Determining Omega from Peculiar Velocities.pdfVIP

a s t r o - p h / 9 3 0 9 0 2 8 1 9 S e p 1 9 9 3 In Cosmic Velocity Fields (IAP, Paris, July 1993), eds. F. Bouchet and Marc Lachieze-Rey.DETERMINING FROM PECULIAR VELOCITIESAVISHAI DEKELRacah Institute of Physics, The Hebrew University of Jerusalem AbstractThe large-scale dynamics of matter is inferred from the observed peculiar velocitiesof galaxies via the POTENT procedure. The smoothed elds of velocity andmass-density uctuations are recovered from the current data of  3; 000 galaxies.The cosmological density parameter can then be constrained in three ways: (a)by comparing the density elds of mass and galaxies, (b) by using the velocity eldin voids, and (c) by investigating quasilinear deviations from Gaussian uctuations.The results indicate a high value of 1; values in the range 0.1-0.3 are rejectedwith high condence.1. IntroductionThe raw data are estimated distances ri and redshifts zi for a set of objects in directionsr?i [34] The distances are estimated by the Tully-Fisher method for spirals, and by theanalogousDn method for ellipticals and SOs. The corresponding radial peculiar velocitiesare ui = czi ri (H0 is set to unity; distances are measured in kms1). Given thesesparsely-sampled radial velocities, POTENT rst computes a smoothed radial-velocity eld,u(r), in a spherical grid using a tensor window function [8,10]. In the current analysis we usea Gaussian window with radius  1200 kms1. Weighting inversely by the local density neareach object mimics equal-volume averaging which minimizes the bias due to the nonuniformsampling, and weighting inversely by the distance variance, 2i , reduces the random eects ofthe measurement errors.The velocity eld is recovered under the assumption of potential ow: v(x) = r(x) [3].According to linear gravitational instability theory (GI) any vorticity mode decays in timeas the universe expands, and based on Kelvins circulation theorem the ow remainsvorticity-free in the mildely-nonlinear r