HOW FAST CAN A GALAXY MIX

Time-dependent solutions to the gravitational N-body problem are unstable in the sense that small initial perturbations tend to be amplified exponentially. This fact, well known from numerical simulations, was "explained" by Gurzadyan and Savvidy, who argued that this instability implies that an N-body system will tend to "mix" on a time scale τGS ∼ N1/3tD, where tD is a typical crossing time. It is shown here that the prediction of Gurzadyan and Savvidy of a "mixing" is right, but that, allowing correctly for the large scale bulk forces present in a self-gravitating system, one anticipates that the effects of this "mixing" should be manifest already on a much shorter time scale ∼tD. It is argued that the result of this "coarse-grained" mixing on a time scale ∼tD should be consistent, at least broadly, with the expected outcome of an epoch of "violent relaxation". It is also emphasized that this time scale τ must be interpreted in an appropriate "average" sense since, as has been observed, e.g., by R.H. Miller, there exist (admittedly special) perturbations which can be amplified on time scales as short as N-1/2tD. © 1990.