No abstract

Recent studies have shown that the cross-correlation coefficient between galaxies and dark matter is very close to unity on scales outside a few virial radii of galaxy halos, independent of the details of how galaxies populate dark matter halos. This finding makes it possible to determine the dark matter clustering from measurements of galaxy-galaxy weak lensing and galaxy clustering. We present new cosmological parameter constraints based on large-scale measurements of spectroscopic galaxy samples from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). We generalise the approach of Baldauf et al. (2010) to remove small scale information (below 2 and 4h −1 Mpc for lensing and clustering measurements, respectively), where the crosscorrelation coefficient differs from unity. We derive constraints for three galaxy samples covering 7131 deg 2 , containing 69150, 62150, and 35088 galaxies with mean redshifts of 0.11, 0.28, and 0.40. We clearly detect scale-dependent galaxy bias for the more luminous galaxy samples, at a level consistent with theoretical expectations. When we vary both σ 8 and Ω m (and marginalise over non-linear galaxy bias) in a flat ΛCDM model, the best-constrained quantity is σ 8 (Ω m /0.25) 0.57 = 0.80 ± 0.05 (1σ, stat. + sys.), where statistical and systematic errors (photometric redshift and shear calibration) have comparable contributions, and we have fixed n s = 0.96 and h = 0.7. These strong constraints on the matter clustering suggest that this method is competitive with cosmic shear in current data, while having very complementary and in some ways less serious systematics. We therefore expect that this method will play a prominent role in future weak lensing surveys. When we combine these data with WMAP7 CMB data, constraints on σ 8 , Ω m , H 0 , w de and m ν become 30-80 per cent tighter than with CMB data alone, since our data break several parameter degeneracies.

Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, E(G), that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to 'galaxy bias' (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of E(G) different from the general relativistic prediction because, in these theories, the 'gravitational slip' (the difference between the two potentials that describe perturbations in the gravitational metric) is non-zero, which leads to changes in the growth of structure and the strength of the gravitational lensing effect. Here we report that E(G) = 0.39 +/- 0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of E(G) approximately 0.4. The measured value excludes a model within the tensor-vector-scalar gravity theory, which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f(R) theory, which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.

In this paper, we derive scaling relations between photometric observable quantities and disc galaxy rotation velocity Vrot or Tully–Fisher relations (TFRs). Our methodology is dictated by our purpose of obtaining purely photometric, minimal‐scatter estimators of Vrot applicable to large galaxy samples from imaging surveys. To achieve this goal, we have constructed a sample of 189 disc galaxies at redshifts z < 0.1 with long‐slit Hα spectroscopy from Pizagno et al. and new observations. By construction, this sample is a fair subsample of a large, well‐defined parent disc sample of ∼170 000 galaxies selected from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7). The optimal photometric estimator of Vrot we find is stellar mass M★ from Bell et al., based on the linear combination of a luminosity and a colour. Assuming a Kroupa initial mass function (IMF), we find: log [V80/(km s−1)] = (2.142 ± 0.004) + (0.278 ± 0.010)[log (M★/M⊙) − 10.10], where V80 is the rotation velocity measured at the radius R80 containing 80 per cent of the i‐band galaxy light. This relation has an intrinsic Gaussian scatter dex and a measured scatter σmeas= 0.056 dex in log V80. For a fixed IMF, we find that the dynamical‐to‐stellar mass ratios within R80, (Mdyn/M★)(R80), decrease from approximately 10 to 3, as stellar mass increases from M★≈ 109 to 1011 M⊙. At a fixed stellar mass, (Mdyn/M★)(R80) increases with disc size, so that it correlates more tightly with stellar surface density than with stellar mass or disc size alone. We interpret the observed variation in (Mdyn/M★)(R80) with disc size as a reflection of the fact that disc size dictates the radius at which Mdyn/M★ is measured, and consequently, the fraction of the dark matter ‘seen’ by the gas at that radius. For the lowest M★ galaxies, we find a positive correlation between TFR residuals and disc sizes, indicating that the total density profile is dominated by dark matter on these scales. For the highest M★ galaxies, we find instead a weak negative correlation, indicating a larger contribution of stars to the total density profile. This change in the sense of the correlation (from positive to negative) is consistent with the decreasing trend in (Mdyn/M★)(R80) with stellar mass. In future work, we will use these results to study disc galaxy formation and evolution and perform a fair, statistical analysis of the dynamics and masses of a photometrically selected sample of disc galaxies.