Clustering in real space and in redshift space

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Abstract
Peculiar velocities distort the clustering pattern in red shift space on all scales. Four consequences of this are: (i) The acceleration vector derived by summing the inverse squared redshifts of galaxies differs significantly from the true acceleration even in linear theory. Estimates of Ω obtained in this manner are only reliable for small Ω. (ii) The power spectrum of large-scale clustering has a quadrupole anisotropy, providing a way to estimate Ω. We calculated, for various assumed power spectra, the line-of-sight correlation function in redshift space, ξυ. We find that ξυ may display a strong anticorrelation feature that has no counterpart in real space. (iii) The density contrast of the local supercluster will appear enhanced in redshift space. Using a simple infall model (with Ω = l), we simulate the Shapley–Ames catalogue. For an infall velocity around 350 km s–1, the apparent density is similar to that observed, so the data do not require Ω⪡ 1, or biasing on large scales. (iv) Turnaround is estimated to occur at a radius ≃1500 km s–1 from a rich cluster, resulting in large transverse features of this scale. Since the velocity field is apparently very coherent, high density caustic surfaces must result. Guided by the appearance of the spherical model, we argue that the shell-like structures seen in some recent redshift surveys are most naturally interpreted as these caustics, rather than as the result of energetic explosions. The model also shows the apparent falling velocity dispersion with radius that is often seen in rich clusters, and suggests that the interpretation of this in terms of equilibrium models is inappropriate.

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