SDSS J120602.09+514229.5 is a gravitational lens system formed by a group of galaxies at redshift z _ { FG } = 0.422 lensing a bright background galaxy at redshift z _ { BG } = 2.001 .
The main peculiarity of this system is the presence of a luminous satellite near the Einstein radius , that slightly deforms the giant arc .
This makes SDSS J120602.09+514229.5 the ideal system to test our grid-based Bayesian lens modelling method , designed to detect galactic satellites independently from their mass-to-light ratio , and to measure the mass of this dwarf galaxy despite its high redshift .
We model the main lensing potential with a composite analytical density profile consisting of a single power-law for the group dominant galaxy , and two singular isothermal spheres for the other two group members .
Thanks to the pixelized source and potential reconstruction technique of we are able to detect the luminous satellite as a local positive surface density correction to the overall smooth potential .
Assuming a truncated Pseudo-Jaffe density profile , the satellite has a mass M _ { sub } = ( 2.75 \pm 0.04 ) \times 10 ^ { 10 } M _ { \odot } inside its tidal radius of r _ { t } = 0.68 \arcsec .
This result is robust against changes in the lens model , with a fractional change in the substructure mass from one model to the other of 0.1 percent .
We determine for the satellite a luminosity of L _ { B } = ( 1.6 \pm 0.8 ) \times 10 ^ { 9 } L _ { \odot } , leading to a total mass-to-light ratio within the tidal radius of ( M / L ) _ { B } = ( 17.2 \pm 8.5 ) M _ { \odot } / L _ { \odot } .
The central galaxy has a sub-isothermal density profile as in general is expected for group members .
From the SDSS spectrum we derive for the central galaxy a velocity dispersion of \sigma _ { \mathrm { kinem } } = 380 \pm 60 \mathrm { km s ^ { -1 } } within the SDSS aperture of diameter 3 \arcsec .
The logarithmic density slope of \gamma = 1.7 ^ { +0.25 } _ { -0.30 } ( 68 % CL ) , derived from this measurement , is consistent within 1- \sigma with the density slope of the dominant lens galaxy \gamma \approx 1.6 determined from the lens model .
This paper shows how powerful pixelized lensing techniques are in detecting and constraining the properties of dwarf satellites at high redshift .