Normalization of the matter power spectrum via higher order angular correlations of luminous red galaxies

We present a novel technique with which to measure σ_g. It relies on measuring the dependence of the second-order bias of a density field on σ₈, using two separate techniques. Each technique employs area-averaged angular correlation functions (ω̄_N), one relying on the shape of W2, the other relying on the amplitude of s₃ (s₃ = ω̄₃/ω̄₂ ²). We confirm the validity of this method by testing it on a mock catalog drawn from Millennium Simulation data and finding a value of σ₈ - σ₈^true = -0.002 ± 0.062. We create a catalog of photometrically selected LRGs from SDSS DR5 and separate it into three distinct data sets by photometric redshift, with median redshifts of 0.47, 0.53, and 0.61. Measurements of c₂ and σ₈ are made for each data set, with the assumption of a flat geometry and WMAP3 best-fit priors on Ω_m, h, and Γ. We find, with increasing redshift, that c₂ = 0.09 ± 0.04,0.09 ± 0.05, and 0.09 ± 0.03, and σ₈ = 0.78 ± 0.08, 0.80 ± 0.09, and 0.80 ± 0.09. We combine these three consistent erg measurements to produce σ₈ = 0.79 ± 0.05. Allowing the parameters Ω_m, h, and Γ to vary within their WMAP3 1 σ error, we find that the best-fit value of σ₈ does not change by more than 8%, and we are thus confident that our measurement is accurate to within 10%. We anticipate that future surveys, such as Pan-STARRS, DES, and LSST, will be able to employ this method in order to measure σ₈ to great precision, and this will serve as an important check, complementarity, on the values determined via more established methods.