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2.7. Velocity Correlations

There has been much discussion on the use of the velocity correlation function (Peebles, 1987; Kaiser, 1988):

Equation 48 (48)

It is on the basis of this function calculated for the S7 sample that Groth, Juskiewicz and Ostriker (1989) argue that the observed velocity field is far more correlated than would be expected on the basis of the CDM model, particularly at large separations.

However, Górski et al. (1989) have made an improvement on this and show how to calculate velocity correlations from observable quantities. They split the velocity correlation tensor into "parallel" and "transverse" components. They show, on the basis of comparison with cosmological N-body simulations, that the scalar version of this by Groth et al. (1989) may give misleading results. The Aaronson et al. and IRAS samples show velocity correlations over scales of 1500 h-1 Mpc. The Burstein et al. elliptical galaxy sample shows the same correlation length scale, but with a considerably greater amplitude. (The elliptical galaxy sample correlations are very sensitive to the velocities of a small number of galaxies in the sample). The correlations in the Aaronson et al. (1982) and IRAS samples are not unusual for CDM models with a bias parameter b = 2 or less, but the CDM models cannot reproduce amplitude of the elliptical galaxy sample. The Peebles baryonic model with isocurvature fluctuation automatically generates long range correlations, but even then cannot come to terms with the S7 elliptical sample.

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