Applications of a new family of solutions of relativistic - - PowerPoint PPT Presentation

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Applications of a new family of solutions of relativistic - - PowerPoint PPT Presentation

Dec 05, 2022 227 likes •650 views

Applications of a new family of solutions of relativistic hydrodynamics T. Csrg 1,2 , G. Kasza 2 , M. Csand 3 and Z. Jiang 4,5 1 Wigner Research Center for Physics, Budapest, Hungary 2 EKE GYKRC, Gyngys, Hungary 3 Etvs University,

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Collisions19@Lund, 2019/02/28 Csörgő, T.

Applications of a new family of solutions

  • f relativistic hydrodynamics
  • T. Csörgő1,2 , G. Kasza2, M. Csanád3 and Z. Jiang4,5

1Wigner Research Center for Physics, Budapest, Hungary 2EKE GYKRC, Gyöngyös, Hungary 3Eötvös University, Budapest, Hungary 4Key Laboratory of Quark and Lepton Physics, Wuhan, China 5IoPP, CCNU, Wuhan, China

Introduction and motivation A New Family of Exact Solutions of Relativistic Hydro Rapidity and pseudorapidity distributions Initial energy density Rlong HBT radius Non-monotonic s-behaviour Outlook Conclusions, summary

Partially supported by NKTIH FK 123842 and FK123959

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A new family of exact solutions

  • f relativistic hydrodynamics
  • T. Csörgő1,2 , G. Kasza2, M. Csanád3 and Z. Jiang4,5

Introduction and motivation A New Family of Exact Solutions of Relativistic Hydro Rapidity and pseudorapidity distributions Rlong HBT radius Outlook to other presentations Conclusions, summary

Partially supported by NKTIH FK 123842 and FK123959 and EFOP 3.6.1-16-2016-00001

arXiv.org:1805.01427 +

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Context

Renowned exact solutions, reviewed in arXiv:1805.01427

Landau-Khalatnikov solution: dn/dy ~ Gaussian Hwa solution (1974) – Bjorken: same solution + e0 (1983) Chiu, Sudarshan and Wang: plateaux, Wong: Landau revisited

Revival of interest: Zimányi, Bondorf, Garpman (1978)

Buda-Lund model + exact solutions (1994-96) Biró, Karpenko, Sinyukov, Pratt (2007) Bialas, Janik, Peschanski, Borsch+Zhdanov (2007) CsT, Csanád, Nagy (2007-2008) CsT, Csernai, Grassi, Hama, Kodama (2004) Gubser (2010-11) Hatta, Noronha, Xiao (2014-16)

New simple solutions Evaluation of dn/dh arXiv:1806.06794 Rapidity distribution Advanced initial e0 arXiv:1806.11309 HBT radii Advanced life-time tf arXiv:1810.00154 Energy scan Non-monotonic e0(s) :arXiv:1811.0999

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Goal

Need for solutions that are:

explicit simple accelerating relativistic realistic / compatible with the data: lattice QCD EoS ellipsoidal symmetry (spectra, v2, v4, HBT) finite dn/dy Generelization of a class that satisfies each of these criteria but not simultaneously

  • T. Cs, M. I. Nagy, M. Csanád, arXiv:nucl-th/0605070, PLB (2008)

M.I. Nagy, T. Cs., M. Csanád, arXiv:0709.3677 , PRC77:024908 (2008)

  • M. Csanád, M. I. Nagy, T. Cs, arXiv:0710.0327 [nucl-th] EPJ A (2008)

New family of exact solutions: CsT, Kasza, Csanád, Jiang, arXiv.org:1805.01427

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Perfect fluid hydrodynamics

Energy-momentum tensor: Relativistic

Euler equation: Energy conservation: Charge conservation: Consequence is entropy conservation:

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Self-similar, ellipsoidal solutions

Publication (for example):

  • T. Cs, L.P.Csernai, Y. Hama, T. Kodama, Heavy Ion Phys. A 21 (2004) 73

3D spherically symmetric HUBBLE flow: No acceleration: Define a scaling variable for self-similarly expanding ellipsoids: EoS: (massive) ideal gas Scaling function n(s) can be chosen freely. Shear and bulk viscous corrections in NR limit: known analytically.

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Auxiliary variables: hx, t, W , hp, y

Consider a 1+1 dimensional, finite, expanding fireball Assume: W=W(hx) Notation T. Cs., G. Kasza, M. Csanád, Z. Jiang, arXiv.org:1805.01427

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Hydro in Rindler coordinates, new sol

Assumptions of TCs, Kasza, Csanád and Jiang, arXiv.org:1805.01427 : From energy-momentum conservation, the Euler and temperature equations are obtained: For the entropy density, the continuity equation is solved.

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A New Family of Exact Solutions of Hydro

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A New Family of Exact Solutions of Hydro

New: not discovered before, as far as we know … Family: For each positive scaling function t(s), a different solution, with same T0, s0, k, l Not self-similar: Coordinate dependenc NOT on scaling variable s ONLY, but additional dependence on H = H(hx) too. Explicit and Exact: Fluid rapidity, temperature, entropy density explicitly given by formulas New feature: Solution is given as parametric curves of H in hx : (hx(H),W(H,t)) Simlification, for now: limit the solution in hx where parametric curves correspond to functions

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Limited in space-time rapidity hx

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Illustration: results for T

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Limited in space-time rapidity hx

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Illustration: results for fluid rapidity W

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Limited in space-time rapidity hx

arXiv.org:1805.01427 : W  l h x

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Approximations near midrapidity

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Observables: rapidity distribution

dn/dy evaluated analytically, in a saddle-point approximation

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Pseudorapidity distribution

dn/dh evaluated analytically, in an advanced saddle-point approximation An important by-product: pT  = pT (y) is rapidity dependent, a Lorentzian just as in Buda-Lund model

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dn/dh for p+p, 7-8 TeV, CMS data

arXiv.org:1805.01427

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dn/dh for Pb+Pb, 5 TeV, ALICE data

arXiv.org:1806.06794

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dn/dh for Xe+Xe, 5.44 TeV, CMS data

NEW (preliminary, too good)

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dn/dh for Au+Au, 200 GeV, PHOBOS

arXiv.org:1806.11309

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dn/dh fits, √sNN = 200 GeV

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Allowed fit region (depends on λ)

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dn/dh fits, √sNN = 130 GeV

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Allowed fit region (depends on λ)

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dn/dh fits, √sNN = 62.4 GeV

25 Allowed fit region (depends

  • n λ)
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dn/dh fits, √sNN = 19.6 GeV

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Rlong fits, √sNN = 62-200 GeV

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Correction factors, √sNN = 62-200 GeV

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Init energy densities, √sNN = 62-200 GeV

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Conclusions

Explicit solutions of a very difficult problem New estimates of initial energy density New exact solution for arbitrary EOS with const e/p after 10 years, finally Non-monotonic initial energy density(s) A lot to do …

more general EoS less symmetry, ellipsoidal solutions rotating viscous solutions New solutions with shear/bulk viscosity …

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Thank you for your attention Questions and Comments ?

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Backup slides

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Rlong systematics

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Teff systematics

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dn/dh systematics

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Rlong systematics

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e0 systematics

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e0 systematics

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e0 systematics

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Time evolution systematics