Modeling of acceleration in heavy-ion collisions: Occurrence of temperature below the Unruh temperature

It has recently been shown that extremely strong electric fields can be created in central collisions of heavy ions, due to which the Schwinger effect can be significant. A direct analog of the electric field in hydrodynamics is the acceleration of the medium. Using the parton-hadron-string dynamics framework we model the Au-Au collisions at intermediate collision energies $\sqrt{{s}_{NN}}=4.5--11.5\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$ and obtain the spatial distribution of acceleration at different time moments. The present study demonstrates that extremely high acceleration of the order of 1 GeV may be generated in both central and noncentral collisions, and that the distribution exhibits a core-corona structure. Consequently, in contrast to the case with an electric field, the Unruh effect is expected to be significant. It is demonstrated that for the confined phase the temperature is less than the Unruh temperature. Conversely, in the deconfined phase, the relationship is inverse. The obtained results thus support the prediction about the existence of states with $T<{T}_{U}$ at the early stages of the collision and the associated complementary description of thermalization in terms of the novel phase transition at the Unruh temperature.