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Register a new userThe 2dF Galaxy Redshift Survey: The power spectrum and the matter content of the universe
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The 2dF Galaxy Redshift Survey has now measured in excess of 160000 galaxy redshifts. This paper presents the power spectrum of the galaxy distribution, calculated using a direct FFT-based technique. We argue that, within the k-space region 0.02<k<0.15 h Mpc^-1, the shape of this spectrum should be close to that of the linear density perturbations convolved with the window function of the survey. This window function and its convolving effect on the power spectrum estimate are analyzed in detail. By convolving model spectra, we are able to fit the power-spectrum data and provide a measure of the matter content of the universe. Our results show that models containing baryon oscillations are mildly preferred over featureless power spectra. Analysis of the data yields 68% confidence limits on the total matter density times the Hubble parameter Omega_m h = 0.20 +/- 0.03, and the baryon fraction Omega_b/Omega_m = 0.15 +/- 0.07, assuming scale-invariant primordial fluctuations.
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We present a power spectrum analysis of the final 2dF QSO Redshift Survey catalogue containing 22652 QSOs. Utilising the huge volume probed by the QSOs, we can accurately measure power out to scales of ~500Mpc and derive new constraints, at z~1.4, on the matter and baryonic contents of the Universe. Importantly, these new cosmological constraints are derived at an intermediate epoch between the CMB observations at z~1000, and local (z~0) studies of large-scale structure; the average QSO redshift corresponds to a look-back time of approximately two-thirds of the age of the Universe. We find that the amplitude of clustering of the QSOs at z~1.4 is similar to that of present day galaxies. The power spectra of the QSOs at high and low redshift are compared and we find little evidence for any evolution in the amplitude. Assuming a lambda cosmology to derive the comoving distances, r(z), to the QSOs, the power spectrum derived can be well described by a model with shape parameter Gamma=0.13+-0.02. If an Einstein-de Sitter model r(z) is instead assumed, a slightly higher value of Gamma=0.16+-0.03 is obtained. A comparison with the Hubble Volume LCDM simulation shows very good agreement over the whole range of scales considered. A standard (Omega_m=1) CDM model, however, predicts a much higher value of Gamma than is observed, and it is difficult to reconcile such a model with these data. We fit CDM model power spectra (assuming scale-invariant initial fluctuations), convolved with the survey window function, and corrected for redshift space distortions, and find that models with baryon oscillations are slightly preferred, with the baryon fraction Omega_b/Omega_m=0.18+-0.10. The overall shape of the power spectrum provides a strong constraint on Omega_m*h (where h is the Hubble parameter), with Omega_m*h=0.19+-0.05.
We present a power spectrum analysis of the final 2dF Galaxy Redshift Survey, employing a direct Fourier method. The sample used comprises 221,414 galaxies with measured redshifts. We investigate in detail the modelling of the sample selection. A new angular mask is derived, based on revisions to the photometric calibration. The redshift selection function is determined by dividing the survey according to rest-frame colour, and deducing a self-consistent treatment of k-corrections and evolution for each population. The covariance matrix for the power-spectrum estimates is determined using two different approaches to the construction of mock surveys which are used to demonstrate that the input cosmological model can be correctly recovered. We are confident that the 2dFGRS power spectrum can be used to infer the matter content of the universe. On large scales, our estimated power spectrum shows evidence for the `baryon oscillations that are predicted in CDM models. Fitting to a CDM model, assuming a primordial $n_{s}=1$ spectrum, $h=0.72$ and negligible neutrino mass, the preferred parameters are $Omega_{M} h = 0.168 pm 0.016$ and a baryon fraction $Omega_{b} /Omega_{M} = 0.185pm0.046$ (1$sigma$ errors). The value of $Omega_{M} h$ is $1sigma$ lower than the $0.20 pm 0.03$ in our 2001 analysis of the partially complete 2dFGRS. This shift is largely due to the signal from the newly-sampled regions of space, rather than the refinements in the treatment of observational selection. This analysis therefore implies a density significantly below the standard $Omega_{M} =0.3$: in combination with CMB data from WMAP, we infer $Omega_{M} =0.231pm 0.021$. (Abridged.)
We present a detailed analysis of the two-point correlation function, from the 2dF Galaxy Redshift Survey (2dFGRS). We estimate the redshift-space correlation function, xi(s), from which we measure the redshift-space clustering length, s_0=6.82+/-0.28 Mpc/h. We also estimate the projected correlation function, Xi(sigma), and the real-space correlation function, xi(r), which can be fit by a power-law, with r_0=5.05+/-0.26Mpc/h, gamma_r=1.67+/-0.03. For r>20Mpc/h, xi drops below a power-law as is expected in the popular LCDM model. The ratio of amplitudes of the real and redshift-space correlation functions on scales of 8-30Mpc/h gives an estimate of the redshift-space distortion parameter beta. The quadrupole moment of xi on scales 30-40Mpc/h provides another estimate of beta. We also estimate the distribution function of pairwise peculiar velocities, f(v), including rigorously the effect of infall velocities, and find that it is well fit by an exponential. The accuracy of our xi measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of xi(r) and the two redshift-space distortion effects parameterized by beta and velocity dispersion, a. We find beta=0.49+/-0.09 and a=506+/-52km/s, though the best fit values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(sigma), and find that the shape is consistent with models and simulations. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that beta(L=L*,z=0)=0.47+/-0.08, and that the present day matter density of the Universe is 0.3, consistent with other 2dFGRS estimates and independent analyses.
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).
We measure the clustering of galaxy groups in the 2dFGRS Percolation-Inferred Galaxy Group (2PIGG) catalogue. The 2PIGG sample has 29,000 groups with at least two members. The clustering amplitude of the full 2PIGG catalogue is weaker than that of 2dFGRS galaxies, in agreement with theoretical predictions. We have subdivided the 2PIGG catalogue into samples that span a factor of 25 in median total luminosity. Our correlation function measurements span an unprecedented range of clustering strengths, connecting the regimes probed by groups fainter than L* galaxies and rich clusters. There is a steady increase in clustering strength with group luminosity; the most luminous groups are ten times more strongly clustered than the full 2PIGG catalogue. We demonstrate that the 2PIGG results are in very good agreement with the clustering of groups expected in the LCDM model.
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