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In this section, we test the VELMOD method on simulated data sets. Kolatt et al. (1996) have produced simulated catalogs that mimic the properties of both the IRAS redshift survey and the Mark III samples. We briefly review the salient points here.

The mass density distribution of the simulated universe is based on the distribution of IRAS galaxies in the real universe. This was achieved by first taking the present redshift distribution of IRAS galaxies and solving for a 500 km s-1 smoothed, real-space distribution via an iterative procedure that applies nonlinear corrections and a power-preserving filter (Sigad et al. 1997). The smoothed, filtered IRAS density field was then "taken back in time" using the Zeldovich-Bernoulli algorithm of Nusser & Dekel (1992) to obtain the linear initial density field. The method of constrained realization (Hoffman & Ribak 1991; Ganon & Hoffman 1993) was used to restore small-scale power down to galactic scales. The resulting initial conditions were then evolved forward as an Omega = 1 N-body simulation using the PM code of Gelb & Bertschinger (1994). The present-day density field resulting from this procedure is displayed in Figure 6 of Kolatt et al. (1996).

We generated a suite of 20 mock Mark III and mock IRAS catalogs from this simulated universe. (9) Each mock Mark III TF sample was constructed to mimic the distribution on the sky and in redshift space of the corresponding real sample, and the TF relations and scatters of the mock samples were chosen to be similar to the observed ones. The mock TF samples were subject to selection criteria similar to those imposed on the real samples. The mock IRAS redshift catalogs were generated so as to resemble the actual IRAS 1.2 Jy redshift survey. They have the true IRAS selection and luminosity functions applied, and lack data in the IRAS-excluded zones (cf. Strauss et al. 1990). These data were then put through exactly the same code that is used to derive predicted peculiar velocity and density fields for the real data (Appendix A). To simplify the interpretation of the mock catalog tests, the mock IRAS galaxies were generated with probability proportional to the mass density itself. Thus, the mock IRAS galaxies are unbiased relative to the mass, i.e., for the mock catalogs bI = 1, and therefore the true value of betaI for the simulated data is unity.

9 The 20 catalogs (of both types) are different statistical realizations of the same simulation. As a result, our simulations fully probe the effects of statistical variance, because of distance indicator scatter, spatial inhomogeneities, etc. However, they do not include the effects of cosmic variance, because the density field of the region of space surveyed may not be characteristic of the universe as a whole. However, as we shall argue in Section 6, we expect that cosmic variance will have minimal effect on our beta-determination. Back.

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