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

We present a novel technique with which to measure sigma(8). It relies on measuring the dependence of the second-order bias of a density field on sigma(8), using two separate techniques. Each technique employs area-averaged angular correlation functions ((omega) over bar (N)), one relying on the shape of (omega) over bar (2), the other relying on the amplitude of s(3) (s(3) = (omega) over bar (3)/(omega) over bar (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 sigma(8) - sigma(true)(8) = -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 c(2) and sigma(8) are made for each data set, with the assumption of a flat geometry and WMAP3 best-fit priors on Omega(m), h, and Gamma. We find, with increasing redshift, that c(2) = 0.09 +/- 0.04, 0.09 +/- 0.05, and 0.09 +/- 0.03, and sigma(8) = 0.78 +/- 0.08, 0.80 +/- 0.09, and 0.80 +/- 0.09. We combine these three consistent sigma(8) measurements to produce sigma(8) = 0.79 +/- 0.05. Allowing the parameters Omega(m), h, and Gamma to vary within their WMAP3 1 sigma error, we find that the best-fit value of sigma(8) 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 sigma(8) to great precision, and this will serve as an important check, complementarily, on the values determined via more established methods.