We study the local structure of the vorticity field and the $\mathrm{\Lambda }$ polarization in Au+Au collisions in the energy range $\sqrt{s_{\mathrm{NN}}}=7.7–200\mathrm{GeV}$ and Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2760\mathrm{GeV}$ using a multiphase transport model. We focus on the vorticity field arising from the nonuniform expansion of the fireball, which gives the circular structure of the transverse vorticity ${\mathbf{\omega }}_{\perp }=({\omega }_x,{\omega }_y)$ around the $z$ direction as well as the quadrupole pattern of the longitudinal vorticity ${\omega }_z$ in the transverse plane. As a consequence, the three components of the polarization vector $\mathbf{P}=(P_x,P_y,P_z)$ for $\mathrm{\Lambda }$ hyperons show harmonic behaviors as $\mathrm{sgn}\left(Y\right)sin{\varphi }_p$, $-\mathrm{sgn}\left(Y\right)cos{\varphi }_p$, and $-sin\left(2{\varphi }_p\right)$, where ${\varphi }_p$ and $Y$ are the azimuthal angle and rapidity in momentum space. These patterns of the local $\mathrm{\Lambda }$ polarization are expected to be tested in future experiments.

• Received 4 March 2018

DOI:https://doi.org/10.1103/PhysRevC.98.024905