Comparison of Velocity and Gravity Fields: The Mark III Tully‐Fisher Catalog versus theIRAS1.2 Jy Survey

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Abstract
We consider a measure of the peculiar velocity field derived from the Mark III compilation of 2900 spiral galaxies (Willick et al.), using an analysis method that is substantially free of bias (Nusser & Davis). We expand the velocity field in a set of orthogonal, smooth modes, reducing the data to a set of 56 coefficients fitted to a maximum redshift of 6000 km s–1, and maximum spherical harmonic of l = 3. The radial resolution of the modes degrades with redshift, from 800 km s–1 locally to 3000 km s–1 at 4000 km s–1 redshift. Equivalent mode coefficients can be computed for the gravity field derived from any whole-sky redshift catalog of galaxies, such as the IRAS 1.2 Jy survey (Fisher et al.). Given the coefficients of the expansions, one can compare the velocity and gravity fields on a galaxy-by-galaxy basis, or on a mode-by-mode basis. Detailed comparison shows the two independent fields to be remarkably aligned in general. There are, however, systematic discrepancies in the fields that lead to considerable coherence in the residuals between them. These residuals take the form of a dipole field in the Local Group (LG) frame that grows with distance; it is not consistent with a bulk flow residual. We perform a likelihood analysis in the mode-mode comparison to determine which value of β≡ Ω0.6/b for the IRAS gravity field is the best fit to the Mark III velocity field, considering the errors and covariance in both the velocity and gravity coefficients. We find that the most likely value lies in the range β = 0.4-0.6. However, in contrast with results we obtain using simulated galaxy catalogs, the x2 per degree of freedom for the fit is well in excess of unity, primarily because of the coherent dipole residuals at cz 3000 km s–1. Thus, despite the general alignment of the Mark III velocity and IRAS gravity fields, they do not agree in detail, precluding a firm determination of β from these data sets at present. The method is capable of measuring β to an accuracy of 10%, but without understanding these systematic discrepancies, we cannot infer a value of β from these data.