We describe a new scenario (first introduced in [G. Torrieri, B. Tomášik and I. Mishustin, Phys. Rev. C \textbf{77}, 034903 (2008)]) for freezeout in heavy ion collisions that could solve the lingering problems associated with the so-called HBT puzzle. We argue that bulk viscosity increases as $T$ approaches $T_c$. The fluid {then} becomes unstable against small perturbations, and fragments into clusters of a size much smaller than the total size of the system. These clusters maintain the pre-existing outward-going flow, as a spray of droplets, but develop no flow of their own, and hadronize by evaporation. We show that this scenario can explain HBT data and suggest how it can be experimentally tested.
We introduce a new scenario for heavy ion collisions that could solve the lingering problems associated with the so-called HBT puzzle. We postulate that the system starts expansion as the perfect quark-gluon fluid but close to freeze-out it splits into clusters, due to a sharp rise of bulk viscosity in the vicinity of the hadronization transition. We then argue that the characteristic cluster size is determined by the viscosity coefficient and the expansion rate. Typically it is much smaller and independent of the total system volume. These clusters maintain the pre-existing outward-going flow…
We investigate particle spectra and elliptic flow coefficients in relativistic heavy ion collisions by taking into account the distortion of phase space distributions due to bulk viscosity at freezeout. We first calculate the distortion of phase space distributions in a multi-component system within the Grad's fourteen moment method. We find some subtle issues when one matches macroscopic variables with microscopic momentum distributions in a multi-component system and develop a consistent procedure to uniquely determine the corrections in the phase space distributions. Next, we calculate part…
Freeze-out and spectral running of primordial gravitational waves in viscous cosmology
Libera Università Mediterranea (LUM) “Giuseppe Degennaro”（利贝拉地中海大学（卢姆）“朱塞佩·德真纳罗”）；Università di Bari（巴里大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Bari（意大利国家核物理研究所，巴里分部）
We solve the relativistic Navier-Stokes equations with homogeneous boost-invariant boundary conditions, and perform a stability analysis of the solution. We show that, if the bulk viscosity has a peak around $T_c$ as inferred from QCD-based arguments, the background solution "freezes" at $T_c$ to a nearly constant temperature state. This state is however highly unstable with respect to certain inhomogeneous modes. Calculations show that these modes have enough time to blow up and tear the system into droplets. We conjecture that this is how freeze-out occurs in the QGP created in heavy ion col…
Effects of viscosity and thermal conductivity on the dynamics of first-order phase transitions are studied. The nuclear gas-liquid and hadron-quark transitions in heavy-ion collisions are considered. We demonstrate that at non-zero thermal conductivity, $κ\neq 0$, onset of spinodal instabilities occurs on an isothermal spinodal line, whereas for $κ=0$ instabilities take place at lower temperatures, on an adiabatic spinodal.
We investigate the form of the viscous correction to the equilibrium distribution function in the context of a Cooper-Frye freeze out prescription for viscous hydrodynamic simulations of relativistic heavy ion collisions. The standard quadratic ansatz used by all groups for the case of shear viscosity is found to be disfavored by experimental data for v4/(v2)^2 at the Relativistic Heavy Ion Collider, and is unlikely to be correct for the hadron resonance gas present at freeze out. Instead, data for v2(pt) along with v4/(v2)^2 favor a momentum dependence between linear and quadratic.
Using a viscosity-based survival scale for geometrical perturbations formed in the early stages of relativistic heavy-ion collisions, we model the radial flow velocity during freeze-out. Subsequently, we employ the Cooper-Frye freeze-out prescription, with first-order viscous corrections to the distribution function, to obtain the transverse momentum distribution of particle yields and flow harmonics. For initial eccentricities, we use the results of Monte Carlo Glauber model. We fix the blast-wave model parameters by fitting the transverse momentum spectra of identified particles at the Large…
The interplay between shear and bulk viscosities on the flow harmonics, $v_n$'s, at RHIC is investigated using the newly developed relativistic 2+1 hydrodynamical code v-USPhydro that includes bulk and shear viscosity effects both in the hydrodynamic evolution and also at freeze-out. While shear viscosity is known to attenuate the flow harmonics, we find that the inclusion of bulk viscosity decreases the shear viscosity-induced suppression of the flow harmonics bringing them closer to their values in ideal hydrodynamical calculations. Depending on the value of the bulk viscosity to entropy den…
Effects of the bulk viscosity on the elliptic flow are studied. To introduce a realistic equation of state and transport coefficients, we apply the results of the lattice QCD and hadron resonance gas calculations for these quantities. We found that the bulk viscosity acts in a non trivial manner on the elliptic flow $v_{2}$. The reduction of $v_{2}$ is more effective at low $p_{T}$ compared to the case of shear viscosity, whereas at high $p_{T}$, the situation is reversed, leading to $v_{2}$ enhancement. We argue that this is caused by the competition of the critical behaviors of the equation …
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 (SPH) 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 $% p_{T}\sim 1-3$ GeV…
We have calculated microscopically bulk viscosity of hadronic matter, where equilibrium thermodynamics for all hadrons in medium are described by Hadron Resonance Gas (HRG) model. Considering pions and nucleons as abundant medium constituents, we have calculated their thermal widths, which inversely control the strength of bulk viscosities for respective components and represent their in-medium scattering probabilities with other mesonic and baryonic resonances, present in the medium. Our calculations show that bulk viscosity increases with both temperature and baryon chemical potential, where…
The agreement of hydrodynamic predictions of differential elliptic flow and radial flow patterns with Au+Au data is one of the main lines of evidence suggesting the nearly perfect fluid properties of the strongly coupled Quark Gluon Plasma, sQGP, produced at RHIC. We study the sensitivity of this conclusion to different hydrodynamic assumptions on chemical and thermal freezeout after the sQGP hadronizes. We show that if chemical freezeout occurs at the hadronization time, the differential elliptic flow for pions increase with proper time in the late hadronic phase until thermal freezeout and l…
In the proximity of the QCD critical point the bulk viscosity of quark-gluon matter is expected to be proportional to nearly the third power of the critical correlation length, and become significantly enhanced. This work is the first attempt to study the phenomenological consequences of enhanced bulk viscosity near the QCD critical point. For this purpose, we implement the expected critical behavior of the bulk viscosity within a non-boost-invariant, longitudinally expanding $1+1$ dimensional causal relativistic hydrodynamical evolution at non-zero baryon density. We demonstrate that the crit…
We study the effects of bulk viscosity on pT spectra and elliptic flow in heavy ion collisions. For this purpose we compute the dissipative correction df to the single particle distribution functions in leading-log QCD, and in several simplified models. We consider, in particular, the relaxation time approximation and a kinetic model for the hadron resonance gas. We implement these distribution functions in a hydrodynamic simulation of Au + Au collisions at RHIC. We find significant corrections due to bulk viscosity in hadron pT spectra and the differential elliptic flow parameter v2(pT). Thes…
We study the effect of separate chemical and kinetic freeze-outs to the ideal hydrodynamical flow in Au+Au collisions at RHIC (sqrt(s_NN) = 200 GeV energy). Unlike in earlier studies we explore how these effects can be counteracted by changes in the initial state of the hydrodynamical evolution. We conclude that the reproduction of pion, proton and antiproton yields necessitates a chemical freeze-out temperature of T = 150 MeV instead of T = 160 - 170 MeV motivated by thermal models. Unlike previously reported, this lower temperature makes it possible to reproduce the p_T-spectra of hadrons if…
We study the effects of the shear and bulk viscosities in the hadronic phase on the expansion of the fireball and on the particle production in relativistic heavy ion collisions. Comparing simulation with or without viscosity in the hadronic matter we find that elliptic flow observables strongly dependent on dissipative effects in the late stage. On the other hand, interferometry radii are sensitive, through the early transverse flow, on the value of the viscosity at high temperatures. We present first calculations including the effects of bulk viscosity in the hadronic phase and in the hadron…
Within a parton cascade we investigate the dependence of anisotropies in momentum space, namely the elliptic flow $v_2=<cos(2ϕ)>$ and the $v_4=<cos(4ϕ)>$, on both the finite shear viscosity $η$ and the freeze-out (f.o.) dynamics at the RHIC energy of 200 AGeV. In particular it is discussed the impact of the f.o. dynamics looking at two different procedures: switching-off the collisions when the energy density goes below a fixed value or reducing the cross section according to the increase in $η/s$ from a QGP phase to a hadronic one. We address the relation between the scaling of $v_2(p_T)$ wit…
The space-time evolution of the (1+1)-dimensional viscous hydrodynamics with an initial quark-gluon plasma (QGP) produced in ultrarelativistic heavy ion collisions is studied numerically. The particle-emitting sources undergo a crossover transition from the QGP to hadronic gas. We take into account a usual shear viscosity for the strongly coupled QGP as well as the bulk viscosity which increases significantly in the crossover region. The two-pion Hanbury-Brown-Twiss (HBT) interferometry for the viscous hydrodynamic sources is performed. The HBT analyses indicate that the viscosity effect on th…
The bulk viscosity ($ζ$) of the hadronic medium has been estimated within the ambit of the Hadron Resonance Gas (HRG) model including the Hagedorn density of states. The HRG thermodynamics within a grand canonical ensemble provides the mean hadron number as well as its fluctuation. The fluctuation in the chemical composition of the hadronic medium in the grand canonical ensemble can result in non-zero divergence of the hadronic fluid flow velocity, allowing us to estimate the $ζ$ of the hadronic matter upto a relaxation time. We study the influence of the hadronic spectrum on $ζ$ and find its …
We consider a rotating neutron star with the presence of hyperons in its core, using an equation of state in an effective chiral model within the relativistic mean field approximation. We calculate the hyperonic bulk viscosity coefficient due to nonleptonic weak interactions. By estimating the damping timescales of the dissipative processes, we investigate its role in the suppression of gravitationally driven instabilities in the $r$-mode. We observe that $r$-mode instability remains very much significant for hyperon core temperature of around $10^8 $K, resulting in a comparatively larger inst…
Within a parton cascade approach we investigate the scaling of the differential elliptic flow $v_2(p_T)$ with eccentricity $ε_x$ and system size and its sensitivity to finite shear viscosity. We present calculations for shear viscosity to entropy density ratio $η/s$ in the range from $1/4π$ up to $1/π$, finding that the $v_2$ saturation value varies by about a factor 2. Scaling of $v_2(p_T)/ε_x$ is seen also for finite $η/s$ which indicates that it does not prove a perfect hydrodynamical behavior, but is compatible with a plasma at finite $η/s$. Introducing a suitable freeze-out condition, we …
We compute the bulk viscosity of a mixed quark-hadron phase. In the first scenario to be discussed, the mixed phase occurs at large densities and we assume that it is composed of a mixing of hyperonic matter and quarks in the Color Flavor Locked phase. In a second scenario, the mixed phase occurs at lower densities and it is composed of a mixing of nucleons and unpaired quark matter. We have also investigated the effect of a non-vanishing surface tension at the interface between hadronic and quark matter. In both scenarios, the bulk viscosity is large when the surface tension is absent, while …
The bulk viscosity in quark matter is sufficiently high to reduce the effective pressure below the corresponding vapor pressure during density perturbations in neutron stars and strange stars. This leads to mechanical instability where the quark matter breaks apart into fragments comparable to cavitation scenarios discussed for ultra-relativistic heavy-ion collisions. Similar phenomena may take place in kaon-condensed stellar cores. Possible applications to compact star phenomenology include a new mechanism for damping oscillations and instabilities, triggering of phase transitions, changes in…
The bulk viscosity of three-flavor color-superconducting quark matter originating from the nonleptonic process u+s <-> u+d is computed. It is assumed that up and down quarks form Cooper pairs while the strange quark remains unpaired (2SC phase). A general derivation of the rate of strangeness production is presented, involving contributions from a multitude of different subprocesses, including subprocesses that involve different numbers of gapped quarks as well as creation and annihilation of particles in the condensate. The rate is then used to compute the bulk viscosity as a function of the …
We evaluate the viscous damping of anisotropic flow in heavy-ion collisions for arbitrary temperature-dependent shear and bulk viscosities. We show that the damping is solely determined by effective shear and bulk viscosities, which are weighted averages over the temperature. We determine the relevant weights for nucleus-nucleus collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and 200 GeV, corresponding to the maximum LHC and RHIC energies, by running ideal and viscous hydrodynamic simulations. The effective shear viscosity is driven by temperatures below $210$ MeV at RHIC, and below $280$ MeV at th…
The specific shear viscosity (eta/s)_QGP of a Quark-Gluon-Plasma (QGP) at temperatures T_c < T < 2T_c is extracted from the centrality dependence of the eccentricity-scaled elliptic flow measured in ultra-relativistic heavy-ion collisions. Coupling viscous fluid dynamics for the QGP with a microscopic transport model for hadronic freeze-out we find that the eccentricity-scaled elliptic flow is a universal function of charged multiplicity per unit overlap area, (1/S)(dN_ch/dy), that depends only on the viscosity but not on the model used for computing the initial fireball eccentricity. Comparin…
