new exact solutions of rel hydro - indico.lucas.lu.secollisions19@lund, 2019/02/28 csörgő, t. a...
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Applications of a new family of solutionsof relativistic hydrodynamics
T. Csörgő1,2 , G. Kasza2, M. Csanád3 and Z. Jiang4,5
1Wigner Research Center for Physics, Budapest, Hungary2EKE GYKRC, Gyöngyös, Hungary
3Eötvös University, Budapest, Hungary4Key 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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Collisions19@Lund, 2019/02/28 Csörgő, T.
A new family of exact solutionsof 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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Collisions19@Lund, 2019/02/28 Csörgő, T.
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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Collisions19@Lund, 2019/02/28 Csörgő, T.
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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Collisions19@Lund, 2019/02/28 Csörgő, T.
Perfect fluid hydrodynamics
Energy-momentum
tensor:
Relativistic
Euler equation:
Energy conservation:
Charge conservation:
Consequence is entropy conservation:
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Collisions19@Lund, 2019/02/28 Csörgő, T.
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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Collisions19@Lund, 2019/02/28 Csörgő, T.
Auxiliary variables: hx, t, W , hp, y
Consider a 1+1 dimensional, finite, expanding fireballAssume: W=W(hx)
Notation T. Cs., G. Kasza, M. Csanád, Z. Jiang, arXiv.org:1805.01427
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Hydro in Rindler coordinates, new sol
Assumptions of TCs, Kasza, Csanád and Jiang, arXiv.org:1805.01427 :
From energy-momentum conservation, theEuler and temperature equations are obtained:
For the entropy density, the continuity equation is solved.
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Collisions19@Lund, 2019/02/28 Csörgő, T.
A New Family of Exact Solutions of Hydro
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Collisions19@Lund, 2019/02/28 Csörgő, T.
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, butadditional dependence on
H = H(hx) too.
Explicit and Exact:Fluid rapidity, temperature,
entropy density explicitly givenby 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 curvescorrespond to functions
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Limited in space-time rapidity hx
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Illustration: results for T
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Limited in space-time rapidity hx
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Illustration: results for fluid rapidity W
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Limited in space-time rapidity hx
arXiv.org:1805.01427 : W l h x
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Approximations near midrapidity
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Observables: rapidity distribution
dn/dy evaluatedanalytically,
in a saddle-pointapproximation
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Pseudorapidity distribution
dn/dh evaluatedanalytically,
in an advanced saddle-pointapproximation
An important by-product:pT = pT (y) is rapiditydependent, a Lorentzian
just as in Buda-Lund model
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh for p+p, 7-8 TeV, CMS data
arXiv.org:1805.01427
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh for Pb+Pb, 5 TeV, ALICE data
arXiv.org:1806.06794
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh for Xe+Xe, 5.44 TeV, CMS data
NEW (preliminary, too good)
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh for Au+Au, 200 GeV, PHOBOS
arXiv.org:1806.11309
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh fits, √sNN = 200 GeV
23
Allowed fit region(depends on λ)
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh fits, √sNN = 130 GeV
24
Allowed fit region(depends on λ)
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh fits, √sNN = 62.4 GeV
25
Allowed fit region (dependson λ)
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh fits, √sNN = 19.6 GeV
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Rlong fits, √sNN = 62-200 GeV
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Correction factors, √sNN = 62-200 GeV
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Init energy densities, √sNN = 62-200 GeV
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Collisions19@Lund, 2019/02/28 Csörgő, T.
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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Collisions19@Lund, 2019/02/28 Csörgő, T.
Thank you for your attention
Questions and Comments ?
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Backup slides
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Rlong systematics
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Teff systematics
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Collisions19@Lund, 2019/02/28 Csörgő, T.
dn/dh systematics
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Rlong systematics
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Collisions19@Lund, 2019/02/28 Csörgő, T.
e0 systematics
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Collisions19@Lund, 2019/02/28 Csörgő, T.
e0 systematics
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Collisions19@Lund, 2019/02/28 Csörgő, T.
e0 systematics
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Collisions19@Lund, 2019/02/28 Csörgő, T.
Time evolution systematics