Combining strong lensing and dynamics in galaxy clusters: integrating MAMPOSSt within LENSTOOL

International audienceContext. The mass distribution in galaxy clusters and groups is an important cosmological probe. It has become clear in recent years that mass profiles are best recovered when combining complementary probes of the gravitational potential. Strong lensing (SL) is very accurate in the inner regions, but other probes are required to constrain the mass distribution in the outer regions, such as weak lensing or studies of dynamics. Aims. We constrain the mass distribution of a cluster showing gravitational arcs by combining a strong lensing method with a dynamical method using the velocities of its 24 member galaxies. Methods. We present a new framework in which we simultaneously fit SL and dynamical data. The SL analysis is based on the LENSTOOL software and the dynamical analysis uses the MAMPOSSt code, which we integrated into LENSTOOL. After describing the implementation of this new tool, we applied it to the galaxy group SL2S J02140-0535 (z(spec) = 0.44), which we had previously studied. We used new VLT/FORS2 spectroscopy of multiple images and group members, as well as shallow X-ray data from XMM. Results. We confirm that the observed lensing features in SL2S J02140-0535 belong to different background sources. One of these sources is located at zspec = 1.017 +/- 0.001, whereas the other source is located at z(spec) = 1.628 +/- 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(-17)(+44) kpc, c(200) = 10.0(-2.5,)(+1:7) and M-200 = 1.0(-0.2)(+0.5) x 10(14) M-circle dot respectively. These parameters are better constrained when we fit SL and dynamical information simultaneously. 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. Conclusions. 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. The similarities in shape and alignment of the centroids of the total mass, light, and intracluster gas distributions add to the picture of a non-disturbed system