Vortex rings in fragmentation regions in heavy-ion collisions at $\sqrt{s_{NN}}=$ 39 GeV

Vorticity generated in heavy-ion collisions at energy of $\sqrt{s_{NN}}=$ 39 GeV is studied. Simulations are performed within a model of the three-fluid dynamics. A peculiar structure consisting of two vortex rings is found: one ring in the target fragmentation region and another one in the projectile fragmentation region. These rings are also formed in central collisions. The matter rotation is opposite in this two rings. These vortex rings are already formed at the early stage of the collision together with primordial fragmentation regions. The average vorticity, responsible for the global polarization of the observed $\Lambda$ and $\bar{\Lambda}$, is also studied. In the semi-central collisions the average vorticity in the midrapidity region turns out to be more than an order of magnitude lower than the total one. The total vorticity is dominated by the contributions of the fragmentation regions and is produced because of asymmetry of the vortex rings in noncentral collisions. This suggests that in semi-central collisions the global polarization in the fragmentation regions should be at least an order of magnitude higher than that observed by the STAR collaboration in the midrapidity. This polarization should be asymmetrical in the reaction plain and correlate with the corresponding directed flow.