The origin of very wide binary stars
M.B.N. Kouwenhoven, S.P. Goodwin, Melvyn B. Davies, Richard J. Parker, P. Kroupa, D. Malmberg
aa r X i v : . [ a s t r o - ph . S R ] A ug Proceedings of the 9th Pacific-Rim Conference on Stellar AstrophysicsASP Conference Series, Vol. c (cid:13) The origin of very wide binary stars
M.B.N. Kouwenhoven , S.P. Goodwin , Melvyn B. Davies ,Richard J. Parker , , P. Kroupa , and D. Malmberg Kavli Institute for Astronomy and Astrophysics, Peking University,Yi He Yuan Lu 5, Haidian District, Beijing 100871, P.R. China Department of Physics and Astronomy, University of She ffi eld, HicksBuilding, Hounsfield Road, She ffi eld S3 7RH, United Kingdom Lund Observatory, Box 43, SE-221 00, Lund, Sweden Institute for Astronomy, ETH Z ¨urich, Wolfgang-Pauli-Strasse 27, 8093 Z ¨urich,Switzerland Argelander Institute for Astronomy, University of Bonn, Auf dem H ¨ugel 71,53121 Bonn, Germany
Abstract.
A large population of fragile, wide ( > AU) binary systems exists inthe Galactic field and halo. These wide binary stars cannot be primordial because of thehigh stellar density in star forming regions, while formation by capture in the Galacticfield is highly improbable. We propose that these binary systems were formed duringthe dissolution phase of star clusters (see Kouwenhoven et al. 2010, for details). Starsescaping from a dissolving star cluster can have very similar velocities, which can leadto the formation of a wide binary systems. We carry out N -body simulations to testthis hypothesis. The results indicate that this mechanism explains the origin of widebinary systems in the Galaxy. The resulting wide binary fraction and semi-major axisdistribution depend on the initial conditions of the dissolving star cluster, while thedistributions in eccentricity and mass ratio are universal. Finally, since most stars areformed in (relatively tight) primordial binaries, we predict that a large fraction of thewide “binary stars” are in fact higher-order multiple systems.
1. Wide binary systems in the Galactic field and halo
The large majority of stars are thought to form as part of a binary or multiple stellarsystem (e.g., Duquennoy & Mayor 1991; Fischer & Marcy 1992; Goodwin & Kroupa2005; Kouwenhoven et al. 2005, 2007). The general consensus is that most star formin embedded star clusters and loosely-bound associations (e.g., Lada & Lada 2003;Bastian 2011), which initially exhibit a significant amount of substructure (e.g., Allison et al.2009). Following proto-star formation, the properties of the binary population evolveover time, primarily due to the e ff ects pre-main sequence evolution (Kroupa 1995) anddynamical interactions with other stars (e.g., Heggie & Hut 2003; Marks et al. 2011).Most star clusters dissolve within 10 −
50 Myr after their formation (see de Grijs & Parmentier2007, and references therein). The field star population is therefore thought to be theresult of a mixture of stars originating from di ff erent star clusters (Goodwin 2010).1 Kouwenhoven, Goodwin, Davies, Parker, Kroupa &MalmbergOver the last decades a significant number of wide ( > AU) binary systems havebeen discovered (see Fig. 1). In the log-normal period distribution of Duquennoy & Mayor(1991), for example, ∼
15% of the binary systems have a semi-major axis larger than10 AU. Individual wide binary systems are often identified in proper motion studies,and occasionally combined with parallaxes, radial velocity measurements and back-ground star statistics (e.g., Makarov et al. 2008; Quinn & Smith 2009; Shaya & Olling2011, and numerous others). The overall properties of the wide binary population canalso be obtained statistically (e.g., Longhitano & Binggeli 2010). Wide binary sys-tems are extremely fragile, and those wider than 0 . − . cannot have formed as primordial binaries in star clus-ters, simply because their orbital separation is comparable to the size of a typicalembedded cluster. Moreover, the typical size of a star forming core is ∼ AU(Ward-Thompson et al. 2007), which sets an absolute maximum to the size of a pri-mordial wide binary system. Even if they were somehow able to form, they would bedestroyed immediately due to stellar encounters (Kroupa 2001; Parker et al. 2009).The fact that it is not possible to form primordial binary systems with semi-majoraxes in the range 10 AU − . N B of binary systems via three-bodyencounters is given by ˙ N B = . G M n σ , (1)(Goodman & Hut 1993), where G is the gravitational constant, M is the typical stellarmass, n the stellar number density, and σ the velocity dispersion. The value of ˙ N B isnegligible for stars in the Galactic field and halo. On the other hand, capture is possiblein the dense cores of star clusters, but this will never result in the formation of long-lived wide binary systems, due to the crowded stellar environment.In Kouwenhoven et al. (2010) we proposed that wide binary systems form duringthe dissolution phase of star clusters. This mechanism can result in a significant pop-ulation of binary systems (see also Moeckel & Bate 2010; Moeckel & Clarke 2011).In this scenario, an unbound pair of escaping stars can form a binary system whentheir relative velocity is small . Our N -body simulations (see below) result in a pop-ulation of wide binary systems with semi-major axes comparable to their initial sepa-ration, a thermal eccentricity distribution, and a mass ratio distribution resulting from(gravitationally-focused) random pairing of components from the initial mass function. Following Kouwenhoven et al. (2010), we define systems with an orbital separation in the range 10 AU ≤ a ≤ . A large population of comets may also be captured by stars via a similar mechanism, during clusterdissolution (e.g., Eggers et al. 1997; Levison et al. 2010) heorigin of verywide binary stars 3 Semi-major axis (au)110100 S e m i - m a j o r a x i s d i s t r i bu t i on PAH2007LB2007DM1991CRC1990 CG2004 HaloCG2004 Disk10 au 0.1 pc 0.2 pc Figure 1. The observed semi-major axis distribution for wide binary systems,compiled from the catalogues of Duquennoy & Mayor (1991); Close et al. (1990);L´epine & Bongiorno (2007); Chanam´e & Gould (2004) and Poveda et al. (2007).
2. Method, initial conditions and N -body simulations To test our hypothesis that wide binary systems are formed during the dissolutionphase of star clusters, we carry out N -body simulations using the STARLAB package(Portegies Zwart et al. 2001). For each star cluster were draw N stars from a Kroupa(2001) mass distribution in the range 0 . −
50 M ⊙ . We study the properties of the result-ing binary population as a function of the number of member stars N (10 ≤ N ≤ R of the star clusters (0.1 pc ≤ R ≤ B (0% ≤ B ≤ Q ≡ E K / E p of the clus-ter, where E k and E p are the kinetic and potential energy of the cluster, respectively.We study the cases Q = / Q = / ff erent stellar density distributionsof the stars: (i) spherical Plummer (1911) models, and (ii) models with substructuredinitial conditions with fractal parameter α = . Q = 1/2 Semi-major axis (AU)0.00.20.40.60.81.0 S e m i - m a j o r a x i s d i s t r i bu t i on Semi-major axis (AU)0.00.20.40.60.81.0 M a ss r a t i o (M sun )0.00.20.40.60.81.0 M a ss r a t i o Q = 3/2 Semi-major axis (AU)0.00.20.40.60.81.0 S e m i - m a j o r a x i s d i s t r i bu t i on Semi-major axis (AU)0.00.20.40.60.81.0 M a ss r a t i o (M sun )0.00.20.40.60.81.0 M a ss r a t i o Figure 2. The semi-major axis distribution ( left ), the correlation between massratio q and semi-major axis a ( middle ) and between primary mass M and mass ratio q ( right ). The properties of the orbits of binary systems and higher-order multiplesystems are indicated with the dots and triangles, respectively. For each multiplesystem with n stellar components, we have included all n − N = R = . Q = / top ) and Q = / bottom ). The vertical dashed lines indicate a = AUand a = . q min ( M ) = M min / M . negative, and (ii) both stars are each others mutual nearest neighbor. In our analysiswe only consider binary systems with a semi-major axis a ≤ . ≥ a out / a in > Q st for multiple stellar systems, where a in and a out are the inner and outerorbits of a (sub)system, respectively, and Q st ≈ −
10 is a stability parameter whichdepends on the orbital configuration. For wide higher-order system with (outer) orbitalperiods of order ∼
3. The wide binary fraction, orbital elements and higher-order multiplicity
A summary of the results of our N -body simulations is listed below. For an extensivedescription of the results we refer to Kouwenhoven et al. (2010). To illustrate the re-sults, we show the orbital properties of a selected sample of the simulations in Figs. 2and 3. (a) The wide binary fraction. After cluster dissolution, the wide binary fraction (i.e.,heorigin of verywide binary stars 5
Q = 1/2 Semi-major axis (AU)0.00.20.40.60.81.0 S e m i - m a j o r a x i s d i s t r i bu t i on Semi-major axis (AU)0.00.20.40.60.81.0 M a ss r a t i o (M sun )0.00.20.40.60.81.0 M a ss r a t i o Q = 3/2 Semi-major axis (AU)0.00.20.40.60.81.0 S e m i - m a j o r a x i s d i s t r i bu t i on Semi-major axis (AU)0.00.20.40.60.81.0 M a ss r a t i o (M sun )0.00.20.40.60.81.0 M a ss r a t i o Figure 3. Same as Fig. 2, but now for substructured models (fractal parameter α = .
5) with N = R = . Q = / top ) and Q = / bottom ); in each case fifty realisations have been simulated. the fraction of wide binary systems as compared to the total number of systems) rangesbetween 1% and 30% for an individual star cluster. The exact value depends the prop-erties of the star cluster at the time of dissolution. The structure of the star cluster at themoment of dissolution, as well as the number of stars, a ff ects the final number of widebinary stars. Substructured star clusters (e.g., Fig. 3) generate significantly more widebinary systems than spherical star clusters (e.g., Fig. 2). The wide binary fraction in-creases with decreasing cluster membership and with increasing initial virial ratio. Thewide binary population in the Galactic field ( ∼ ff erent types of star clusters. Its properties can therefore,in principle, be used to constrain the properties of young star clusters. (b) The semi-major axis distribution. The resulting semi-major axis distribution forwide binary systems is mainly in the range (0 . − R , where R is size of the star clusterat the moment of dissolution. The semi-major axis distribution of the newly formedbinaries typically shows two peaks: a dynamical peak at small values of a , resultingfrom three-body interactions, and an dissolution peak of wide binary systems formedduring the dissolution phase of the star cluster (this is clearly shown in the left-handpanels in Fig. 3). The ratio of the number of binary stars in the dynamical peak and the dissolution peak depends on the initial conditions of the star cluster (see above). (c) The eccentricity distribution. The capture process which results in wide binaryformation is chaotic. The eccentricity distribution for wide binary systems is thereforeexpected to be thermal: f ( e ) = e for 0 ≤ e < (%)020406080100 H i ghe r- o r de r m u l t i p li c i t y o f w i de " b i na r y " sys t e m s ( % ) Binary systemsTriple systemsQuadruple systems
Figure 4. Most stars form as a member of a primordial binary system. Many wide“binary” systems formed during the star cluster dissolution process are thereforeexpected to be higher-order multiple systems. The relative multiplicities of widesystems can in principle be used to constrain the binary fraction B at the time of starcluster dissolution. (d) The mass ratio distribution. The mass ratio distribution for wide binary systems re-sults from gravitationally-focused random pairing (e.g., Kouwenhoven et al. 2009, andreferences therein) of the individual components. This implies that wide binaries witha high-mass primary star have a small mass ratio, while those with a low-mass binaryhave a high mass ratio (see Figs. 2 and 3). In addition, the wide binary fraction slowlyincreases with increasing primary star mass. (e) Orientation of the orbits.
The orientation of the stellar spins of the two stars ina wide binary system are randomly aligned. In the case of a wide multiple system, theorbital orientations of the inner orbits are also randomly aligned with respect to eachother, and with respect to the orbit of the wide orbit. (f) Implications for higher-order multiplicity.
A significant fraction of star form aspart of a primordial binary system. Both components of a wide “binary” system aretherefore expected to be binary themselves. Recent observations suggest indeed thatwide “binary” systems are frequently triple or quadruple systems (Makarov et al. 2008;Mamajek et al. 2010; Faherty et al. 2010; Law et al. 2010). The multiplicity ratiosamong wide systems can therefore be used to constrain the primordial binary fraction,or more specifically, the binary fraction at the moment of star cluster dissolution (seeFig. 4).There is an ongoing debate about the wide binary formation mechanism itself. Kouwenhoven et al.heorigin of verywide binary stars 7(2010) shows that a pair of (previously unbound) stars can form a wide binary systemduring the dissolution phase, while the study of Moeckel & Clarke (2011) shows thata small (but transient) population of wide binary systems is always present in a starcluster, and that this wide binary population is frozen in when a star cluster dissolves.It may well be possible that both mechanisms contribute to the formation of the widebinary population in the Galactic field and halo.
4. Summary
Approximately 15% of the known binary systems in the Galaxy have an orbital sepa-ration larger than 10 AU. These systems cannot be primordial, simply because theirorbital separations are comparable to the size of young embedded clusters. Moreover,if they were able to form in such environments, they would immediately be destroyedby dynamical interactions with other stars. Dynamical capture in the Galactic field orhalo is highly improbable due to the low stellar density and high velocity dispersion,and cannot explain the observed wide binary population either.We propose that wide binary systems form during the dissolution phase of starclusters (see Kouwenhoven et al. 2010, for details). In this scenario, an escaping pair ofstars with a small relative velocity can form a wide binary system. N -body simulationsconfirm this hypothesis, and allow us to predict the prevalence and orbital properties ofthe wide binary population ( § Acknowledgments.
M.B.N.K. was supported by the Peter and Patricia GruberFoundation through the IAU-PPGF fellowship, by the Peking University One HundredTalent Fund (985), and by the National Natural Science Foundation of China (grants11010237 and 11043007). The authors acknowledge the She ffi eld-Bonn Royal SocietyInternational Joint Project grant, which provided financial support and the collaborativeopportunities for this work. References
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