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The infall of cold dark matter onto a galaxy produces cold collisionlessflows and caustics in its halo. If a signal is found in the cavity detector ofdark matter axions, the flows will be readily apparent as peaks in the energyspectrum of photons from axion conversion, allowing the densities, velocityvectors and velocity dispersions of the flows to be determined. We discuss theevolution of velocity dispersion along cold collisionless flows in one and twodimensions. A technique is presented for obtaining the leading behaviour of thevelocity dispersion near caustics. The results are used to derive an upperlimit on the energy dispersion of the Big Flow from the sharpness of its nearbycaustic, and a prediction for the dispersions in its velocity components.

Evolution of velocity dispersion along cold collisionless flows