For galaxy clustering to provide robust constraints on cosmological parameters and galaxy formation models, it is essential to make reliable estimates of the errors on clustering measurements. We present a new technique, based on a spatial Jackknife
(JK) resampling, which provides an objective way to estimate errors on clustering statistics. Our approach allows us to set the appropriate size for the Jackknife subsamples. The method also provides a means to assess the impact of individual regions on the measured clustering, and thereby to establish whether or not a given galaxy catalogue is dominated by one or several large structures, preventing it to be considered as a fair sample. We apply this methodology to the two- and three-point correlation functions measured from a volume limited sample of M* galaxies drawn from data release seven of the Sloan Digital Sky Survey (SDSS). The frequency of jackknife subsample outliers in the data is shown to be consistent with that seen in large N-body simulations of clustering in the cosmological constant plus cold dark matter cosmology. We also present a comparison of the three-point correlation function in SDSS and 2dFGRS using this approach and find consistent measurements between the two samples.
We present a test of different error estimators for 2-point clustering statistics, appropriate for present and future large galaxy redshift surveys. Using an ensemble of very large dark matter LambdaCDM N-body simulations, we compare internal error e
stimators (jackknife and bootstrap) to external ones (Monte-Carlo realizations). For 3-dimensional clustering statistics, we find that none of the internal error methods investigated are able to reproduce neither accurately nor robustly the errors of external estimators on 1 to 25 Mpc/h scales. The standard bootstrap overestimates the variance of xi(s) by ~40% on all scales probed, but recovers, in a robust fashion, the principal eigenvectors of the underlying covariance matrix. The jackknife returns the correct variance on large scales, but significantly overestimates it on smaller scales. This scale dependence in the jackknife affects the recovered eigenvectors, which tend to disagree on small scales with the external estimates. Our results have important implications for the use of galaxy clustering in placing constraints on cosmological parameters. For example, in a 2-parameter fit to the projected correlation function, we find that the standard bootstrap systematically overestimates the 95% confidence interval, while the jackknife method remains biased, but to a lesser extent. The scatter we find between realizations, for Gaussian statistics, implies that a 2-sigma confidence interval, as inferred from an internal estimator, could correspond in practice to anything from 1-sigma to 3-sigma. Finally, by an oversampling of sub-volumes, it is possible to obtain bootstrap variances and confidence intervals that agree with external error estimates, but it is not clear if this prescription will work for a general case.
We identify a large sample of isolated bright galaxies and their fainter satellites in the 2dF Galaxy Redshift Survey (2dFGRS). We analyse the dynamics of ensembles of these galaxies selected according to luminosity and morphological type by stacking
the positions of their satellites and estimating the velocity dispersion of the combined set. We test our methodology using realistic mock catalogues constructed from cosmological simulations. The method returns an unbiased estimate of the velocity dispersion provided that the isolation criterion is strict enough to avoid contamination and that the scatter in halo mass at fixed primary luminosity is small. Using a maximum likelihood estimator that accounts for interlopers, we determine the satellite velocity dispersion within a projected radius of 175 kpc/h. The dispersion increases with the luminosity of the primary and is larger for elliptical galaxies than for spiral galaxies of similar bJ luminosity. Calibrating the mass-velocity dispersion relation using our mock catalogues, we find a dynamical mass within 175 kpc/h of M_175 ~ 4.0^{+2.3}_{-1.5} 10^12 (L_bJ/L_*) M_sol/h for elliptical galaxies and M_175 ~ 6.3^{+6.3}_{-3.1} 10^11 (L_bJ/L_*)^1.6 Msol/h for spiral galaxies. Finally, we compare our results with recent studies and investigate their limitations using our mock catalogues.
