Table 1: The non-dimensional times ($\xi _k$), positions ($\lambda _k$), thicknesses ( $\Delta r_k$), maximum densities ( $\rho _{\rm max}$) of the first ten caustics, the halo density itself ( $\rho _{\rm halo}$) at the positions of these caustics and other parameters used in expressions (3), (5)-(7). The present velocity dispersion is that for neutralinos which is about 0.03 cm s-1. It is worth emphasizing that the thicknesses of the caustics do not depend on the halo parameters but only on the velocity dispersion of dark matter [see expression (6)]. It is instructive to compare the last two columns, which show that for a cluster-size halo with $r_{\rm vir}\sim 1$ Mpc, the caustic density can be many orders of magnitude higher than the halo density itself.
k $\xi _k$       $\lambda _k$       $\left({\rm d}^2\lambda/{\rm d}\xi^2\right)_k$ $\Lambda_k$          $\Delta r_k$ (pc)          $\rho_{\rm max}/\rho_{\rm H}/(\!\sqrt{r_{\rm vir}})~~{\rm pc}^{-1/2}$ $\rho_{\rm halo}/\rho_{\rm H}$
1 0.985 0.368 -5.86 -0.0704 $5.6\times 10^{-4}$ 233 12
2 1.46 0.237 -11.2 -0.0254 $2.6\times 10^{-4}$ 431 39
3 1.76 0.179 -16.7 -0.0135 $1.7\times10^{-4}$ 640 82
4 1.98 0.146 -22.3 -0.00854 $1.2\times10^{-4}$ 850 139
5 2.16 0.124 -28.0 -0.00591 $9.1\times 10^{-5}$ 1067 210
6 2.31 0.108 -33.9 -0.00437 $7.3\times 10^{-5}$ 1290 297
7 2.43 0.096 -39.8 -0.00337 $6.0\times10^{-5}$ 1532 398
8 2.55 0.087 -45.7 -0.00266 $5.1\times 10^{-5}$ 1749 513
9 2.64 0.079 -51.7 -0.00221 $4.4\times 10^{-5}$ 2010 640
10 2.73 0.073 -57.8 -0.00182 $3.8\times 10^{-5}$ 2253 785


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