Bulk Viscous Corrections Research Articles

Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation

We investigate whether early and late time attractors for non-conformal kinetic theories exist by computing the time-evolution of a large set of moments of the one-particle distribution function. For this purpose we make use of a previously obtained exact solution of the 0+1D boost-invariant massive Boltzmann equation in relaxation time approximation. We extend prior attractor studies of non-conformal systems by using a realistic mass- and temperature-dependent relaxation time and explicitly computing the effect of varying both the initial momentum-space anisotropy and initialization time on the time evolution of a large set of integral moments. Our findings are consistent with prior studies, which found that there is an attractor for the scaled longitudinal pressure, but not for the shear and bulk viscous corrections separately. We further present evidence that both late- and early-time attractors exist for all moments of the one-particle distribution function that contain greater than one power of the longitudinal momentum squared.

Quarkonium in a bulk viscous QGP medium

The non-equilibrium properties of a quark-gluon plasma (QGP) have been a topic of intensive research. In this contribution, we explore the nature of heavy quarkonia immersed in a QGP with bulk viscosity. We incorporate the bulk viscous effect through the deformation of the distribution functions of thermal quarks and gluons, with which the color dielectric permittivity can be computed. We use the color dielectric permittivity to compute the heavy quark potential inside a bulk viscous plasma, and solve the Schr\"odinger equation using the potential to obtain the physical properties such as binding energies and decay widths. We discuss the effect of the bulk viscous correction on the quarkonium properties and the melting temperatures.

Hydrodynamic attractor in the nonconformal Bjorken flow

Nonconformal attractor behavior is studied by solving nonconformal second-order viscous hydrodynamics with respect to boost-invariant plasmas. Numerical solutions of the relative decay rate of the enthalpy density, the inverse shear and bulk Reynolds numbers all exhibit universal patterns towards an ideal fluid description at late stages, demonstrating the existence of a nonconformal hydrodynamic attractor. However, as a generic feature, the nonconformal hydrodynamic attractor emerges only at late times, which differs drastically from the behavior observed in conformal systems. The absence of the early-time attractor in nonconformal fluids is a consequence of the early-time unstable mode, which arises from a positive-valued eigenmode associated with the free-streaming dynamics. The early-time attractor can be restored in a mixture of the shear and bulk viscous corrections, in which early-time unstable modes cancel approximately. However, to support practical simulations of hydrodynamics in high-energy heavy-ion collisions, for which the early-time nonconformal attractor is approachable in all independent modes, the quadratic coupling between the bulk pressure and the expansion rate should be enhanced by at least a factor of two through the transport coefficient ${\ensuremath{\delta}}_{\mathrm{\ensuremath{\Pi}}\mathrm{\ensuremath{\Pi}}}$.

First order dissipative hydrodynamics and viscous corrections to the entropy four-current from an effective covariant kinetic theory

The first order hydrodynamic evolution equations for the shear stress tensor, the bulk viscous pressure and the charge current have been studied for a system of quarks and gluons, with a non-vanishing quark chemical potential and finite quark mass. The first order transport coefficients have been obtained by solving an effective Boltzmann equation for the grand-canonical ensemble of quasiquarks and quasigluons. We adopted temperature dependent effective fugacity for the quasiparticles to encode the hot QCD medium effects. The non-trivial energy dispersion of the quasiparticles induces mean field contributions to the transport coefficients whose origin could be directly related to the realization of conservation laws from the effective kinetic theory. Both the QCD equation of state and chemical potential are seen to have a significant impact on the quark-gluon plasma evolution. The shear and bulk viscous corrections to the entropy-four current have been investigated in the framework of the effective kinetic theory. The effect of viscous corrections to the entropy density have been quantified in the case of one dimensional boost-invariant expansion of the system. Further, the first order viscous corrections to the time evolution of temperature along with the description of pressure anisotropy and Reynolds number of the system have been explored for the longitudinal boost-invariant expansion.

Bulk viscous corrections to photon production in the quark–gluon plasma

Photons radiated in heavy-ion collisions are a penetrating probe, and as such can play an important role in the determination of the quark-gluon plasma (QGP) transport coefficients. In this work we calculate the bulk viscous correction to photon production in two-to-two scattering reactions. Phase-space integrals describing the bulk viscous correction are evaluated explicitly in order to avoid the forward scattering approximation which is shown to be poor for photons at lower energies. We furthermore present hydrodynamical simulations of AA collisions focusing on the effect of this calculation on photonic observables. Bulk corrections are shown to reduce the elliptic flow of photons at higher pT.

Quasiparticle anisotropic hydrodynamics for central collisions

We use quasiparticle anisotropic hydrodynamics to study an azimuthally-symmetric boost-invariant quark-gluon plasma including the effects of both shear and bulk viscosities. In quasiparticle anisotropic hydrodynamics, a single finite-temperature quasiparticle mass is introduced and fit to the lattice data in order to implement a realistic equation of state. We compare results obtained using the quasiparticle method with the standard method of imposing the equation of state in anisotropic hydrodynamics and viscous hydrodynamics. Using these three methods, we extract the primordial particle spectra, total number of charged particles, and average transverse momentum for various values of the shear viscosity to entropy density ratio eta/s. We find that the three methods agree well for small shear viscosity to entropy density ratio, eta/s, but differ at large eta/s. We find, in particular, that when using standard viscous hydrodynamics, the bulk-viscous correction can drive the primordial particle spectra negative at large p_T which is clearly unphysical. Such a behavior is not seen in either anisotropic hydrodynamics approach, irrespective of the value of eta/s.

Quasiparticle anisotropic hydrodynamics

We study an azimuthally-symmetric boost-invariant quark-gluon plasma using quasiparticle anisotropic hydrodynamics including the effects of both shear and bulk viscosities. We compare results obtained using the quasiparticle method with the standard anisotropic hydrodynamics and viscous hydrodynamics. We consider the predictions of the three methods for the differential particle spectra and mean transverse momentum. We find that the three methods agree for small shear viscosity to entropy density ratio, η/s, but show differences at large η/s. Additionally, we find that the standard anisotropic hydrodynamics method shows suppressed production at low transverse-momentum compared to the other two methods, and the bulk-viscous correction can drive the primordial particle spectra negative at large pT in viscous hydrodynamics.

Bulk viscous corrections to screening and damping in QCD at high temperatures

Non-equilibrium corrections to the distribution functions of quarks and gluons in a hot and dense QCD medium modify the “hard thermal loops” (HTL). The HTLs determine the retarded, advanced, and symmetric (time-ordered) propagators for gluons with soft momenta as well as the Debye screening and Landau damping mass scales. We compute such corrections to a thermal as well as to a non-thermal fixed point. The screening and damping mass scales are sensitive to the bulk pressure and hence to (pseudo-) critical dynamical scaling of the bulk viscosity in the vicinity of a second-order critical point. This could be reflected in the properties of quarkonium bound states in the deconfined phase and in the dynamics of soft gluon fields.

Onset of cavitation in the quark-gluon plasma

We study the onset of bubble formation (cavitation) in the quark-gluon plasma as a result of the reduction of the effective pressure from bulk-viscous corrections. By calculating velocity gradients in typical models for quark-gluon plasma evolution in heavy-ion collisions, we obtain results for the critical bulk viscosity above which cavitation occurs. Since present experimental data for heavy-ion collisions seems inconsistent with the presence of bubbles above the phase transition temperature of QCD, our results may be interpreted as an upper limit of the bulk viscosity in nature. Our results indicate that bubble formation is consistent with the expectation of hadronisation in low-temperature QCD.

Bulk viscosity effects in event-by-event relativistic hydrodynamics

Bulk viscosity effects on the collective flow harmonics in heavy-ion collisions are investigated, on an event-by-event basis, using a newly developed 2+1 Lagrangian hydrodynamic code named v-usphydro, which implements the smoothed particle hydrodynamics algorithm for viscous hydrodynamics. A new formula for the bulk viscous corrections present in the distribution function at freeze-out is derived, starting from the Boltzmann equation for multi-hadron species. Bulk viscosity is shown to enhance the collective flow Fourier coefficients from ${v}_{2}({p}_{T})$ to ${v}_{5}({p}_{T})$ when ${p}_{T}\ensuremath{\sim}1$--2.5 GeV, even when the bulk viscosity to entropy density ratio, $\ensuremath{\zeta}/s$, is significantly smaller than $1/(4\ensuremath{\pi})$.