Parametric strong gravitational lensing analysis of Abell 1689

We have derived the mass distribution of galaxy cluster Abell 1689 within 0.3 h(70)(-1) Mpc of the cluster centre using its strong lensing (SL) effect on 32 background galaxies, which are mapped in altogether 107 multiple images. The multiple images are based on some from the literature with modifications to both include new and exclude some of the original image systems. The cluster profile is explored further out to similar to 2.5h(70)(-1) Mpc with weak lensing (WL) shear measurements from the literature. The masses of similar to 200 cluster galaxies are measured with the Fundamental Plane (FP) in order to model accurately the small-scale mass structure in the cluster. The cluster galaxies are modelled as elliptical truncated isothermal spheres. The scalings of the truncation radii with the velocity dispersions of galaxies are assumed to match those of: (i) field galaxies; and (ii) theoretical expectations for galaxies in dense environments. The dark matter (DM) component of the cluster is described by either non-singular isothermal ellipsoids (NSIE) or elliptical versions of the universal DM profile (elliptical Navarro, Frenk & White, ENFW). To account for substructure in the DM we allow for two DM haloes. The fitting of a non-singular isothermal sphere (NSIS) to the smooth DM component results in a velocity dispersion of 1450(-31)(+39) km s(-1) and a core radius of 77(-8)(+10) h(70)(-1) kpc, while a Navarro, Frenk & White (NFW) profile has an r(200) of 2.86 +/- 0.16 h(70)(-1) Mpc (M-200 = 3.2 x 10(15)M(circle dot) h(70)) and a concentration of 4.7(-0.5)(+0.6). The total mass profile is well described by either a NSIS profile with sigma = 1514(-17)(+18) km s(-1) and a core radius of r(c) = 71 +/- 5 h(70)(-1) 70 kpc, or an NFW profile with C = 6.0 +/- 0.5 and r(200) = 2.82 +/- 0.11 h(70)(-1) Mpc (M-200 = 3.0 x 10(15)M(circle dot) h(70)). The errors are assumed to be due to the error in assigning masses to the individual galaxies in the galaxy component. Their small size is due to the very strong constraints imposed by multiple images and the ability of the smooth DM component to adjust to uncertainties in the galaxy masses. The agreement in the total mass profile between this work and that of the literature is better than 1 sigma at all radii, despite the considerable differences in the methodology used. Using the same image configuration as used in the literature, we obtain a SL model that is superior to some in the literature (rms of 2.7 compared to 3.2 arcsec). This is very surprising considering the larger freedom in the surface mass profile in their grid modelling. The difference is most likely a result of the careful inclusion of the cluster galaxies. Using also WL shear measurements from the literature, we can constrain the profile further out to r similar to 2.5 h(70)(-1) Mpc. The best-fitting parameters change to s = 1499 +/- 15 km s(-1) and r(c) = 66 +/- 5 h(70)(-1) kpc for the NSIS profile and C = 7.6 +/- 0.5 and r(200) = 2.55 +/- 0.07 h(70)(-1) Mpc (M-200 = 2.3 x 10(15)M(circle dot) h(70)) for the NFW profile.