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

TL;DR

The paper uses the PHSD transport framework to map the spatial distribution of acceleration in Au-Au collisions across intermediate energies, computing the Unruh temperature $T_{ m U} = a/(2\pi)$ and comparing it with the local thermodynamic temperature $T$ from a hadronic EoS. The results reveal a core–corona structure where hadronic corona regions reach $T < T_{ m U}$ while the QGP core maintains $T > T_{ m U}$, with $T_{ m U}$ peaking at early times and decreasing as the system expands. These findings support the presence of states with $T < T_{ m U}$ in the early stages of heavy-ion collisions and suggest a complementary description of thermalization via a phase transition at $T_{ m U}$, intimately linked to confinement/deconfinement dynamics. The work also discusses the possible origins of large acceleration in the corona, including relativistic boundary effects, geometry, and Luttinger-type forces, and highlights the potential of heavy-ion collisions as a gravitational laboratory for studying acceleration-induced thermodynamics in QCD matter.

Abstract

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 analogue of the electric field in hydrodynamics is the acceleration of the medium. Using the parton-hadron-string dynamics (PHSD) framework we model the Au-Au collisions at intermediate collision energies $\sqrt{s_{NN}}=4.5-11.5\,$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 non-central 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.

Figures (7)

• Figure 1: Profiles of temperature $T$ (first column), characteristic Unruh temperature $T_{\rm U}$ (second column) in the $z = 0$ plane, calculated at different times after the collision for Au + Au collisions at $\sqrt{s_{NN}} = 7.7\,$GeV. The profiles of $T$ and $T_{\rm U}$ shown in (a) are calculated for a central collision ($b = 0\,$fm); in (b) for an off-center collision ($b = 7.5\,$fm). The dotted curves show two contours in the $xy$ plane, limiting the medium in energy density to the value $\varepsilon = 500\,$MeV/fm$^3$ (inner contour) and $\varepsilon = 50\,$MeV/fm$^3$ (outer contour).
• Figure 2: Evolution of the temperature $T$ and the characteristic Unruh temperature $T_{\rm U}$, calculated in PHSD for Au + Au collisions at energies $\sqrt{s_{NN}} = 4.5, 7.7$ and $11.5\,$GeV. For the collision energy $\sqrt{s_{NN}} = 7.7\,$GeV, two impact parameters are considered: $b = 0\,$fm, which corresponds to a central collision, and $b = 7.5\,$fm, which corresponds to an off-center collision of nuclei. The results are presented for a full fireball $\varepsilon > 50\,$MeV/fm$^3$ (first panel); for partonic phase only (second panel) and for hadronic phase only (third panel).
• Figure 3: $T^2-T_{\rm U}^2$ profiles for different $z$-cuts calculated at various times after the collision for Au + Au central collisions ($b=0\,$fm) at $\sqrt{s_{NN}} = 7.7\,$GeV, averaged over all events. Only positive $z$ is shown due to symmetry. The dotted curves on the $T^2-T_{\rm U}^2$ profiles show two contours in the $xy$ plane, limiting the medium in energy density to the value $\varepsilon = 500\,$MeV/fm$^3$ (inner contour) and $\varepsilon = 50\,$MeV/fm$^3$ (outer contour).
• Figure 4: The same as Fig. \ref{['fig:T2-Tu2-b0.0']} but for the non-central collisions ($b=7.5\,$fm).
• Figure 5: Three-dimensional distribution of the three-dimensional part of the acceleration vector $a^{\mu} = u^{\nu}\partial_{\nu} u^{\mu}$ for a non-central collision $b=7.5\,$fm at $t-t_{coll} =5\,$fm/$c$.