Determination of Malmquist Bias and Selection Effects from Monte Carlo Simulations

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Abstract
Maps of the peculiar velocity field derived from distance relations are affected by Malmquist type bias and selection effects. Because of the large number of interdependent effects, they are in most cases difficult to treat analytically. Monte Carlo simulations are used to understand and evaluate these effects. In these simulations the ``true'' spatial distribution and relevant properties of galaxies as well as selection effects and observational uncertainties are realistically modeled. The results of the simulation can directly be applied to correct observed peculiar velocity maps. The simulation is used to investigate biases in samples of measured peculiar velocities by Lynden-Bell et al. (1988), Willick (1990) and the new sample of spiral galaxies by Haynes et al. (1993). Based on the results obtained from the application of our method to toy models we find that the method is a useful tool to estimate the bias induced both by inhomogeneities and selection effects. This is a crucial step for the analysis of the Haynes etal sample which was selected with a redshift dependent criterion.Comment: accepted for publication in The Astronomical Journal, LaTex file using aaspptwo.sty macros, 18 pages + 15 figures, figures not included. A postscript version including all figures can be obtained from ftp://ecf.hq.eso.org/pub/preprints/malmquist.ps (2.8 MByte or 0.9 Mbyte for the compressed version
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