CLUSTERING OF GALAXIES IN REDSHIFT SPACE - VELOCITY DISTORTION OF THEPOWER SPECTRUM AND CORRELATION-FUNCTION

Large-scale N-body simulations are used to investigate the distorting effects of peculiar velocities on the shape of the power spectrum and correlation function of galaxies as measured in redshift space. The di stortion effect is studied over a large range of scales, from the nonl inear small scales of approximately 1 h-1 Mpc to the linear regime of 400 h-1 Mpc. The distortions cause the redshift space power spectrum t o be steeper than the real spectrum; the redshift space spectrum is en hanced over the real spectrum on large scales, in agreement with linea r theory (Kaiser 1987), and is suppressed on small scales. The transit ion scale to the linear regime depends on the density parameter, OMEGA . For OMEGA = 0.2, the redshift space power spectrum is linearly enhan ced on scales greater-than-or-equal-to 60 h-1 Mpc; for OMEGA = 1, the linear enhancement is reached only for approximately 200 h-1 Mpc. An a nalytic expression relating the redshift space power spectrum to the r eal space spectrum is derived; it is a function of OMEGA and of scale. The ratio of the redshift to real space correlation functions for sep arations 1-20 h-1 Mpc is also investigated. A comparison of observatio ns with simulations in redshift space reveals that the power spectrum of IRAS and optical galaxies are consistent with the spectrum of the s tandard OMEGA = 1 CDM model, as well as with the power spectra of the OMEGA almost-equal-to 0.2 CDM model and the OMEGA = 1 HDM model. Consi stency is also found for the correlation functions.