Where are the Luminous Red Galaxies (LRGs)? Using correlation measurements and lensing to relate LRGs to dark matter haloes

Non-linear redshift-space distortions, the Finger-of-God (FoG) effect, can complicate the interpretation of the galaxy power spectrum. Here, we demonstrate the method proposed by Hikage, Takada & Spergel to use complimentary observations to directly constrain this effect on the data. We use catalogues of Luminous Red Galaxies (LRGs) and photometric galaxies from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) to measure the redshift-space power spectrum of LRGs, the cross-correlation of LRGs with the shapes of background photometric galaxies (galaxy-galaxy weak lensing) and the projected cross-correlation of LRGs with photometric galaxies having similar photometric redshifts to the LRG spectroscopic redshift. All of these measurements use a reconstructed halo field. While we use the position of each LRG for single LRG systems, we compare the measurements using different halo-centre proxies for multiple-LRG systems (4.5 per cent of all the haloes): the brightest LRG position (BLRG), the faintest LRG position (FLRG) and their arithmetical mean position (Mean), respectively, in each system. We find significant differences in the measured correlations of different centres, showing consistent off-centring effects in the three observables. By comparing the measurements with a halo model that treats the satellite photometric galaxies as being distributed according to a generalized Navarro, Frenk and White profile, we find that similar to 40 (70) per cent of BLRGs (FLRGs) are off-centred satellite galaxies in the multiple-LRG systems. The satellite LRGs have typical off-centring radius of similar to 400 kpc h(-1), and velocity dispersion of about 500 km s(-1) in host haloes with a mean mass of 1.6 x 10(14) M-circle dot h(-1). We show that, if LRGs in the single LRG systems have similar offsets, the residual FoG contamination in the LRG power spectrum can be significant at k greater than or similar to 0.1 h Mpc(-1), which may cause a bias in cosmological parameters determined by the shape of the power spectrum, such as the neutrino mass. Our results demonstrate that overlapping spectroscopic and imaging galaxy surveys can be used to observationally calibrate the FoG contamination and more robustly use the galaxy power spectrum for cosmological measurements.