Tobias Heinemann and Chris Hamilton analysed how a stellar system responds to a moving perturbing mass. Their homogeneous-system calculation includes both the gravitational wake and collective Landau modes, whose apparent divergences cancel near marginal stability.[ref]
The result shows why retaining only the steady wake can misrepresent a slowly relaxing system. The assumptions about background distribution and the order of time and stability limits are part of the calculation.

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