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4.3. Velocity versus Density

The peculiar velocity data is compared with the distribution of galaxies in redshift space to obtain beta. The comparison can be performed either at the density level (e.g., velocity-inferred mass density a la POTENT versus real-space density of galaxies as extracted from redshift surveys [45]), or at the velocity level [46], [47], or simultaneously [48] (reviews: [35], [42]).

New developments: The methods are being improved to better take into account the random and systematic errors. The comparison is done in several different ways.

Pro: Some of the comparison methods allow a direct mapping of the biasing field. bullet Certain versions of the method are straightforward to implement.

Con: It is hard to impose the same effective smoothing on the two data sets. This may cause a bias in the estimate of beta, and a complication due to possible scale dependence in the biasing scheme. bullet The estimation is contaminated by the possible complexity of the biasing scheme. Each method may actually refer to a somewhat different beta [44]. bullet It is hard to distinguish nonlinear biasing from nonlinear gravitational effects.

Current Results: For IRAS galaxies, the current best estimates vary in the range 0.5 leq betaI leq 1.2, depending on the method, the volume used, the weighting of the different data, the smoothing scale, etc. The comparisons at the density level [45] tend to yield higher estimates than the comparisons at the velocity level [46]. One of the velocity comparisons indicates a possible inconsistency in the data at large distances [47]. The value of betaI seems to grow with smoothing scale, from betaI ~ 0.5 - 0.6 at Gaussian smoothing scales of 3 - 6 h-1Mpc [46], [48] to betaI ~ 1 on scales of ~ 12 h-1Mpc [45], [48]. The estimates for optical galaxies indicate a biasing parameter that is typically larger by ~ 30%.

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