THE COSMIC MACH NUMBER - DIRECT COMPARISONS OF OBSERVATIONS AND MODELS

The cosmic Mach number M is the ratio of the bulk flow of the galaxy v elocity field on some scale R to the small-scale velocity dispersion w ithin regions of scale R. Because M is the ratio of two velocities, it is independent of the amplitude of the power spectrum and of the bias parameter in linear theory. We develop a robust method to derive this statistic from existing peculiar velocity data sets. For the infrared Tully-Fisher distances of spirals in the Local Supercluster of Aarons on and collaborators. we find M = 1.03 and a characteristic distance f rom the Local Group of 1464 km s-1; for the elliptical galaxy sample o f Faber et al., we find M = 0.57 with a characteristic distance of 257 2 km s-1, and for the R-band Tully-Fisher sample of Willick in the Pis ces-Perseus region, we find M = 1.05 with a characteristic distance of 5265 km s-1. The bulk flow of the Willick sample is 717 km s-1, appre ciably larger than in the other two data sets. We compare these result s with Monte Carlo simulations of the observational realizations drawn from numerical simulations of the universe based on various scenarios , including the standard cold dark matter (CDM) scenario. The galaxies of the simulations mimic the distribution of the real galaxies in bot h position and environment. We find the effect of velocity bias on the derived Mach number to be small. Only 5% of the CDM simulations have M as large as or larger than that observed for the Aaronson et al. sam ple. We test three further models: the standard hot dark matter model, the primordial isocurvature baryon model, and the tilted CDM model, i n which the logarithmic index of the primordial fluctuation spectrum i s n = 0.7 rather than the simplest inflationary prediction of unity. A ll three models are able to match the observed Mach number for the Aar onson et al. sample in more than 15% of realizations. The Mach number test is a powerful discriminator between models for the origin of cosm ological structure, and it rejects the standard CDM scenario at the 94 % confidence level.