We consider three extensions of the Navarro, Frenk and White (NFW) profile and investigate the intrinsic degeneracies among the density profile parameters on the gravitational lensing effect of satellite galaxies on highly magnified Einstein rings. I
n particular, we find that the gravitational imaging technique can be used to exclude specific regions of the considered parameter space, and therefore, models that predict a large number of satellites in those regions. By comparing the lensing degeneracy with the intrinsic density profile degeneracies, we show that theoretical predictions based on fits that are dominated by the density profile at larger radii may significantly over- or underestimate the number of satellites that are detectable with gravitational lensing. Finally, using the previously reported detection of a satellite in the gravitational lens system JVAS B1938+666 as an example, we derive for this detected satellite values of r_max and v_max that are, for each considered profile, consistent within 1sigma with the parameters found for the luminous dwarf satellites of the Milky Way and with a mass density slope gamma < 1.6. We also find that the mass of the satellite within the Einstein radius as measured using gravitational lensing is stable against assumptions on the substructure profile. In the future thanks to the increased angular resolution of very long baseline interferometry at radio wavelengths and of the E-ELT in the optical we will be able to set tighter constraints on the number of allowed substructure profiles.
SDSS J120602.09+514229.5 is a gravitational lens system formed by a group of galaxies at redshift z=0.422 lensing a bright background galaxy at redshift z=2.001. The main peculiarity of this system is the presence of a luminous satellite near the Ein
stein 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. Thanks to the pixelized source and potential reconstruction technique of Vegetti and Koopmans 2009a 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=(2.75+-0.04)10^10 M_sun inside its tidal radius of r_t=0.68. We determine for the satellite a luminosity of L_B=(1.6+-0.8)10^9 L_sun, leading to a total mass-to-light ratio within the tidal radius of (M/L)_B=(17.2+-8.5) M_sun/L_sun. 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_kinem=380+-60 km/s within the SDSS aperture of diameter 3. 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~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.
