Milky Way Galaxy

Sinking Star Clusters Near Sgr A^*

The theory that the bright stars found orbiting within 1 parsec of Sgr A^* are born dozens of parsecs from the black hole must explain how these stars are transported from their birth place to their current orbits. Dynamical friction acting on single stars does not provide this explanation, as it acts over a 1 billion year timescale, a timescale that is 100 times the age of the B main-sequence star found within 1,000 AU of the black hole. One line of attack that improves upon dynamical friction acting on single stars is to place the massive stars into a stellar cluster and allow dynamical friction to act on the whole cluster.^[1]

The timescale for a star to sink to the central black hole is inversely proportional to the mass of the star. A drift timescale below the 10 million year age of the largest B main-sequence stars requires a stellar mass of over 100 solar masses, far larger than the 15 solar masses carried by the largest B main-sequence stars. One way around this difficulty is to place a B main-sequence star into a gravitationally-bound cluster of stars, and let the cluster itself drift inward through the action of dynamical friction. A tightly-bound star cluster acts on the surrounding stars in the same way as a single star of the same mass. With enough mass, a cluster can drift into the inner parsec of the Galaxy before the largest stars in the cluster die of old age. To drift inward in less than a million years, a cluster must have a mass of several million solar masses.

A star cluster does not sink to the Galactic center without damage. Think of the effect of friction on any body, whether it be a block of wood sliding on a flat surface, or a spacecraft reentering Earth's atmosphere. The kinetic energy lost to friction appears as heat in these objects. When dynamical friction acts on a star cluster, the kinetic energy from the cluster's orbit is converted into kinetic energy of individual stars within the cluster. The cluster is effectively ?heated? by the friction. This leads to evaporation, as the stars in the outer regions of the cluster are pushed above the cluster's escape velocity. Dynamical friction therefore causes the cluster to lose stars.

The decay of a star cluster's orbit amplifies the evaporation of stars from the cluster by increasing the tidal force of the Galaxy's gravitational field on the cluster. The tidal force becomes stronger as one approaches the center of the Galaxy. As the cluster's orbit shrinks, the outer stars in the cluster feel a greater tug from the Galaxy than from the star cluster. The Galaxy tidally strips the star cluster of its outermost stars.

During this whole process, the largest stars are tucked safely in the core of the cluster. As with the Galactic core, a star cluster segregates itself, so that the largest stars are at the center of the cluster and the lightest stars are in the outer regions of the cluster. This is a consequence of thermodynamics: the energy within the cluster becomes equally distributed among the stars, which gives the massive stars lower velocities that the low-mass stars. As the cluster's orbit decays, the cluster loses its least-massive stars first through evaporation and tidal stripping. Eventually the cluster contains only massive stars. When the diminished cluster is finally ripped apart, it releases these massive stars onto individual orbits around the central black hole.

Where a cluster deposits its largest stars in its self-destructive journey to the central black hole depends on the cluster's mass and density. To place massive stars within a parsec of the black hole, the star cluster must satisfy several criteria. The cluster must be able to thermalize rapidly, so that the massive stars have time to sink to the center of the cluster before the cluster is stripped of stars; this criteria is satisfied for clusters massive enough to sink to the inner parsec of the Galaxy. The cluster must also shrink away to nothing in about the time it takes to travel from several tens of parsecs to inside 1 parsec; if the cluster is stripped of stars too fast, it is destroyed before it travels far. This second condition places a severe constraint on the density of the star cluster that limit the usefulness of the theory as an explanation for stars such as S2. A cluster with a core density of 10⁶ solar masses per cubic parsec is completely disrupted at 1 parsec from the central black hole. This is not too bad, as theorists who study the evolution of stellar clusters believe that the densities of cluster cores can reach 10⁷ solar masses per cubic parsec. A stellar cluster seen in the Galactic core has a central density estimated at just under 10⁶ solar masses per cubic parsec. The problem is that the density required to reach a given point from the black hole is inversely proportional to the cube of the distance to the black hole. If the cluster is to be disrupted inside 20,000 AU (0.1 parsecs), the central density of the cluster must be greater than 10¹⁰ solar masses per cubic parsec. To be disrupted inside 2,000 AU, where the star S2 is found, the cluster must have a central density of 10¹³ solar masses per cubic parsec. These densities are outside the range of plausibility.

The end result is that stellar clusters can at best provide a partial solution to the problem of rapidly transporting massive stars to the vicinity of Sgr A^*. Sinking stellar clusters can account for the massive stars seen at 1 parsec from the black hole, but not for stars such as S2 that are only hundreds of AU from the black hole. This may imply a second process that can carry massive stars several tens of parsecs to within 1,000 AU of the black hole. But if sinking clusters are transporting stars to within 1 parsec of the black hole, all that is needed is a mechanism to carry stars over that final parsec.