The cosmic Mach number: Direct comparisons of observations and models

The comic Mach number M is the ratio of the bulk flow of the galaxy velocity field on some scale R to the small-scale velocity dispersion within 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 Aaronson and collaborators, we find M = 1.03 and a characteristic distance from the Local Group of 1464 Km s^-1; for the elliptical galaxy samp of Willick in M = 0.57 with a characteristic distance of 2572 Km s^-1, and for the R-band Tully-Fisher sample of Willick in the Pisces-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, appreciably larger than in the other two data sets. We compare these results with Monte Carlo simulations of the observational realizations drawn from numerical simulations of the universe based on varioud scenarios, including the standard cold dark matter (CDM) scenario. The galaxies of the simulations mimic the distribution of the real galaxies in both 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. Sample. We test three further models: the standard hot dark matter model, the primordial isocurvature baryon model, and the tilted CDM model, in which the logarithmic index of the primordial fluctuation spectrum is n = 0.7 rather than the simplest inflationary prediction on unity. All three models are able to match the observed Mach number for the Aaronson et al. sample in more than 15% of realizations. The Mach number test is a powerful discriminator between models for the origin of cosmological structure, and it rejects the standard CDM scenario at the 94% confidence level.