scholarly journals The Problem of Three Stars: Stability Limit

2007 ◽  
Vol 3 (S246) ◽  
pp. 209-217 ◽  
Author(s):  
M. Valtonen ◽  
A. Mylläri ◽  
V. Orlov ◽  
A. Rubinov
Keyword(s):  
Analytical Formula ◽  
Analytical Calculation ◽  
Stability Limit ◽  
Stellar Dynamics ◽  
Energy Change ◽  
Orbital Energy ◽  
Single Star ◽  
Triple Systems ◽  
Numerical Orbit ◽  
Three Body

AbstractThe problem of three stars arises in many connections in stellar dynamics: three-body scattering drives the evolution of star clusters, and bound triple systems form long-lasting intermediate structures in them. Here we address the question of stability of triple stars. For a given system the stability is easy to determine by numerical orbit calculation. However, we often have only statistical knowledge of some of the parameters of the system. Then one needs a more general analytical formula. Here we start with the analytical calculation of the single encounter between a binary and a single star by Heggie (1975). Using some of the later developments we get a useful expression for the energy change per encounter as a function of the pericenter distance, masses, and relative inclination of the orbit. Then we assume that the orbital energy evolves by random walk in energy space until the accumulated energy change leads to instability. In this way we arrive at a stability limit in pericenter distance of the outer orbit for different mass combinations, outer orbit eccentricities and inclinations. The result is compared with numerical orbit calculations.

scholarly journals Three-Body Problem and Multiple Stellar Systems

2004 ◽  
Vol 191 ◽  
pp. 146-151
Author(s):  
M. Valtonen
Keyword(s):  
Binary Stars ◽  
Body Problem ◽  
Star Clusters ◽  
Point Of View ◽  
Stellar Systems ◽  
Three Body Problem ◽  
Single Star ◽  
Triple Systems ◽  
Break Up ◽  
Three Body

AbstractThree-body processes go on in star clusters where binary stars meet single stars and frequently form temporary triple systems. The triples are typically unstable and break up into a new binary and a single star. Also a simple scattering of a single star from a binary may take place. Both processes can be handled by the statistical theories of three-body break-up and scattering. Here we apply the theory to binary stars, assuming that binaries have been involved in the three-body process. The distributions of binary periods, eccentricities and mass ratios are discussed from this point of view and compared with observational samples.

scholarly journals Binary Interactions in Star Clusters

1988 ◽  
Vol 126 ◽  
pp. 669-670
Author(s):  
Stephen L. W. McMillan
Keyword(s):  
Numerical Experiments ◽  
Binary Systems ◽  
Star Clusters ◽  
Stellar Dynamics ◽  
Single Star ◽  
The Past

Over the past decade, a very considerable amount of effort in stellar dynamics has gone into the study of interactions between binary systems and other stars. The asymptotic analytic results obtained by Heggie (1975) for binary-single star encounters have been largely confirmed and extended by later numerical experiments (Hills 1975, Hut and Bahcall 1983). Binary-binary interactions have been studied by Mikkola (1983).

scholarly journals Electromagnetic transients and gravitational waves from white dwarf disruptions by stellar black holes in triple systems

2020 ◽  
Vol 495 (1) ◽  
pp. 1061-1072
Author(s):  
Giacomo Fragione ◽  
Brian D Metzger ◽  
Rosalba Perna ◽  
Nathan W C Leigh ◽  
Bence Kocsis
Keyword(s):  
White Dwarf ◽  
Gamma Ray ◽  
High Energy ◽  
Stellar Mass ◽  
Compact Objects ◽  
Electromagnetic Transients ◽  
Tidal Disruption ◽  
Single Star ◽  
Triple Systems ◽  
Nearby Galaxies

ABSTRACT Mergers of binaries comprising compact objects can give rise to explosive transient events, heralding the birth of exotic objects that cannot be formed through single-star evolution. Using a large number of direct N-body simulations, we explore the possibility that a white dwarf (WD) is dynamically driven to tidal disruption by a stellar-mass black hole (BH) as a consequence of the joint effects of gravitational wave (GW) emission and Lidov–Kozai oscillations imposed by the tidal field of an outer tertiary companion orbiting the inner BH–WD binary. We explore the sensitivity of our results to the distributions of natal kick velocities imparted to the BH and WD upon formation, adiabatic mass loss, semimajor axes and eccentricities of the triples, and stellar-mass ratios. We find rates of WD–tidal disruption events (TDEs) in the range 1.2 × 10−3 − 1.4 Gpc−3 yr−1 for z ≤ 0.1, rarer than stellar TDEs in triples by a factor of ∼3–30. The uncertainty in the TDE rates may be greatly reduced in the future using GW observations of Galactic binaries and triples with LISA. WD–TDEs may give rise to high-energy X-ray or gamma-ray transients of duration similar to long gamma-ray bursts but lacking the signatures of a core-collapse supernova, while being accompanied by a supernova-like optical transient that lasts for only days. WD–BH and WD–NS binaries will also emit GWs in the LISA band before the TDE. The discovery and identification of triple-induced WD–TDE events by future time domain surveys and/or GWs could enable the study of the demographics of BHs in nearby galaxies.

Simplified Analytical Calculation and Modification of the Crushing Forces of Intersection Units in Vessel-Bridge Collisions

2020 ◽  
Author(s):  
Yin Faqiang ◽  
Pan Jin ◽  
Huang Shiwen ◽  
Xu Mingcai
Keyword(s):  
Small Angle ◽  
Large Angle ◽  
Analytical Formula ◽  
Analytical Calculation ◽  
Typical Structure ◽  
Analytical Formulas ◽  
Ship Collision ◽  
Collision Force ◽  
Inclined Angle ◽  
The Impact

Abstract Because of the increasingly busy maritime trade, the number of bridges damaged by ship-bridge collision also increases. In order to reduce the serious losses caused by ship-bridge collision incidents, it is necessary to make a rapid estimation of ship collision forces. The simplified analytical formulas can be used to rapidly evaluate the collision force in ship collision accidents, but it is found that the existing simplified formulas are only applicable to bulb structures including small-angle inclined elements and not suitable for large-angle inclined elements which exist in ship-bridge collision. In this paper, the quasi-static crushing simulation of the bulbous structure with small-angle inclined angle elements is carried out, and the applicability of the simplified analytical formula of the intersection unit to the typical structure is verified. By comparing the simplified analytical results of the bow with the quasi-static simulation results and the ratio of the strength reduction factor to the effective crushing distance, it is found that the inclined angle of the inclined element will affect the impact force of the simplified analytical calculation. Then, finite element analysis of the truncated-type intersection structure with different element inclination angles are carried out, and the results show that the existing simplified analytical formula is no longer suitable for the calculation of collision force when the inclined angle is greater than 40°. For this reason, the existing simplified analytical formulas are modified for the large-angle inclined elements, and it can provide a certain reference calculation value for the collision force of vessel-bridge collision which includes large-angle inclined elements.

scholarly journals The Formation of Multiple Systems by Dynamical Interaction in Clusters

1977 ◽  
Vol 33 ◽  
pp. 199-206
Author(s):  
S. J. Aarseth
Keyword(s):  
Large Fraction ◽  
Close Binaries ◽  
Formation Mechanisms ◽  
Dynamical Interaction ◽  
Multiple Systems ◽  
Triple Systems ◽  
Hyades Cluster ◽  
Binary Formation ◽  
Formation And Evolution ◽  
Three Body

AbstractThis review is mainly devoted to a discussion of binary formation and evolution in stellar systems, as described by N-body techniques. The simplest formation mechanisms consist of ejection from bound triple systems and capture arising from hyperbolic three-body encounters. However, the large number of astrophysically close binaries cannot be accounted for in this way unless most stars are formed in compact groups. Numerical calculations show that the evolution of clusters containing several hundred members is invariably dominated by one central binary which absorbs a large fraction of the total energy. It is suggested that a visual binary in the core of the Hyades cluster may have been associated with this process.

scholarly journals Review of the Dynamical Aspects of Triple Systems

1977 ◽  
Vol 33 ◽  
pp. 145-150
Author(s):  
V. Szebehely
Keyword(s):  
Fundamental Problem ◽  
Stellar Dynamics ◽  
Close Approach ◽  
Type Systems ◽  
Computational Results ◽  
Transient Phenomena ◽  
Triple Systems ◽  
Families Of Periodic Orbits ◽  
Negative Total Energy

AbstractA classification of possible motions of triple systems is presented emphasizing the transient phenomena occurring in addition to the final (asymptotic) outcome and clarifying the discrepancies between the astronomical and mathematical formulations. A conjectured possible instability is described and it is shown that systems with negative total energy and low angular momentum may lead to instability and to the formation of binaries. The ejected or escaping star may have high velocity if the triple close approach preceding the escape is sufficiently close. The computational results of several systematic series of such escapes are applied to various stellar configurations.The present status of the fundamental problem of partitioning the phase-space into stable and unstable regions is reviewed and a recently developed technique, applicable to stellar dynamics is described. Recently discovered families of periodic orbits and previously established classical configurations are shown to weaken the general instability conjecture.The possible existence of triple systems in states of dissolution offer intriguing observational challenges regarding the discovery of these projected temporary trapezium type systems.

scholarly journals The Binaries from Unstable Triples. Dynamical Processes of Formation

1989 ◽  
Vol 8 ◽  
pp. 143-144
Author(s):  
Joanna P. Anosova
Keyword(s):  
Computer Simulations ◽  
Dynamical Evolution ◽  
Close Binary ◽  
Close Binaries ◽  
State University ◽  
Dynamical Processes ◽  
Triple Systems ◽  
Gravitational Problem ◽  
Three Body

The dynamical processes of formation, evolution and disruption of binaries may be effectively studied by computer simulations in the N > 3-body gravitational problem. As a result of analysis of these investigations of diverse authors, the classification of the dynamical processes of formation of wide and close binaries may be proposed (see Table 1). This Table shows the following general processes: I-triple approaches of the single bodies; II-approaches of binaries with single bodies; Ill-escape from physical triples. The actions of these processes, and kinetics of a frequency of binaries in general field were studied at the Astronomical Observatory of the Leningrad State University (1965-1988) by computer simulations in the three-body problem. More than 3.104 orbits with negative total energy E < 0 and 5.104 with E > 0 have been run on the computers. The film “Dynamical evolution of triple systems” was produced. Part I of this movie shows the evolution of the unstable non-hierarchical triplet as well as the processes of formation, evolution, and disruption of temporary wide and final close binaries inside the physical triples. Part II of film presents in detail the trajectories of the bodies on the triple approaches of “fly-by”-and of “exchange”-types. The triple approach of “fly-by”-type results often in an escape from triple as well as the formation of final close binary. The triple approach of “exchange”-type consists as a rule of a few close double approaches of bodies and rarely results in an escape from triplet, it results in formation of temporary wide binary inside triplet. Part III of movie presents the trajectories of the different-mass bodies: an escape of the minimum-mass body, the intermediate-mass body, and the maximum-mass body as well as a formation of binaries with different-mass components.

scholarly journals A Review of the Dynamics of Classical Triple Stars

1977 ◽  
Vol 33 ◽  
pp. 139-143
Author(s):  
R. S. Harrington
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Triple Systems ◽  
Numerical Experimentation ◽  
The Stability ◽  
Von Zeipel’S Method ◽  
Three Body ◽  
Triple Stars

AbstractFour ways of studying the dynamics of triple systems are outlined, namely the analytical, the qualitative, the numerical, and the observational approach. A discussion of the stability of classical (revolutional, hierarchical) triples summarizes the results of analytical developments, based on the application of von Zeipel’s method to the general three-body problem, and of numerical experimentation. Finally, a summary is given of recent investigations concerning the dynamics of triples other than the revolutional systems.

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