A New Approach to Probing Large-Scale Power with Peculiar Velocities

We propose a new strategy for probing the power spectrum on large scales using galaxy peculiar velocities. We explore the properties of surveys that cover only two small fields in opposing directions on the sky. Surveys of this type have several advantages over those that attempt to cover the entire sky; in particular, by concentrating on galaxies in narrow cones, these surveys are able to achieve the density needed to measure several moments of the velocity field with only a modest number of objects, even for surveys designed to probe scales ≳100 h-1 Mpc. We construct mock surveys with this geometry and analyze them in terms of the three moments to which they are most sensitive. We calculate window functions for these moments and construct a χ2 statistic that can be used to put constraints on the power spectrum. In order to explore the sensitivity of these surveys, we calculate the expectation values of the moments and their associated measurement noise as a function of the survey parameters such as density and depth for several popular models of structure formation. In addition, we have studied how well these kinds of surveys can distinguish between different power spectra and found that, for the same number of objects, cone surveys are as good as or better than full-sky surveys in distinguishing between popular cosmological models. We find that a survey with 200-300 galaxy peculiar velocities with distance errors of 15% in two cones with an opening angle of ~10° could put significant constraints on the power spectrum on scales of 100-300 h−1 Mpc, where few other constraints exist. We believe that surveys of the kind we describe here could provide a valuable tool for the study of large-scale structure on these scales and present a viable alternative to full-sky surveys.