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

Abstract

We present a novel technique to measure $\ddot{I}{ƒ}_8$, by measuring the dependence of the second-order bias of a density field on $\ddot{I}{ƒ}_8$ using two separate techniques. Each technique employs area-averaged angular correlation functions ($\bar{\ddot{I}}{‰}_N$), one relying on the shape of $\bar{\ddot{I}}{‰}_2$, the other relying on the amplitude of $s_3$ ($s_3=\bar{\ddot{I}}{‰}_3/\bar{\ddot{I}}{‰}_2^2$). We confirm the validity of the method by testing it on a mock catalog drawn from Millennium Simulation data and finding $\ddot{I}{ƒ}_8^{measured}-\ddot{I}{ƒ}_8^{true}=-0.002\pm 0.062$. 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 $\ddot{I}{ƒ}_8$ are made for each data set, assuming flat geometry and WMAP3 best-fit priors on $\hat{I}{\text{c◯}}_m$, $h$, and $\hat{I}“$. We find, with increasing redshfit, $c_2=0.09\pm 0.04$, $0.09\pm 0.05$, and $0.09\pm 0.03$ and $\ddot{I}{ƒ}_8=0.78\pm 0.08$, $0.80\pm 0.09$, and $0.80\pm 0.09$. We combine these three consistent $\ddot{I}{ƒ}_8$ measurements to produce the result $\ddot{I}{ƒ}_8=0.79\pm 0.05$. Allowing the parameters $\hat{I}{\text{c◯}}_m$, $h$, and $\hat{I}“$ to vary within their WMAP3 1$\ddot{I}ƒ$ error, we find that the best-fit $\ddot{I}{ƒ}_8$ 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 $\ddot{I}{ƒ}_8$ 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