Density profiles of galaxy groups and clusters from SDSS galaxy-galaxy weak lensing

We present results of a measurement of the shape of the density profile of galaxy groups and clusters traced by 43 335 Luminous Red Galaxies (LRGs) with spectroscopic redshifts from the Sloan Digital Sky Survey (SDSS). The galaxies are selected such that they are the brightest within a cylindrical aperture, split into two luminosity samples and modelled as the sum of stellar and dark matter components. We present a detailed investigation of many possible systematic effects that could contaminate our signal and develop methods to remove them, including a detected intrinsic alignment for galaxies within 100 h(-1) kpc of LRGs which we remove using photometric redshift information. The resulting lensing signal is consistent with NFW (Navarro, Frenk & White) profile dark matter haloes; the singular isothermal sphere (SIS) profile is ruled out at the 96 (conservatively) and 99.96 per cent confidence level (CL) for the fainter and brighter lens samples (respectively) when we fit using lensing data between 0.4 and 2 h(-1) Mpc with total signal-to-noise ratio of 19 and 25 for the two lens samples. The lensing signal amplitude suggests that the faint and bright sample galaxies typically reside in haloes of mass (2.9 +/- 0.4) x 10(13) and (6.7 +/- 0.8) x 10(13) h(-1) M-circle dot, respectively, in good agreement with predictions based on halo spatial density with normalization lower than the 'concordance' sigma(8) = 0.9. When fitting for the concentration parameter in the NFW profile, we find c = 5.0 +/- 0.6 (stat) +/- 1 (sys), and c = 5.6 +/- 0.6 (stat) +/- 1 (sys) for the faint and bright samples, consistent with Lambda cold dark matter (CDM) simulations. We also split the bright sample further to determine masses and concentrations for cluster-mass haloes, finding mass (1.3 +/- 0.2) x 10(14) h(-1) M-circle dot for the sample of LRGs brighter than -22.6 in r. We establish that on average there is a correlation between the halo mass and central galaxy luminosity relation that scales as M proportional to L-2.