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Elliptic Flow in Heavy-Ion Collisions at Energies $\sqrt{s_{NN}}=$ 2.7--39 GeV

The transverse-momentum integrated elliptic flow of charged particles at midrapidity, $v_2$(charged), and that of identified hadrons from Au+Au collisions are computed in a wide range of incident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The simulations are performed within a three-fluid model employing three different equations of state (EoS's): a purely hadronic EoS and two versions of the EoS involving the deconfinement transition---a first-order phase transition and a smooth crossover one. The present simulations demonstrate low sensitivity of $v_2$(charged) to the EoS. All considered scenarios equally well reproduce recent STAR data on $v_2$(charged) for mid-central Au+Au collisions and properly describe its change of sign at the incident energy decrease below $\sqrt{s_{NN}}\approx$ 3.5 GeV. The predicted integrated elliptic flow of various species exhibits a stronger dependence on the EoS. A noticeable sensitivity to the EoS is found for anti-baryons and, to a lesser extent, for $K^-$ mesons. In particular, the $v_2$ excitation functions of anti-baryons exhibit a non-monotonicity within the deconfinement scenarios that was predicted by Kolb, Sollfrank and Heinz. However, low multiplicities of anti-baryons at $\sqrt{s_{NN}}\leq$ 10 GeV result in large fluctuations of their $v_2$ which may wash out this non-monotonicity.