\begin{table}%t1
\caption{\label{table:caustic-parameters}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~(\ref{Gk}), (\ref{eq:rho3Ddef})$-$(\ref{eq:maxdens}). 
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~(\ref{eq:thickness})].
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.}
%\centering
\par
\begin{tabular}{cccccccc}
\hline\hline
$k$ &  $\xi_k$~~~~~~   &  $\lambda_k$~~~~~~ &
$\left({\rm d}^2\lambda/{\rm d}\xi^2\right)_k$ & $\Lambda_k$  & \qquad $\Delta r_k$ (pc) 
& \qquad $\rho_{\rm max}/\rho_{\rm H}/(\!\sqrt{r_{\rm vir}})~~{\rm  pc}^{-1/2}$ & $\rho_{\rm halo}/\rho_{\rm H}$\\[1mm]
\hline
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  \\
\hline\end{tabular}
\end{table}