin dust is required to match. For a white dwarf of temperature $10^{4}$K and
radius $10^{9}$cm, surrounded by a population of $10\mu$m radius dust
particles, we require $N\sim 2\times 10^{28}$ particles to intercept enough
light to reradiate the observed flux in the infrared. Assuming a dust density
of 3g.cm-3, this means a mass of $\sim 2\times 10^{20}$g, which is very small
– comparable to an average Solar system asteroid. A similar calculation yields
a mass in dust $\sim 5\times 10^{21}$g to match the observed flux of HD 87978
at 24$\mu$m. This represents an upper limit as there is no evidence of excess
in the HD 87978 flux.

Infrared excesses are a common feature of young planetary systems, as the dust
from the late, collisional, stage of planetary assembly. Some fragments must
survive to late stages, because there is evidence for surviving rocky material
in orbit around a significant fraction of white dwarfs (Zuckerman et al.,
2010). Thus, we anticipate the rocky material from a surviving asteroid belt
may be available for the construction of interstellar transport vehicles. Any
estimate of the required mass is wildly speculative given our current lack of
knowledge, but we can set a baseline by considering what might be required for
transportation of humans in such an episode. Given the expense and danger
involved, we can imagine that construction would opt for extremes of
efficiency. If the spaceships were constructed by hollowing out asteroids
(less expensive than boosting material from a planetary surface to space) we
anticipate the smallest volume per capita that is feasible. A contender for
the highest population density long-term settlement is the Kowloon Walled City
slum of Hong Kong (Nosowitz, 2013), with a population density of $\sim$ 1
million people per square km. The walled city was also 15 storeys high, or
about 60m, so that the volume associated with 1 million people is $\sim
6\times 10^{7}m^{3}$, or a volume of about 60 $m^{3}$ per person. The
excavation of such a volume of rock implies a mass $\sim 2\times 10^{8}$g per
capita. If this were all converted to dust, it would still allow for the
construction of habitats for $\sim 10^{12}$ people. This does not allow for
volumes for storage, or engines or many other necessary items, but it
illustrates that an alien construction need not produce an enormous infrared
signature. The only substantive conclusion we can draw is that we have no
significant evidence for anything unusual observed in the infra-red output of
this sample of stars.

###  3.2 Astrophysical Effects

We have also noted the possibility that close stellar encounters might induce
comet showers. The extent of the Solar Oort cloud is believed to extend well
beyond the $10^{4}$ AU threshold we have adopted, so it is natural to expect
the stellar encounters identified here to affect any equivalent Oort clouds
around these stars, should they exist. However, the observable signals to be
expected from such a comet shower require that gas or dust be released from
the comet to yield infrared excesses or transient spectral features in
absorption, and this requires the comets to get close enough to the star to
begin to sublimate, which essentially requires getting within 5 AU (Whipple,
1950), in the case of a Sun-like star. Such a requirement imposes a delay
$\sim 1\rm Myr$ between the actual encounter and the peak of any expected
signal (Hut et al., 1987; Dybczyński, 2002) – corresponding roughly to the
orbital timescale at the original location of the scattered comets. Thus, it
is likely far too early to expect much of a signal in the case of the sample
of stars shown here.

Nevertheless, we can still estimate the size of the effect. Starting with a
Sun-like Oort cloud, we take a total of $10^{12}$ comets distributed uniformly
within $5\times 10^{4}$ AU of the host star. Several authors have made more
detailed models of the actual Solar Oort cloud, but this simple model captures
the basic population demographics (e.g. Weissman (1996)). In such a model, the
local density of comets is $n\sim 2\times 10^{-3}\rm AU^{-3}$. If we ask how
close to the perturbing star, of mass $M_{pert}$, does a comet need to get to
be strongly scattered, we can determine this by calculating the $\Delta
V_{\perp}$ due to a scattering encounter (e.g. from Binney & Tremaine (1987))
and set it to be comparable to the orbital velocity of the comet, at a
distance $a$ from the host star of mass $M_{*}$. This yields an impact
parameter (relative to the scatterer) of

$b\sim 36AU\left(\frac{M_{pert}}{0.3M_{\odot}}\right)\left(\frac{1\rm
M_{\odot}}{M_{*}}\right)^{1/2}\left(\frac{50\rm
km.s^{-1}}{V_{0}}\right)\left(\frac{a}{10^{4}\rm AU}\right)^{1/2}$ (2)

In passing through the cloud, the interloper perturbs a fraction $\sim
10^{-5}$ of the comets, assuming $M_{pert}=1\rm M_{\odot}$, which is
comparable to more detailed estimates (e.g. Dybczyński (2002)). This is not
likely to be observable amongst the sample identified here – because of the
delay between perturbation and post-perturbation perihelion – but it suggests
that the space density of stars experiencing comet showers should be similar
to the density of stellar perturbations identified here.

One hope for an immediate signal is for the perturber itself to cause
sublimation in comets that pass close to it during its passage through the
Oort cloud. This has not been estimated in the above papers, so let us
estimate the size of the effect within the context of our simple comet cloud
model outlined above. If we adopt the Whipple threshold of $\sim 5$ AU for the
sublimation of water in Solar system comets, this amounts to an equivalent
temperature of $T_{eq}=150$K on the sunward facing side of the comet. This
implies the perturber must pass within

$b_{sub}=0.6AU\left(\frac{R_{pert}}{0.3\rm
R_{\odot}}\right)\left(\frac{T_{pert}}{3550\rm
K}\right)^{2}\left(\frac{T_{eq}}{150\rm K}\right)^{-2}$ (3)

to generate gas and dust by sublimation. Consideration of gravitational
focussing increases this estimate by only 10 per cent. Therefore, for M dwarf
perturbers, there is rarely a comet within a sufficiently large volume to
generate any mass loss. In the case of a G-star perturber, the volume gets
larger, and there is $\sim 1$ comet within the sublimation radius at any given
time. However, the odds of this object passing across the line of sight of the
observer is small. Over the course of a month, the line of sight intersecting
a solar mass star will sweep out a volume $\sim 0.04\rm AU^{3}$ (travelling at
50 km.s-1), which is small compared to the volume $\sim 500\,\rm AU^{3}$ per
comet.

Therefore, we conclude that the odds are negligible of seeing a transient
absorption in one of these systems due to the perturber directly sublimating a
comet in the Oort cloud.

##  4 Conclusions

HZ21 argue that the difficulties involved in migration between stars is
minimized during close stellar encounters, and that the possibility of
observing the operation of extraterrestrial technologies may be enhanced
during such episodes. As a result, in this paper we have searched the GAIA
database of stars within 100 pc in order to identify those unbound stellar
pairs that are likely to have close encounter in the recent past or near
future. . We identify a total of 132 pairs with either a better than 1 per
cent chance of passing within $10^{4}$AU of one another, or with a mean value
$\langle 1/r_{min}^{2}\rangle<0.1$. Of these, 16 pairs feature a star of
spectral type between K1–F3. These approximately Sun-like stars are the ones
that correspond most directly to our original hypothesis. Many of these pairs
have measured radial velocities, and we have used this information, where
available, to improve our estimates of the interaction metrics.

The motivation to undertake interstellar migration may also be reduced if the
star has a bound companion, as such a body would be much easier to reach.
Examination of our preferred sample for indications of binary companions
leaves only 8/16 of the primaries in the most constrained sample as having no
evidence for binarity. As a result, our preferred candidate systems for
observing signs of interstellar migration are HD 87978, HD 92577, HD 50669, HD
44006, HD 80790, LSPM J2126+5338, LSPM J0646+1829 and HD 192486. The highest
probability candidates amongst known planet hosts are the stars GJ 433 and HR
858. We suggest that searches for extraterrestrial technology include these
stars in their search, as they provide a rationale for a hypothesis-driven
search instead of the traditional blind search and thus may motivate deeper
observations. Indeed, the full sample of 16 systems in Table 1 are worthy of
studying in this regard. In appendix A we provide finding charts for each of
these pairs, as well as for a few additional systems of potential interest
(such as the most extreme members of the lower mass sample in Table 2).

As an example of such a search, we have searched the 2MASS and WISE databases
for the stars in Table 1 to look for the possibility of infrared excesses due
to large-scale astroconstruction in these systems. We find no evidence for an
infrared excess in any of the G star systems. We also examined the encounters
in the expanded sample (Table 2) that involved white dwarfs – since most of
these stars are evolved from G or F main sequence stars. We find one marginal
detection of a W3 excess around GD 84, but this must be regarded as tentative
given the uncertainties in the background level at these wavelengths. From
these non-detections we can constrain the mass in 10$\mu$m dust around these
stars to be $<10^{21}$g.

Our study bears obvious resemblance to studies searching for the stars that
will make close encounters with the Sun (Bailer-Jones et al., 2018; Bobylev &
Bajkova, 2021). Those studies focus on stars close to the Sun, whose
parallaxes are often more accurate than those used here, and for which a much
larger fraction have radial velocities available. In our case, we are limited
primarily by the accuracy of the parallax and the unknown line-of-sight
velocity, which renders our sample statistical in nature. It is likely that
only one or two of the candidates in Table 1 will actually experience an
encounter within $10^{4}$ AU, but the benefits of having a well-defined,
manageable sample compensate for this.

The author thanks the anonymous referee and Ben Zuckerman for advice and
comments on the manuscript. This research was supported in part by grants to
UCLA from NASA. This research has made use of NASA’s Astrophysics Data System
and the results of the RECONS consortium, which can be found at
www.recons.org. 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, in particular the institutions
participating in the Gaia Multilateral Agreement. This research has made use
of the NASA/IPAC Infrared Science Archive, which is funded by the National
Aeronautics and Space Administration and operated by the California Institute
of Technology. This publication makes use of data products from the Two Micron
All Sky Survey, which is a joint project of the University of Massachusetts
and the Infrared Processing and Analysis Center/California Institute of
Technology, funded by the National Aeronautics and Space Administration and
the National Science Foundation. The Digitized Sky Survey was produced at the
Space Telescope Science Institute under U.S. Government grant NAG W-2166. The
images of these surveys are based on photographic data obtained using the
Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The
plates were processed into the present compressed digital form with the
permission of these institutions. This research has made use of the NASA
Exoplanet Archive, which is operated by the California Institute of
Technology, under contract with the National Aeronautics and Space
Administration under the Exoplanet Exploration Program.

##  Appendix A Finding Charts

Here we present the finding charts for the 16 systems in Table 1, along with a
handful of additional, potentially interesting, systems. We show the relative
proper motions of each of the members of the close encounter pair, to
illustrate the nature of each encounter. Note that the magnitudes of the
vectors are proportional to the relative amplitude of the proper motions in
each chart, but not between charts (i.e. there is no uniform scaling in proper
motion that has been applied across all charts). In the cases where radial
velocities are measured for these stars, their direction is indicated as
moving towards ($\bigodot$) or away from ($\bigotimes$) the observer. All
images are taken from the ALADIN archive (Bonnarel et al., 2000) of DSS2
images, except where specifically indicated.

###  A.1 Encounters featuring Sun-like Stars

Figure 11: The left panel shows the field surrounding the interacting pair HD
157393 and LSPM J1722+1513. The purple arrows indicate the two stars involved
in the interaction, while the black arrows indicate the proper motions of the
two stars involved. The field is $10^{\prime}\times 10^{\prime}$ and the co-
ordinates of HD 157393 are 17h22m24s.9726448248, +15∘08′12′′.868453175 (epoch
J2000). HD157393 is suspected to be a binary, based on the proper motion
anomaly between Hipparcos and GAIA (Kervella et al., 2019). The right hand
panel shows the field surrounding the pair HD 159902 and CD-45 11747. The
field is a little smaller here ($4^{\prime}\times 4^{\prime}$) because this
pair is much closer together. The position of HD 159902 is
17h39m27s.8792739684, -45∘53′10′′.985009447 at epoch J2000. The red arrow
indicates the probable proper motion companion to HD 159902.

Figure 12: The left panel shows the field surrounding the interacting pair
involving the G1 star HD 187154 and the K1 star HD 187084. The purple arrows
indicate the two stars involved in the interaction, while the black arrows
indicate the proper motions of the two stars involved. The field is
$11^{\prime}\times 11^{\prime}$. The position of HD 187154 is
19h49m44s.0761820458, -32∘45′50′′.287392501 at epoch J2000. HD187154 is
suspected to be a binary, based on the proper motion anomaly between Hipparcos
and GAIA (Kervella et al., 2019). The right hand panel shows the field
surrounding the G6IV star HD 87978 and the M dwarf J10090601-1109290. The
field is $12.7^{\prime}\times 12.7^{\prime}$. The star HD 87978 is a
potentially single Sun-like star, nearing the end of its main sequence
lifetime. It’s position is 10h08m26s.5768781632, -11∘06′54′′.743846694 at
epoch J2000.

Figure 13:  The left panel shows the field surrounding the pair involving the
F2 star HD 92577 and the M dwarf J104111261-1418509. The field is a
$5^{\prime}\times 5^{\prime}$. The star HD 92577 is one of the potentially
single Sun-like stars in our table and its position is 10h41m06s.1151098272
,-14∘21′29′′.265485777 at epoch J2000. The right panel shows the field
surrounding the interacting pair TYC 5786-123-1 and J21335912-0746358. The
purple arrows indicate the two stars involved in the interaction, while the
black arrows indicate the proper motions of the two stars involved. The field
is $2.5^{\prime}\times 2.5^{\prime}$ and was taken from the PanSTARRs survey
because of the better angular resolution. The position of TYC 5786-123-1 is
21h34m06s.3864435104, -07∘47′35′′.460488485 at epoch J2000. Both stars
involved in this encounter have common proper motion companions in the GAIA
data, whose positions are marked by red arrows.

Figure 14: The left panel shows the encounter between the F5 star HD 143332
and the M star J16000455-0712125. The field is $10^{\prime}\times
10^{\prime}$. The position of HD 143332 is 16h00m02s.6498506984,
-07∘07′21′′.680091901 at epoch J2000. The right hand panel shows the encounter
between the binary star HD 26770 and the M dwarf J04132532-2830440. The red
arrow indicates the presence of a binary companion. The field is
$10^{\prime}\times 10^{\prime}$. The position of HD 26770 is 04h13m00s.52912,
-28∘32′26′′.2934 at epoch J2000.

Figure 11 shows the finding charts for the first two entries in Table 1. The
left hand panel shows the encounter involving the F8 star HD 157393. In this
case, the closest approach is estimated to lie in the future, and the proper
motion vectors appear to be converging. In the right hand panel, we see the
encounter involving the G5 star HD 159902. The pair, in this case, is much
closer and the closest approach is estimated to have occurred in the recent
past. Thus, the proper motions now appear to be diverging. The star HD 159902
also appears to have a wide ($a_{\perp}\sim 1000$ AU) proper motion companion
in the GAIA data.

Figure 12 shows two more finding charts, for the star HD 187154 (left panel)
and HD 87978 (right panel). The former case now shows diverging proper motions
and the closest approach is estimated to have occurred in the past. The latter
case is currently showing converging proper motions and is estimated to
undergo close approach in the future. HD 87978 is also one of the stars in
Table 1 for which there is, as yet, no evidence of a bound companion.

The left panel of Figure 13 shows the finding chart for the encounter
featuring the F2V star HD 92577. The right panel of Figure 13 shows the
finding chart for a binary-binary encounter. In this case, the minimum
encounter distance is expected to be much wider than either of the binary
separations ($a_{\perp}=712$ AU for TYC-5786-123-1 and $a_{\perp}=310$AU for
the M dwarf pair).

The left hand panel of Figure 14 shows the encounter of HD 143332 with another
M dwarf. This is projected to reach closest approach $\sim 10^{4}$ years in
the future, consistent with the evidently converging proper motions. HD 143332
is also suspected to be a binary (Kervella et al., 2019). The right hand panel
shows the encounter of the G0V star HD 26770 with an M dwarf. The HD 26770
system is actually a wide binary containing two G stars.

Figure 15: The left panel shows the pair involving the G8IV star HD 50669 and
the M star J06540919-0148118. The purple arrows indicate the two stars, while
the black arrows indicate the proper motions. The field is $2.2^{\prime}\times
2.2^{\prime}$, and is drawn from the PanSTARRS survey. The position of HD
50669 is 06h54m08s.8776552042, -01∘49′20′′.549547800 at epoch J2000. The right
hand panel shows the encounter between the F5 star HD 143332 and the M star
J16000455-0712125. The field is $10^{\prime}\times 10^{\prime}$. The position
of HD 143332 is 16h00m02s.6498506984, -07∘07′21′′.680091901 at epoch J2000.

Figure 16: The left panel shows the encounter between the binary star HD210974
and the star UCAC2 18317515. The purple arrows indicate the two stars, while
the black arrows indicate the proper motions. The field is $7.5^{\prime}\times
7.5^{\prime}$. The position of HD 210974 is 22h14m38s.26886, -32∘12′23′′.2520
at J2000. The right hand panel shows the encounter between the F6 star HD
80790 and the M star J09191695-5901597. The field is $10^{\prime}\times
10^{\prime}$. The position of HD 80890 is 09h19m19s.9662065270,
-58∘55′45′′.646644916 at epoch J2000.

The left hand panel of Figure 15 shows the interaction of the G8IV star HD
50669 with an M star. This is an apparently single star approaching the end of
its main sequence lifetime and thus another prime candidate for an
interstellar migration event such as those postulated in HZ21. The right hand
panel of Figure 15 shows the finding chart for the star HD 44006, another
isolated G star undergoing an encounter with an M dwarf.

The left hand panel of Figure 16 shows an encounter between another binary
featuring G8 and K0V stars, with a fainter star UCAC2 18317515. This system
likely went through its closest approach fairly recently. The right hand panel
shows the field around the HD 80790. This star underwent a close passage with
the M star J09191695-5901597 a few thousand years ago and is now diverging.
The star HD 80790 is identified as a binary in the literature.

The left hand panel of Figure 17 shows the field of the encounter featuring
the star LSPM J2126+5338 with an M dwarf binary. This is actually the highest
probability encounter in Table 1. Finally, the right hand panel shows the
encounter featuring the star LSPM J0646+1829. This is another of the single
Sun-like stars undergoing a close encounter.

Figure 17: The left panel shows the field containing the star LSPM J2126+5338
and the M star J21265700+5343001. The purple arrows indicate the two stars,
while the black arrows indicate the proper motions. The field is
$8^{\prime}\times 8^{\prime}$. The position of LSPM J2126+5338 is
21h26m52s.8508484028, +53∘38′22′′.323798302 at epoch J2000. The right hand
panel shows the pair of stars LSPM J0646+1829 and J06464503+1828391. The field
is $5^{\prime}\times 5^{\prime}$. The position of LSPM J0646+1829 is
06h46m36s.3522038800, +18∘29′43′′.045073347 at epoch J2000.

Figure 18:  The left panel shows the encounter of the wide proper motion pair
HD 29836 and HD 28570 (indicated with the red arrow) with the M dwarf LP
415-358. The principals in the encounter are indicated by purple arrows and
the proper motions by the black arrows. The field shown here is
$8.8^{\prime}\times 8.8^{\prime}$. The position of HD 29836 is
04h59m37s.3055400488, +83∘11′46′′.005522306 at epoch J2000. The right hand
panel shows the encounter between HD 192486 and HD 192527. The field size here
is $24.5^{\prime}\times 24.5^{\prime}$. The position of HD 192486 is
20h16m26s.4481841445, -35∘11′54′′.476960125 at epoch J2000.

The final figure in this section contains the final two entries in Table 1.
Neither of these encounters has a minimum likely passage within $10^{4}$AU,
but both have $<(1/r_{min})^{2}>$ above the threshold value of 0.1. The left
hand panel shows the encounter of a GV star HD 29836, with an M dwarf LP
415-358. HD 29836 has a wide K7 proper motion companion, HD 285970. Despite
the low values of $P_{\mu}$ and $P_{rv}$, this encounter has the equal fifth
highest value of $\langle 1/r_{min}^{2}\rangle$ in Table 1. The right hand
panel shows the encounter of an F2V star HD 192486 and a G5V star HD 192527.
The two stars share a common radial velocity, but clearly discrepant proper
motions. This pair lies close to the lower limit of our $\Delta v$ cutoff, but
there is no indication of excess astrometric noise that would suggest one of
the sources is a partially resolved binary whose motion may have distorted the
relative proper motions.

###  A.2 Other Systems of Interest

The encounter involving the white dwarf GD 84 features a marginal detection of
an infra-red excess. Figure 19 shows this encounter and also indicates the
star tentatively identified by Farihi et al. (2005) as a companion – see
Figure 4.4 of Farihi (2004) for the original finding chart. The identification
was tentative because the stellar proper motion measurement was compromised by
confusion with the nearby background star. GAIA measurements now reveal that
this is not at the same distance nor does it share the proper motion of GD 84.

The right hand panel of Figure 19 shows the identification of the two stars
taking part in the encounter that is closest to the Sun – that of HD 331161B
and G125-30. This pair is so close to the Sun (14 pc away) that a full finding
chart that spans the region between the pair includes so many stars as to be
essentially unreadable. Thus, in this chart we provide two zooms in on the
stars in question, separated by $\sim 23^{\prime}$ on the sky.

Figure 19: The left panel shows the interacting pair involving the white dwarf
GD 84 and the M star LP 162-1. The purple arrows indicate the two stars, while
the black arrows indicate the proper motions. The green arrow in this field
indicates the star initially identified as a possible companion by Farihi et
al. (2005) but which now lies definitively farther away. The inset at the
upper right shows the finding chart from Farihi (2004), which identifies the
putative companion as star B. The red dashed square indicates the
corresponding field of view in our image. The dotted arrow shows the proper
motion for this star as well. The field is $5^{\prime}\times 5^{\prime}$. The
position of GD 84 is 07h18m01s.9005268754, +45∘47′53′′.06535215 at epoch
J2000. The right hand panel shows the encounter between the M dwarfs HD
331161B and the M star G125-30. Here we show only postage stamp images around
each star, because these stars are separated by 23 arcminutes on the sky. Of
all the pairs in our sample, this is the closest to the Sun. The position of
HD 331161B is 19h46m24s.2211145800, +32∘00′57′′.783307309 at J2000. The fields
here are taken from the PanSTARRS survey.

Figure 20 shows the encounters with the most extreme parameters. In the left
panel, we see the interaction of the two M-dwarfs J07315294+0633251 and
J07321651+0628319, whose minimum likely close passage distance is estimated to
be $\sim 105$ AU. The converging nature of the proper motions indicates that,
with the right radial velocities, this can have a very close passage in $\sim
10^{4}$ years. The right hand panel shows the pair with the highest estimated
probability of a close interaction. In this case, the high probability is not
driven by the proper motions necessarily, but rather by the close
correspondence in the distances to the two stars.

Figure 20: The left hand panel shows the approach that has the smallest likely
perihelion of our entire sample, with a possible minimum of only 105 AU,
featuring two M dwarfs J07315294+0633251 and J07321651+0628319. The field of
view here is $11^{\prime}\times 11^{\prime}$. The right hand panel shows the
pair that has the highest estimated probability of a passage within
$10^{4}$AU, namely the pair J05100438+3306067 and J05100212+3303535. The field
of view here is $5.3^{\prime}\times 5.3^{\prime}$.

Our final finding charts , in Figure 21, show the two exoplanet host systems
that have the closest encounters within the context of our analysis. The left
hand panel shows the star GJ 433, which hosts three planets, and its
trajectory relative to a binary containing a K0V star and a white dwarf. The
closest approach here likely happened a few thousand years ago and the pair is
now diverging. On the right hand side of Figure 21, we show the encounter
featuring HR 858. This system is likely converging towards its closest
approach in the future. This encounter is once again an encounter between two
binaries.

Figure 21: The left hand panel shows the encounter featuring the planet host
star GJ433, a $\sim 0.5M_{\odot}$ M2V star that hosts two short period Super-
Earths and a long period, Saturn-class planet. The field of view of this
figure is $11^{\prime}\times 11^{\prime}$. The position of star GJ 433 is
11h35m26s.9474098036, -32∘32′23′′.883014588 at epoch J2000. The right hand
panel shows the encounter featuring HR 858, a $\sim 1.2M_{\odot}$, F6V star,
which hosts three short-period Super-Earths discovered by TESS. This star is
converging to an encounter with another binary pair in the near future. The
field of view here is $24^{\prime}\times 24^{\prime}$. The position of HR 858
is 02h51m56s.2464213292 ,-30∘48′52′′.259083285 at epoch J2000.

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