On the other hand, the same Mark III and IRAS data, when analyzed by the POTENT procedure, lead to estimates of ß consistent with unity (27), well above the limits from the velocity-gravity field comparisons. The POTENT algorithm has had at least as much validation studies applied to it as any of the competing algorithms, and tests show that it is fully capable of recovering the underlying true value of ß in a noisy field of data. How is it that the same data can lead to such divergent conclusions when analyzed using different procedures?

The answer is currently unknown but might result from the very different weighting applied to the density-density algorithms vs. the velocity-gravity algorithms. In the former case, the procedure is most sensitive to the divergence of the velocity field and is insensitive to the largest scale components of the field. In the Fourier domain, the divergence of velocity is proportional to (k vk), so the highest Fourier modes remaining after the smoothing are given maximal weight. The velocity-gravity algorithms, on the other hand, are seeking the reflex dipole of the motion of the local group and are dominated by the largest wavelength Fourier modes in the volume. Thus the weightings of the alternative procedures could not be more different!

Because, as argued above, the Mark III data do not really fit the predictions of the IRAS inferred gravity field for any value of ß, it should therefore not be a surprise when very differently weighted analyses of the data lead to differing conclusions. The prudent course of action is to work to understand why the fields are so inconsistent, to search for systematic errors in one or both of the fields, and to restrain from drawing overly strong cosmological conclusions until the competing algorithms lead to consistent solutions.

This work was supported by National Science Foundation Grant AST95–28340 and National Aeronautics and Space Administration Grant NAG 5–1360.

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