Strong Lensing as a Probe of the Mass Distribution Beyond the Einstein
  Radius. Mass & Light in SL2S J08544-0121, a Galaxy Group at z=0.35
  Precise modelling of strong lensing systems can be affected by external mass
distributions, e.g. the group or cluster within which the lens is embedded. In
this article, we propose to turn this limitation to our advantage and to use
precise strong lensing modelling to probe external mass distributions
surrounding the lens. We consider SL2S J08544-0121, a galaxy group at z=0.35
that contains a strong lensing system. A simple elliptical isothermal potential
cannot reproduce satisfactorily the strong lensing constraints. We include an
external mass perturbation corresponding to the group within which the lens is
embedded. The lensing properties of this perturbation are parametrised by its
total mass M and a smoothing scale s that quantifies the characteristic scale
over which M is distributed. For a range of these parameters, we are able to
reproduce accurately the observations. This suggests that light is a good
tracer of mass. Interestingly, this also shows that a localised strong lensing
analysis (on scales of ~10") allows us to constrain global properties of the
group as a whole (on scales of ~100). Indeed, we constrain the group
mass-to-light ratio to be M/L=98+-27 (i band, solar units, not corrected for
evolution) and s=20" +- 9 (2sigma confidence level). We demonstrate that these
strong lensing only constraints are due to the perturbed strong lensing
configuration, where the main arc is located at ~5" from the galaxy, whereas
its counter-image is found at ~8". To test independently our resulting strong
lensing model, we pursue an independent weak lensing analysis of the group and
find a mass-to-light ratio in the range 66-146 (1sigma confidence level).
