Combining Strong Lensing and Dynamics in Galaxy Clusters: integrating
  MAMPOSSt within LENSTOOL I. Application on SL2S J02140-0535
  We present a new framework were we simultaneously fit strong lensing (SL) and
dynamical data. The SL analysis is based on LENSTOOL, and the dynamical
analysis uses MAMPOSSt code, which we have integrated into LENSTOOL. After
describing the implementation of this new tool, we apply it on the galaxy group
SL2S\,J02140-0535 ($z_{\rm spec}=0.44$), which we have already studied in the
past. We use new VLT/FORS2 spectroscopy of multiple images and group members,
as well as shallow X-ray data from \xmm. We confirm that the observed lensing
features in SL2S\,J02140-0535 belong to different background sources. One of
this sources is located at $z_{\rm spec}$ = 1.017 $\pm$ 0.001, whereas the
other source is located at $z_{\rm spec}$ = 1.628 $\pm$ 0.001. With the
analysis of our new and our previously reported spectroscopic data, we find 24
secure members for SL2S\,J02140-0535. Both data sets are well reproduced by a
single NFW mass profile: the dark matter halo coincides with the peak of the
light distribution, with scale radius, concentration, and mass equal to $r_s$
=$82^{+44}_{-17}$ kpc , $c_{200}$ = $10.0^{+1.7}_{-2.5}$, and $M_{200}$ =
$1.0^{+0.5}_{-0.2}$ $\times$ 10$^{14}$M$_{\odot}$ respectively. These
parameters are better constrained when we fit simultaneously SL and dynamical
information. The mass contours of our best model agrees with the direction
defined by the luminosity contours and the X-ray emission of SL2S\,J02140-0535.
The simultaneous fit lowers the error in the mass estimate by 0.34 dex, when
compared to the SL model, and in 0.15 dex when compared to the dynamical
method.The combination of SL and dynamics tools yields a more accurate probe of
the mass profile of SL2S\,J02140-0535 up to $r_{200}$. However, there is
tension between the best elliptical SL model and the best spherical dynamical
model.
