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The galaxy density field extracted from a complete redshift survey of IRAS galaxies brighter than 1. 936 Jy is compared with the mass-density field reconstructed by the POTENT procedure from the observed peculiar velocities of 493 objects. Both density fields have been filtered with a Gaussian of smoothing length 1200 km s^-1^. Noise considerations limit the present analysis to a volume ~ (5300 km s^-1^) ³^ containing ~12 independent density samples. We find a strong correlation between the galaxy and mass-density fields; both feature the Great Attractor, part of the Perseus-Pisces supercluster, and the large void between them. Monte Carlo noise simulations show that the data are consistent with the hypotheses that the smoothed fluctuations of galaxy and mass densities at each point are proportional to each other with a "biasing" factor of IRAS galaxies bI_, and that the peculiar velocity field is related to the mass-density field as expected according to gravitational instability theory. Under these hypotheses, the two density fields can be related by specifying two parameters, bI_ and the cosmological density parameter OMEGA. The Monte Carlo simulations are then used to estimate the random errors, to correct for systematic errors in POTENT, and to constrain the parameters via a likelihood analysis. Our strongest result is OMEGA⁰. 6^/bI_ = 1. 28_-0. 59_^+0. 75^ at 95% confidence. Small nonlinear effects allow weaker, separate constraints on OMEGA and on bI_. Thus, if OMEGA = 1, then bI_ = 0. 7_-0. 2_^+0. 6^, and if bI_ > 0. 5, then OMEGA > 0. 46, both at the 95% confidence level. Inhomogeneous Malmquist bias could cause an overestimate of OMEGA; our 95% confidence limit for bI_ > 0. 5 could be reduced by correction for this bias at most to OMEGA > 0. 3. The constraints on OMEGA are limited to the simple biasing relation assumed, but the effect of undersampling cluster cores by IRAS is negligible, and the results are independent of the cosmological constant LAMBDA.
Dekel et al. (Thu,) studied this question.