The 2dF Galaxy Redshift Survey: The bias of galaxies and the density of the Universe

TL;DR

The paper demonstrates that the bispectrum of the 2dF Galaxy Redshift Survey can simultaneously constrain the linear and nonlinear galaxy bias parameters and the matter density. By developing a fast estimator and using two triangle configurations, the authors extract $b_1\approx1.04$ and $b_2\approx-0.054$ on large scales, and derive $\Omega_m\approx0.27$ at the effective redshift $z\approx0.17$ from redshift-space distortions. The results show that optically selected galaxies trace the underlying mass distribution with little to no scale-dependent bias over the probed $k$-range. The analysis, supported by mock catalogs, provides a robust, survey-alone measurement of cosmological parameters and supports a consistent picture with other cosmological probes.

Abstract

We compute the bispectrum of the 2dF Galaxy Redshift Survey (2dFGRS) and use it to measure the bias parameter of the galaxies. This parameter quantifies the strength of clustering of the galaxies relative to the mass in the Universe. By analysing 80 million triangle configurations in the wavenumber range 0.1 < k < 0.5 h/Mpc (i.e. on scales roughly between 5 and 30 Mpc/h) we find that the linear bias parameter is consistent with unity: b_1=1.04 pm 0.11, and the quadratic (nonlinear) bias is consistent with zero: b_2=-0.054 pm 0.08. Thus, at least on large scales, optically-selected galaxies do indeed trace the underlying mass distribution. The bias parameter can be combined with the 2dFGRS measurement of the redshift distortion parameter beta = Omega_m^{0.6}/b_1, to yield Omega_m = 0.27 pm 0.06 for the matter density of the Universe, a result which is determined entirely from this survey, independently of other datasets. Our measurement of the matter density of the Universe should be interpreted as Omega_m at the effective redshift of the survey (z=0.17).

Figures (4)

• Figure 1: Measured (redshift-space) 2dFGRS dimensionless bispectrum from the SGP and NGP for the two chosen configurations. The dotted line shows the perturbation theory prediction for $b_1=1$, $b_2=0$ while the dashed and dot-dashed lines show the shot noise contributions. The error bars are obtained via Monte Carlo simulation of 16 mock 2dFGRS catalogues (see text for details).
• Figure 2: Error on the linear bias parameter from $\Lambda$CDM mock galaxy catalogues in the SGP (left) and NGP (right). The average bias in the estimator is consistent with zero for the SGP: $-0.01 \pm 0.03$, but shows a small bias of $0.10\pm 0.04$ for the NGP. The sample rms of $0.11$ for the SGP and $0.16$ for the NGP are used in the analysis of the 2dFGRS.
• Figure 3: $1/b_1$ recovered with the bispectrum method versus the underlying (true) $1/b_1\equiv \sqrt{P/P_g}$ for 16 mock SGP simulations for the $\tau$CDM and $\Lambda$CDM models. $1/b_1$ is the natural quantity in the analysis of the bispectrum (see equation \ref{['eq:bispectrum1']}). Note that the 2dFGRS has data in the NGP and SGP, reducing the error bar compared to these mock catalogues.
• Figure 4: Ratio of the average measured bispectrum and the average perturbation theory predictions, relative to the bispectrum for a fiducial unbiased model ($B_{\rm fid}$). Dashed line $b_1=1.3, b_2=0$, dot-dashed line $b_1=1.0, b_2=0.5$. To produce this figures only the SGP data were used and only configurations with two wavevectors of common length. This means that only 12 million triangles were used from the total 80 millions. Inclusion of the remainder excludes both models at high confidence. The error bars are obtained via Monte Carlo from the 16 N-body simulations, and are placed centrally on the mean of the estimates from the mock catalogues. This illustrates the level of bias in the estimator. The figure also shows that there is no evidence of scale dependent bias.