On the vorticity of flow in redshift space

Given an irrotational (vorticity free) velocity field in real space, we prove that, in the distant observer limit and in the absence of multi-valued zones, the associated velocity field in redshift space is also irrotational. The proof does not rely on any approximation to gravitational dynamics. The result can be particularly useful for the analysis of redshift distortions and for reconstruction methods of cosmological velocity fields from galaxy redshift surveys, in the nonlinear regime. Although the proof is restricted to the distant observer limit, we show that the POTENT method can be modified to derive the full real space velocity field as a function of the redshift space coordinate, thus avoiding spatial Malmquist biases.