Theoretical implications of deviations from Hubble flow

The net streaming solution found by Dressler et al. for their sample of elliptical galaxies can be modelled as the convolution of the peculiar velocity field with a tensor window function. For the cold dark matter spectrum normalized to unit mass variance in 8 h−1 Mpc spheres the prediction is in good agreement with the observation (previous indications to the contrary resulted from an inappropriate choice of smoothing window). If galaxy clustering is biased upward this will reduce the predictions, and a bias factor b>2 gives an unacceptably small prediction. An attempt is made to normalize the amplitude directly to form rich clusters, and this gives a prediction which is smaller than the unbiased model but still acceptable. In an attempt to extract more information from the data we have combined the elliptical data with the cluster spirals of Aaronson et al. to form a sample of 35 clusters or loose clumps and we have calculated the likelihood function for a family of theoretical velocity power spectra characterized by a coherence length Rc, and 3D velocity dispersion υ3. The models include an additional spatially incoherent velocity field of amplitude σ*; this parameter allows for some tolerance to small departures from the predictions of the model, as might arise from motions associated with small-scale non-linear clustering, or from measurement errors in excess of the formal error bars. With σ* = 350 km s−1, the most likely models have large Rc and υ3≃500−700 km s−1, but models with much smaller coherence length and the same υ3 are essentially equally likely. There may be coherent large-scale streaming motions, and these would be difficult to reproduce in models such as cold dark matter, but they are not required by the data. If σ*, is substantially reduced, only models with small coherence length remain viable.