Normalization of the Matter Power Spectrum via Higher-Order Angular Correlations of Luminous Red Galaxies

We present a novel technique to measure $\sigma_8$, by 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 ($\bar{\omega}_N$), one relying on the shape of $\bar{\omega}_2$, the other relying on the amplitude of $s_3$ ($s_3 =\bar{\omega}_3/\bar{\omega}_2^2$). We confirm the validity of the method by testing it on a mock catalog drawn from Millennium Simulation data and finding $\sigma_8^{measured}- \sigma_8^{true} = -0.002 \pm 0.062$. 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, assuming flat geometry and WMAP3 best-fit priors on $\Omega_m$, $h$, and $\Gamma$. We find, with increasing redshfit, $c_2 = 0.09 \pm 0.04$, $0.09 \pm 0.05$, and $0.09 \pm 0.03$ and $\sigma_8 = 0.78 \pm 0.08$, $0.80 \pm 0.09$, and $0.80 \pm 0.09$. We combine these three consistent $\sigma_8$ measurements to produce the result $\sigma_8 = 0.79 \pm 0.05$. Allowing the parameters $\Omega_m$, $h$, and $\Gamma$ to vary within their WMAP3 1$\sigma$ error, we find that the best-fit $\sigma_8$ does not change by more than 8% and we are thus confident 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 to measure $\sigma_8$ to great precision, and will serve as an important check, complementary, on the values determined via more established methods.