Burgers equation for the bulk viscous pressure of quark matter

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.

Figures (4)

• Figure 1: The relaxation times $\tau_\pm$ in seconds, for the bag model and pQCD at $\mu_d = 400$ and $850~\,\mathrm{MeV}$ respectively. We have marked the millisecond scale, relevant for mergers or stellar oscillation modes, and shown the uncertainty bands obtained by varying the renormalization scale in pQCD.
• Figure 2: The bulk viscosity components $\zeta_\pm$ for the bag model and pQCD at $\mu_d = 400$ and $850~\,\mathrm{MeV}$ respectively. Values of the bulk viscosity are given in CGS units. The uncertainty bands describe the dependence on the renormalization scale in pQCD.
• Figure 3: The approximate crossing temperature $T_\mathrm{cross}$ at which the two Green's functions $G_\alpha$ coincide as a function of baryon density $n_B$. Only the central value of the renormalization scale is shown for pQCD. The band represents the time scales $t=10^{-4}\ldots 10 ^{-2}\,\mathrm{s}$, with the thick line corresponding to the millisecond scale. For $T \ll T_\mathrm{cross}$ dissipation is dominated by the nonleptonic processes.
• Figure 4: $\zeta_\pm$ at $m_s\in\lbrace 94,1.5\times 94,2.0\times 94\rbrace\,\mathrm{MeV}$ in the bag model. Everything evaluated at $\mu_d=400\,\mathrm{MeV}, a_4=0.7$.