along the ring (see fig. \[fig:alma\_COandcont\]), the velocity distribution pattern (see the second panel in fig. \[fig:alma\_momenta\]) shows a clear geometrical offset in the velocity components that could be associated with two separated emitting components. In some of the knots a bimodal distribution of the line is clearly visible: in such cases the difference in velocity among the two components is $\sim300$km/s.

![image](Final_HST.pdf){width="\textwidth"} ![image](Final_ALMA.pdf){width="\textwidth"}

  --------------- --------------- ----------------- --------------- -------------------- --------------------
                    $r_{\rm E}$        $\phi$             $q$        $\Delta x_{\rm L}$   $\Delta y_{\rm L}$
                         ”             $\circ$                               ”                    ”
  HST $1.6\mu$m    0.66$\pm$0.02   142.51$\pm$7.51   0.77$\pm$0.02    -0.09$\pm$ 0.02      -0.04$\pm$ 0.05
  ALMA $1.3$ mm    0.65$\pm$0.04   143.19$\pm$9.09   0.77$\pm$0.04    -0.10$\pm$ 0.03      +0.01$\pm$ 0.03
  --------------- --------------- ----------------- --------------- -------------------- --------------------

  --------------- ----------------- ----------------- --------------- --------------- ----------------- -----------------
                   $\mu_{3\sigma}$   $\mu_{5\sigma}$   $A_{3\sigma}$   $A_{5\sigma}$    $r_{3\sigma}$     $r_{5\sigma}$
                                                          kpc$^2$         kpc$^2$            kpc               kpc
  HST $1.6\mu$m     7.80$\pm$0.44     8.32$\pm$0.49    20.43$\pm$1.8   11.45$\pm$1.6   2.550$\pm$0.117   1.909$\pm$0.144
  ALMA $1.3$ mm    17.39$\pm$3.86    18.73$\pm$4.43    0.82$\pm$0.34   0.44$\pm$0.16   0.510$\pm$0.098   0.375$\pm$0.064
  --------------- ----------------- ----------------- --------------- --------------- ----------------- -----------------

![image](allmodels.png){width="\textwidth"}

Modeling the emission of SDP9
=============================

We perform lens modeling, in order to obtain the lens parameters, reconstruct the source emission and retrieve other useful informations such as the total magnification $\mu$. There are mainly two different approaches to lens modeling. The so called ‘parametric’ methods describe both the 