Ideal Relativistic Hydrodynamics Research Articles

Phenomenological Relativistic Second-Order Hydrodynamics for Multiflavor Fluids

In this work, we perform a phenomenological derivation of the first- and second-order relativistic hydrodynamics of dissipative fluids. To set the stage, we start with a review of the ideal relativistic hydrodynamics from energy–momentum and particle number conservation equations. We then go on to discuss the matching conditions to local thermodynamical equilibrium, symmetries of the energy–momentum tensor, decomposition of dissipative processes according to their Lorentz structure, and, finally, the definition of the fluid velocity in the Landau and Eckart frames. With this preparatory work, we first formulate the first-order (Navier–Stokes) relativistic hydrodynamics from the entropy flow equation, keeping only the first-order gradients of thermodynamical forces. A generalized form of diffusion terms is found with a matrix of diffusion coefficients describing the relative diffusion between various flavors. The procedure of finding the dissipative terms is then extended to the second order to obtain the most general form of dissipative function for multiflavor systems up to the second order in dissipative fluxes. The dissipative function now includes in addition to the usual second-order transport coefficients of Israel–Stewart theory also second-order diffusion between different flavors. The relaxation-type equations of second-order hydrodynamics are found from the requirement of positivity of the dissipation function, which features the finite relaxation times of various dissipative processes that guarantee the causality and stability of the fluid dynamics. These equations contain a complete set of nonlinear terms in the thermodynamic gradients and dissipative fluxes arising from the entropy current, which are not present in the conventional Israel–Stewart theory.

A chiral mean-field equation-of-state in UrQMD: effects on the heavy ion compression stage

It is shown that the initial compression in central heavy ion collisions at beam energies of E_{mathrm {lab}}=1-10A GeV depends dominantly on the underlying equation of state and only marginally on the model used for the dynamical description. To do so, a procedure to incorporate any equation of state in the UrQMD transport model is introduced. In particular we compare the baryon density, temperature and pressure evolution as well as produced entropy in a relativistic ideal hydrodynamics approach and the UrQMD transport model, where the same equation of state is used in both approaches. Not only is the compression similar if the same equation of state is used in either dynamical model, but it also strongly depends on the actual equation of state. These results indicate that the equation of state can be studied with observables which are sensitive to the initial compression phase and maximum compression achieved in heavy ion collisions at these beam energies.

Out-of-equilibrium photon production in the late stages of relativistic heavy-ion collisions

In this work, we assess the importance of nonequilibrium dynamics in the production of photons from the late stages of relativistic heavy-ion collisions. The ${p}_{\mathrm{T}}$-differential spectra and ${v}_{2}$ of photons from the late hadronic stage are computed within a nonequilibrium hadron transport approach, and compared to the results of a local equilibrium evolution using ideal relativistic hydrodynamics. It is found that nonequilibrium dynamics enhance the late-stage photon production at low ${p}_{\mathrm{T}}$ and decreases it at higher ${p}_{\mathrm{T}}$ compared to the estimate from hydrodynamics. This same comparison points to a significant increase in the momentum anisotropies of these photons due to nonequilibrium dynamics. Once combined with photons produced above the particlization temperature in the hydrodynamics evolution, the differences between the two approaches appear modest for the ${p}_{\mathrm{T}}$ differential spectra, but are clearly noticeable at low ${p}_{\mathrm{T}}$ for the elliptic flow: nonequilibrium dynamics enhance the photon ${v}_{2}$ below ${p}_{\mathrm{T}} \ensuremath{\approx}1.4$ GeV.

Family of new exact solutions for longitudinally expanding ideal fluids

We report on the discovery of new analytical solutions of the equations of relativistic ideal hydrodynamics. In this solution, the fluid expands in the longitudinal direction and contains a plateau structure that extends over a finite range in rapidity and can be either symmetric or asymmetric in that variable. We further calculate the corresponding pseudo-rapidity distribution of hadron yields, and find decent agreement with experimental measurements in high-energy Pb+Pb, Au+Au, p+Pb, and d+Au collisions.

Photon production in Pb + Pb collisions at [formula omitted] TeV

We calculate the high energy photon production from the Pb + Pb collisions for different centrality classes at sNN=2.76 TeV Large Hadron Collider (LHC) energy. The jet energy loss in the jet fragmentation, jet-photon conversion and jet bremsstrahlung is considered by using the Wang–Huang–Sarcevic (WHS) and Baier–Dokshitzer–Mueller–Peigne–Schiff (BDMPS) models. We use the (1+1)-dimensional ideal relativistic hydrodynamics to study the collective transverse flow and space–time evolution of the quark gluon plasma (QGP). The numerical results agree well with the ALICE data of the direct photons from the Pb + Pb collisions (sNN=2.76 TeV) for 0–20%, 20–40% and 40–80% centrality classes.

Numerical simulation of anomalous wave phenomena in hot nuclear matter

The collective dynamic phenomena accompanying the collision of high-energy heavy ions are suggested to be approximately described in the framework of ideal relativistic hydrodynamics. If the transition from hadron state to quark-gluon plasma is the first-order phase transition (presently this view is prevailing), the hydrodynamic description of the nuclear matter must demonstrate several anomalous wave phenomena—such as the shock splitting and the formation of rarefaction shock and composite waves, which may be indicative of this transition. The present work is devoted to numerical study of these phenomena.

A new shock-capturing numerical scheme for ideal hydrodynamics

We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.

Noether’s Theorem of Relativistic-Electromagnetic Ideal Hydrodynamics

We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with the conserved quantity derived from the Noether theorem. We further show that our formulation can reproduce the usual electromagnetic hydrodynamics which is obtained so as to satisfy the conservation of the inertia of fluid motion.

Vorticity and magnetic field production in relativistic ideal fluids

In the framework of relativistic ideal hydrodynamics, we study the production mechanism for vorticity and magnetic field in relativistic ideal fluids. It is demonstrated that in the uncharged fluids the thermal vorticity will always satisfy the Kelvin's theorem and the circulation must be conserved. However, in the charged fluids, the vorticity and magnetic field can be produced by the interaction between the entropy gradients and the fluid velocity gradients. Especially, in the multiple charged fluids, the vorticity and magnetic field can be produced by the interaction between the inhomogenous charge density ratio and the fluid velocity gradients even if the entropy distribution is homogeneous, which provides another mechanism for the production of vorticity and magnetic field in relativistic plasmas or in the early universe.

Ideal hydrodynamics outside and inside a black hole: Hamiltonian description in Painlevé-Gullstrand coordinates

We show that when the Painlevé-Gullstrand coordinates are used in their Cartesian version, the Hamiltonian of relativistic ideal hydrodynamics in the vicinity of a nonrotating black hole differs by only one simple term from the corresponding Hamiltonian in a flat spacetime. The interior region of the black hole is also described in a unified way, because there is no singularity on the event horizon in Painlevé-Gullstrand coordinates. We present the exact solution describing the steady accretion of extremely hard matter (ɛ ∝ n 2) onto a moving black hole up to the central singularity. In the local induction approximation, we derive the equation of motion for a thin vortex filament against the background of such an accretion flow. We explicitly calculate the Hamiltonian for a fluid with an ultrarelativistic equation of state, ɛ ∝ n 4/3, and solve the problem of a centrally symmetric steady flow of such matter.

Elliptic flow of charged and strange hadrons in PbAu collisions at 158 AGeV/c measured in CERES experiment

Differential elliptic flow of v2(pT ) for π − , K 0 , p and Λ is measured at center- of-mass energy of √ sNN=17.3 GeV near the mid-rapidity region in rather central PbAu collisions collected by the CERES/NA45 experiment at CERN. The proton v2(pT )i s ex- tracted from π + sample and particle ratios measured by NA49 experiment adapted to CERES conditions. The proton v2(pT ) data show a downward swing towards low pT with excursions into negative v2 values which was not observed earlier. The results are com- pared with corresponding measurements performed at NA49 and STAR experiments as well as with theoretical predictions from ideal relativistic hydrodynamics. The obtained results for baryons are below hydrodynamic predictions even at the kinetic freeze-out temperature of T f =160 MeV which needs introducing of a viscous hydrodynamics at the late hadronic phase.

Analytical relativistic ideal hydrodynamical solutions in (1+3)D with longitudinal and transverse flows

A new method for solving relativistic ideal hydrodynamics in ($1+3$)D is developed. Longitudinal and transverse radial flows are explicitly embedded into the ansatz for the velocity field and the hydrodynamic equations are reduced to a single equation for the transverse velocity field only, which is analytically more tractable as compared to the full hydrodynamic equations. As an application we use the method to find analytically all possible solutions whose transverse velocity fields have power dependence on the proper time and transverse radius. The possible applications to relativistic heavy ion collisions and possible generalizations of the method are discussed.

Radiative and collisional energy loss, and photon-tagged jets at RHIC

The suppression of single jets at high transverse momenta in a quark-gluon plasma is studied at RHIC energies, and the additional information provided by a photon tag is included. The energy loss of hard jets traversing through the medium is evaluated in the AMY formalism, by consistently taking into account the contributions from radiative events and from elastic collisions at leading order in the coupling. The strongly-interacting medium in these collisions is modelled with (3+1)-dimensional ideal relativistic hydrodynamics. Putting these ingredients together with a complete set of photon-production processes, we present a calculation of the nuclear modification of single jets and photon-tagged jets at RHIC.

Hydrodynamic radial and elliptic flow in heavy-ion collisions from AGS to LHC energies

Using ideal relativistic hydrodynamics in 2+1 dimensions, we study the collision-energy dependence of radial and elliptic flow, of the emitted hadron spectra, and of the transverse momentum dependence of several hadronic particle ratios, covering the range from Alternating Gradient Synchrotron (AGS) to Large Hadron Collider (LHC) energies. These calculations establish an ideal-fluid dynamic baseline that can be used to assess non-equilibrium features manifest in future LHC heavy-ion experiments. Contrary to earlier suggestions we find that a saturation and even decrease of the differential elliptic flow v2(pT) with increasing collision energy cannot be unambiguously associated with the QCD phase transition.

Onset of J/ψ melting in quark–gluon fluid at RHIC

We have developed a hydro+J/ψ model to study the sequential suppression of charmonia at RHIC energy. The (3+1)-dimensional relativistic ideal hydrodynamics is employed to describe the spacetime evolution of hot and dense matter, and charmonia are treated as impurity traversing through the matter. The observed J/ψ suppression at mid-rapidity in Au+Au collisions at RHIC is reproduced well by the sequential melting of χc, ψ′ and J/ψ in the medium. The melting temperature of directly produced J/ψ is well determined to be ∼2Tc. Azimuthal anisotropy of J/ψ (v2) is calculated with this model. Survival probability and azimuthal anisotropy in the ‘hot-wind scenario’ are also presented.

High-resolution shock capturing scheme for ideal hydrodynamics in general relativity optimized for quasistationary solutions

In this article, we present a numerical scheme for relativistic ideal hydrodynamics on arbitrary curved spacetimes in up to three spatial dimensions. The aim of this scheme is an improved treatment of stationary or quasistationary scenarios without loss of general applicability. This is achieved by treating pressure and gravitational forces, which are usually computed with unrelated numerical methods, within a unified framework. We derive a special formulation of the source terms in the hydrodynamic evolution equations, which is then utilized to construct the new scheme. For single star simulations, the optimizations take full effect only for rigidly rotating isentropic stars in a corotating coordinate frame. To test the algorithm, simulations of single polytropic neutron stars (rigidly rotating and nonrotating) have been carried out, demonstrating its usefulness for studies of stellar oscillation modes. We found that most of the numerical error is caused by the treatment of the stellar surface. To study the evolution scheme itself, we introduce a test bed involving an artificial spacetime without a fluid-vacuum boundary. The oscillation modes of the stellar models used here have already been investigated in the literature. A comparison with our results is given, exhibiting good agreement.

Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics

Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by tran

The phase transition to the quark-gluon plasma and its effect on hydrodynamic flow

It is shown that in ideal relativistic hydrodynamics a phase transition from hadron to quark and gluon degrees of freedom in the nuclear matter equation of state leads to a minimum in the excitation function of the transverse collective flow.