4.3. Velocity versus Density

The peculiar velocity data is compared with the distribution of galaxies in redshift space to obtain . 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. 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 , and a complication due to possible scale dependence in the biasing scheme. The estimation is contaminated by the possible complexity of the biasing scheme. Each method may actually refer to a somewhat different [44]. 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 _I 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 _I seems to grow with smoothing scale, from _I ~ 0.5 - 0.6 at Gaussian smoothing scales of 3 - 6 h^-1Mpc [46], [48] to _I ~ 1 on scales of ~ 12 h^-1Mpc [45], [48]. The estimates for optical galaxies indicate a biasing parameter that is typically larger by ~ 30%.