A fundamental hypothesis for the interpretation of the measured large-scale
line-of-sight peculiar velocities of galaxies is that the large-scale cosmic
flows are irrotational. In order to assess the validity of this assumption, we
estimate, within the frame of the gravitational instability scenario, the
amount of vorticity generated after the first shell crossings in large-scale
caustics. In the Zel'dovich approximation the first emerging singularities form
sheet like structures. Here we compute the expectation profile of an initial
overdensity under the constraint that it goes through its first shell crossing
at the present time. We find that this profile corresponds to rather oblate
structures in Lagrangian space. Assuming the Zel'dovich approximation is still
adequate not only at the first stages of the evolution 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 time and for different cosmologies.
The average vorticity created in these caustics is small: of the order of one
(in units of the Hubble constant). To illustrate this point we compute the
contribution of such caustics to the probability distribution function of the
filtered vorticity at large scales. We find that this contribution that this
yields a negligible contribution at the 10 to 15 h−1Mpc scales. It becomes
significant only at the scales of 3 to 4 h−1Mpc, that is, slightly above
the galaxy cluster scales.Comment: 25 pages 16 figures; accepted for publication by A&A vol 342 (1999
