A Measurement of the Quadrupole Power Spectrum in the Clustering of the 2dF QSO Survey

TL;DR

This paper addresses measuring the quadrupole component of the redshift-space power spectrum to extract information about velocity fields and cosmology from the 2dF QSO survey. It develops a fast, optimal estimator for multipole moments $P_l(k)$ that does not require computing the correlation function, using a weighted fluctuation field with the minimum-variance weight $\psi(s,k)=1/[1+\bar{n}(s)P(k,|s|)]$ and yielding the estimator ${\mathcal{P}}_l(k)$. Applied to the 2QZ data, the authors model the full redshift-space power spectrum, including light-cone effects, geometric distortions, FoG, and redshift errors, finding a best-fit bias $b_0$ around 1.4–1.5 and a quadrupole signal detected but with large uncertainties, consistent with LCDM and previous analyses. They conclude that while 2QZ provides limited dark-energy constraints due to shot noise, the proposed method is viable for larger surveys (e.g., SDSS, KAOS/WFMOS) to improve cosmological inferences from the quadrupole of the power spectrum.

Abstract

We report a measurement of the quadrupole power spectrum in the two degree field (2dF) QSO redshift (2QZ) survey. The analysis uses an algorithm parallel to that for the estimation of the standard monopole power spectrum without first requiring computation of the correlation function or the anisotropic power spectrum. The error on the quadrupole spectrum is rather large but the best fit value of the bias parameter from the quadrupole spectrum is consistent with that from previous investigations of the 2dF data.

Figures (4)

• Figure 1: A Sketch for the definition of the variables.
• Figure 2: Theoretical prediction for the monopole power spectrum ${\@fontswitch\mathcal{P}}_0(k)$ (left panel) and quadrupole ${\@fontswitch\mathcal{P}}_2(k)/{\@fontswitch\mathcal{P}}_0(k)$ (right panel). The dashed curve is the linear modeling (\ref{['lin']}), while the solid curve is the nonlinear modeling (\ref{['nonlin']}). The upper (lower) panels assume $b_0=1~(b_0=2)$ in the bias formula (\ref{['bias']}). Theoretical model is the $\Lambda$CDM model with the cosmological parameters $\Omega_m=0.28$, $\Omega_b=0.045$, $h=0.7$, $\sigma_8=0.9$ and $n=1$.
• Figure 3: The monopole power spectrum ${\@fontswitch\mathcal{P}}_0(k)$ (upper panels) and quadrupole divided by monopole ${\@fontswitch\mathcal{P}}_2(k)/{\@fontswitch\mathcal{P}}_0(k)$ (lower panels) from the 2dF QSO sample. The left (right) panels are from the SGC (NGC) sample, respectively. The curves assume the $\Lambda$CDM model with the cosmological parameters $\Omega_m=0.28$, $\Omega_b=0.045$, $h=0.7$, $\sigma_8=0.9$ and $n=1$. Concerning the bias model, the solid curve assumes (\ref{['bias']}) with $b_0=1.5$, but the dashed curve uses (\ref{['biasbest']}).
• Figure 4: The $\chi^2$ for ${\@fontswitch\mathcal{P}}_0(k)$ (dashed curve) and ${\@fontswitch\mathcal{P}}_2(k)$ (solid curve) as a function of the bias parameter $b_0$. The left (right) panels are for the South Galactic Cap (North Galactic Cap) sample, respectively.