Binary and Multi-Star Systems

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Hierarchical systems


Triple star systems

         In a physical triple star system,stars usally follows an arrangement called hierarchical, in which each star orbits the center of mass of the system. Usually, two of the stars form a close binary system, and the third orbits this pair at a distance much larger than that of the binary orbit.The reason for this arrangement is that if the inner and outer orbits are comparable in size, the system may become dynamically unstable, leading to a star being ejected from the system.

Higher multiplicities

   Mobile diagrams: (a) multiplex; (b) simplex, binary system; (c) simplex, triple system; (d) simplex, quadruple system, hierarchy 2; (e) simplex, quadruple system, hierarchy 3; (f) simplex, quintuple system, hierarchy 4.

         Hierarchical multiple star systems with more than three stars can produce a number of more complicated arrangements, which can be illustrated by a mobile diagram(1968).

          Each level of the diagram illustrates the decomposition of the system into two or more systems with smaller size. Since, as we have already seen for triple stars, this may be unstable, multiple stars are expected to be simplex, meaning that at each level there are exactly two children.

         A real example of a system with hierarchy 3 is Castor, which we will dicuss inBinary_and Multi Star Systems in the universe. It consists of what appears to be a visual binary star which, upon closer inspection, can be seen to consist of two spectroscopic binary stars. By itself, this would be a quadruple hierarchy 2 system as in (d), but it is orbited by a fainter more distant component, which is also a close red dwarf binary. This forms a sextuple system of hierarchy 3.

         The maximum hierarchy occurring in A. A. Tokovinin's Multiple Star Catalogue, as of 1999, is 4.For example, the stars Gliese 644A and Gliese 644B form what appears to be a close visual binary star; since Gliese 644B is a spectroscopic binary, this is actually a triple system. The triple system has the more distant visual companion Gliese 643 and the still more distant visual companion Gliese 644C, which, because of their common motion with Gliese 644AB, are thought to be gravitationally bound to the triple system. This forms a quintuple system whose mobile diagram would be the diagram of level 4 appearing in (f).

         Higher hierarchies are also possible. Most of these higher hierarchies either are unstable or suffer from internal perturbations. Others consider complex multiple stars will in time theoretically disintegrate into less complex multiple stars.

 

Trapezia


         A second known class of multiple stars consists of the young trapezia, named after the multiple star known as the Trapezium in the heart of the Orion Nebula.Such systems are not rare, and commonly appear close to or within bright nebulae. These stars have no standard hierarchical arrangements, but compete for stable orbits, where the center of gravity is not fixed at some point but moves as the stars change their mutual positions. This relationship is called interplay. Such stars eventually settle down to a close binary with a distant companion, with the other star(s) previously in the system ejected into interstellar space at high velocities. Example of such events may explain the runaway stars that might have been ejected during a collision of two binary star groups or a multiple system. This event is credited with ejecting AE Aurigae, Mu Columbae and 53 Arietis at above 200 kms?1 and has been traced to the Trapezium cluster in the Orion Nebula some two million years ago.

Orbital motion in multiple stars


Calculating the center of mass in binary stars

         In a simple binary case, r1, the distance from the center of the first star to the center of mass, is given by:

   

where: a is the distance between the two stellar centers and m1 and m2 are the masses of the two stars. If a is taken to be the semimajor axis of the orbit of one body around the other, then r1 will be the semimajor axis of the first body's orbit around the center of mass or barycenter, and r2 = a C r1 will be the semimajor axis of the second body's orbit. When the center of mass is located within the more massive body, that body will appear to wobble rather than following a discernible orbit.

Center of mass animations

Images are representative, not simulated. The position of the red cross indicates the center of mass of the system.

   

(a.) Two bodies of similar mass orbiting around a common center of mass, or barycenter.

   

(b.) Two bodies with a difference in mass orbiting around a common barycenter, like the Charon-Pluto system

   

(c.) Two bodies with a major difference in mass orbiting around a common barycenter (similar to the Earth-Moon system)

   

(d.) Two bodies with an extreme difference in mass orbiting around a common barycenter (similar to the Sun-Earth system)

   

(e.) Two bodies with similar mass orbiting in an ellipse around a common barycenter.