\begin{table}%t1 \caption{\label{tab_densitylaws}Density laws and associated parameters. } \small%\centering \par \begin{tabular}{lccc} \hline\hline\noalign{\smallskip} &Density law & Constants & $\rho_{\rm c}$ \\ & & (kpc) & ($M_{\odot}~\rm pc^{-3}$) \\ \hline\noalign{\smallskip} Bulge &${\rm e}^{-(r/r_{0})^{2}}$ &$r_{0}=0.5$ & $\frac{M_{\rm b}}{4\pi r_{0}^{3}}=12.73$ \\ \\ Thin disc &${\rm e}^{-R/h_{R}}\textrm{sech}^{2}(-z/h_{z})$ &$h_{R}=2.5$ & $\frac{M_{\rm tn}}{4\pi h_{R}^{2}h_{z}}=1.881$ \\ & &$h_{z}=0.352$ & \\ \\ Thick disc &${\rm e}^{-R/h_{R}}{\rm e}^{-z/h'_{z}}$ & $h_{R} = 2.5$ & $\frac{M_{\rm tk}}{4\pi h_{R}^{2}h'_{z}}=0.0286$\\ & & $h'_{z}=1.158$ & \\ \\ Halo &$ [(1+(\frac{a}{a_{0}})^{2})]^{-1}$ &$a_{0} = 2.7$ & 0.108\\ \hline \end{tabular} \tablefoot{$r$ is the spherical radius from the center of the Galaxy and $r_{0}$ is bulge scale length; $R$ and $z$ are the natural cylindrical coordinates of the axisymmetric disc, $h_{R}$ is the scale length of the disc, $h_{z}$ is the scale height of the thin disc, $h'_{z}$ is the scale height of the thick disc; $a$ is the radius of the halo and $a_{0}$ is a constant; $\rho_{\rm c}$ is the central mass density.} \end{table}