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Using Multipoles of the Correlation Function to Measure H(z), D_A(z), and eta(z) from Sloan Digital Sky Survey Luminous Red Galaxies | Chia-Hsun Chuang
; Yun Wang
; | Date: |
24 May 2012 | Abstract: | Galaxy clustering data can be used to measure H(z), D_A(z), and eta(z).
Here we present a method for using effective multipoles of the galaxy two-point
correlation function (xi_0(s), xi_2(s), xi_4(s), and xi_6(s), with s
denoting the comoving separation) to measure H(z), D_A(z), and eta(z), and
validate it using LasDamas mock galaxy catalogs. Our definition of effective
multipoles explicitly incorporates the discreteness of measurements, and treats
the measured correlation function and its theoretical model on the same
footing. We find that for the mock data, xi_0 + xi_2 + xi_4 captures nearly
all the information, and gives significantly stronger constraints on H(z),
D_A(z), and eta(z), compared to using only xi_0 + xi_2.
We apply our method to the sample of LRGs from the SDSS DR7 without assuming
a dark energy model or a flat Universe. We find that xi_4(s) deviates on
scales of s<60,Mpc/h from the measurement from mock data (in contrast to
xi_0(s), xi_2(s), and xi_6(s)), leading to a significant difference in the
measured mean values of H(z), D_A(z), and eta(z) from xi_0 + xi_2 and xi_0
+ xi_2 + xi_4, thus it should not be used in deriving parameter constraints.
We obtain {H(0.35),D_A(0.35),Omega_mh^2,eta(z)} = {79.6_{-8.7}^{+8.3}km
s^{-1}Mpc^{-1}, 1057_{-87}^{+88}Mpc, 0.103pm0.015, 0.44pm0.15} using xi_0 +
xi_2. We find that H(0.35)r_s(z_d)/c and D_A(0.35)/r_s(z_d) (where r_s(z_d) is
the sound horizon at the drag epoch) are more tightly constrained:
{H(0.35)r_s(z_d)/c, D_A(0.35)/r_s(z_d)} =
{0.0437_{-0.0043}^{+0.0041},6.48_{-0.43}^{+0.44}} using xi_0 + xi_2. We
conclude that the multipole method can be used to isolate systematic
uncertainties in the data, and provide a useful cross-check of parameter
measurements from the full correlation function. | Source: | arXiv, 1205.5573 | Services: | Forum | Review | PDF | Favorites |
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