Vorticity generation in large-scale structure caustics

A fundamental hypothesis for the interpretation of the measured large-scale line-of-sight peculiar velocities of galaxies is that the large-scale cosm ic flows are irrotational. In order to assess the validity of this assumpti on, we estimate, within the frame of the gravitational instability scenario , the amount of vorticity generated after the first shell crossings in larg e-scale caustics. In the Zel'dovich approximation the first emerging singul arities form sheet like structures. Here we compute the expectation profile of an initial overdensity under the constraint that it goes through its fi rst shell crossing at the present time. We find that this profile correspon ds to rather oblate structures in Lagrangian space. Assuming the Zel'dovich approximation is still adequate not only at the first stages of the evolut ion but also slightly after the first shell crossing, we calculate the size and shape of those caustics and their vorticity content as a function of t ime and for different cosmologies. The average vorticity created in these caustics is small: of the order of o ne (in units of the Hubble constant). To illustrate this point we compute t he contribution of such caustics to the probability distribution function o f the filtered vorticity at large scales. We find that this contribution th at this yields a negligible contribution at the 10 to 15 h(-1) Mpc scales. It becomes significant only at the scales of 3 to 4 h(-1) Mpc, that is, sli ghtly above the galaxy cluster scales.