# The Census of Exoplanets in Visual Binaries: population trends from a
volume-limited Gaia DR2 and literature search

Clémence Fontanive Center for Space and Habitability, University of Bern,
Bern, Switzerland  Daniella Bardalez Gagliuffi American Museum of Natural
History, New York, NY, USA

(Received November 2, 2020; Accepted January 28, 2021)

###### Abstract

We present results from an extensive search in the literature and Gaia DR2 for
visual co-moving binary companions to stars hosting exoplanets and brown
dwarfs within 200 pc. We found 218 planet hosts out of the 938 in our sample
to be part of multiple-star systems, with 10 newly discovered binaries and 2
new tertiary stellar components. This represents an overall raw multiplicity
rate of $23.2\pm 1.6\,\%$ for hosts to exoplanets across all spectral types,
with multi-planet systems found to have a lower stellar duplicity frequency at
the 2.2-$\sigma$ level. We found that more massive hosts are more often in
binary configurations, and that planet-bearing stars in multiple systems are
predominantly observed to be the most massive component of stellar binaries.
Investigations of the multiplicity of planetary systems as a function of
planet mass and separation revealed that giant planets with masses above 0.1
MJup are more frequently seen in stellar binaries than small sub-Jovian
planets with a 3.6-$\sigma$ difference, a trend enhanced for the most massive
($>$7 MJup) short-period ($<$0.5 AU) planets and brown dwarf companions.
Binarity was however found to have no significant effect on the demographics
of low-mass planets ($<$0.1 MJup) or warm and cool gas giants ($>$0.5 AU).
While stellar companion mass appears to have no impact on planet properties,
binary separation seems to be an important factor in the resulting structure
of planetary systems. Stellar companions on separations $<$1000 AU can play a
role in the formation or evolution of massive, close-in planets, while planets
in wider binaries show similar properties to planets orbiting single stars.
Finally, our analyses indicate that numerous stellar companions on separations
smaller than 1–3 arcsec likely remain undiscovered to this date. Continuous
efforts to complete our knowledge of stellar multiplicity on separations of
tens to hundreds of AU are essential to confirm the reported trends and
further our understanding of the roles played by multiplicity on exoplanets.

exoplanets, multiplicity, visual, binaries, companions, formation,
demographics, statistics

††journal: Frontiers in Astronomy and Space Sciences - Exoplanets: The Effect
of Stellar Multiplicity on Exoplanetary Systems

##  1 Introduction

The architectures of stellar, sub-stellar, and planetary systems are relics of
their formation and evolutionary processes. By studying the orbital parameters
and configurations of hierarchical systems as an ensemble we can in principle
trace back to the formation mechanisms that originated them. Planet formation
is a direct consequence of star formation, yet it can be severely influenced
by the presence of a stellar companion. The existence of planets in orbit
around one or both components of binary systems are stringent probes of planet
formation process. Radial velocity measurements estimate that $18\pm 1\,\%$ of
FGK stars will have a giant planet within 20 AU (Cumming et al., 2008). About
$44\,\%$ of FGK stars are found in multiple systems, with $33\,\%$ in binary
systems, and $11\,\%$ in higher-order architectures (Raghavan et al., 2010).
Hence roughly half of potential planet hosts are in multiple-star systems,
arguing that the fraction of giant planets orbiting a stellar component of a
binary system is likely not negligible.

A number of campaigns have thus searched for planets in and around stellar
binaries, including radial velocity programs (e.g., Konacki et al., 2009),
transit discoveries (e.g., Doyle et al., 2011) and direct imaging surveys
(e.g., Asensio-Torres et al., 2018; Hagelberg et al., 2020), leading to the
detection of a number of circumstellar (orbiting one star) and circumbinary
(orbiting two stars) planets. Despite these efforts, most exoplanet searches
routinely exclude stars in binary or multiple systems to avoid systematic
errors in planet detection, and the first systems of this type were identified
serendipitously (see e.g., Patience et al., 2002; Mugrauer et al., 2006). The
distinct demographics of the first planets discovered in binary star systems
hinted at the possibility that binary companions could dramatically reorient
the orbital configuration of planetary systems (Zucker & Mazeh, 2002).
Approaching the question from the opposite end, numerous high-resolution
imaging studies have also searched for stellar companions to known planetary
systems, either to validate or refine the nature of identified planets
(Everett et al., 2015; Furlan et al., 2017; Hirsch et al., 2017), or to
purposely investigate the effect of stellar duplicity on planetary populations
(Colton et al., 2021; Horch et al., 2014; Matson et al., 2018; Wang et al.,
2014).

Dedicated studies of circumstellar planets in binary systems rapidly revealed
a lack of stellar companions within 20–50 AU (e.g., Bergfors et al., 2013;
Kraus et al., 2016). Close stellar companions on this separation range are
generally accepted to prevent planet formation, although early examples of
giant planets in $<$20 AU binaries (Queloz et al., 2000; Hatzes et al., 2003)
demonstrated that such systems do exist. Consistent with the observed
shortfall of planets of tight binaries, theoretical models predict that the
presence of a very close binary companion can truncate a protoplanetary disk
(Kraus et al., 2012; Pichardo et al., 2005), hence obstructing the formation
of a planet by core accretion, or ejecting the planet in unstable systems
(Kaib et al., 2013). Binary companions at large separations (beyond several
hundreds to thousands of AU) from planet hosts, on the other hand, have been
argued to have no impact on the formation and evolution of planets (Desidera &
Barbieri, 2007; White & Ghez, 2001).

Meanwhile, the effects of binary companions at intermediate (around
$\sim$100–300 AU) separations are more debated. Such companions could truncate
circumprimary disks by opening large gaps, hence redirecting the material to
the primary stars’ circumstellar disks and leaving the secondaries with no or
depleted disks (Artymowicz & Lubow, 1994; Bate & Bonnell, 1997), consistent
with observations of binary systems among T Tauri stars (Jensen & Akeson,
2003). Theoretical simulations also showed that perturbations from secondary
stars may assist the formation and evolution of giant planets by enhancing
mass accretion and orbital migration rates in circumstellar disks (Kley,
2001). The Kozai-Lidov mechanism (Kozai, 1962; Lidov, 1962) could also play a
role in the inward migration and final orbital properties of planets through
secular interactions induced by an outer stellar companion on such
separations. This process has indeed been invoked to explain the formation of
hot Jupiters (Fabrycky & Tremaine, 2007; Winn et al., 2010).

In this study, we present an overview of the current census of circumstellar
exoplanets in visual binaries, with separations from tens of AU out to 20 000
AU, within a volume limited to 200 pc. The goal of this compilation is to
gather information of stellar multiplicity for a large sample of exoplanets,
which will hopefully serve in future investigations, rather than to perform a
detailed statistical analysis of these populations. In particular, this work
extends previous such studies of exoplanets orbiting one component of a binary
system to all stellar spectral types and all types of extra-solar planets and
brown dwarf companions. In Section 2, we describe the construction of our
exoplanet sample (Section 2.1), followed by a search for co-moving companions
to exoplanet hosts (Section 2.2) in the literature and in Gaia. Section 3
presents our results, in which we explore differences between the demographics
of planets in binaries and around single stars (Section 3.2), as well as
potential trends in planet properties based on binary separation and mass, for
the population of planets in multiple-star systems (Section 3.3). Section 4
discusses the completeness of our sample and the observed effects of stellar
duplicity on various exoplanetary populations. Our conclusions are presented
in Section 5.

##  2 Materials and Methods

We describe in this Section the construction of our studied exoplanet sample
(Section 2.1) and the searches performed for wide binary companions to all
selected planet hosts (Section 2.2). In the context of this work, we consider
brown dwarfs and extra-solar planets orbiting stars as a unique population of
sub-stellar companions. We thus make no distinction between companions below
and above the deuterium burning limit (13 MJup), and will use the term sub-
stellar companion to denote planetary and brown dwarf companions in general,
unless otherwise specified. Similarly, double and multiple stellar systems
will often be referred to as binaries throughout most of this work for
conciseness. Finally, given the exoplanet-oriented approach of this study, the
term host will always refer to the planet-bearing star in a system,
independently of whether or not it is the higher-mass component of a multiple-
star system.

###  2.1 Exoplanet Compilation

We gathered a sample of extra-solar planets and brown dwarfs from the NASA
Exoplanet Archive111https://exoplanetarchive.ipac.caltech.edu, the Extrasolar
Planets Encyclopaedia222http://exoplanet.eu (Schneider et al., 2011), the
Exoplanet Orbit Database333http://exoplanets.org (Han et al., 2014) and the
Open Exoplanet Catalogue444http://www.openexoplanetcatalogue.com. The data
from these libraries were collected on June 23, 2020, and cross-matched to
identify all systems with at least one planet or brown dwarf companion
reported as confirmed in at least one of these databases. We gathered from
these catalogs all available information about the sub-stellar companions and
stellar hosts, and only kept systems with robust companion mass (or minimum
mass) and semi-major axis measurements. We imposed a cut of 0.1 M⊙ on the
minimum mass of the host, based on primary masses supplied in the considered
databases, in order to focus our study on stellar hosts only. We also removed
all circumbinary (P-type) systems, orbiting both stars from a binary system,
as our study concentrates on circumstellar (S-type) planets and brown dwarfs,
found around a single component of a binary system.

We cross-matched the resulting sample with the Gaia Data Release 2 (DR2; Gaia
Collaboration et al., 2016, 2018) catalog, obtaining positions, parallaxes,
proper motions, Gaia magnitudes and effective temperatures for all hosts found
in Gaia DR2. Astrometric information was taken from the SIMBAD Astronomical
Database (Wenger et al., 2000) for the few targets that are not part of Gaia
DR2 or do not have full astrometric solutions from the Gaia mission. Based on
the obtained stellar parallaxes, we restricted our sample to systems with
parallax measurements larger than 5 mas, corresponding to a maximum distance
of 200 pc for our volume-limited investigation. This cut allows us to focus on
relatively nearby stars, thus limiting the range of probed inner working
angles around different targets when searching for stellar companions, while
keeping a sufficiently large sample for a statistically significant study.

The final sample consists of 938 host stars, harboring a total of 1316
exoplanets and brown dwarfs, and contains 693 single-planet systems and 245
multi-planetary systems. Stellar hosts have masses ranging from 0.1 to 3.09
M⊙, with a median of 0.95 M⊙. Most primaries are along the main sequence,
covering spectral types from B to M, with 171 giants or sub-giants and 8 white
dwarfs. We show in Figure 1 the Gaia Hertzsprung-Russell diagrams for all
primaries in our sample with Gaia DR2 parallaxes and G, BP, and RP magnitudes
(926 stars), with the color scale indicating the host mass. Tables for the
final samples are provided as supplementary material and are available online,
with separate tables for the stellar hosts and sub-stellar companions.

Figure 1: Gaia color-magnitude diagrams of planet hosts stars, showing
absolute G magnitudes against BP-RP colors (left) and G-RP (right). Symbols
plotted with black rings represent planet hosts found to be part of multiple-
star systems. The colorbar indicates the mass of each planet host, using a
logarithmic scale. The gray background population shows the 200-pc volume-
limited cleaned sample from Gaia DR2.

###  2.2 Binary Search

In this work, we focus on co-moving visual binaries or higher-order
hierarchical stellar systems, that is, systems with two or more stars
confirmed to be moving together in the sky. The co-moving nature of two
gravitationally-bound objects can be determined in two ways. The first
approach is via proper motion (and parallax) measurements, where the
components of a multiple system will show astrometric parameters consistent
with one another. The second method consists in comparing images taken over a
sufficiently-long time baseline to demonstrate that two sources show the same
displacement over time compared to fixed background objects. Both approaches
require the two (or more) stars to be spatially resolved in imaging
observations, and such visual binaries are thus typically widely-separated
systems. We place an outer limit of 20 000 AU on the projected separation in
our search for multiple systems.

In the following sections, we describe the searches we performed for wide, co-
moving visual companions to all stellar hosts from our gathered sample of
exoplanetary systems. The full compilation of binary systems is provided as
online supplementary material.

####  2.2.1 Binaries in Surveys and the Literature

The catalogs used to compile our studied sample contain some information about
stellar binarity. We complemented the multiplicity data from these databases
with the Catalogue of Exoplanets in Binary Star
Systems555https://www.univie.ac.at/adg/schwarz/multiple.html (Schwarz et al.,
2016). We added to this all systems from published surveys searching for
visual stellar companions to circumprimary planetary systems (Adams et al.,
2012, 2013; Bergfors et al., 2013; Bohn et al., 2020; Coker et al., 2018;
Daemgen et al., 2009; Deacon et al., 2016; Dietrich & Ginski, 2018;
Eggenberger et al., 2007, 2011; Faedi et al., 2013; Fontanive et al., 2019;
Furlan et al., 2017; Ginski et al., 2012, 2016, 2020; Kraus et al., 2016;
Lillo-Box et al., 2012; Lodieu et al., 2014; Luhman & Jayawardhana, 2002;
Moutou et al., 2017; Mugrauer et al., 2006, 2007a, 2007b; Mugrauer & Ginski,
2015; Mugrauer & Neuhäuser, 2009; Mugrauer, 2019; Ngo et al., 2016, 2017;
Patience et al., 2002; Raghavan et al., 2006; Southworth et al., 2020; Udry et
al., 2004; Wang et al., 2014; Wöllert et al., 2015; Ziegler et al., 2018) or
reviews of planets in binaries (Bonavita & Desidera, 2007, 2020; Desidera &
Barbieri, 2007; Eggenberger & Udry, 2007; Eggenberger, 2010; Roell et al.,
2012; Thebault & Haghighipour, 2015) that we could find, and finally any other
serendipitous discovery we were aware of that may have been missing from the
above compilations.

In parallel, we cross-matched our host star sample with large-scale catalogs
of stellar multiplicity like the Washington Double Star Catalog (WDS; Mason et
al., 2001), the Catalog of Components of Double & Multiple stars (CCDM;
Dommanget & Nys, 2002), the Tycho Double Star Catalogue (TDSC; Fabricius et
al., 2001) and the Updated Multiple Star Catalog (MSC; Tokovinin, 2018), as
well as surveys for wide stellar binaries conducted with direct imaging
(Deacon et al., 2014; Janson et al., 2012, 2014, 2017; Raghavan et al., 2010;
Tokovinin & Lépine, 2012; Tokovinin, 2014a, b; Ward-Duong et al., 2015;
Winters et al., 2019).

Each reported multiple system was then checked individually in the literature
to ensure the S-type nature of the planets and brown dwarfs, and confirm that
the binary or multiple system was indeed visual (with resolved components),
and astrometrically confirmed to be co-moving, either via consistent relative
astrometry in multi-epoch observations or through similar kinematics (as
opposed to optical binaries with a probabilistic bound nature from the chance
of alignment). A total of 184 stars in our sample were mentioned in the
considered surveys to have at least one companion satisfying these criteria
(excluding the recent Gaia search performed by Mugrauer, 2019; see Section
2.2.2). For all identified systems, we gathered, when available, binary
separations, companion masses, and companion spectral types.

####  2.2.2 Companions in Gaia DR2

To complement the literature search performed above, we searched for bright
companions in the Gaia DR2 catalog to all stars in our compilation. Using the
collected positions, proper motions and parallaxes for the stellar hosts, we
searched for Gaia sources within angular distances corresponding to
separations of 20 000 AU from our primaries, and displaying consistent
kinematics. Following the approach from Fontanive et al. (2019), we used
thresholds of $20\,\%$ disparity in parallax, and offsets of $<20\,\%$ of the
total proper motion in one direction and $<50\,\%$ in the other coordinate.
These cuts allow to account for the fact the short-term astrometric
measurements from Gaia DR2 may capture the reflex motion of binary systems, or
may have spurious solutions for unresolved binaries (see Fontanive et al.,
2019 for details).

For systems part of young moving groups, other members of the same association
may appear nearby in the sky and display similar proper motions and
parallaxes, consistent with the average moving group kinematics. To avoid the
inclusion of unassociated close-by group members in our binary list, we
checked that no more than one other astrometric match was found on angular
separations up to 20 times the identified binary radius. We consider that a
co-moving source within 20 000 AU projected separation is statistically
unlikely to be an unrelated member of the same group if no other members are
found within a 400-fold sky area. We thus regard such sources as bonafide
bound companions for the purpose of this study. When one other match was
found, we applied the same procedure centered on this outer source, with the
same search radius, to establish whether other group members were found
nearby, in which case all sources were taken to be unrelated moving group
members. If no additional sources with consistent kinematics were found, we
considered the outer source to be the tertiary component of a triple system.
Finally, we checked that identified binary companions were different from the
sub-stellar companions in our exoplanet list, as some young and bright brown
dwarfs discovered with direct imaging on wide separations may be detected at
the low-mass end of the Gaia DR2 completeness (Reylé, 2018).

This analysis yielded 175 companions around 172 hosts stars. For all
identified systems, we measured the binary separation from the respective Gaia
DR2 positions of co-moving components, and collected Gaia photometry for the
companions. The majority (139) of identified Gaia companions were already
known from the literature (excluding findings from Mugrauer, 2019) and were
included in our compilation from Section 2.2.1. Based on our literature
findings, 19 of the detected Gaia companions were in fact tight binaries
themselves, unresolved in Gaia. Mugrauer (2019) recently performed a very
similar search for wide companions to exoplanet host stars in Gaia DR2, which
presents a useful comparison survey to validate our approach. We found that
all binaries reported in that work and present in our sample list (121
systems) were also retrieved in our Gaia analysis. From these, 23 systems and
a tertiary companion to the WASP-11 system (unresolved in Gaia) were never
reported prior to that study. We however retrieved 51 additional Gaia systems
missing from the Mugrauer (2019) compilation, which is likely due to different
target samples between that study and ours. Finally, 10 of our identified Gaia
co-moving systems were not found to have been previously reported in the
literature (up to early September 2020): CoRoT-7, HD 13167, HD 23472, HIP
73990, K2-228, L2 Pup, TOI-132, WASP-189, WASP-29, WASP-59. In addition, new
tertiary components were discovered around HIP 65A and V 1298 Tau. These
companions are presented in Table 1, with additional information about the
systems provided within the full catalogs available online.

Table 1: New stellar companions to planet host stars identified in this work using the Gaia DR2 catalog. The new system components are marked in bold in the System column, which is only indicative of the overall system architecture, and do not represent proposed naming conventions. Following the approach in the main tables, component A systematically denotes the planet host irrespectively of the relative component masses, unless already named differently in the literature. Indices 1 in the stellar mass and spectral type columns refer to the planet hosts, and indices 2 refer to the considered stellar companions. This is a highlight of full tables available as supplementary material, which provide additional information about these systems, together with the rest of our compilation. System | Parallax | Separation | Separation | SpT1 | Mass1 | SpT2 | Mass2
---|---|---|---|---|---|---|---
| [mas] | [arcsec] | [AU] |  | [M⊙] |  | [M⊙]
New binary companions |  |  |  |  |  |
CoRoT-7 Abc + B | 6.23 | 75.7 | 12160 | K0V | 0.93 | M4 | 0.23
HD 13167 Ab + B | 6.69 | 20.1 | 3001 | G3V | 1.35 | M4 | 0.21
HD 23472 Abc + B | 25.59 | 9.6 | 374 | K3.5V | 0.75 | M6 | 0.14
HIP 73990 Abc + B | 9.03 | 47.3 | 5234 | F2IV | 1.72 | M2 | 0.50
K2-228 Ab + B | 7.71 | 22.6 | 2933 | K6 | 0.71 | G3 | 1.08
L2 Pup Ab + B | 15.61 | 32.8 | 1998 | M5IIIe | 0.66 | M5 | 0.20
TOI-132 Ab + B | 6.08 | 19.6 | 3231 | G8V | 0.97 | M4 | 0.17
WASP-189 Ab + B | 10.00 | 9.4 | 942 | A4/5IV/V | 1.89 | M2 | 0.45
WASP-29 Ab + B | 11.39 | 125.2 | 10994 | K4V | 0.82 | M3 | 0.38
WASP-59 Ab + B | 8.60 | 81.8 | 9512 | K5V | 0.72 | K7 | 0.62
New tertiary companions |  |  |  |  |  |
HIP 65 (Ab + B) + C | 16.16 | 73.6 | 4557 | K4V | 0.78 | M7.5 | 0.11
V 1298 Tau Ab-e + (BC) | 9.21 | 117.0 | 14795 | K1 | 1.10 | K7 | 0.66

For all new Gaia systems, we checked whether the wide stellar companions were
known (seemingly single) objects in SIMBAD, and gathered additional mass and
spectral type information from the literature for these components when
available. In addition, for all components known from the literature but
missing from our Gaia binary list, we searched for these wide companions in
Gaia DR2 in case these stars were in the catalog but with no astrometric
solutions, and thus not detectable as co-moving sources in our Gaia search.
From these, 14 companions were recovered without Gaia DR2 astrometry, and
available Gaia magnitudes and relative positions of components were added to
our catalog for these additional companions.

####  2.2.3 Properties of Stellar Companions

As a number of literature systems (mostly from WDS) and Gaia binaries had no
existing stellar classification or measured mass, we estimated these
characteristics for all identified Gaia components based on their positions in
the Gaia color-magnitude diagrams. Hertzsprung-Russell diagrams were made for
all binary companions with measured magnitudes in the G, BP and RP bands,
using the sources’ parallaxes if available, and the astrometry from the
associated planet hosts otherwise.

From these, 6 sources populated the white dwarf part of the parameter space,
and were all found in the Gaia DR2 white dwarf study by Gentile Fusillo et al.
(2019). The white dwarf classifications and masses were thus taken from this
work for these companions.

All other companions appeared to fall along the main sequence. For these
systems, we used the TESS Input Catalog (TIC; Stassun et al., 2018) to map the
parameter space of the Gaia color-magnitude diagrams to stellar masses and
spectral types, based on TIC stellar masses and queried SIMBAD spectral types
for all sources from the catalog out to 200 pc. As clear and continuous trends
in mass and spectral type were seen along the Gaia main sequences of the TIC
sample (similar to our host sample in Figure 1), the masses and spectral types
of wide companions could be inferred directly based on their location along
these Gaia main sequences. Quantities were interpolated using the mean mass
and spectral type from the TIC sample in a box of size 0.2 mag centered on the
companion’s absolute magnitude and color, provided that at least 10 sources
were found in that box. For each detected Gaia companion, masses (rounded to
0.01 M⊙) and spectral types (to 1 sub-type) were obtained from the TIC BP–RP
and G–RP parameter spaces, and averaged for more robust final values. For
sources characterized in this way from their colors and magnitudes, the
average offset and scatter between literature values and our Gaia-derived
estimates was $+0.3\pm 1.5$ sub-type in spectral type, and $-0.01\pm 0.05$ M⊙
in mass (removing known unresolved sources). We also validated this method by
applying it to our main sequence host star sample, and observed comparably
negligible offsets to values collected in the planet-host catalog.

For companions that fell outside the TIC main sequence due to unusual Gaia
colors (14 objects), or for sources with no BP and RP magnitudes (16 objects),
we used the median intersection of the absolute G magnitude with the TIC main
sequences instead, assuming that these objects were single, main sequence
stars, similar to the approach followed in the recent Gaia study by Mugrauer
(2019). For companions classified from their absolute magnitudes alone, the
average scatter was $-0.4\pm 2.4$ sub-types in spectral type and $-0.2\pm
0.07$ M⊙ in mass for sources truly on the main sequence, with very similar
results in mass to Mugrauer (2019) for overlapping systems. Larger offsets
were seen for known white dwarf companions with no Gaia colors, which were
hence assimilated to M dwarfs on the main sequence based on their absolute
G-band magnitudes.

Based on these results, we consider that our Gaia-inferred quantities are
robust measurements for main sequence components. We adopt these as final
values when no previous mass and spectral type estimates were available for
the retrieved companions, and use existing literature estimates otherwise. The
literature, Gaia, and final adopted values are all reported in our tables.

##  3 Results

Many surveys looking for extra-solar planets, in particular with the radial
velocity method, are affected by or biased against binaries with separation
$\leq 2$–6 arcsec, excluding known multiple systems in target selection
processes (see e.g., Eggenberger, 2010; Ngo et al., 2017). As a result,
measurements of multiplicity rates for exoplanetary systems are particularly
challenging, as these selection biases are not trivial to quantify and correct
for (see e.g., Moe & Kratter, 2019). This typically means that studies like
ours, investigating the binarity of planetary systems discovered partly by
such surveys, cannot be used to derive the true frequency of planets in
binaries, nor to probe the existence of planets in very tight binaries. With
this in mind, the goal of this work is thus to provide an overview the current
census of sub-stellar companions in wide visual binaries, rather than to
achieve robust statistical results, and we will therefore not attempt to
account for these biases here.

Our studied sample of planetary systems was nonetheless compiled independently
from the binary nature (known or unknown) of the systems. The gathered
compilation should thus not be biased toward or against the existence of
binary star systems beyond the intrinsic biases from exoplanet detection
campaigns. Our Gaia search for wide companions is also homogeneous across the
host star sample, limited only in inner working angle by the distance to each
star, and by the inherent completeness of Gaia DR2. Our ability to recover
stellar companions in Gaia is therefore, in principle, independent of the
architecture of the planetary systems themselves. Similarly, the existing
literature surveys considered spanned a large range of planet host stars and
probed various distinct planetary populations. We thus consider that while
strong biases remain in our binary list, which should be taken into account
for detailed statistics and the derivation of absolute occurrence rates, our
compilation does not strongly discriminate between different types of sub-
stellar companions (i.e., planet or brown dwarf masses, separations or
detection methods) in the potential to detect wide visual companions. Our
compilation can hence be used to search for raw trends within the obtained
sample of binaries and highlight potential correlations between multiplicity
and the properties of planetary and sub-stellar companions.

###  3.1 Overall Compilation

From the compilation gathered in Section 2.2.1, combining an extensive
literature search and a Gaia DR2 investigation, 218 planet hosts were found to
have at least one visual co-moving stellar companion: 186 host stars were
found to be in binary systems, and 32 host stars in higher-order hierarchical
systems. From these, 4 binaries and 1 triple system are composed of 2 planet-
hosting stars, organizing the 218 planet hosts into 213 unique multiple
systems. The architecture of each planet-bearing multiple-star system is
presented in Figure LABEL:f:architectures, which illustrates the relative
separations and masses of sub-stellar and stellar companions within each
system. Figure 2 presents the distribution of spectral types among the planet
hosts stars, showing relative numbers of single stars and planet hosts in
multiple systems for each spectral type, and compared to the sample of
detected stellar companions. Companion masses range from 2.37 M⊙ down to the
hydrogen-burning limit ($\sim$0.07 M⊙). Binary projected separations extend
from 0.85 AU (GJ 682) out to our 20 000 AU search limit, with a median value
of 678 AU. A total of 19 binaries were found in the range 10–50 AU, and 27
systems were identified on separations shorter than 100 AU.

Figure 2: Distribution of spectral types from B through M, plus white dwarfs,
for single-star planet hosts (blue), multiple-star planet hosts (magenta) and
stellar companions (yellow). Hatched sections of the plotted bars represents
giants and sub-giants, with the remaining systems being on the main sequence.
Each color-coded histogram is independently normalized so that the sum of the
bars within each individual group adds up to 1.

Table 2 summarizes the numbers and raw fractions of sub-stellar companions in
single and multiple-star systems, where binaries and triples are counted
similarly as hierarchical multiple systems. We emphasize once again that no
completeness or selection bias corrections have been performed, and the quoted
numbers simply provide an overview of the collected catalogs. From the 1316
exoplanets and brown dwarfs in our compilation, 286 were found to be around
one component of a multiple-star system ($21.7\pm 1.3\,\%$). In terms of
individual planetary systems, 218 out of 938 planet host stars ($23.2\pm
1.6\,\%$) are part of multiple-star systems. Interestingly, a marginally
higher fraction (2.2-$\sigma$) of single-planet systems are in hierarchical
stellar systems ($25.1\pm 1.9\,\%$) compared to multi-planet systems ($18.0\pm
2.7\,\%$).

Table 2: Summary of results, providing the number of single and multiple (binary or higher-order) systems hosting various planetary sub-populations. Raw occurrence rates are given in parentheses with uncertainties computed as Poisson noise. Planetary population | Total | Single-star systems | Multiple-star systems
---|---|---|---
All Planets | 1316 | 1030 ($78.3\pm 2.4\,\%$) | 286 ($21.7\pm 1.3\,\%$)
All Planetary Systems | 938 | 720 ($76.8\pm 2.9\,\%$) | 218 ($23.2\pm 1.6\,\%$)
Single-Planet Systems | 693 | 519 ($74.9\pm 3.3\,\%$) | 174 ($25.1\pm 1.9\,\%$)
Multi-Planet Systems | 245 | 201 ($82.0\pm 5.8\,\%$) | 44 ($18.0\pm 2.7\,\%$)
M${}_{\mathrm{pl}}<0.1$ MJup | 554 | 462 ($83.4\pm 3.9\,\%$) | 92 ($16.6\pm 1.7\,\%$)
M${}_{\mathrm{pl}}=0.1-7$ MJup | 597 | 444 ($74.4\pm 3.5\,\%$) | 153 ($25.6\pm 2.1\,\%$)
M${}_{\mathrm{pl}}>7$ MJup | 165 | 124 ($75.2\pm 6.7\,\%$) | 41 ($24.8\pm 3.9\,\%$)
a${}_{\mathrm{pl}}<0.5$ AU | 766 | 603 ($78.7\pm 3.2\,\%$) | 163 ($21.3\pm 1.7\,\%$)
a${}_{\mathrm{pl}}=0.5-10$ AU | 476 | 365 ($76.7\pm 4.0\,\%$) | 111 ($23.3\pm 2.2\,\%$)
a${}_{\mathrm{pl}}>10$ AU | 74 | 62 ($83.8\pm 10.6\,\%$) | 12 ($16.2\pm 4.7\,\%$)
M${}_{\mathrm{pl}}\geq 0.1$ MJup, a${}_{\mathrm{pl}}\leq 10$ AU | 688 | 506 ($73.5\pm 3.3\,\%$) | 182 ($26.5\pm 2.0\,\%$)
M${}_{\mathrm{pl}}\geq 0.1$ MJup, a${}_{\mathrm{pl}}\leq 0.5$ AU | 236 | 164 ($69.5\pm 5.4\,\%$) | 72 ($30.5\pm 3.6\,\%$)
M${}_{\mathrm{pl}}\geq 7$ MJup, a${}_{\mathrm{pl}}\leq 10$ AU | 106 | 73 ($68.9\pm 8.1\,\%$) | 33 ($31.1\pm 5.4\,\%$)
M${}_{\mathrm{pl}}\geq 7$ MJup, a${}_{\mathrm{pl}}\leq 0.5$ AU | 28 | 19 ($66.9\pm 15.6\,\%$) | 9 ($32.1\pm 10.7\,\%$)

###  3.2 Multiplicity as a Function of Planet Properties

In this section, we explore the multiplicity of our planet host star sample as
a function of planetary mass and separation. Unfortunately, other orbital
elements (eccentricity, inclination) are not available for the full exoplanet
sample. Investigations involving these parameters would thus be limited to
planetary systems detected with specific methods and are not explored here. In
Figure 3, we show the masses and semi-major axes of all planet and brown
dwarfs in our compilation, with systems found to be in visual stellar binaries
marked in magenta, and apparently single stars in blue.

Figure 3: Planet mass against semi-major axis for all sub-stellar companions
in our exoplanet compilation. Planets identified to be part of multiple-star
systems are shown in magenta, while planets orbiting single stars are plotted
in blue. The dashed lines divide the parameter space into several bins
detailed in the text.

Some previously-known trends associated with specific sub-populations of
planets are visually apparent in Figure 3. One such feature is the lack of
blue scatter points (single-star systems) for sub-stellar companions with
semi-major axis in the range $\sim$0.01–0.10 AU (orbital periods of
$\sim$0.5–10 days around a Sun-like star) and masses larger than $\sim$3 MJup.
This part of the parameter space, representing massive hot Jupiters and brown
dwarfs, is entirely filled with multiple-stars systems (magenta scatter
points), consistent with early observations that these planets and brown
dwarfs are almost exclusively observed in binary stars (Zucker & Mazeh, 2002).
A second notable attribute from Figure 3 is the small group of brown dwarfs
with even shorter orbital separations ($<$0.01 AU) identified around single
stars (top left corner). These sub-stellar companions are all found to orbit
white dwarfs, and correspond to most white dwarf hosts from our compilation.
Such extreme systems are thought to result from the considerable mass loss
stars undergo as they become white dwarfs. This post-main sequence process
drastically changes the star-planet mass ratios, thus altering the dynamics
and stability of brown dwarfs and planets, in particular in multi-planet
systems (e.g., Maldonado et al., 2020).

In order to investigate the effect of stellar multiplicity as a function of
sub-stellar companion mass and separation, we divide the planetary parameter
space into 3 bins in semi-major axis (apl) and 3 bins in mass (Mpl), delimited
by the dashed lines in Figure 3. We chose arbitrary limits of 0.5 and 10 AU in
semi-major axis, and 0.1 and 7 MJup in mass. The boundary at 0.5 AU
corresponds to the observed dearth between two distinct peaks in the
distribution of exoplanet orbital periods, representing the pile-up of hot
planets, and the bulk population near the snow line ($\sim$1–3 AU),
respectively (Udry et al., 2003). The 10-AU threshold corresponds roughly to
the outer detection limit for the radial velocity method, and only massive,
directly-imaged companions are typically identified beyond 10 AU. The 0.1-MJup
mass bound was adopted as the lower limit for the mass of Jovian planets
(Mordasini, 2018), while 7 MJup was taken as the median transition between
core accretion and gravitational instability giant planets (4–10 MJup;
Schlaufman, 2018), a limit also advocated by Moe & Kratter (2019) (see also
Santos et al., 2017).

Table 2 reports the relative numbers of sub-stellar companions in single and
binary systems in each planetary semi-major axis and mass bin. Stars harboring
low-mass, sub-Jovian planets (M${}_{\mathrm{pl}}<0.1$ MJup) appear to have a
substantially lower stellar binary rate, with $16.6\pm 1.7\,\%$ of such
planets being found in multiple-star systems. This compares to $25.5\pm
1.8\,\%$ for higher-mass planets and brown dwarfs, with a 3.6-$\sigma$
difference in raw multiplicity frequency between planetary and sub-stellar
companions below and above 0.1 MJup. A similar trend is seen with planet
orbital distance, where sub-stellar companions with a${}_{\mathrm{pl}}>10$-AU
are less frequently found in stellar binaries, although the smaller number of
such planetary companions reduces the significance of this tendency. This
effect is most likely the result of an enhanced bias against the existence of
wide binaries within 20 000 AU for systems with sub-stellar companions large
orbital distances. Indeed, the presence of a planet or brown dwarf prevents
the possibility of finding a binary companion on comparable or marginally
larger separations than the sub-stellar companion semi-major axis, and
binaries with separations of hundreds to thousands of AU are thus dynamically
impossible for a sizable fraction of these planetary systems. Given these
results, we also report values at the end of Table 2 focusing exclusively on
the close-in (a${}_{\mathrm{pl}}<10$ AU and $<$0.5 AU) giant planet and brown
dwarf populations. While the lower number of systems associated with these
subsets decreases again the significance of observed trends, raw multiplicity
rates seem to increase up to around $30\,\%$ for the very shortest-separation
and most massive sub-stellar companions. We also note that the vast majority
of sub-Jovian planets, with masses below $0.1$ MJup, are found in orbits with
semi-major axes shorter than 0.5 AU.

To better understand these tendencies and the effect of multiplicity with
planet and brown dwarf properties, we explore the distributions of sub-stellar
companions around single and binary stars in the various mass and separation
bins considered. In Figure 4, we show kernel density estimates (KDE) of the
distributions of planet semi-major axis (left panels) and mass (right panel),
for the different regions of the parameter space described above. Planets and
brown dwarfs in single-star systems are shown in blue, and those in
hierarchical stellar systems in magenta. We use KDE bandwidths of 0.3 in all
cases, and consider that such estimates of the probability density functions
should provide good insights into potential underlying trends.

(A) (B)

Figure 4: KDEs of planet properties comparing planets in binaries (magenta)
and planets around single stars (magenta), with the full planetary population
shown in the dotted black lines. Panel A shows the distribution of planetary
semi-major axis, divided between massive giant planets and brown dwarfs (top),
lower-mass giants (middle) and sub-Jovian planets (bottom), following the cuts
in parameter space shown in Figure 3. Panel B shows the distribution of
planetary mass for close-in planets (top), intermediate-separation planets
(middle) and wide-orbit giant planets (bottom).

In terms of planet semi-major axis (Figure 4A), multiplicity appears to have
no effect on the orbital separation of sub-Jovian planets
(M${}_{\mathrm{pl}}<0.1$ MJup), illustrated by the perfectly consistent
distributions for single and binary hosts in the bottom panel, both showing
the same narrow peak in the semi-major axis distribution around 0.1 AU. As we
enter the giant planet regime (M${}_{\mathrm{pl}}=0.1$–7 MJup; middle panel),
the bulk of the planetary population shifts to separations of 1–3 AU, with a
secondary peak at tighter separations (a${}_{\mathrm{pl}}<0.1$ AU). The
relative density of planets in this secondary sub-population seems to be
marginally higher for binary-star systems. Looking at the most massive giant
planets and brown dwarf companions (M${}_{\mathrm{pl}}>7$ MJup; top panel), a
number of new features emerge in the plotted KDEs. While the core of this
exoplanet population still lies at separations of a few AU, comparable to the
lower-mass Jovian planets, a strong over-density of closer-in planets and
brown dwarfs (a${}_{\mathrm{pl}}\sim 0.01$–0.1 AU) is seen among the sample of
multiple-star systems (magenta), corresponding to the population of massive,
small-separation sub-stellar companions in binaries highlighted previously
from Figure 3. The minor peak at even tighter separations around single hosts
corresponds to the sample of extremely short-period brown dwarfs found around
white dwarfs discussed previously. At larger orbital distances, the directly-
imaged population is subdued in the binary-star sample relative to closer-in
planets and brown dwarfs, due to the effect explained above for systems with
wide sub-stellar companions.

Regarding the distribution of planet masses (Figure 4B), stellar binarity
again seems to have no significant effect on the resulting masses for giant
planets and brown dwarfs with separations larger than 0.5 AU (middle and
bottom panels). At small semi-major axes (top panel), two sub-populations are
observed, composed of the sub-Jovian planets with masses below 0.1 MJup
forming the primary peak in the mass distribution, and a broader secondary
population of giant planets and brown dwarfs. Again, we observe a relative
over-abundance of binaries among the more massive planetary population on
small semi-major axes, consistent with the findings deduced from our analysis
as a function of planet orbital separation, and with the values reported in
Table 2.

###  3.3 Planet Properties as a Function of Binary Properties

Based on our results from Section 3.2, suggesting that stellar multiplicity
impacts the existence or properties of Jovian giant planets and brown dwarfs
(M${}_{\mathrm{pl}}>0.1$ MJup) on semi-major axes within 0.5 AU, we further
investigate the properties of these sub-stellar companions as a function of
binary properties and the statistical significance of these results. We will
not look in more details at other planetary systems as the previous analyses
revealed no significant effect of binarity on these planetary populations.

We assess the effect of binary separation by comparing the distribution of
properties for close-in giant planets and brown dwarfs in binaries as a
function of the orbital distance to outer stellar companions. Based on the
size of this subset (66 sub-stellar companions), we arbitrarily define ranges
of $<$250 AU, 250–1000 AU and $>$1000 AU in binary separation
$\rho_{\mathrm{bin}}$, dividing this sample into roughly evenly-populated bins
with 22, 24 and 20 systems, respectively. For hierarchical triple systems in
which the planetary host star is in an inner tight binary, we only consider
the close binary companion, as the outer tertiary component is unlikely to
have a significant effect on the planetary system compared to the nearby
stellar component. For triple systems with a planet host star widely separated
from a closer binary, we count this outer binary as a single companion, using
the mean separation between the planet host and the distant sub-system.
Individual binary systems may be counted more than once, however, if several
sub-stellar companions with masses larger than 0.1 MJup around found within
0.5 AU around the same star.

Figure 5 shows KDEs of the planet semi-major axes (Figure 5A) and mass (Figure
5B), comparing planets and brown dwarfs in the short (yellow), intermediate
(magenta) and wide (blue) binary separation ranges to those around single
stars (dashed black line). Despite the small sample size available for this
restricted planetary population, clear trends are visible in these figures. In
particular, the subset of sub-stellar companions in extremely widely-separated
binaries ($\rho_{\mathrm{bin}}>1000$ AU) shows very similar distributions in
planetary semi-major axis and mass to planets and brown dwarfs found in
single-star systems. In contrast, sub-stellar companions found in tighter
stellar binary systems appear to have smaller semi-major axes and higher
masses. The previously-noted overabundance of massive, close-in giant planets
and brown dwarfs in binaries is hence primarily found in $<$1000 AU binary
systems. We highlight, in particular, that from the 9 massive
(M${}_{\mathrm{pl}}>7$ MJup), close-in (a${}_{\mathrm{pl}}<0.5$ AU) giant
planets and brown dwarfs found in binaries, 8 are in binaries with separations
$<$1000 AU, from which 6 have binary separations $<$250 AU. While these rare
sub-stellar companions only represent $\sim$2$\,\%$ of the full exoplanet
sample, these systems make up about $10\,\%$ of the 64 binaries with
separations under 250 AU identified for the full catalog of planet hosts. We
further assess the significance of these results by performing two-sided
Kolmogorov-Smirnov tests comparing each sub-population of planets in binaries
to the sample of planets around single stars (dashed black lines). We are thus
testing the null hypothesis that the samples are drawn from the same
distribution, and use a threshold of 0.05 on the resulting p-values. We found
that the null hypothesis could be rejected for the distributions of planet
masses and semi-major axes in short and intermediate-separation binaries
($\rho_{\mathrm{bin}}<1000$ AU; yellow and magenta curves), but not for sub-
stellar companions in very wide binaries (blue), confirming that the above
findings are statistically significant (p-values of 0.027 and 0.0003 for the
planet semi-major axes in short and intermediate-separation binaries,
respectively, compared to 0.842 for wider binaries; p-values of 0.005 and
0.013 for the planet masses in short and intermediate-separation binaries, and
0.470 for wide binaries). This result further suggests that close and
intermediate-separation ($<1000$ AU) binary companions have strong effects on
the final semi-major axes of massive planets and brown dwarfs, whereas
planetary systems in very wide ($>1000$ AU) binaries are more likely to evolve
as independent stars.

(A) (B)

Figure 5: Planet properties as a function of binary separation
($\rho_{\mathrm{bin}}$) for all planets with masses above 0.1 MJup and semi-
major axes within 0.5 AU, corresponding to the binary systems plotted in the
magenta distribution in Figure 9. KDEs of planetary semi-major axis are shown
in panel A, and distributions of planet masses are shown in panel B. The
dashed black lines show the distributions for planets in the mass and semi-
major axis ranges found to be orbiting single stars.

(A) (B)

Figure 6: Same as Figure 5 dividing the sample of binary stars by companion
mass (Mc). For triple systems with a tight binary on a wide separation from
the planet host, the total mass of the outer sub-system is considered. The
dashed black lines show the distributions for planets in the mass and semi-
major axis ranges found to be orbiting single stars.

We also investigate potential trends of planet and brown dwarf properties as a
function of binary companion mass, Mc. As for the binary separation, we divide
the available sample into bins of $<$0.3 M⊙, 0.3–0.6 M⊙ and $>$0.6 M⊙. Triple
systems are treated similarly as in the previous analysis, using the total
mass of the outer components in the case of tight binaries on wider
separations from the planet hosts. Figure 6 shows the resulting distributions
of planet semi-major axis (Figure 6A) and mass (Figure 6B) for the various
stellar companion mass bins, together with the overall distributions of
single-star planetary systems (dashed black line). Unlike Figure 5, no clear
trend is observed with binary companion mass. The only marginal tendency is a
rather comparable distribution between the planet orbital distances of single-
star systems and the binaries with the most massive companions (yellow).
Kolmogorov-Smirnov tests performed on these sub-samples confirmed that the
planet separation distribution was statistically different from the single-
star planetary population for binary systems with companion masses below 0.6
M⊙ (p-values of 0.001 and 0.021 for binary companions in the intermediate and
low mass bins, respectively; p-value of 0.859 for high-mass binary
companions). However, this effect is mostly due to the fact that most stellar
companions in this bin are in fact very distant, two-component companions from
triple systems, thus increasing the adopted companion mass, and correspond for
the major part to the systems with separations $>$1000 AU that were found to
match the single-planet population. Kolmogorov-Smirnov tests could not reject
the null hypothesis when comparing the masses of planets and brown dwarfs in
various types of binaries to single-star systems, nor was any evidence found
that sub-stellar companions in binaries with various stellar companion masses
come from different populations (p-values $>$ 0.15 in all cases). Overall, the
excess of smaller-separation and higher-mass giant planets and brown dwarfs in
binaries appears to be distributed across the different binary mass bins
defined, with no robust trend with stellar companion mass.

##  4 Discussion

In this work, we performed analyses of planetary populations as a function of
multiplicity over all spectral types for hosts to exoplanets and brown dwarf
companions. This section similarly presents discussions of our results across
all types of stars, without distinguishing between massive stars, Sun-like
stars and M dwarfs, or main sequence and evolved stars (sub-giants, giants or
white dwarfs), unless explicitly stated otherwise. We note however that only
28 of our stellar hosts (out of 938, i.e. $<3\,\%$) are massive BA stars or
white dwarfs, from which only 5 A stars were found to be in multiple systems
(i.e. $\sim$2$\,\%$ of the binary sample). Excluding these systems would thus
make little difference in the observed results and trends. While giants and
sub-giants represent a more consequent fraction of the sample of host stars
($\sim$25$\,\%$ of the FGK hosts), a sizable number of our host stars have no
luminosity class (giant/sub-giant vs. main sequence) in the spectral types
gathered from the considered exoplanet catalogs or Simbad (e.g. numerous
Kepler/TESS/WASP targets). We are therefore not able to strictly discuss main
sequence stars separately, and our conclusions include a range of stellar
masses and a mixture of stellar evolutionary stages.

###  4.1 Stellar Mass Function and Multiplicity

Figure 2 shows the distribution of spectral types from our planet host sample,
divided between those identified in visual binaries or multiples (magenta) and
seemingly single stars (blue), and compared to the identified stellar
companions (yellow). Absolute numbers are provided at the top of each bar. In
addition, each color-coded histogram is normalized so that the sum of the bars
in a given color add up to 1, i.e. the height of each bar on the y-axis gives
the relative contribution from that spectral type towards to full considered
sub-sample.

Comparing the single and binary stars from our planet hosts, the subset of
binary hosts contains a larger relative fraction of massive A, F and G stars,
with a smaller contribution from lower-mass K and M dwarfs, as demonstrated by
the turnover in the relative heights of the magenta and blue bars from G to K
spectral types. This is consistent with the well-known trend of decreasing
binary rate with decreasing stellar mass, dropping from $\sim$70$\,\%$ for B
and A stars (Kouwenhoven et al., 2007) to around $50\,\%$ for Sun-like stars
(Raghavan et al., 2010), and about 30$\,\%$ for M dwarfs (Janson et al., 2012;
Winters et al., 2019; Ward-Duong et al., 2015). While our survey results were
not corrected for incompleteness and additional binaries may be missing from
our compilation (see Section 4.2), our ability to retrieve wide stellar
companions for our sample can be assumed to be rather independent of the host
spectral types. With raw binary fractions of $37.8\pm 6.5\,\%$, $24.3\pm
2.6\,\%$, $22.4\pm 2.7\,\%$ and $15.7\pm 3.1\,\%$ for F, G, K and M stars,
respectively, these results thus suggest that the population of planet-bearing
stars is representative of the relative multiplicity output of stellar
formation across the stellar spectral sequence. However, without robust
completeness corrections, we are not able to determine whether the differences
between our observed raw fractions and overall stellar multiplicity rates are
due to missing binaries in our samples or to the fact that stars hosting
planets and brown dwarfs are truly less commonly found in binary-star systems.

The distribution of spectral types from companions, on the other hand, peaks
strongly towards low-mass M dwarfs (yellow), which represent over 65$\,\%$ of
our sample of stellar companions. In fact, this resembles closely the stellar
initial mass function, with M dwarfs being the most abundant types of stars
(Chabrier, 2003; Bochanski et al., 2010). This indicates that planet hosts in
multiple systems are more often the most massive component of stellar
binaries. The feature is partly due to a selection effect, as lower-mass stars
are often too faint to be included in target samples for exoplanet campaigns
(Eggenberger, 2010). Nonetheless, although Earth to Neptune-sized planets are
more abundant around M dwarfs (Mulders et al., 2015), giant planet formation
is thought to be more efficient around more massive stars (Mordasini, 2018),
and giant planets are indeed observed to be more frequent around higher-mass
stars (Bonfils et al., 2013; Vigan et al., 2020). Given that binary systems
seem to preferentially host giant planets based on our results, it is not
surprising that most planet hosts in multiple systems would be the most
massive stellar component in these hierarchical systems.

###  4.2 Completeness and Survey Limitations

As mentioned previously, the (in)completeness of our multiplicity search was
not accounted for in the results presented in Section 3, as corrections of
observational biases are beyond the scope of this work. We may nonetheless
look at the properties of our detected systems to understand what biases might
lie in our gathered sample.

Figure 7 shows the angular separation and Gaia G-band magnitude difference for
every visual companion, relative to the planet host star it is bound to. Blue
circles represent companions successfully retrieved in Gaia DR2. Binary
components which are themselves known to be unresolved binaries are marked
with black rings. Magenta triangles correspond to companions known from the
literature but undetected in Gaia. As a $\Delta G$ magnitude difference is
unavailable for these systems, the plotted magnitudes correspond to contrasts
in various visual or infrared filters, and thus correspond to lower limits
compared to the expected magnitude difference values in the G-band. Our
observed recoverability for binaries is consistent with the estimated Gaia
completeness to close binaries (Ziegler et al., 2018): near equal-brightness
binaries ($\Delta G<2$ mag) are consistently retrieved from separations of 1
arcsec (dashed line), binaries down to around $\Delta G=6$ mag are typically
recovered at separations of $\sim$3 arcsec (dotted line), and wider systems
are subject to Gaia DR2 completeness down to the limiting magnitude of $G\sim
21$ mag of the Gaia DR2 survey.

Figure 7: Completeness of the Gaia DR2 binary search showing G-band magnitude
differences against angular separations for all companions retrieved in Gaia
(blue circles). Detected companions known to be themselves close binaries
unresolved inGaia are marked with black circles. Known companions not
recovered in the Gaia DR2 catalog are shown in the magenta triangles, with
plotted magnitude differences corresponding the lower limits in the Gaia
G-band. The dashed and dotted gray lines show inner working angles of 1 arcsec
and 3 arcsec, respectively. Figure 8: Physical projected separations against
distance all identified stellar companions, with the same symbols and color-
codes as in Figure 7, highlighting the completeness of our Gaia binary search
as a function of distance to the Sun. The dashed and dotted gray lines show
inner working angles of 1 arcsec and 3 arcsec, respectively.

A significant number of known tight binaries with angular separation $<$1
arcsec (magenta triangles) were not recovered in Gaia, only known thanks to
high angular-resolution imaging campaigns. As only a small fraction of our
hosts stars have been targeted by such dedicated imaging programs, these
results indicate that additional unresolved sub-arcsecond systems may still be
hidden among our exoplanet host sample. In particular, the 27 binaries for our
sample with projected separations $<$100 AU have a median angular separation
of 0.7 arcsec, and such systems are therefore for the most part not
recoverable in Gaia. Studies like Kraus et al. (2016) or Furlan et al. (2017)
have identified numerous optical candidate companions to Kepler hosts stars on
small angular separations, but additional observational epochs are required to
confirm or refute the bound nature of most of these candidates.

A shortfall of close binaries ($<$50–100 AU) among planet hosts has been
vastly reported in observational surveys (Bergfors et al., 2013; Bonavita &
Desidera, 2020; Kraus et al., 2016; Moe & Kratter, 2019; Roell et al., 2012;
Wang et al., 2014). This feature is generally attributed to a hindrance of
planet formation in very tight binaries, and is also predicted in theoretical
models (Thebault & Haghighipour, 2015). However, our survey is highly
incomplete out to separations of hundreds of AU and thus cannot be used to
probe this feature. Indeed, the resolving limit of $\sim$1–3 arcsec in our
Gaia search corresponds to projected separations of 200–600 AU for the most
distant stars in our study (200 pc). This effect is illustrated in of Figure
8, which plots the physical projected separation of all identified binaries as
a function of distance from the Sun. Detection limits corresponding to inner
working angles of 1 arcsec and 3 arcsec are marked with dashed and dotted
lines, respectively. The figure clearly demonstrates that the range of probed
binary separation is strongly affected by the distance to each star. Our
compilation is only sensitive in Gaia to binary separations below 100 AU for
targets out to 30 pc ($\sim 20\,\%$ of the sample), and only data from
heterogeneous high-angular resolution programs have allowed the detection of
such systems beyond 100 pc.

###  4.3 Impacts of Multiplicity on Exoplanets

####  4.3.1 No Influence on Low-Mass Planets

We found that small planets with masses below 0.1 MJup have a significantly
lower raw binary rate ($16.6\pm 1.7\,\%$) than more massive Jovian planets
($25.5\pm 1.8\,\%$ for planets above 0.1 MJup throughout the brown dwarf mass
range), an offset with a 3.6-$\sigma$ significance. While these numbers
certainly suffer from inherent and observational biases as discussed in
Section 4.2, it is reasonable to assume that these biases do not affect hosts
to different types of planets differently. Indeed, the transit and radial
velocity surveys that yield the detection of these planets are partially
subject to the same inherent selection biases as campaigns discovering more
massive planets with the same methods. As a result, we consider that the
observed trend of lower multiplicity fraction for sub-Jovian planets is a real
feature. Furthermore, terrestrial and Neptunian planets are often found in
tightly-packed multiple-planet systems (Mayor et al., 2011). The fact that
such planets are less frequently seen in hierarchical star systems is thus
also consistent with the observation that multi-planet systems are less
commonly found in stellar binaries.

These results, however, may be a direct consequence of the lower binary
frequency of M dwarfs compared to more massive stars. Since low-mass M stars
host $\sim$2–3 times more close, small planets than Sun-like stars (Howard et
al., 2012; Mulders et al., 2015), and rarely harbor giant planets (Bonfils et
al., 2013), the majority of small sub-Jovian planets and high-order multi-
planet systems are therefore found around M dwarfs. The intrinsic lower
stellar multiplicity rate of M dwarf could hence be responsible, at least
partly, for the observed trends. Nonetheless, Moe & Kratter (2019) found that
the biases from stellar companions against the detection of planets are higher
for F and G stars than M dwarfs. This trend is rooted on the suppression of
planet formation in close binaries and bright stellar companions preventing
transit detections. This suggests that the observed differences in raw binary
fractions between sub-Jovian and giant planet systems would likely be
increased after accounting for these biases, and we conclude that low-mass
planets and tightly-packed systems with multiple small planets are truly less
commonly found in hierarchical stellar systems.

####  4.3.2 The Excess of Massive Close-in Planets and Brown Dwarfs in
Binaries

The substantial prevalence of short-orbit massive planets and brown dwarfs
around members of binary stars was first noted by Zucker & Mazeh (2002), and
later confirmed by numerous observational studies (Eggenberger et al., 2004;
Desidera & Barbieri, 2007; Mugrauer et al., 2007b). More recently, the Friends
of Hot Jupiters survey reported an enhancement of binary frequency for stars
hosting hot Jupiters, with a binary rate 3 times higher that for field stars
over the separation range 50–2000 AU (Ngo et al., 2016). Fontanive et al.
(2019) established the continuity of this trend to the most massive giant
planets and brown dwarfs ($>$7 MJup) found within $\sim$1 AU, constraining the
binary frequency of such systems to be around $80\,\%$ between 20 and 10 000
AU, a result further validated statistically in Moe & Kratter (2019). Results
from these studies demonstrate that stellar companions play an important role
in the formation and/or evolution of these rare planetary systems. These
findings also suggest that the influence of binary companions is strengthened
for higher-mass close-in exoplanets and sub-stellar companions, and that this
effect may be magnified for sub-stellar companions on even tighter orbits.

While the work presented here did not allow us to place any such frequency
constraints, the intrinsic tendencies with planet mass and separation observed
in previous studies are confirmed in our compilation. Indeed, we observed a
larger relative fraction of Jovian planets in binaries within 0.5 AU than for
the bulk of the Jovian planet population around the snow line ($\sim$1–5 AU).
This relative frequency was found to further increase when focusing
exclusively on the most massive planets and brown dwarfs. These trends suggest
that stellar multiplicity affects the orbital separation of massive giant
planets. The presence of an outer wide companion would hence allow for the
inner sub-stellar companion to reach closer-in semi-major axes than planets of
similar masses orbiting single stars, onto an orbital separation regime where
essentially no planets around single stars are observed (Fontanive et al.,
2019).

The influence from outer stellar companions shows a possible dependence on
binary separations. Stellar companions on separations of the order of
thousands of AU seem to have no significant effect on the demographics of
planetary systems, with similar distributions observed between the masses and
semi-major axes of planets and brown dwarfs in such binaries and around single
stars. In contrast, the most massive, close-in giant planets and brown dwarfs
in binaries, in the most extreme planetary configurations, are all in rather
tight binaries, with separations of tens to a few hundreds of AU compared to a
mean $\sim$600 AU for the full binary sample (likely a direct consequence of
uncorrected incompleteness biases as discussed in Sections 4.2 and 4.3.4).
This is consistent with the observed peak in binary separation from Fontanive
et al. (2019) for such systems ($\sim$250 AU), and further supports the idea
that additional binaries may remain undiscovered in our probed sample on this
separation range.

On the other hand, no robust dependence of binary influence on stellar
companion mass was seen in our results. This is not surprising since the
gravitational pull from a companion scales with
M${}_{\mathrm{c}}/\rho_{\mathrm{bin}}^{2}$ (where Mc is the companion mass and
$\rho_{\mathrm{bin}}$ the binary separation). As the companion masses span a
range of about one order of magnitude, compared to over three orders of
magnitude for the separation (which is then squared), binary separation is
thus expected from physical arguments to have larger impact on the
circumstellar planetary system.

####  4.3.3 Very Close Binaries in Triple Systems

The vast majority of main sequence stars in spectroscopic binaries are known
to be the inner binaries of hierarchical triple systems. Tokovinin et al.
(2006) demonstrated that 96% of binaries with orbital periods below $\sim$3
days have tertiary stellar companions. The occurrence of outer components for
these systems is found to steadily decrease with inner binary period, falling
to a rate of 34% triple systems for spectroscopic binaries with periods of
12–30 days. The excess of tertiary companions has been argued (Fabrycky &
Tremaine, 2007; Naoz & Fabrycky, 2014) to allow for the migration of the inner
companions via Kozai-Lidov oscillations in misaligned triples (Kozai, 1962;
Lidov, 1962). Alternatively, these close binary companions have been suggested
to form via disk fragmentation and migration within the circumstellar disk of
the primary star (Moe & Kratter, 2018). The substantial mass required to form
and drive inward such massive inner companions can simultaneously form
additional tertiary companions, leading to such systems being often in triple-
star configurations. These outer components could then allow for more extreme
migrations of the inner companions, leading to the observed negative
correlation between inner binary period and triple architecture frequency (Moe
& Kratter, 2019).

Fontanive et al. (2019) studied hosts to close giant planets and brown dwarf
companions with masses of 7–60 MJup, inferring a tertiary companion fraction
comparatively high to the spectroscopic binaries from Tokovinin et al. (2006).
This population of sub-stellar companions corresponds to the most massive,
short-separation systems found to be predominantly in hierarchical stellar
structures in this work. Moe & Kratter (2019) further confirmed this excess of
triple occurrence rate to be a statistical, real feature, as well as to be
measurably higher than for genuine hot Jupiters ($<$4 MJup) surveyed by Ngo et
al. (2016). The similar demographics between these brown dwarf desert systems
and stellar spectroscopic binaries argues for a common origin for the inner
companions from Tokovinin et al. (2006) and Fontanive et al. (2019),
indicating that these inner giant planet and brown dwarf companions extent the
population of triple stellar systems to sub-stellar masses for the secondary
components of the inner binaries.

Figure 9: Binary separation distribution comparing the full sample of planet-
hosting binaries (thick blue line) to stellar binaries in the Solar-
neighborhood (dashed black line) from Raghavan et al. (2010). The sample of
planet-bearing multiples is further divided between systems hosting a giant
planet of mass $>$0.1 MJup within 0.5 AU (magenta) and all other systems
(yellow). Multi-planet systems with planets falling into the two planetary
categories are counted towards the close-in giant planet subset. Planet host
stars in close binaries with an outer tertiary companion are plotted as the
inner binary only. Triple systems composed of a planet host and a wide tighter
binary are counted as a binary system using the mean separation to the distant
sub-system. The dashed vertical gray lines show the projected separations
probed for the closest 20$\,\%$, 50$\,\%$ and 100$\,\%$ of our sample for
angular separations of 3 arcsec.

####  4.3.4 The Effect of Binary Separation

In Figure 9, we compare the distributions in projected separation of the
planet-hosting wide binaries (solid yellow line) gathered in this work, and
the Solar-type field binaries (dashed black line) from Raghavan et al. (2010).
For multi-planet systems with planets or brown dwarfs falling into the two
planetary categories considered (55 Cancri, HD 38529 A, Upsilon Andromedae A,
WASP-8), we count the binaries only once, towards the close-in giant planet
subset. Triple systems are accounted for in the same way as in Section 3.3.

The binary separations of the planet-bearing systems appears to peak at
significantly larger values, with a peak around 600 AU compared to $\sim$50 AU
for field binaries. Field binaries also show a much broader distribution, with
a log-width of 1.70 compared to 0.75 for planet-hosting multiples. A
Kolmogorov-Smirnov test confirms that the raw observed distributions are
indeed statistically different, with a p-value for the null hypothesis that
they are drawn from the same distribution $<10^{-5}$. These differences are
primarily due to the incompleteness of our compilation on short binary
separations as discussed in Section 4.2. Furthermore, the field binaries from
Raghavan et al. (2010) include unresolved companions detected by spectroscopic
techniques or proper motion accelerations. Such systems are not detectable
with visual detection methods and a number of such tighter binaries could
remain undetected in our studied sample.

The dashed lines in Figure 9 show the projected separations probed for the
closest 20$\,\%$, 50$\,\%$ and 100$\,\%$ of our sample with angular
separations of 3 arcsec, our adopted completeness limit for Gaia. Our observed
peak in the separation distribution (600 pc) roughly coincides with our inner
completeness limit for the full sample (see Section 4.2). This strongly
suggests that a number of undiscovered binaries with separations of tens to
hundreds of AU may still lie in our sample. For example, the planet host stars
DMPP-3 A and HD 59686 from our exoplanet compilation were both found through
significant radial velocity trends to have close stellar companions at 1.22 AU
(Barnes et al., 2020) and 13.56 AU (Ortiz et al., 2016), respectively. These
companions have never been resolved to this date, and these systems were thus
counted as single in the context of this work, which only considered visual,
astrometrically-confirmed systems. Current high-angular resolution efforts and
complementary detection methods, probing smaller binary separation ranges,
must thus be pursued to obtain a more complete picture of the multiplicity of
exoplanet host stars, and understand the true effect of tight binary
companions on the formation and evolution of extra-solar planets and brown
dwarf companions.

Figure 9 also shows the distribution of binary separation, dividing the sample
between binaries hosting a giant planet or brown dwarf within 0.5 AU (magenta)
and the all other systems (blue). The sample of binaries hosting a short-
period gas giant appears to be on somewhat smaller binary separations than the
remaining planet-hosting multiples, with logarithmic means shifting from
$\sim$500 AU to $\sim$700 AU between the two samples, and a slightly tighter
distribution for the former subset. This is representative of our results from
Section 3.3, which showed an enhanced relative fraction of shorter-separation
binaries for systems with close-in planets, an effect that is further
magnified for the most massive planets and brown dwarfs on very tight orbits.
These results are in agreement with previous observations (Desidera &
Barbieri, 2007) that found massive planets in short period orbits to be in
most cases around the components of rather tight binaries. Finally, the larger
relative number of very wide binaries ($>$1000 AU) for hosts to lower-mass and
larger-separation planets is also consistent with the rest of our results. We
indeed found that such widely-separated binaries generally do not impact the
planet properties (see Figure 5), and observed small and wide-orbit planets to
not be significantly affected by the presence of stellar companions,
compatible with the idea that most such planets are only found in very wide
binaries or around single stars. Desidera & Barbieri (2007) similarly
concluded that the properties of exoplanets orbiting components of very wide
binaries are compatible with those of planets orbiting single stars.

###  4.4 Implications for Formation Mechanisms

The final architectures of planetary systems around members of binary stars
strongly depend on how the presence of a close massive body impacts standard
formation and migration processes, through its efficiency to alter the local
disk environment, accretion rates, or tidal interactions between planets and
the host star. The population trends highlighted throughout this study might
provide new clues and insights into the effects of stellar companions on
planet and brown dwarf formation and evolution.

Our findings show that binarity has little effect on the distributions of
planet mass and semi-major axis for the population of sub-Jovian planets found
inside $\sim$1 AU. The impact of stellar duplicity on short binary separations
($<$50 AU) remains to be fully understood theoretically and better constrained
observationally, as such very tight binaries would be more amenable to
influence disks inner regions crucial for small planet formation and stable
orbital behaviors. Nonetheless, our results demonstrate that sub-Jovian
planets that form in binaries with separations of hundreds of AU are
consistent with the population of single-star planets. This suggests that
stellar multiplicity does not need to be extensively accounted for in order to
reproduce the core of this population of small planets, either completely
inhibiting the formation or survival of such planets, or having no visible
effect on the demographics of successfully formed planets.

In contrast, we found that the populations of intermediate-mass giant planets
(M${}_{\mathrm{pl}}=0.1$–7 MJup) and high-mass sub-stellar companions
(M${}_{\mathrm{pl}}>7$ MJup) show different statistical properties between
single-star systems and hosts with stellar companions. Small-separation
planets and brown dwarf companions within the snow line ($<$1–3 AU) were found
to have somewhat larger masses and/or tighter separations when in binary
stars. This trend is enhanced for the most massive and closest-separation sub-
stellar companions, that also have inflated raw stellar multiplicity rates
compared to lower-mass and wider planets, consistent with previous studies
(Fontanive et al., 2019; Moe & Kratter, 2019). This strongly indicates that
the identified stellar binary companions likely affect the formation and/or
migration of these massive sub-stellar objects, either allowing for more
massive planets to exist at similar separations than planets around single
stars, or enabling similar-mass planets to form or migrate to shorter semi-
major axes in stellar binaries.

Understanding the true nature and extend of these effects is a challenging
task. Unfortunately, available data provide little insight at this stage into
the details of the possible underlying processes, with few prospects to
disentangle between planetary formation and evolution, and missing information
about most orbital elements for binary orbits. Likewise, modeling the
formation and evolution of planets in binaries requires to explore a very wide
parameter space, including binary separations, mass ratios, inclinations and
eccentricities. The large variety of possible binary configurations likely
impacts the existence and properties of planetary systems differently for each
combination of these key binary parameters, from detrimental to perturbing or
even favorable effects.

For circumstellar planets, which represent the focus of this study, a nearby
stellar companion is expected to primarily affect the outer parts of typical
planet formation locations, where the gravitational influence from the stellar
companions will be enhanced. The outskirts of protoplanetary disks are
believed to predominantly harbor more massive planets, with mostly rare, cold
Jovian planets predicted beyond a few tens of AU in the core accretion
paradigm (Emsenhuber et al., 2020), and the formation of massive planets and
brown dwarfs by gravitational disk fragmentation occurring preferentially in
the cool outer regions of disks, from separations of several tens to hundreds
of AU (Rafikov, 2005; Hall et al., 2017). Following this reasoning, giant
planets and brown dwarfs forming at large orbital separations are thus more
likely to be affected by the presence of an outer star in the system than
small planets forming and accreting within a few AU from the host star. The
observed population of wide-orbit ($>$10 AU) planets and brown dwarfs was
found to have a lower raw binary rate than similar-mass sub-stellar companions
on shorter orbits, and no significant differences were observed in planetary
properties between single and multiple-star systems. The effect from outer
companion stars would thus likely be in facilitating inward migration
processes, bringing massive giant planets and brown dwarfs onto extremely
tight orbits typically unreachable in single-star environments, via e.g. the
Kozai-Lidov mechanism (Naoz & Fabrycky, 2014; Winn et al., 2010) or other
triggered dynamical perturbations.

Alternately, binarity could impact separate planet formation channels
differently, i.e., influencing the conditions for gravitational disk
instability, but with little effect on the results of core accretion
mechanisms if they proceed, thus affecting the very most massive planets and
brown dwarfs only. For example, the presence of a nearby companion star within
$\sim$100–300 AU could tidally truncate protoplanetary disks (Kraus et al.,
2012) and lead to faster disk dissipation rates (Müller & Kley, 2012). This
effect would be particularly problematic for giant planet formation by core
accretion, which requires significantly longer timescales to operate than disk
fragmentation. Formation by core accretion would therefore only take place if
the outer companion has little effect on the disk and forming planetary
system, thus not significantly impacting the final planet properties compared
to single star conditions. Similarly, binary companions have been suggested to
be able to trigger instabilities in otherwise stable disks (Boss, 2006), hence
favorably modifying formation environments for in-situ disk fragmentation, but
inconsequential for core accretion. This idea is reconcilable with the high
masses of the outlying population of sub-stellar companions observed to be
predominantly in binaries, which seemingly formed differently from the
population of lower-mass planets on similar orbits, most likely through
gravitational disk fragmentation (Moe & Kratter, 2019).

Finally, our results regarding the separation distribution of binaries might
help to narrow down the effect of at least one binary parameter. As mentioned
previously, there is reliable observational evidence that close binarity
($<$50 AU) hinders planet formation around a host star (Fontanive et al.,
2019; Kraus et al., 2016; Wang et al., 2014), although this feature could not
be robustly investigated in the present work. We also found stellar
multiplicity of very large separations (thousands of AU) to have no
significant impact on observed planetary populations, suggesting that planet
formation and evolutionary patterns in such systems behave similarly as around
single stars. Intermediate separations, from several tens to a few hundreds of
AU, therefore appear to be a key region of the parameter space to explore in
order to further our perspective of exoplanets in stellar binaries.
Examinations of physical quantities in these systems such as binding energy
may be especially interesting to study for a better physical understanding of
the processes in play, and we particularly advocate for investigations to be
conducted in the theoretical context of gravitational disk instability based
on our results.

##  5 Summary

In this work, we have compiled a sample of 938 stars hosting a total of 1316
extra-solar planets and brown dwarf companions, out to 200 pc. We searched for
visual co-moving companions to these systems via an extensive search in the
literature and using the Gaia DR2 catalog to identify common proper motion
sources. This analysis yielded a total of 218 planet hosts in multiple-star
systems, including 186 binaries and 32 hierarchical triple systems, with 10
newly-discovered binary companions and 2 new tertiary components. From these,
4 binaries and 1 triple system contain 2 planet-bearing stars. Stellar
companions have masses ranging from the brown dwarf/star boundary at 0.07 M⊙
up to 2.27 M⊙, with separations ranging from $<$1 AU to 20 000 AU with a
median of $\sim$600 AU.

Investigating our gathered sample of binaries, we found that:

  1. $\bullet$

More massive planet hosts are more often part of multiple-star systems,
consistent with the population of planet-bearing stars following the overall
relative multiplicity outcome of stellar formation.

  2. $\bullet$

Planet hosts in multiple systems were also predominantly observed to be the
most massive component of stellar binaries.

  3. $\bullet$

A total of 27 binary systems have separations $<$100 AU, from which 20 have
binary separations smaller than 50 AU, with 1 system in an extreme $<$1 AU
configuration. Most of these close binaries, however, were only identified
thanks to dedicated high-angular resolution campaigns, and could not, for the
most part, be retrieved with the resolving limit of Gaia (1–3 arcsec), in
particular for the most distant targets in our sample.

  4. $\bullet$

As only a small fraction of planet hosts have been targeted by such imaging
programs, a significant number of sub-arcsecond binaries and companions on
separations of a few arcseconds could still be missing from our catalog,
further supported by the concurrence of our measured peak in binary separation
and our estimated Gaia completeness limit.

Assuming that the selection and observational biases lying in and limiting our
gathered compilation of stellar binaries affect various subsets of planetary
populations and planet hosts in a reasonably homogeneous way, we investigated
possible correlations between planet properties and the existence and
properties of outer stellar companions. Our main results are:

  1. $\bullet$

From our identified sample of binary companions, we measured a raw
multiplicity rate of $23.2\pm 1.6\,\%$ for planet hosts.

  2. $\bullet$

Multi-planet systems were found to have a somewhat lower stellar duplicity
frequency ($18.0\pm 2.7\,\%$) compared to single-planet systems ($25.1\pm
1.9\,\%$) with a 2.2-$\sigma$ significance.

  3. $\bullet$

Dividing the planet parameter space into various sub-populations, we found
that giant planets and brown dwarfs with masses above 0.1 MJup have a
substantially larger (3.6-$\sigma$) raw stellar multiplicity fraction
($25.5\pm 1.8\,\%$) than lower-mass planets ($16.6\pm 1.7\,\%$), consistent
with the fact that these small sub-Jovian planets are typically organized in
tightly-packed multi-planet systems.

  4. $\bullet$

This trend appears to further increase up to about $\sim$30$\,\%$ for massive
planet and brown dwarfs (M${}_{\mathrm{pl}}>7$ MJup) on very short orbital
separations (a${}_{\mathrm{pl}}<0.5$ AU), with the most massive and shortest-
period sub-stellar companions almost exclusively observed in multiple-star
systems. These results are consistent with previous studies of these
populations (Fontanive et al., 2019; Moe & Kratter, 2019), which appear to
follow the architectures of stellar spectroscopic binaries, systematically
observed as part of hierarchical triple systems (Tokovinin et al., 2006).

In terms of planet properties, our results suggest that:

  1. $\bullet$

Stellar duplicity has no significant effect on the demographics of low-mass
planets (M${}_{\mathrm{pl}}<0.1$ MJup) or the core population of warm giant
exoplanets on separations neighboring the snow line (a${}_{\mathrm{pl}}>0.5$
AU).

  2. $\bullet$

Only high-mass, small-separation planets were observed to have different
distributions of planet properties between the subset of planets in binaries
and single-star systems, with an over-density of planets and brown dwarfs of
several Jupiter masses found on semi-major axes of $\sim$0.01–0.1 AU
identified in multiple-star systems.

  3. $\bullet$

These extreme planetary systems with few or no single-star analogues were
predominantly found to be in rather tight binary configurations $<$1000 AU,
and mostly on separations $<$250 AU for sub-stellar companions with masses
$>$7 MJup. These systems represent a sizable fraction of such tight binaries
in our compilation ($\sim$10$\,\%$), despite the rarity of these planets and
brown dwarfs in our overall exoplanet catalog ($\sim$2$\,\%$).

  4. $\bullet$

In contrast, the subset of these planets in binaries with separations $>$1000
AU showed similar distributions in mass and semi-major axis to planets and
brown dwarfs orbiting single stars. This indicates that short ($<$250 AU) or
intermediate-separation ($<$1000 AU) binaries play a role the formation or
evolution of these massive planets and brown dwarfs, but that very wide
binaries do not influence the architectures of planetary systems.

  5. $\bullet$

Binary companion mass, on the other hand, was found to have no significant
effect on planetary properties.

Between the upcoming generation of telescopes and future Gaia data releases,
the next decade promises to lead to unprecedented discoveries and new
characterisation possibilities. These findings will arguably yield
unparalleled information and new robust constraints on system architectures
and population demographics, which will in turn provide key probes into
formation histories and dynamical evolution processes. We hope that the
gathered compilation of exoplanets in visual binaries will be useful to future
studies in this constantly-growing research area, and will motivate the need
to pursue existing campaigns searching for small-separation binary companions
to known planetary systems. With a more comprehensive picture of stellar
multiplicity on the separation ranges demonstrated here to remain highly
incomplete, we will be able to confirm and better understand the tentative
trends highlighted in this paper, and improve our fundamental understanding of
stellar, sub-stellar and planetary formation and evolution.

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

C.F. led this study, performing the catalog compilations and binary searches
and leading the data analyses. D.B.G. contributed to the search for trends
within the obtained catalogs, scientific interpretation of results, and
writing of the paper.

## Acknowledgments

C.F. acknowledges support from the Center for Space and Habitability (CSH).
This work has been carried out within the framework of the NCCR PlanetS
supported by the Swiss National Science Foundation. D.B.G. acknowledges
support from the NASA ADAP award No. 80NSSC19K0532. 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. This research has made
use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at
exoplanets.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). This research has made
use of the SIMBAD database and the VizieR catalogue access tool, operated at
CDS, Strasbourg, France.

## Data Availability Statement

The catalogs compiled in this work and used throughout this study are provided
as supplementary online material. The compilations are also made publicly
available online at
https://docs.google.com/spreadsheets/d/11b29RREm_rTWcpUGvh7M_-
wOQgH8aTiyoxDPHieqXBo/edit?usp=sharing, in a catalog that we plan to update
regularly.

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