47 - Orbit segregation

Summary

Up and down, and in and out, Here and there, and round about

Gilbert and Sullivan

Any process, such as mass segregation, mass loss, or core–halo instability which redistributes the density of a gravitating system will also produce orbit segregation. Orbit segregation is caused primarily by changes in the mean gravitational field. It affects orbits according to their eccentricity.

In a globular cluster, for example, the timescale for mass segregation to redistribute density falls between the dynamical crossing timescale and the relaxation timescale for stars of average mass. Therefore orbits of average or light stars undergo secular changes governed by the slowly changing mean field. (We are isolating changes in the mean field which, averaged over orbits, lead to orbit segregation, so we now ignore close encounters and dynamical friction for the test stars.) Suppose, for clarity, we compare the extremes of eccentricity: circular and radial orbits. Let the cluster's density increase toward the center, as usual. If the cluster were in stationary equilibrium, stars in circular orbits would just go around and around, and those in radial orbits would just go in and out through the center, in equilibrium with the mean field. Stars with intermediate eccentricities, but constant angular momentum, would generally follow open orbits with constant amplitude.

Now suppose part of the cluster begins to contract slowly compared with the timescale for free fall.