  In a concurrent work, Villois et al. 2020 reported the evidence that vortex
reconnections in quantum fluids follow an irreversible dynamics, namely
vortices separate faster than they approach; such time-asymmetry is explained
by using simple conservation arguments. In this work we develop further these
theoretical considerations and provide a detailed study of the vortex
reconnection process for all the possible geometrical configurations of the
order parameter (superfluid) wave function. By matching the theoretical
description of incompressible vortex filaments and the linear theory describing
locally vortex reconnections, we determine quantitatively the linear momentum
and energy exchanges between the incompressible (vortices) and the compressible
(density waves) degrees of freedom of the superfluid. We show theoretically and
corroborate numerically, why a unidirectional density pulse must be generated
after the reconnection process and why only certain reconnecting angles,
related to the rates of approach and separations, are allowed. Finally, some
aspects concerning the conservation of centre-line helicity during the
reconnection process are discussed.
