Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions (1007.0130v1)

Abstract: We introduce a new framework of highly-anisotropic hydrodynamics that includes dissipation effects. Dissipation is defined by the form of the entropy source that depends on the pressure anisotropy and vanishes for the isotropic fluid. With a simple ansatz for the entropy source obeying general physical requirements, we are led to a non-linear equation describing the time evolution of the anisotropy in purely-longitudinal boost-invariant systems. Matter that is initially highly anisotropic approaches naturally the regime of the perfect fluid. Thus, the resulting evolution agrees with the expectations about the behavior of matter produced at the early stages of relativistic heavy-ion collisions. The equilibration is identified with the processes of entropy production.

• The paper introduces an anisotropic hydrodynamics model that distinguishes transverse and longitudinal pressures to accurately describe early-stage collision dynamics.
• It employs an entropy-based dissipation mechanism tied to pressure anisotropy and solves complex evolution equations both numerically and analytically.
• The model accounts for rapid thermalization in heavy-ion collisions and paves the way for future studies in higher-dimensional and gauge dynamics frameworks.

Highly-Anisotropic and Strongly-Dissipative Hydrodynamics for Early Stages of Relativistic Heavy-Ion Collisions

The paper by Florkowski and Ryblewski introduces a novel theoretical framework for modeling the early stages of relativistic heavy-ion collisions through a highly-anisotropic hydrodynamics approach that incorporates dissipation effects. This research is motivated by the need to reconcile the rapid equilibration observed in heavy-ion collisions at facilities like RHIC and LHC with the highly anisotropic conditions theorized to exist immediately after such collisions.

Key Aspects and Methodology:

1. Anisotropic Hydrodynamics: The authors propose an anisotropic form of hydrodynamics where the transverse and longitudinal pressures, $P_\perp$ and $P_\parallel$, are treated as distinct variables due to their significant difference in early collision stages. This distinction is a departure from isotropic hydrodynamics, which assumes equal pressures in all directions, akin to perfect-fluid scenarios.
2. Entropy-Based Dissipation: Central to this model is the concept of an entropy source term $\Sigma$, which vanishes in isotropic conditions but dictates the system's evolution otherwise. The authors express the entropy source in terms of pressure anisotropy, leading to a non-linear equation for the evolution of the anisotropy parameter $x$.
3. Boost-Invariant Framework: The paper focuses on purely-longitudinal boost-invariant systems, simplifying the scenario to provide a more tractable analysis of the anisotropic dynamics. This assumption aligns with Bjorken-type scenarios, often used in modeling high-energy nuclear collisions.
4. Numerical and Analytical Insights: The authors solve the evolution equations both numerically for different initial anisotropies and analytically in certain limits. They demonstrate that their model inherently drives the system towards isotropy, aligning theoretical predictions with phenomenological observations of rapid thermalization in heavy-ion collisions.

Implications and Future Directions:

This research provides a structured approach to understanding the transition from highly anisotropic initial conditions to isotropic and equilibrated states in relativistic heavy-ion collisions. The inclusion of dissipation through an entropy source term marks a significant development, allowing the model to approximate real thermodynamic processes more closely. The results suggest a strong dependency of isotropization time scales on the relaxation parameter, $\tau_{\text{eq}}$, implicating that the precise measurement or theoretical understanding of this parameter could offer deeper insights into the initial stages of quark-gluon plasma formation.

The framework opens the path for future exploration of anisotropic hydrodynamics in more complex 2+1 and 3+1 dimensional systems, offering potential applicability to a wider range of experimental observables. Further, integrating aspects such as color fields or gauge dynamics, potentially guided by the principles of ADS/CFT correspondence, could enrich the model, enhancing its utility and accuracy in depicting early high-energy collision dynamics. Researchers may also investigate alternative forms of the entropy source function, inspired by different physical principles, to capture specific aspects of the early-stage dynamics of heavy-ion collisions.