Milky Way Galaxy

Three-Body Interactions Near Sgr A^*

The problem of transporting a star that is many parsecs away from the central Galactic black hole into close orbit around it in less than 10 million years is the primary problem facing theories that assert stars such as S2, which appears to be a large, short-lived B main-sequence star, are born far from the black hole. Curiously, a host of theories ignore this principal question, focusing instead on a secondary question: why does a star like S2 have such a relatively ?low? eccentricity? The orbit of S2 has an eccentricity of 0.88?a circular orbit has an eccentricity of 0, and a parabolic orbit has an eccentricity of 1)?with a periapsis (the orbital point closest to the black hole) of 122 AU and an apoapsis (the orbital point farthest from the black hole) of 1,838 AU. By solar system standards, this is a very eccentric orbit. Mercury, the planet with the most eccentric orbit, has an eccentricity of only 0.21. Comets are the Solar System bodies with eccentricities matching that of S2?the orbit of Halley's Comet has an eccentricity of 0.97. But the eccentricity of S2 is low if one believes stars such as S2 originate at 1 parsec or beyond.

The assumption of some theorists is that the B main-sequence stars such as S2 were at one time in orbits with apoapsides out at 206,000 AU (1 parsec) and periapsides at several hundred AU, for an eccentricity of better than 0.999. Presumably, this orbit is the outcome of transporting these stars from their birthplace tens of parsecs from the central black hole. The problem is then lowering the apoapsis to 1,000 AU.

To efficiently change the apoapsis of a star, or spacecraft for that matter, you remove kinetic energy at the opposite point in the orbit, the periapsis. For instance, a spacecraft orbiting the Sun would fire its engines at its periapsis (perihelion) to move its apoapsis (aphelion) either high or lower in altitude; conversely, it would fire its engines at its aphelion to raise or lower its perihelion. For a star to alter its apoapsis efficiently, it must interact with another body near its periapsis. These interactions are inherently three-body interactions, involving the redistribution of energy among the star, the central black hole, and a third body. Each possible or improbable third body motivates its own theory.

In the simplest versions of this brand of theory, the star in the highly eccentric orbit gives up a large fraction of its kinetic energy to a second star during a close encounter at periapsis. The second target star is kicked into a larger orbit, and the apoapsis of the first star drops in altitude over the central black hole.

This simple version of the theory, of course, presupposes that there are a large number of target stars orbiting within 100 AU of the black hole. If the density of target stars is too small, encounters between target stars and stars in highly-eccentric orbits become too rare to place many B main-sequence stars into close orbit around the central black hole. The target stars also need to be very long-lived, so that they have time to drift into close orbit around the central black hole; dynamical friction is generally assumed to act on the target stars. Plausible suggestions for targets are black hole of several solar masses and neutron stars.^[1] These objects are heavy enough to drop to the bottom of the gravitational potential well, and because they live forever, they can populate the 100 AU region over the age of the Galaxy. An implausible suggestion is a black hole of intermediate mass, of 10³ to 10⁴ solar masses, orbiting Sgr A^*.^[2] Only one such black hole is needed to alter the orbits of many stars, but how does one create this second large black hole?

In another version of the three-body theory, a star carries the third body with it: the star is a member of a binary star system, and binary system is in the highly-eccentric orbit.^[3] The companion to the B main-sequence star is a main-sequence star with a mass above 60 solar masses. As the binary system orbits the central black hole, the tidal force exerted by the black hole pumps energy into the system, eventually disrupting it, and leaving the B main-sequence star in a close orbit around the black hole. The companion star is left in a somewhat more eccentric orbit than the binary system. The advantage of this theory over the previous theory is that one does not rely on the existence of a multitude of scattering targets close to the black hole.

Despite the cleverness of many of these three-body theories, they all suffer from their neglect of the basic problem: how do stars, whether binary or single, born tens of parsecs away from the central black hole, come to have highly-eccentric orbits that bring them within 1,000 AU of the black hole. The theorists presenting three-body theories generally pass this issue off in a couple of vague statements or stick a discussion of possible mechanisms in the appendices of their papers. Once can plausibly argue that the B main-sequence stars are carried from their birthplace to within 1 parsec of the central black hole by a star cluster. Whether the cluster places massive stars into orbits with periapsides inside 1,000 AU is unknown. Other mechanisms, such as scattering with another star that drops the periapsis to less than 1,000 AU has been suggested, but these mechanisms generally rely on low probability events. The transport of B main-sequence stars remains the principal issue in these theories. If a mechanism cannot be found that rapidly and naturally moves these stars into highly-eccentric orbits, with periapsides of order 100 AU and apoapsides of several parsecs, there is little point in developing such theories.