Burgers equation for the bulk viscous pressure of quark matter

TL;DR

This paper derives a new evolution equation for bulk viscous pressure in quark matter, revealing its behavior as a two-component Burgers fluid and identifying key transport coefficients relevant for modeling compact star mergers.

Contribution

It introduces a novel formulation for bulk viscous effects in quark matter, including explicit transport coefficients and their dependence on physical parameters, applicable to astrophysical simulations.

Findings

Bulk viscous pressure behaves like a two-component Burgers fluid.

Transport coefficients are expressed in terms of decay rates and equilibrium parameters.

The formulation is applicable to different equations of state and density regimes.

Abstract

The dissipative properties of relativistic strongly interacting nuclear matter significantly influence the damping of stellar oscillations and density fluctuations during compact star mergers. In this work, we derive the evolution equation for the bulk viscous pressure in unpaired quark matter under small deviations from equilibrium. Our analysis reveals that it behaves like a two-component Burgers fluid. We identify four key transport coefficients -- two relaxation times and two bulk viscosity coefficients -- expressed in terms of equilibrium parameters and electroweak nonleptonic and semi-leptonic decay rates. The transport coefficients are evaluated for two distinct equations of state: one based on perturbative quantum chromodynamics and the other on a modified MIT bag model, valid in different density regimes. We also determine the temperature and density region where nonleptonic electroweak processes dominate the dissipation. Our formulation establishes a new way of describing bulk viscous effects in quark matter, applicable for numerical simulations of compact star mergers.