New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

Csörgő, T.; Kasza, G.; Csanád, M.; Jiang, Ze-Fang

doi:10.3390/universe4060069

Cited by 18 publications

(90 citation statements)

References 73 publications

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“…To check this conjecture, it is necessary to search for suitable generalizations or extensions of the CKCJ family of solutions. 16 However, the detailed investigation of such possible generalizations of an already published exact solution goes also well beyond the limitations of our current manuscript.…”

Section: Pseudorapidity Densitymentioning

confidence: 76%

“…As reviewed recently in Ref. 16, the longitudinal momentum spectra of high energy collisions can a posteriori be very well described by exact solutions of 1+1 dimensional solutions of perfect fluid hydrodynamics, the central theme of our current investigation.…”

Section: Introductionmentioning

confidence: 84%

“…This new family of exact solutions, the CKCJ solution was discovered by Csörgő, Kasza, Csanád and Jiang and presented first in Ref. 16. The first part of this manuscript series 17 connects the CKCJ solution to experimentally measured quantities by evaluating the rapidity and pseudorapidity density distributions.…”

Section: Introductionmentioning

confidence: 89%

“…We expect that these nearly Gaussian approximations are valid only in a certain limited range of rapidities or pseudo-rapidities, typically up to 2, 2.5 units away from mid-rapidity, as detailed in Refs. 16,17. We also expect that the range of validity of the more precise Eq.…”

Section: Pseudorapidity Densitymentioning

confidence: 98%

“…where the mean multiplicity is given by Eq. (16), also as a function of the parameters of the embedded exact solutions is given by Eq. (36) of Ref.…”

Section: Pseudorapidity Densitymentioning

confidence: 99%

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Lifetime estimations from RHIC Au+Au data

Kasza

Csörgő

2019

Int. J. Mod. Phys. A

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We discuss a recently found family of exact and analytic, finite and accelerating, 1+1 dimensional solutions of perfect fluid relativistic hydrodynamics to describe the pseudorapidity densities and longitudinal HBT-radii and to estimate the lifetime parameter and the initial energy density of the expanding fireball in Au+Au collisions at RHIC with √ s N N = 130 GeV and 200 GeV colliding energies. From these exact solutions of relativistic hydrodynamics, we derive a simple and powerful formula to describe the pseudorapidity density distributions in high energy proton-proton and heavy ion collisions, and derive the scaling of the longitudinal HBT radius parameter as a function of the pseudorapidity density. We improve upon several oversimplifications in Bjorken's famous initial energy density estimate, and apply our results to estimate the initial energy densities of high energy reactions with data-driven pseudorapidity distributions. When compared to similar estimates at the LHC energies, our results indicate a surprising and non-monotonic dependence of the initial energy density on the energy of heavy ion collisions.

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Section: Pseudorapidity Densitymentioning

confidence: 76%

Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 89%

Section: Pseudorapidity Densitymentioning

confidence: 98%

“…where the mean multiplicity is given by Eq. (16), also as a function of the parameters of the embedded exact solutions is given by Eq. (36) of Ref.…”

Section: Pseudorapidity Densitymentioning

confidence: 99%

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Lifetime estimations from RHIC Au+Au data

Kasza

Csörgő

2019

Int. J. Mod. Phys. A

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Evolution of magnetic fields from the 3 + 1 dimensional self-similar and Gubser flows in ideal relativistic magnetohydrodynamics

Shokri

Sadooghi

2018

J. High Energ. Phys.

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Motivated by the recently found realization of the 1 + 1 dimensional Bjorken flow in ideal and nonideal relativistic magnetohydrodynamics (MHD), we use appropriate symmetry arguments, and determine the evolution of magnetic fields arising from the 3 + 1 dimensional self-similar and Gubser flows in an infinitely conductive relativistic fluid (ideal MHD). In the case of the 3 + 1 dimensional self-similar flow, we arrive at a family of solutions, that are related through a differential equation arising from the corresponding Euler equation. To find the magnetic field evolution from the Gubser flow, we solve the MHD equations of a stationary fluid in a conformally flat dS 3 ×E 1 spacetime. The results are then Weyl transformed back into the Minkowski spacetime. In this case, the temporal evolution of the resulting magnetic field is shown to exhibit a transition between an early time 1/t decay to a 1/t 3 decay at a late time. Here, t is the time coordinate. Transverse and longitudinal components of the magnetic fields arising from these flows are also found. The latter turns out to be sensitive to the transverse size of the fluid. In contrast to the result arising from the Gubser flow, the radial domain of validity of the magnetic field arising from the self-similar flow is highly restricted. A comparison of the results suggests that the (conformal) Gubser MHD may give a more appropriate qualitative picture of the magnetic field decay in the plasma of quarks and gluons created in heavy ion collisions. PACS numbers: 12.38.Mh, 47.75.+f, 52.27.Ny, 52.30.Cv * m shokri@physics.sharif.ir † sadooghi@physics.sharif.ir 1 Here, e is the electric charge and mπ ∼ 140 MeV the pion mass.

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Perturbation solutions of relativistic viscous hydrodynamics forlongitudinally expanding fireballs *

et al. 2020

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The solutions of the relativistic viscous hydrodynamics for longitudinally expanding fireballs are investigated with the Navier-Stokes theory and Israel-Stewart theory. The energy and the Euler conservation equations for the viscous fluid are derived in Rindler coordinates, by assuming that the longitudinal expansion effect is small. Under the perturbation assumption, an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented. The temperature evolution with both shear viscous effect and longitudinal acceleration effect in the longitudinal expanding framework are presented. The specific temperature profile shows symmetric Gaussian shape in the Rindler coordinates. Further, we compare the results from the Israel-Stewart approximation with the results from the Bjorken and the Navier-Stokes approximations, in the presence of the longitudinal acceleration expansion effect. We found that the Israel-Stewart approximation gives a good description of the early stage evolutions than the Navier-Stokes theory.

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New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

Cited by 18 publications

References 73 publications

Lifetime estimations from RHIC Au+Au data

Lifetime estimations from RHIC Au+Au data

Evolution of magnetic fields from the 3 + 1 dimensional self-similar and Gubser flows in ideal relativistic magnetohydrodynamics

Perturbation solutions of relativistic viscous hydrodynamics forlongitudinally expanding fireballs *

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