Dynamical states and dynamical evolution of the selected triple star systems

The general problem of investigating multiple stellar systems is formulated. It is shown that the complete solution of this problem requires 1) a complex of astrometric and astrophysical observations of multiple stars, and the 2) maximum attainable precision of such observations. The conditions under which this precision can be achieved are discussed.The most important characteristics of the dynamical states of multiple systems are the total energy E and the relative energies E_ij of the bodies in these systems. For eight triple systems (ADS 1630, 2926, 6175, 6650, 6811, 7114, 9626, 9909), statistical tests — a method of calculating the uncertainties _E and _Eij from the errors of the observational data — are used to find the probabilities for dynamical states and the values E_tr±E_tr and E_bin±E_bin.Only three triple stars appear certain to be physical systems with a dynamical connection between the components — ADS 6175 and 9909 with the probabilities P>0.80 are dynamical non-hierarchical unstable triple systems with a complicated motions of the components; the final state of these systems is an escape. In the triple system ADS 1630 a qualitative course of the component motions has not been determined because of the larger errors in the observed data. The dynamical evolution of the triple system ADS 9909 is under study.     

New Data on the Paleoproterozoic Age of Metamorphism in the Yelabuga Deformation Zone of Volgo-Uralia,East European Craton

Doklady Earth Sciences - This data on the age of metamorphism of rocks of the Yelabuga zone and the geochronological data on detrital zircon from paragneisses of the same zone are presented, and...     

Mineralogy of silicate inclusions in the Elga IIE iron meteorite

The petrography, mineral modal data and major and trace element compositions of 15 silicate inclusions in the Elga iron meteorite (chemical group IIE) show that these inclusions represent chemically homogeneous zoned objects with highly variable structures, reflecting the sequence of crystallization of a silicate melt during cooling of the metal host. The outer zones of inclusions at the interface with their metal host have a relatively medium-grained hypocrystalline texture formed mainly by Cr-diopside and merrillite crystals embedded in high-silica glass, whereas the central zones have a fine-grained hypocrystalline texture. Merrillite appears first on the liquidus in the outer zones of the silicate inclusions. Na and REE concentrations in merrillite from the outer zones of inclusions suggest that it may have crystallized as α-merrillite in the temperature range of 1300–1700°С. Merrillite tends to preferentially accumulate Eu without Sr. Therefore, strongly fractionated REE patterns are not associated with prolonged differentiation of the silicate melt source but depend on crystallization conditions of Н-chondrite droplets in a metallic matrix. The systematic decrease in Mg# with increasing Fe/Mn in bronzite may indicate partial reduction of iron during crystallization of the inclusion melt. The modal and bulk compositions of silicate inclusions in the Elga meteorite, as well as the chemical composition of phases are consistent with the model equilibrium crystallization of a melt, corresponding to 25% partial melting of H-chondrite, and the crystallizing liquidus phase, merrillite, and subsequent quenching at about 1090°С. Despite a high alkali content of the average weighted bulk inclusion composition, La/Hf and Rb/Th fall within the field of H chondrites, suggesting their common source. Our results reveal that silicate inclusions in the Elga (IIE) iron meteorite originated by mixing of two impact melts, ordinary chondrite and Ni-rich iron with а IIE composition, which were produced by impact event under near-surface conditions on a partially differentiated parent asteroid.     

Close triple approaches and escape in the three-body problem

We have studied a total of 5000 close triple approaches resulting in escape, for equal-mass systems with zero initial velocities. Escape is shown to take place in the majority of the cases after a fly-by close triple approach when the escaper passes near the centre of mass along an almost straight-line orbit. A number of configurational and kinematical parameters are introduced in order to characterize the triple approach. The distributions of these parameters are investigated. A comparison with 831 examples in the vicinity of the so-called Pythagorean problem is carried out. We find that the general features of close triple approaches which result in escape are the same for both types of systems.     

Initial conditions and dynamics of triple systems

The dynamical evolution of triple systems with equal-mass components and zero initial velocities is studied. We consider two regions of initial conditions: a regionD of all possible configurations of triples and a circleR. The configurations are distributed uniformly within these regions. The calculations have been carried out until a time when escape or conditional escape (i.e. distant ejection) of one component takes place. The accuracy has been checked by doing time-reversed integration. Types of predictable and non-predictable systems are revealed. Averages for a number of evolution parameters are presented: the life-time, minimum perimeter during the last triple approach resulting in escape, semi-major axis and eccentricity of the final binary, and the smallest separation between the components during the evolution. It is shown that the statistical results for the regionsD andR do not differ significantly for the most part. Our results, which have been obtaned by a three-body regularization method, are in good agreement with previous work based on the RK4 integrator and Sundman's time smoothing.     

Dynamical evolution of triple systems with big differences in the masses of bodies. A criterion for stability

The dynamical evolution of about 1.5 million planar hierarchical triple systems with a negative total energy and different-mass bodies is investigated by computer simulations. We considered both cases — prograde and retrograde motions of bodies. For every system, calculations were carried out either till a time when the Marchal'set al. (1984) criterion of escape of a body from a triple system was satisfied (the unstable triple systems) or during 1000 rotations of a total system (the stable triple systems). Computations were carried out on three computers-Sunstations in the Physical Research Laboratory, Ahmedabad, India during several months continuously. We changed smoothly the initial value of the coefficient of hierarchy of triples $$q = r_{3 - 12} /r_{12} $$ Wherer ₁₂ is a distance between close bodiesM1,M2 andr _3–12 is a distance between their center of masses and a distant bodyM3. We define critical (minimum) values of the coefficientq of hierarchy of stable triple systems with a relative accuracy δq=1%. Ratios of masses of bodies belong to the interval [0.13, 244.00]. A possibility of extention of these results for hierarchical subsystems with different multiplicities inside clusters is discussed.     

Distribution of minima of the current size of the triple systems and their disruption

The dynamical evolution of triple systems has been studied by computer simulations. A function (t) has been defined, where p is the maximum distance of the components from their centre of inertia, and t is the time. The value of is used to indicate the current size of the triple system. The minima of have been followed during the course of evolution of the triples. A distribution of f(_min) has been obtained, which is described by the following statistical parameters: the mode is equal to 0.65d, the mean value _min= 0.750d, r.m.s. is 0.477d, the asymmetry is 0.218, the excess is 2.04 where d is the mean harmonic distance between the bodies in the equilibrium state of the triple system. As a rule, escapes from triples occur only after close three-body approaches.     

A search and classification of multiple systems in the general field

Summary The general problems are formulated, and the classification of the multiple star and galaxy systems is proposed. The dynamical states of eight nearby triple stars are ascertained. Presented by S. Vereshchagin.