The dynamical decay of unstable 4-body systems

Unstable 4-body systems with negative energy can ultimately decay to (1) a binary plus two single stars, (2) two separate binaries, or (3) a stable triple plus a single star. One hundred random 2-dimensional and one hundred random 3-dimensional 4-body systems have been numerically integrated to determine the statistics of the end products. Of the final stable triples and binaries, 19% were triples, which agrees well with observational estimates of the ratio of triples to binaries. The results were essentially the same for 2- and 3- dimensional systems.     

Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood

The stars that populate the solar neighbourhood were formed in stellar clusters. Through N -body simulations of these clusters, we measure the rate of close encounters between stars. By monitoring the interaction histories of each star, we investigate the singleton fraction in the solar neighbourhood. A singleton is a star which formed as a single star, has never experienced any close encounters with other stars or binaries, or undergone an exchange encounter with a binary. We find that, of the stars which formed as single stars, a significant fraction is not singletons once the clusters have dispersed. If some of these stars had planetary systems, with properties similar to those of the Solar System, the planets' orbits may have been perturbed by the effects of close encounters with other stars or the effects of a companion star within a binary. Such perturbations can lead to strong planet–planet interactions which eject several planets, leaving the remaining planets on eccentric orbits. Some of the single stars exchange into binaries. Most of these binaries are broken up via subsequent interactions within the cluster, but some remain intact beyond the lifetime of the cluster. The properties of these binaries are similar to those of the observed binary systems containing extrasolar planets. Thus, dynamical processes in young stellar clusters will alter significantly any population of Solar System-like planetary systems. In addition, beginning with a population of planetary systems exactly resembling the Solar System around single stars, dynamical encounters in young stellar clusters may produce at least some of the extrasolar planetary systems observed in the solar neighbourhood.     

Accretion and dynamical interactions in small-N star-forming clusters: N= 5

We present results from high-resolution hydrodynamical simulations that explore the effects of small-scale clustering in star-forming regions. A large ensemble of small- N clusters with five stellar seeds have been modelled and the resulting properties of stars and brown dwarfs statistically derived and compared with observational data.
Close dynamical interactions between the protostars and competitive accretion driven by the cloud collapse are shown to produce a distribution of final masses that is bimodal, with most of the mass residing in the binary components. When convolved with a suitable core mass function, the final distribution of masses resembles the observed initial mass function, in both the stellar and substellar regimes. Binaries and single stars are found to constitute two kinematically distinct populations, with about half of the singles attaining velocities ≥2 km s⁻¹, which might deprive low-mass star-forming regions of their lightest members in a few crossing times. The eccentricity distribution of binaries and multiples is found to follow a distribution similar to that of observed long-period (uncircularized) binaries.
The results obtained support a mechanism in which a significant fraction of brown dwarfs form under similar circumstances as those of normal stars but are ejected from the common envelope of unstable multiple systems before their masses exceed the hydrogen burning limit. We predict that many close binary stars should have wide brown dwarf companions. Brown dwarfs, and, in general, very low-mass stars, would be rare as pure binary companions. The binary fraction should be a decreasing function of primary mass, with low-mass or substellar primaries being scarce. Where such binaries exist, they are expected either to be close enough (semimajor axis ∼10 au) to survive strong interactions with more massive binaries or to be born in very small molecular cloud cores.     

How well do starlab and nbody4 compare? I. Simple models

N -body simulations are widely used to simulate the dynamical evolution of a variety of systems, among them star clusters. Much of our understanding of their evolution rests on the results of such direct N -body simulations. They provide insight in the structural evolution of star clusters, as well as into the occurrence of stellar exotica. Although the major pure N -body codes starlab/kira and nbody4 are widely used for a range of applications, there is no thorough comparison study yet.
Here, we thoroughly compare basic quantities as derived from simulations performed either with starlab/kira or nbody4 .
We construct a large number of star cluster models for various stellar mass function settings (but without stellar/binary evolution, primordial binaries, external tidal fields, etc.), evolve them in parallel with starlab/kira and nbody4 , analyse them in a consistent way and compare the averaged results quantitatively. For this quantitative comparison, we develop a bootstrap algorithm for functional dependencies.
We find an overall excellent agreement between the codes, both for the clusters' structural and energy parameters as well as for the properties of the dynamically created binaries. However, we identify small differences, like in the energy conservation before core collapse and the energies of escaping stars, which deserve further studies.
Our results reassure the comparability and the possibility to combine results from these two major N -body codes, at least for the purely dynamical models (i.e. without stellar/binary evolution) we performed. Further detailed comparison studies for more complex systems, e.g. including stellar/binary evolution, are required.     

The tightening of wide binaries in dSph galaxies through dynamical friction as a test of the dark matter hypothesis

We estimate the time-scales for orbital decay of wide binaries embedded within dark matter haloes, due to dynamical friction against the dark matter particles. We derive analytical scalings for this decay and calibrate and test them through the extensive use of N -body simulations, which accurately confirm the predicted temporal evolution. For density and velocity dispersion parameters as inferred for the dark matter haloes of local dSph galaxies, we show that the decay time-scales become shorter than the ages of the dSph stellar populations for binary stars composed of  1 M_⊙  stars, for initial separations larger than 0.1 pc. Such wide binaries are conspicuous and have been well measured in the solar neighbourhood. The prediction of the dark matter hypothesis is that they should now be absent from stellar populations embedded within low velocity dispersion, high-density dark mater haloes, as currently inferred for the local dSph galaxies, having since evolved into tighter binaries. Relevant empirical determinations of this will become technically feasible in the near future, and could provide evidence to discriminate between dark matter particle haloes or modified gravitational theories, to account for the high dispersion velocities measured for stars in local dSph galaxies.     

On evolution of contact eclipsing binaries

It is shown that during contact eclipsing binaries evolution under the influence of stellar wind, magnetic stellar wind and with matter transfer by gas flow, in binary stellar systems there may take place a process of star merger (low mass stars) within 10⁵–10⁷ yr and a fast increase of distance between stars of massive binaries. W UMa-type stars are a finite evolutionary stage of very close and low mass binary pairs. As for contact systems of early spectral types (CE-systems), they are more varied in evolution.     

Dynamics of rotating triple systems

We investigate the dynamical evolution of 100 000 rotating triple systems with equal-mass components. The system rotation is specified by the parameter ω=?c²E, where c and E are the angular momentum and total energy of the triple system, respectively. We consider ω=0.1,1, 2, 4, 6 and study 20 000 triple systems with randomly specified coordinates and velocities of the bodies for each ω. We consider two methods for specifying initial conditions: with and without a hierarchical structure at the beginning of the evolution. The evolution of each system is traced until the escape of one of the bodies or until the critical time equal to 1000 mean system crossing times. For each set of initial conditions, we computed parameters of the final motions: orbital parameters for the final binary and the escaping body. We analyze variations in the statistical characteristics of the distributions of these parameters with ω. The mean disruption time of triple systems and the fraction of the systems that have not been disrupted in 1000 mean crossing times increase with ω. The final binaries become, on average, wider at larger angular momenta. The distribution of their eccentricities does not depend on ω and generally agrees with the theoretical law f(e)=2e. The velocities of the escaping bodies, on average, decrease with increasing angular momentum of the triple system. The fraction of the angles between the escaping-body velocity vector and the triple-system angular momentum close to 90° increases with ω. Escapes in the directions opposite to rotation and prograde motions dominate at small and large angular momenta, respectively. For slowly rotating systems, the angular momentum during their disruption is, on average, evenly divided between the escaping body and the final binary, whereas in rapidly rotating systems, about 80% of the angular momentum is carried away by the escaping component. We compare our numerical simulations with the statistical theory of triple-system disruption.     

GG Tau: the ringworld and beyond

In binary stellar systems, exoplanet searches have revealed planetary mass companions orbiting both in circumstellar and in circumbinary orbits. Modelling studies suggest increased dynamical complexity around the young stars that form such systems. Circumstellar and circumbinary disks likely exhibit different physical conditions for planet formation, which also depends on the stellar separation. Although binaries and higher order multiple stars are relatively common in nearby star-forming regions, surprisingly few systems with circumbinary distributions of proto-planetary material have been found. With its spectacular ring of dust and gas encircling the central triple star, one such system, GG Tau A, has become a unique laboratory for investigating the physics of circumsystem gas and dust evolution. We review here its physical properties.     

Be/X射线双星包层性质的研究

Be单星和Be/X射线双星作为一类特殊早型天体和特殊的大质量X射线双星 ,在各个波段都有与其它相同光谱型的B型天体显著不同的特征 ,因此长期以来引起中外天文学者的关注。首先在可见光波段发射线的存在 ,就是对仅产生吸收线的经典大气的挑战 ;其次Be星作为一类早型带有包层天体 ,研究Be星包层的性质 ,对研究原恒星包层性质和进一步了解早型星其它光谱型的性质是非常重要的 ;再者可以研究Be星的存在与星际磁场或湍流的星际介质是否有关 ;最后研究Be/X射线双星 ,对双星的演化模型也有很重要的作用。随着天文观测手段的不断完善和理论模型的发展 ,我们对Be星的现象有了更深的了解 ,并且产生了一些模型。研究内容包括Be星包层和星风的性质 ,以及包层形成机制 ,Be/X射线双星物质相互作用等。本文共分五章 ,第一章主要概要介绍Be和Be/X射线双星历史和目前已经取得的成就 ;第二章介绍Be单星多波段观测结果 ;第三章介绍Be/X射线双星的观测结果 ;第四章介绍目前主要的Be单星和Be/X射线双星模型 ;第五章给出Be/X射线双星XPer/ 4U0 352 30的分光观测结果 ,并结合单臂振动盘模型给出定性解释。     

Evolutionary Processes in Low-Mass Binary Systems

We consider the evolution of certain low-mass binaries, incorporating models of (a) internal evolution, (b) tidal friction, (c) dynamo activity driven by an elementary α,Ω dynamo, (d) stellar wind driven by the activity, and (e) magnetic braking as a consequence of wind and poloidal dynamo-generated magnetic field. In some circumstances the stellar wind is found to remove mass on a nuclear timescale, as is necessary to explain some observed systems. We can hope that various uncertainties in the model may be clarified by a careful comparison of the models with such observed quantities as rotation periods. These are modified by processes (a), (b) and (e). Assuming that stellar evolution is slow, rotation rate should in some circumstances represent a balance between magnetic braking trying to slow the star down and tidal friction trying to spin it up. Preliminary attempts are promising, but indicate that some fine tuning is necessary. When there is a third body present, in an orbit which is inclined but not necessarily of short period, the eccentricity of a close binary can be strongly modified by ‘Kozai cycles’. We show that this may complicate attempts to account for spin rates of stars in close binaries.     

Massive stars

We describe the present state of massive star research seen from the viewpoint of stellar evolution, with special emphasis on close binaries. Statistics of massive close binaries are reasonably complete for the Solar neighbourhood. We defend the thesis that within our knowledge, many scientific results where the effects of binaries are not included, have an academic value, but may be far from reality. In chapter I, we summarize general observations of massive stars where we focus on the HR diagram, stellar wind mass loss rates, the stellar surface chemistry, rotation, circumstellar environments, supernovae. Close binaries can not be studied separately from single stars and vice versa. First, the evolution of single stars is discussed (chapter I). We refer to new calculations with updated stellar wind mass loss rate formalisms and conclusions are proposed resulting from a comparison with representative observations. Massive binaries are considered in chapter II. Basic processes are briefly described, i.e. the Roche lobe overflow and mass transfer, the common envelope process, the spiral-in process in binaries with extreme mass ratio, the effects of mass accretion and the merging process, the implications of the (asymmetric) supernova explosion of one of the components on the orbital parameters of the binary. Evolutionary computations of interacting close binaries are discussed and general conclusions are drawn. The enormous amount of observational data of massive binaries is summarized. We separately consider the non-evolved and evolved systems. The latter class includes the semi-detached and contact binaries, the WR binaries, the X-ray binaries, the runaways, the single and binary pulsars. A general comparison between theoretical evolution and observations is combined with a discussion of specially interesting binaries: the evolved binaries HD 163181, HD 12323, HD 14633, HD 193516, HD 25638, HD 209481, Per and Sgr; the WR+OB binary V444 Cyg; the high mass X-ray binaries Vela X-1, Wray 977, Cyg X-1; the low mass X-ray binaries Her X-1 and those with a black hole candidate; the runaway Pup, the WR+compact companion candidates Cyg X-3, HD 50896 and HD 197406. We finally propose an overall evolutionary model of massive close binaries as a function of primary mass, mass ratio and orbital period. Chapter III deals with massive star population synthesis with a realistic population of binaries. We discuss the massive close binary frequency, mass ratio and period distribution, the observations that allow to constrain possible asymmetries during the supernova explosion of a massive star. We focuss on the comparison between observed star numbers (as a function of metallicity) and theoretically predicted numbers of stellar populations in regions of continuous star formation and in starburst regions. Special attention is given to the O-type star/WR star/red supergiant star population, the pulsar and binary pulsar population, the supernova rates. Received 17 July 1998     

Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers

In the present paper we combine an N-body code that simulates the dynamics of young dense stellar systems with a massive star evolution handler that accounts in a realistic way for the effects of stellar wind mass loss. We discuss two topics.

1. The formation and the evolution of very massive stars (with masses >120 M_⊙) is followed in detail. These very massive stars are formed in the cluster core as a consequence of the successive (physical) collisions of the 10–20 most massive stars in the cluster (this process is known as ‘runaway merging’). The further evolution is governed by stellar wind mass loss during core hydrogen and core helium burning (the WR phase of very massive stars). Our simulations reveal that, as a consequence of runaway merging in clusters with solar and supersolar values, massive black holes can be formed, but with a maximum mass ≈70 M_⊙. In low-metallicity clusters, however, it cannot be excluded that the runaway-merging process is responsible for pair-instability supernovae or for the formation of intermediate-mass black holes with a mass of several 100 M_⊙.
2. Massive runaways can be formed via the supernova explosion of one of the components in a binary system (the Blaauw scenario), or via dynamical interaction of a single star and a binary or between two binaries in a star cluster. We explore the possibility that the most massive runaways (e.g. ζ Pup, λ Cep, BD+43°3654) are the product of the collision and merger of two or three massive stars.

     

Main features of dynamical escape from three-dimensional triple systems

The dynamical evolution of triple systems with equal and unequal-mass components and different initial velocities is studied. It is shown that, in general, the statistical results for the planar and three-dimensional triple systems do not differ significantly. Most (about 85%) of the systems disrupt; the escape of one component occurs after a triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (about 15%) of stable or long-lived systems is formed if the angular momentum is non-zero. Averages, distributions and coefficients of correlations of evolutionary characteristics are presented: the life-time, angular momentum, numbers of wide and close triple approaches of bodies, relative energy of escapers, minimum perimeter during the last triple approach resulting in escape, elements of orbits of the final binary and escaper.     

Short Gamma Ray Bursts as electromagnetic counterpart of coalescing binary systems

Coalescing binary systems, consisting of two collapsed objects, are among the most promising sources of high frequency gravitational waves signals detectable, in principle, by ground-based interferometers. Binary systems of Neutron Star or Black Hole/Neutron Star mergers should also give rise to short Gamma Ray Bursts, a subclass of Gamma Ray Bursts. Short-hard-Gamma Ray Bursts might thus provide a powerful way to infer the merger rate of two-collapsed object binaries. Under the hypothesis that most short Gamma Ray Bursts originate from binaries of Neutron Star or Black Hole/Neutron Star mergers, we outline here the possibility to associate short Gamma Ray Bursts as electromagnetic counterpart of coalescing binary systems.     

The dynamical stability of W Ursae Majoris-type systems

Theoretical study indicates that a contact binary system would merge into a rapidly rotating single star due to tidal instability when the spin angular momentum of the system is more than a third of its orbital angular momentum. Assuming that W Ursae Majoris (W UMa) contact binary systems rigorously comply with the Roche geometry and the dynamical stability limit is at a contact degree of about 70 per cent, we obtain that W UMa systems might suffer Darwin's instability when their mass ratios are in a region of about 0.076–0.078 and merge into the fast-rotating stars. This suggests that the W UMa systems with mass ratio   q ≤ 0.076  cannot be observed. Meanwhile, we find that the observed W UMa systems with a mass ratio of about 0.077, corresponding to a contact degree of about 86 per cent would suffer tidal instability and merge into the single fast-rotating stars. This suggests that the dynamical stability limit for the observed W UMa systems is higher than the theoretical value, implying that the observed systems have probably suffered the loss of angular momentum due to gravitational wave radiation (GR) or magnetic stellar wind (MSW).     

Optical spectroscopy of XMEGA targets in the Carina Nebula – III. The multiple system Tr 16-104 (≡CPD −59° 2603)

We discuss the orbital elements of the multiple system Tr 16-104 which is usually believed to be a member of the open cluster Trumpler 16 in the Carina complex. We show that Tr 16-104 could be a hierarchical triple system consisting of a short-period (2.15 d) eclipsing O7 V+O9.5 V binary bound to a B0.2 IV star. Our preliminary orbital solution of the third body indicates that the B star most probably describes an eccentric orbit with a period of ∼285 or ∼1341 d around the close binary. Folding photometric data from the literature with our new ephemerides, we find that the light curve of the close binary exhibits rather narrow eclipses indicating that the two O stars must be well inside their Roche lobes. Our analysis of the photometric data yields a lower limit on the inclination of the orbit of the close binary of i ≥77° . The stellar radii and luminosities of the O7 V and O9.5 V stars are significantly smaller than expected for stars of this spectral type. Our results suggest that Tr 16-104 lies at a distance of the order of 2.5 kpc and support a fainter absolute magnitude for zero-age main-sequence O stars than usually adopted. We find that the dynamical configuration of Tr 16-104 corresponds to a hierarchical system that should remain stable provided that it suffers no strong perturbation. Finally, we also report long-term temporal variations of high-velocity interstellar Ca  ii absorptions in the line of sight towards Tr 16-104.     

Frequency of Be and Ae stars in spectroscopic binaries

The frequency of Be and Ae stars in spectroscopic binaries and Algol binaries is examined based on the available catalogue data, and compared with that of stars in theBright Star Catalogue. It is shown that in binary systems Be and Ae stars reveal different statistical behaviours. The frequency of Be stars in spectroscopic binaries shows a notable peak in its orbital-period distribution in the range of 100–300 days, suggesting a statistical group separated from Algol systems. In contrast, most of Ae stars in spectroscopic binaries belong to the Algol systems.     

On the onset of runaway stellar collisions in dense star clusters – I. Dynamics of the first collision

We study the circumstances under which first collisions occur in young and dense star clusters. The initial conditions for our direct N -body simulations are chosen such that the clusters experience core collapse within a few million years, before the most massive stars have left the main sequence. It turns out that the first collision is typically driven by the most massive stars in the cluster. Upon arrival in the cluster core, by dynamical friction, massive stars tend to form binaries. The enhanced cross-section of the binary compared to a single star causes other stars to engage the binary. A collision between one of the binary components and the incoming third star is then mediated by the encounters between the binary and other cluster members. Due to the geometry of the binary–single star engagement the relative velocity at the moment of impact is substantially different than in a two-body encounter. This may have profound consequences for the further evolution of the collision product.     

A 3D dynamical model of the colliding winds in binary systems

We present a three-dimensional (3D) dynamical model of the orbital-induced curvature of the wind–wind collision region in binary star systems. Momentum balance equations are used to determine the position and shape of the contact discontinuity between the stars, while further downstream the gas is assumed to behave ballistically. An Archimedean spiral structure is formed by the motion of the stars, with clear resemblance to high-resolution images of the so-called 'pinwheel nebulae'. A key advantage of this approach over grid or smoothed particle hydrodynamic models is its significantly reduced computational cost, while it also allows the study of the structure obtained in an eccentric orbit. The model is relevant to symbiotic systems and γ-ray binaries, as well as systems with O-type and Wolf–Rayet stars.
As an example application, we simulate the X-ray emission from hypothetical O+O and WR+O star binaries, and describe a method of ray tracing through the 3D spiral structure to account for absorption by the circumstellar material in the system. Such calculations may be easily adapted to study observations at wavelengths ranging from the radio to γ-ray.     

Analysis of Two-Parameter Families of Triple Close ApproachesOccurring in Stellar Systems (I)

The analysis of two-parameter families of triple close approaches occurring in stellar systems is studied in a series of three papers. This paper deals with the role of triple encounters with low initial velocities and equal masses in the evolution of stellar systems. It shows how a condition of complete collapse may be perturbed to obtain well-established two-parameter families of asymmetric triple close approaches with the formation of a binary and with systematic regularity of escape of the third body. Our results also indicate that the conjecture of Szebehely viz., `The measure of escaping orbits is significantly higher than the measure of stable orbits' is likely to be true. Further our results differ from that of Agekian's escape probability criterian. The second paper deals with the role of triple encounters with low initial velocities and equal masses in the evolution of stellar systems in 3D space. The third and last paper offers applications in stellar systems. This revised version was published online in July 2006 with corrections to the Cover Date.