\begin{table}%t8
\caption{\label{king_t}Physical parameters of the Arches cluster.} 
\small%\centerline
 {
\begin{tabular}{l c c l}
\hline\hline
Parameter & & Value & Comments \\
\hline
 Core radius		&$R_{\rm c}$  			& $0.14\pm0.05$ pc	& Derived by fitting the empirical King density law \\
& & &to the observed $\Sigma(R)$\\ 
 Tidal radius		&$R_{\rm t}$  			& ${\sim}1$ pc 		& Derived by Kim et~al. (\cite{kim2}) \\
 Central concentration	&$c= \log \frac{R_{\rm t}}{R_{\rm c}}$	& $0.84$		& Comparable to the less concentrated galactic globulars\\
& & &according to Harris (\cite{harris})\\
 Central surface density&$\Sigma_{0}$ 			& $2.2({\pm}0.4)\times10^{3}~{\rm stars~pc}^{-2}$		& Derived by fitting the empirical King density law \\
& & &to the observed $\Sigma(R)$\\
 Central volume density	&$\rho_{0}$ 			& $8.0({\pm}1.5)\times10^{3}~{\rm stars~pc}^{-3}$		& \\
 Central mass density	&$\rho_{\rm m,0}$ 			& $2.0({\pm}0.4)\times10^{5}~M_{\odot}~{\rm pc}^{-3}$		& For an average mass of $25.4~M_{\odot}$ in the ${>}10~M_{\odot}$ range \\
 Cluster mass		&$M_{\rm cl,1}$ 			& ${\sim}2.0(\pm0.6)\times10^{4}~M_{\odot}$			& For an extrapolation of the photometric mass down to $1~M_{\odot}$\\
\quad &$M_{\rm cl,2}$&${\sim}3.1(\pm0.6)\times10^{4}~M_{\odot}$&For an extrapolation down to $0.08~M_{\odot}$ using a Kroupa IMF (\cite{kroupa})\\
 Predicted & & &\\
velocity dispersion$^{a}$	&$\sigma=\left(\frac{0.4~GM_{\rm cl}}{R_{\rm hm}}\right)^{1/2}$	& $9~{\rm km~s}^{-1}$			& Using $M_{\rm cl,1}$ and a half mass radius of $0.4$~pc derived in SGB02\\[4pt]
 \hline
\end{tabular}}
\medskip
$^{{a}}$ Equations~(4)--(80b) of Binney \& Tremaine (\cite{binney}).
\end{table}