Vorticity in peripheral collisions at the Facility for Antiproton and Ion Research and at the JINR Nuclotron-based Ion Collider fAcility

The flow vorticity development is studied in the reaction plane of peripheral relativistic heavy-ion reactions at energies just above the threshold of the transition to a quark-gluon plasma (QGP). Earlier calculations at higher energies with larger initial angular momentum predicted significant vorticity leading to measurable $\Lambda$ polarization. Here we discuss the possibility of vorticity and circulation in dense plasma at lower temperatures. In low-viscosity QGP this vorticity still remains significant.

Figure 1

The classical weighted vorticity ${\Omega }_{zx}$, calculated in the reaction [$x$-$z$] plane at $t=0.17$ fm/$c$ and at $t=3.56$ fm/$c$. The energy of the $\mathrm{Au}+\mathrm{Au}$ collision is $\sqrt{s_{NN}}=4.65+4.65$ GeV, $b=0.5b_{\max }$, and the cell size is $dx=dy=dz=0.575$ fm. The average vorticity ${\Omega }_{zx}$ is 0.1345 and 0.0773 $c$/fm for the two selected times, respectively. The vorticity in the other directions is significantly weaker.

Figure 2

The classical weighted vorticity ${\Omega }_{zx}$, calculated in the reaction [$x$-$z$] plane at $t=0.34$ fm/$c$ and $t=3.72$ fm/$c$. The energy of the $\mathrm{U}+\mathrm{U}$ collision is $\sqrt{s_{NN}}=4.0+4.0$ GeV, $b=0.5b_{\max }$, and the cell size is $dx=dy=dz=0.610$ fm. The average vorticity ${\Omega }_{zx}$ is 0.1297 and 0.0736 $c$/fm for the two selected times, respectively.

Figure 3

The relativistic weighted thermal vorticity ${\Omega }_{zx}$, calculated in the reaction [$x$-$z$] plane at $t=0.17$ fm/$c$ and at $t=3.56$ fm/$c$. The energy of the $\mathrm{Au}+\mathrm{Au}$ collision is $\sqrt{s_{NN}}=4.65+4.65$ GeV, $b=0.5b_{\max }$, and the cell size is $dx=dy=dz=0.575$ fm. The average thermal vorticity ${\Omega }_{zx}$ is 0.0847 and 0.0739 for the two selected times, respectively. The thermal vorticity decreases much slower than the standard vorticity due to the decreasing temperature.

Figure 4

The relativistic weighted thermal vorticity ${\Omega }_{zx}$, calculated in the reaction [$x$-$z$] plane at $t=0.34$ fm/$c$ and at $t=3.72$ fm/$c$. The energy of the $\mathrm{U}+\mathrm{U}$ collision is $\sqrt{s_{NN}}=4.0+4.0$ GeV, $b=0.5b_{\max }$, and the cell size is $dx=dy=dz=0.610$ fm. The average vorticity ${\Omega }_{zx}$ is 0.0856 and 0.0658 for the two selected times, respectively.