Bayesian inference of nuclear incompressibility from collective flow in mid-central Au+Au collisions at 400--1500 MeV/nucleon
The incompressibility $K$ of symmetric nuclear matter (SNM) is determined through a Bayesian analysis of collective flow data from Au + Au collisions at beam energies $E = 400 -1500$ MeV/nucleon. This analysis utilizes a Gaussian process (GP) emulator applied to the isospin-dependent quantum molecular dynamics (IQMD) model for heavy-ion collisions, both with and without incorporating the momentum dependence of the single-nucleon potentials. Specifically, the inferred incompressibility values are $K=188.9^{+2.9}_{-4.5}$ MeV and $256.1^{+8.2}_{-8.7}$ MeV at $E = 400$ MeV/nucleon, respectively, at the 68\% confidence level using rapidity and transverse velocity dependence of proton elliptic flow data, with and without consideration of the momentum dependence. When the transverse momentum dependence of proton-like directed flow data is included, the inferred incompressibility values become $K=222.3^{+9.0}_{-9.9}$ MeV and $K=285.5^{+6.7}_{-7.3}$ MeV, respectively. Furthermore, we found that the value of $K$ derived from observables of proton elliptic flow increases with beam energy. This indicates that the equation of state (EoS) of nuclear matter hardens at higher densities and temperatures in reactions with higher beam energies.