The Three‐Point Correlation Function of Galaxies Determined from the Two‐Degree Field Galaxy Redshift Survey

Abstract

In a detailed analysis of the three-point correlation function (3PCF) for the 2dF Galaxy Redshift Survey (2dFGRS), we have accurately measured the 3PCF for galaxies of different luminosities. The 3PCF amplitudes [Qred or Qproj ] of the galaxies generally decrease with increasing triangle size and increase with the shape parameter v, in qualitative agreement with the predictions for the clustering of dark matter (DM) in popular hierarchical cold dark matter (CDM) models. The 2dFGRS results agree well with our results for the Las Campanas Redshift Survey (LCRS), although the measurement accuracy is greatly improved in the present study because the 2dFGRS is much larger in size than the LCRS. The dependence of the 3PCF on luminosity is not significant, but there seems to be a trend for the brightest galaxy sample to have a lower amplitude than the fainter ones. Comparing the measured 3PCF amplitudes [Qred or Qproj ] to the prediction of a WMAP (Wilkinson Microwave Anisotropy Probe) concordance model, we find that the measured values are consistently lower than the predicted ones for DM. This is most pronounced for the brightest galaxies (sample I), for which about one-half of the predicted Q-value provides a good description of Qproj for the 2dFGRS data. For the less luminous sample (sample II), the Q-values are also smaller than in the DM model on small scales, but on scales larger than s = 8 h-1 Mpc and rp = 3.25 h-1 Mpc they reach the model values. Therefore, the galaxies of sample II are unbiased tracers on linear scales, but the bright galaxies (sample I) have a linear bias factor of ~1.5. As for the LCRS data, we may state that the best-fit DM model gives higher values for the 3PCF than observed. This indicates that the simple DM models must be refined, by using either more sophisticated bias models or a more sophisticated combination of model parameters.