Normalization of the Matter Power Spectrum via Higher-Order Angular Correlations of Luminous Red Galaxies
We present a novel technique to measure $σ_8$, by measuring the dependence of the second-order bias of a density field on $σ_8$ using two separate techniques. Each technique employs area-averaged angular correlation functions ($\barω_N$), one relying on the shape of $\barω_2$, the other relying on the amplitude of $s_3$ ($s_3 =\barω_3/\barω_2^2$). We confirm the validity of the method by testing it on a mock catalog drawn from Millennium Simulation data and finding $σ_8^{measured}- σ_8^{true} = -0.002 \pm 0.062$. 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 $σ_8$ are made for each data set, assuming flat geometry and WMAP3 best-fit priors on $Ω_m$, $h$, and $Γ$. We find, with increasing redshfit, $c_2 = 0.09 \pm 0.04$, $0.09 \pm 0.05$, and $0.09 \pm 0.03$ and $σ_8 = 0.78 \pm 0.08$, $0.80 \pm 0.09$, and $0.80 \pm 0.09$. We combine these three consistent $σ_8$ measurements to produce the result $σ_8 = 0.79 \pm 0.05$. Allowing the parameters $Ω_m$, $h$, and $Γ$ to vary within their WMAP3 1$σ$ error, we find that the best-fit $σ_8$ 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 $σ_8$ to great precision, and will serve as an important check, complementary, on the values determined via more established methods.