The Muenster Redshift Project. I. Simulations of Power Spectra and Analytical Corrections

Random point realizations of Gaussian fluctuation fields are simulated and analyzed in order to illustrate the effects of redshift errors on inhomogeneous galaxy distributions. It is shown that, e.g., for 106 galaxies with redshifts z < 0.3 and errors 001 < _ < 0.03 (similar to the present catalog of the Muenster Redshift Project), volume-averaging statistical methods such as power-spectrum analysis yield small statistical errors. Monte Carlo simulations are supplemented by analytical considerations, showing that with simple relations the measured power spectra can be corrected for the smoothing effect of redshift errors. The most important result of our simulations is the sensitivity of large samples (106 galaxies with z < 0.3) to the expected turnover of the power spe⁶trum (here assumed to be located at 200 h -1 Mpc for H_{0 }= 100 h km s 1 Mpc -1), even with redshift errors as large as = 0.03. For global cosmological investigations, basic sampling parameters are the size and shape of the total survey volume and the number of objects located within this volume, while random redshift errors of individual galaxies are of minor importance.