Quantifying dwarf satellites through gravitational imaging: the case of SDSS J120602.09+514229.5

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, which 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 Galaxy satellites independently of 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 Vegetti and Koopmans, we are able to detect the luminous satellite as a local positive surface density correction to the overall smooth mass model. Assuming a truncated pseudo-Jaffe density profile, the satellite has a mass M-sub = (2.75 +/- 0.04) x 1010 M-circle dot inside its tidal radius of r(t) = 0.68 arcsec. This result is robust against changes in the lens model. We determine for the satellite a luminosity of L-B = (1.6 +/- 0.8) x 109 L-circle dot, leading to a total mass-to-light ratio within the tidal radius of (M/L)(B) = (17.2 +/- 8.5) M-circle dot/L-circle dot. The central galaxy has a sub-isothermal density profile as in general is expected for group members. From the Sloan Digital Sky Survey (SDSS) spectrum, we derive for the central galaxy a velocity dispersion of Sigma(kinem) = 380 +/- 60 km s-1 within the SDSS aperture of a diameter of 3 arcsec. The logarithmic density slope of gamma = 1.7+0.25(-0.30) [68 per cent confidence limit (CL)], derived from this measurement, is consistent within 1 Sigma with the density slope of the dominant lens galaxy gamma approximate to 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.