COMPARISON OF VELOCITY AND GRAVITY FIELDS - THE MARK-III TULLY-FISHERCATALOG VERSUS THE IRAS-1.2 JY SURVEY

We consider a measure of the peculiar velocity held derived from the M ark 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 held in a set of orthogonal, smooth modes, redu cing 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) loc ally to 3000 km s(-1) at 4000 km s(-1) redshift. Equivalent mode coeff icients can be computed for the gravity held derived from any whole-sk y redshift catalog of galaxies, such as the IRAS 1.2 Jy survey (Fisher et al.). Given the coefficients of the expansions, one can compare th e velocity and gravity fields on a galaxy-by-galaxy basis, or on a mod e-by-mode basis. Detailed comparison shows the two independent fields to be remarkably aligned in general. There are, however, systematic di screpancies in the fields that lead to considerable coherence in the r esiduals between them. These residuals take the form of a dipole held in the Local Group (LG) frame that grows with distance; it is not cons istent with a bulk flow residual. We perform a likelihood analysis in the mode-mode comparison to determine which value of beta = Omega(0.6) /b for the IRAS gravity held is the best fit to the Mark III velocity held, considering the errors and covariance in both the velocity and g ravity coefficients. We find that the most likely value lies in the ra nge beta = 0.4-0.6. However, in contrast with results we obtain using simulated galaxy catalogs, the chi(2) per degree of freedom for the fi t is well in excess of unity, primarily because of the coherent dipole residuals at cz greater than or similar to 3000 km s(-1). Thus, despi te the general alignment of the Mark III velocity and IRAS gravity fie lds, they do not agree in detail, precluding a firm determination of b eta from these data sets at present. The method is capable of measurin g beta to an accuracy of 10%, but without understanding these systemat ic discrepancies, we cannot infer a value of beta from these data.