64 - Gravitational shocks

Summary

Awaiting the sensation of a short sharp shock

Gilbert and Sullivan

Leaving behind the properties of a single isolated system we now begin to examine what happens when two systems interact. Sections 48.2 and 58 already showed how tides can transfer energy and angular momentum. Now we explore some effects of tidal transfer on the internal structure of stellar systems. Since stellar systems have many more degrees of freedom than the interior of an individual star they may respond to external forces in more varied ways. This section describes the basic response of a spherical cluster which passes quickly through the plane of a flat galaxy. Section 65 describes the distortions of two flat systems as they attempt to move slowly past one another.

‘Quick’ and ‘slow’ are relative terms. We saw in Section 47 that what counts is the ratio of the orbital period (or quasi-period) to the timescale for external forces to change. If this ratio is small we can use adiabatic invariants or, more generally, multiple timescale expansions to examine such phenomena as orbit segregation. If this ratio is large we can use the impulsive approximation. A sudden impulsive change of the external field produces a gravitational shock.

it is certainly possible, and probably even common, for a system to contain some orbits which respond smoothly, and others which are shocked, by the same external change. Different parts of the system may respond differently, leading to complicated internal behavior.