All Tables

Table 1: Two mass density/shape models considered in this study. For model 9 1, an exact expression for both $\breve{\kappa}_Z$ and g_Z can be derived analytically from Eqs. (8) and (9) provided $H=\rm const.$ (see the Appendix B, Eq. (B.2); the kernel and field are finite for $k^\pm \ne 1$ ). Model 2 is a vertically parabolic profile. In this case, there is no solution in a closed form, whatever the shape of the system. Note that $\rho _1 \propto 1/a^2$ for $R \ll a$ whereas $\rho _1 \sim \rm const.$ for $R \gg a$ .
Table 2: Three systems to check the full method.
Table 3: Theoretical formulae for the physical resolution ${\cal R}_Z$ in the vertical direction as functions of the number M of source points,s-parameter and disc semi-thickness h. The last column corresponds to a 3-point, finite-difference method.
Table 4: Same legend as for Table 3 but for the physical resolution ${\cal R}_R$ in the radial direction ( $\ell =h$ for all examples). $N_{\rm left}$ , $N_{\rm local}$ and $N_{\rm right}$ denote the number of cylinders populating the left-side, long-range, the local and right-side, long-range contributions respectively (see the Appendix C).