Determination of the nuclear incompressibility from the rapidity-dependent elliptic flow in heavy-ion collisions at beam energies 0.4\emph{A} - 1.0\emph{A} GeV

Heavy-ion-collision measurements in combination with transport model simulations serve as important tools for extracting the nuclear incompressibility. However, uncertainties in transport models (or model dependence) partly affect the reliability of the extracted result. In the present work, by using the recently measured data of rapidity-dependent flows, we constrain the incompressibility of nuclear matter and analyse the impact of model uncertainties on the obtained value. The method is based on the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model in which the Skyrme potential energy-density functional is introduced. Three different Skyrme interactions which give different incompressibilities varying from $K_0$=201 to 271 MeV are adopted. The incompressibility is deduced from the comparison of the UrQMD model simulations and the FOPI data for rapidity-dependent elliptic flow in Au+Au collisions at beam energies 0.4\emph{A} - 1.0\emph{A} GeV. The elliptic flow $v_2$ as a function of rapidity $y_0$ can be well described by a quadratic fit $v_2=v_{20} + v_{22}\cdot y_0^2 $. It is found that the quantity $v_{2n}$ defined by $v_{2n}=|v_{20}|+|v_{22}|$ is quite sensitive to the incompressibility $K_0$ and the in-medium nucleon-nucleon cross section, but not sensitive to the slope parameter $L$ of the nuclear symmetry energy. With the FU3FP4 parametrization of the in-medium nucleon-nucleon cross section, an averaged $K_0 = 220 \pm 40$~MeV is extracted from the $v_{2n}$ of free protons and deuterons. However, remaining systematic uncertainties, partly related to the choice of in-medium nucleon-nucleon cross sections, are of the same magnitude ($\pm 40$~MeV). Overall, the rapidity dependent elliptic flow supports a soft symmetric-matter equation-of-state.