Hydrodynamic attractors for the speed of sound in holographic Bjorken flow

Abstract

The speed of sound is a central quantity in the exploration of the phase diagram of quantum chromodynamics, specifically through heavy ion collisions analyzed in the Beam Energy Scan at the Relativistic Heavy Ion Collider. Such collisions push the system generically far away from equilibrium, where thermodynamic quantities are not well-defined and the thermodynamic definition for the speed of sound becomes unreliable. In addition, the plasma is approximately boost invariant along the beamline, leading to initially large anisotropy between that direction and the transverse plane. Here, we extend the standard thermodynamic definition to calculate the speed of sound when the system is out of equilibrium, in particular, undergoing Bjorken flow. Then, we compute this out-ofequilibrium speed of sound in a holographic plasma, and demonstrate remarkable agreement with the hydrodynamic prediction. We show by Borel resummation that the holographic system has one attractor for this speed of sound longitudinal, and another transverse, to the direction of Bjorken expansion. Attractor times for various initial flow conditions show that reaching an attractor does not imply or require local thermal equilibrium. In the cases studied, reaching an attractor implies hydrodynamization (quantities evolve approximately according to hydrodynamics), justifying the name hydrodynamic attractor.

Constraining the initial stages of ultrarelativistic nuclear collisions

“…The attractor apparent in the pressure anisotropy A(w) is particularly striking, but it is a manifestation of an intrinsic feature of this dynamical system, as well as many other like it, however one chooses to describe them. It also has implications for other observables, such as the speed of sound away from equilibrium [75].…”