The document summarizes simulations showing that perturbations from the Milky Way can disrupt planetary systems in wide binary star systems (average separations over 1,000 AU) by driving variations in the binary orbit. Specifically: - Simulations found that 30-60% of planetary systems in wide binaries experience instabilities causing planetary ejections over 10 billion years due to low binary pericentre passages driven by Galactic tides. - The eccentricity distribution of giant exoplanets in wide binaries is significantly higher than around single stars, consistent with additional scattering triggered by time-varying binary companions. - Additional simulations reproduced the observed eccentricity distributions by assuming similar initial planetary systems that undergo scattering both in isolation and with a distant

1. LETTER doi:10.1038/nature11780
Planetary system disruption by Galactic
perturbations to wide binary stars
Nathan A. Kaib1,2{, Sean N. Raymond3,4 & Martin Duncan1
Nearly half the exoplanets found within binary star systems reside1 To investigate this scenario, we use the Mercury simulation package
in very wide binaries with average stellar separations greater than to perform 2,600 simulations modelling the orbital evolution of our
1,000 astronomical units (one astronomical unit (AU) being the Sun’s four giant planets (on their current orbits) in the presence of a
Earth–Sun distance), yet the influence of such distant binary com- very wide binary companion10. These simulations are listed as set A in
panions on planetary evolution remains largely unstudied. Unlike Table 1, which briefly summarizes the initial conditions of our dif-
their tighter counterparts, the stellar orbits of wide binaries con- ferent simulations (see Supplementary Information for details). An
tinually change under the influence of the Milky Way’s tidal field example simulation is shown in Fig. 1. Initially, the binary companion
and impulses from other passing stars. Here we report numerical has no effect on the planets’ dynamics because its starting pericentre
simulations demonstrating that the variable nature of wide binary (q; solid black line in Fig. 1) is ,3,000 AU. However, after 1 Gyr of
star orbits dramatically reshapes the planetary systems they host, evolution, Galactic perturbations drive the binary pericentre near
typically billions of years after formation. Contrary to previous 100 AU, exciting the eccentricities of Neptune and Uranus. Once again,
understanding2, wide binary companions may often strongly perturb at 3.5 Gyr, the binary passes through another low-pericentre phase,
planetary systems, triggering planetary ejections and increasing the this time triggering the ejection of Uranus. Last, at 7.2 Gyr, the binary
orbital eccentricities of surviving planets. Although hitherto not makes a final excursion to low q, causing Neptune’s ejection.
recognized, orbits of giant exoplanets within wide binaries are statis- Such behaviour is not unusual. Depending on the binary’s mass and
tically more eccentric than those around isolated stars. Both eccent- semimajor axis (mean separation, or a*), Fig. 2a demonstrates that
ricity distributions are well reproduced when we assume that isolated ,30–60% of planetary systems in simulation set A experience instabi-
stars and wide binaries host similar planetary systems whose outer- lities causing one or more planetary ejections after 10 Gyr (the approx-
most giant planets are scattered beyond about 10 AU from their imate age of our Galaxy’s thin disk). Even though binaries with smaller
parent stars by early internal instabilities. Consequently, our results semimajor axes are less affected by Galactic perturbations, Fig. 2a
suggest that although wide binaries eventually remove the most dis- shows that the influence of binary semimajor axis on planetary insta-
tant planets from many planetary systems, most isolated giant exo- bility rates is weak. This is because tighter binaries make pericentre
planet systems harbour additional distant, still undetected planets. passages at a higher frequency. In addition, when they reach low-q
Unlike binary stars with separations below ,103 AU, very widely phases they remain stuck there for a much longer time than wider
separated binaries (‘wide binaries’) are only weakly bound by self- binaries. As Fig. 2b shows, both of these effects cause tighter binaries
gravity, leaving them susceptible to outside perturbations. As a result, to become lethal (that is, destabilizing) at a much larger pericentre,
the Milky Way’s tide and impulses from other passing stars strongly offsetting the Galaxy’s diminished influence. Most binary-triggered
perturb wide-binary orbits3,4. These perturbations, which are fairly instabilities are very delayed. For binaries with aà >2,000 AU, Fig. 2c
independent of the orbiting object’s mass, are also known to dramati- shows that well over 90% of instabilities occur after at least 100 Myr of
cally affect the dynamics of Solar System comets at similar orbital evolution, well after planet formation is complete. For tighter binaries,
distances5,6. Galactic perturbations drive a pseudo-random walk in many more begin in orbits that destabilize the planets nearly instantly.
the pericentres of these comets (the closest approach distances to the Although planets are believed to form on nearly circular orbits11,
Sun)5,7. The same effect will occur in wide-binary orbits. Thus, even if a most known giant planets (m sin i . 1 MJup, where m is the planet’s
very wide binary’s initial pericentre is quite large, it will inevitably mass, i its orbital inclination and MJup is Jupiter’s mass) have signi-
become very small at some point if it remains gravitationally bound ficant non-zero orbital eccentricities (eccentricities of less massive
and evolves long enough. Such low-pericentre phases will pro- planets are known to be lower, or ‘colder’)12. This observed eccentricity
duce close stellar passages between binary members, with potentially distribution can be reproduced remarkably well when systems of
devastating consequences for planetary systems in these binaries8,9. circularly orbiting planets undergo internal dynamical instabilities
Counterintuitively, we therefore suspect that wide binary compa- causing planet–planet scattering events that eject some planets and
nions could more dramatically affect planetary system evolution than excite the survivors’ eccentricities13–16. For planetary systems within
tight binaries. wide binaries, Fig. 2a predicts that many should undergo additional
Table 1 | Initial conditions of simulation sets
Name of simulation set Number of planets Planet masses (MJup) Planet a-range (AU) Binary mass (M[) Binary a* (AU) External perturbations included
A 4 SS SS 0.1–1.0 1,000–30,000 Tide 1 stars
B1 3 0.5 to ,15 2 to ,15 None None None
B2 3 0.5 to ,15 2 to ,15 0.4 1,000–30,000 Tide 1 stars
B3 3 0.5 to ,15 2 to ,15 0.4 1,000–30,000 None
SS refers to planetary systems resembling the Solar System’s four giant planets. Tide 1 stars refers to perturbations from the Galactic tide and passing field stars. MJup, mass of Jupiter; a, semimajor axis; M[, solar mass.
1
Department of Physics, Queen’s University, Kingston, Ontario K7L 3N6, Canada. 2Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada. 3Universite de
´
Bordeaux, Observatoire Aquitain des Sciences de l’Univers, 2 rue de l’Observatoire, BP 89, F-33271 Floirac Cedex, France. 4CNRS, UMR 5804, Laboratoire d’Astrophysique de Bordeaux, 2 rue de
l’Observatoire, BP 89, F-33271 Floirac Cedex, France. {Present address: Center for Interdisciplinary Exploration and Research in Astrophysics and Department of Physics and Astronomy, Northwestern
University, 2131 Tech Drive, Evanston, Illinois 60208, USA.
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2. RESEARCH LETTER
104 a
0.7
1.0 HD 80606
HD 20782 0.6
103 0.8
Instability fraction
Distance (AU)
0.5
m (Mʘ)
0.6
*
0.4
102
0.4
N 0.3
U
0.2
S
101 0.2
J
0 2 4 6 8 b
Time (Gyr) 250
1.0 HD 80606
Figure 1 | Typical binary-triggered disruption. Simulation of a binary-
triggered instability in a planetary system resembling our own Solar System. HD 20782
200
Critical pericentre (AU)
The pericentre and apocentre are plotted for Jupiter (J; red lines), Saturn (S; 0.8
gold), Uranus (U; cyan) and Neptune (N; blue). The binary’s semimajor axis
m (Mʘ)
(dotted black line) and pericentre (solid black line) are also shown. 150
0.6
*
dynamical instabilities triggered by their stellar companions. Thus,
these systems should experience an even greater number of planet– 0.4 100
planet scattering events than isolated planetary systems.
This raises the possibility that the eccentricities of exoplanets may 0.2 50
hold a signature of the dynamical process illustrated in Fig. 1. Indeed,
the overall distribution of exoplanet eccentricities provides com-
pelling evidence of our disruptive mechanism. Figure 3a compares c
the observed eccentricity distribution of all Jovian-mass (m sin
i . 1 MJup) exoplanets found in binaries1 with the distribution of 1.0 HD 80606
Jovian-mass planets around isolated stars. As can be seen, the distri-
HD 20782 0.9
Delayed instability fraction
bution of planets within wide binaries is significantly hotter (or more
0.8
biased to higher eccentricities) than planetary systems without known
stellar companions. A Kolmogorov-Smirnov test returns a probability
m (Mʘ)
(P-value) of only 0.6% that such a poor match between the two data sets 0.6 0.7
*
will occur if they sample the same underlying distribution. Thus, we
reject the null hypothesis that the distributions are the same. Although 0.4
it consists of just 20 planets, our wide-binary planetary sample contains
0.5
the two most eccentric known exoplanet orbits, HD 80606b and HD 0.2
20782b (see Fig. 2). Furthermore, these excited eccentricities seem to be
confined to only very wide binary systems. Figure 3a also shows the
1,000 3,000 10,000 30,000
eccentricity distribution of planets residing in binaries with average
a (AU)
separations below 103 AU. Unlike the case for wider binaries, here we *
see that these eccentricities match very closely with the isolated distri- Figure 2 | Disruption as a function of binary mass and separation.
bution. (A Kolmogorov-Smirnov test returns a P-value of 91%.) This a–c, Maps of the fraction of systems in set A (see Table 1) that lost at least one
suggests that the variable nature of distant binary orbits is crucial to planet via instability (a), the median binary pericentre below which an instability
exciting planetary orbits. Large eccentricities of planets within binaries is induced in planetary systems (b) and the fraction of instabilities that occur after
have previously been explained with the Kozai resonance17–20, yet this the first 100 Myr of evolution (c). In each panel, binary mass (m*) is plotted on the
effect should be most evident in these tighter binary systems. y axis, and the binary semimajor axis (a*) is plotted on the x axis; black data points
We perform additional simulations, attempting to explain the mark the masses and presumed semimajor axes of the HD 80606 and HD 20782
observed eccentricity excitation in Fig. 3a with the mechanism illu- binaries, which host the two most eccentric known planetary orbits26,27. Although
HD 80606b has been reproduced with a Kozai-driven mechanism, this process is
strated in Fig. 1. These additional simulation sets are summarized in markedly slower in even wider binaries such as HD 20782b28. Moreover, the
Table 1 (B1–B3). Unlike the internally stable planetary systems in presence of more than one planet suppresses these Kozai oscillations28–30.
simulation set A, these simulated systems consist of three approximately However, our disruptive mechanism naturally collapses many systems to one
Jovian-mass planets started in unstable configurations (to induce planet, still enabling Kozai resonances to contribute to eccentricity excitation.
planet–planet scattering) and evolved for 10 Gyr (see Supplemen- Panel a suggests that binary-triggered instability rates become extremely high as
tary Information). In the simulation sets presented in Fig. 3b, we binary semimajor axes drop below ,103 AU, which could mean that tighter
naturally reproduce both observed eccentricity distributions using binaries trigger planetary system instabilities even more efficiently than those
the same initial planetary systems. When our planetary systems are plotted here. However, the initial conditions assumed for both our planetary
orbits (Solar System-like) and binary orbits (isotropic) become questionable for
run in isolation (set B1 in Table 1) planet–planet scattering caused by binary semimajor axes below ,103 AU (see Supplementary Information).
internal instabilities yields the observed planetary eccentricities for Another interesting aspect not immediately obvious in c is that instability times
isolated stars (Kolmogorov-Smirnov test P-value of 42%). Then when decrease at the largest binary semimajor axes. This is because such binaries are
a 0.4M[ binary companion is added to each system (set B2 in Table 1) rapidly unbound (or ‘ionized’) by stellar impulses, making it impossible for these
the eccentricity distribution is heated further, and again the match to binaries to trigger instabilities at very late epochs (see Supplementary Information).
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3. LETTER RESEARCH
1.0 1.0 much more excited eccentricities compared to the compact systems.
a b This is because binaries do not have to evolve to such low pericentres to
0.8 0.8 disrupt extended systems. In fact, the observed wide-binary plane-
Cumulative fraction
tary eccentricity distribution cannot be matched without using wide
0.6 0.6 binaries with planets beyond 10 AU (P 5 1.6% from a Kolmogorov-
Smirnov test). Assuming planets form similarly in wide binaries and
0.4 0.4 isolated systems, the planetary eccentricity excitation observed within
wide binaries may offer new constraints on the bulk properties of
0.2 0.2 isolated giant exoplanet systems, which dominate the giant exoplanet
Simulation set B1
Observed a < 1,000 AU Simulation set B2 catalogue. Whereas most detection efforts are currently insensitive to
*
0.0 0.0 planets with periods beyond ,10 yr, our work suggests that massive,
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
longer-period planets (beyond ,10 AU) should be common around
1.0 1.0 isolated stars. Indeed, such distant planets have recently been directly
c d observed21 and microlensing results suggest many such planets reside
0.8 0.8 far from host stars22.
Cumulative fraction
Owing to the variable nature of their orbits, very distant binary
0.6 0.6 companions may affect planetary evolution at least as strongly as their
tighter counterparts. This represents a paradigm shift in our under-
0.4 0.4 standing of planet-hosting binaries, because previous work tended to
assume that only tighter binaries strongly influence planetary system
0.2 0.2 B2: rpl < 10 AU
evolution2,23. Intriguingly, the eccentricities of planets in wide binaries
Simulation set B1
Simulation set B3 B2: rpl > 10 AU may provide new constraints on the intrinsic architectures of all plane-
0.0 0.0 tary systems. To develop this prospect further, searches for common
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 proper motion companions to planet-hosting stars should be con-
Eccentricity Eccentricity tinued and expanded2,23–25.
Figure 3 | Eccentricity excitation of planets of wide binaries. Comparison of Received 27 July; accepted 1 November 2012.
planetary eccentricity distributions. In all panels, pale red lines correspond to
Published online 6 January 2013.
observed systems with very wide (a* . 103 AU) companions and pale blue lines
are for observed isolated systems. Dashed lines describe the innermost planets 1. Roell, T., Neuha ¨user, R., Seifahrt, A. & Mugrauer, M. Extrasolar planets in stellar
in our simulated systems (sets B1–B3 in Table 1). In all distributions, planets multiple systems. Astron. Astrophys. 542, A92 (2012).
with a , 0.1 AU are excluded to remove tidally circularized orbits. a, A 2. Desidera, S. & Barbieri, M. Properties of planets in binary systems. The role of
comparison of observed exoplanet eccentricities within tighter (a* , 103 AU) binary separation. Astron. Astrophys. 462, 345–353 (2007).
binaries (solid black line) to those observed in very wide (a* . 103 AU) binaries 3. Heggie, D. C. & Rasio, F. A. The effect of encounters on the eccentricity of binaries in
clusters. Mon. Not. R. Astron. Soc. 282, 1064–1084 (1996).
and isolated systems. b, Eccentricities of simulated three-planet systems after
4. Jiang, Y.-F. & Tremaine, S. The evolution of wide binary stars. Mon. Not. R. Astron.
10 Gyr of evolution (sets B1 and B2 in Table 1). c, Simulations from b rerun Soc. 401, 977–994 (2010).
with no Galactic perturbations (set B3 in Table 1). d, The final eccentricities of 5. Oort, J. H. The structure of the cloud of comets surrounding the Solar System and a
two different subgroups of wide binary simulations from b: systems that hypothesis concerning its origin. Bull. Astron. Inst. Neth. 11, 91–110 (1950).
consisted of two planets extending beyond 10 AU at 10 Myr (black line), and 6. Heisler, J. & Tremaine, S. The influence of the galactic tidal field on the Oort comet
two-planet systems confined inside 10 AU at 10 Myr (green). Notice in b that the cloud. Icarus 65, 13–26 (1986).
presence of a wide binary does not seem to enhance the production of very 7. Kaib, N. A. & Quinn, T. Reassessing the source of long-period comets. Science 325,
1234–1236 (2009).
extreme planetary eccentricities. However, one-quarter of our wide binary
8. Adams, F. C. & Laughlin, G. Constraints on the birth aggregate of the Solar System.
systems have planets driven into the central star (1.7 times the rate within Icarus 150, 151–162 (2001).
isolated systems). Tidal dissipation not included in our models could strand 9. Zakamska, N. L. & Tremaine, S. Excitation and propagation of eccentricity
these planets in very eccentric orbits before they collide with the central star19,20. disturbances in planetary systems. Astron. J. 128, 869–877 (2004).
Interestingly, binaries also completely strip 20% of our systems of planets, 10. Chambers, J. E., Quintana, E. V., Duncan, M. J. & Lissauer, J. J. Symplectic integrator
yielding naked stars that once hosted planets (see Supplementary Information). algorithms for modeling planetary accretion in binary star systems. Astron. J. 123,
2884–2894 (2002).
11. Lissauer, J. J. Planet formation. Annu. Rev. Astron. Astrophys. 31, 129–172
observations is quite good, with a Kolmogorov-Smirnov test P-value (1993).
of 46%. 12. Wright, J. T. et al. Ten new and updated multiplanet systems and a survey of
In Fig. 3c, the match to observed planetary eccentricities is much exoplanetary systems. Astrophys. J. 693, 1084–1099 (2009).
poorer. Here we rerun our binary simulations with Galactic perturba- 13. ´
Juric, M. & Tremaine, S. Dynamical origin of extrasolar planet eccentricity
distribution. Astrophys. J. 686, 603–620 (2008).
tions shut off to yield static binary orbits (set B3 in Table 1). In this 14. Ford, E. B. & Rasio, F. A. Origins of eccentric extrasolar planets: testing the planet-
case, the eccentricity distribution is barely more excited than the iso- planet scattering model. Astrophys. J. 686, 621–636 (2008).
lated cases, indicating that the variable nature of wide-binary orbits is 15. Malmberg, D. & Davies, M. B. On the origin of eccentricities among extrasolar
crucial to heating planetary eccentricities. Otherwise, most stellar com- planets. Mon. Not. R. Astron. Soc. 394, L26–L30 (2009).
16. Raymond, S. N., Armitage, P. J. & Gorelick, N. Planet-planet scattering in
panions always remain far from the planets. planetesimal disks. II. Predictions for outer extrasolar planetary systems.
In Fig. 3d we reexamine simulation set B2 to determine which types Astrophys. J. 711, 772–795 (2010).
of planetary systems are most influenced by wide binary companions. 17. Kozai, Y. Secular perturbations of asteroids with high inclination and eccentricity.
Astron. J. 67, 591–598 (1962).
By examining the planetary systems after only 10 Myr, we can view 18. Holman, M., Touma, J. & Tremaine, S. Chaotic variations in the eccentricity of the
them after most have experienced internal instabilities but before the planet orbiting 16 Cygni B. Nature 386, 254–256 (1997).
binary has played a large role (because its effects are delayed). We find 19. Wu, Y. & Murray, N. Planet migration and binary companions: the case of HD
that 70% of our planetary systems have collapsed to two planets. (The 80606b. Astrophys. J. 589, 605–614 (2003).
20. Fabrycky, D. & Tremaine, S. Shrinking binary and planetary orbits by Kozai cycles
remaining systems are composed of nearly equal numbers of one- with tidal friction. Astrophys. J. 669, 1298–1315 (2007).
planet and three-planet systems.) We then split these two-planet sys- 21. Marois, C., Zuckerman, B., Konopacky, Q. M., Macintosh, B. & Barman, T. Images of
tems into those with the outer planet beyond 10 AU and those with both a fourth planet orbiting HR 8799. Nature 468, 1080–1083 (2010).
planets confined inside 10 AU. In Fig. 3d, the final (t 5 10 Gyr) eccen- 22. The Microlensing Observations in Astrophysics (MOA) Collaboration & The Optical
Gravitational Lensing Experiment (OGLE) Collaboration. Unbound or distant
tricity distribution is shown for both subgroups of planetary systems. planetary mass population detected by gravitational microlensing. Nature 473,
As can be seen, the more extended planetary systems eventually yield 349–352 (2011).
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4. RESEARCH LETTER
23. Eggenberger, A. et al. The impact of stellar duplicity on planet occurrence and 30. Kaib, N. A., Raymond, S. N. & Duncan, M. J. 55 Cancri: a coplanar planetary system
properties. I. Observational results of a VLT/NACO search for stellar companions to that is likely misaligned with its star. Astrophys. J. 742, L24 (2011).
130 nearby stars with and without planets. Astron. Astrophys. 474, 273–291
(2007). Supplementary Information is available in the online version of the paper.
24. Raghavan, D. et al. Two suns in the sky: stellar multiplicity in exoplanet systems.
ˇ
Acknowledgements We thank J. Chambers and R. Roskar for discussions. This work
Astrophys. J. 646, 523–542 (2006).
was funded by a CITA National Fellowship and Canada’s NSERC. S.N.R. thanks the PNP
25. Mugrauer, M. et al. A search for wide visual companions of exoplanet host stars: the
programme of CNRS and the NASA Astrobiology Institute’s Virtual Planetary
Calar Alto survey. Astron. Nachr. 327, 321–327 (2006).
Laboratory team. Our computing was performed on the SciNet General Purpose
26. Jones, H. R. A. et al. High-eccentricity planets from the Anglo-Australian Planet
Cluster at the University of Toronto.
Search. Mon. Not. R. Astron. Soc. 369, 249–256 (2006).
27. Naef, D. et al. HD 80606 b, a planet on an extremely elongated orbit. Astron. Author Contributions N.A.K. performed the simulations and analysis and was the
Astrophys. 375, L27–L30 (2001). primary writer of this paper. S.N.R. and M.D. helped initiate the project and advised on
28. Innanen, K. A., Zheng, J. Q., Mikkola, S. & Valtonen, M. J. The Kozai mechanism and simulations and analysis.
the stability of planetary orbits in binary star systems. Astron. J. 113, 1915–1919
(1997). Author Information Reprints and permissions information is available at
29. Batygin, K., Morbidelli, A. & Tsiganis, K. Formation and evolution of planetary www.nature.com/reprints. The authors declare no competing financial interests.
systems in presence of highly inclined stellar perturbers. Astron. Astrophys. 533, A7 Readers are welcome to comment on the online version of the paper. Correspondence
(2011). and requests for materials should be addressed to N.A.K. (nkaib@astro.queensu.ca).
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