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

Abstract

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.

23 pages, 4 figures, preprint, accepted to ApJ

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• The Search for a Primordial Magnetic Field
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• Primordial Magnetic Field Effects on the CMB and Large Scale Structure
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