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Csörgő, T.1
Observables and initial conditions from exact rotational hydro solutions
T. Csörgő 1 , I. Barna 1 and M.I. Nagy 1,3
1 MTA Wigner Research Center for Physics, RMKI3 ELTE University, Budapest, Hungary
New exact rotating hydro solutionsTwo different family of equations of state
Summary: new rotating solutionsSingle particle spectra
Elliptic and higher order flowsOscillations of HBT radii
Summary: effects on observables
arXiv:1309.4390v2 PRC 89, 044901 (2014)+ manuscript in preparation
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Csörgő, T.2
Motivation: initial angular momentum
Observation of conserved quantities: importantExample from L. Cifarelli, L.P. Csernai, H. Stöcker,
EPN 43/22 (2012) p. 91
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Csörgő, T.3
Hydrodynamics: basic equations
Basic equations of non-rel hydrodynamics: Euler equation needs to be modified for lattice QCD EoS
Use basic thermodynamical relations for lack of conserved charge (baryon free region)
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Csörgő, T.4
Rewrite for v, T and (n, or s)
lattice QCD EoS: modification of the dynamical equations:
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Csörgő, T.5
Ansatz for rotation and scaling
The case without rotation:known self-similar solutionT. Cs, hep-ph/00111139S. V. Akkelin et al, hep-ph/0012127, etc.
Let’s try to add rotation!
First good news: scaling variable remains good→ a hope to find ellipsoidal rotating solutions!
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Csörgő, T.6
For details, see arXiv:1309.4390
From self-similarity
Ellipsoidal ->spheroidal
time dependence ofR and w coupled
Conservation law!
Common properties of solutions
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Csörgő, T.7
Solutions for conserved particle n
For details, see arXiv:1309.4390
Similar to irrotational case:
Family of self-similar solutions, T profile free
T. Cs, hep-ph/00111139
Rotation leads to increased transverse acceleration!
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Csörgő, T.8
Role of temperature profiles
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Csörgő, T.9
1B: conserved n, T dependent e/p
Rotation: increases transverse acceleration
Works only if T is T(t) only
But more general EoS
Similar to
T. Cs. et al,
hep-ph/0108067
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Csörgő, T.10
Solutions for lattice QCD type EoS
Two different class of solutions: p/e = const(T) or p/e = f(T)Notes: increased acceleration (vs conserved n)Observables calculable if s ~ n(final) (Landau)
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Csörgő, T.11
First integrals: Hamiltonian motion
1A: n is conserved2A: n is not conseerved
Angular momentum conservedEnergy in rotation → 0
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Csörgő, T.12
Summary so far: rotating solutions
New and rotatingexact solutions of fireball hydro
Also for lattice QCD family of EoSNow analyzed in detail
(after 53 years)
Important observation:
Rotation leads to stronger radial expansionlQCD EoS leads to stronger radial expansion
Perhaps connected to large radial flowsin RHIC and LHC data
Observables:Next slides
arXiv:1309.4390 (v2)
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Csörgő, T.13
Observables from rotating solutions
Note: (r’, k’) in fireball frame rotated wrt lab frame (r,k)
Note: in this talk, rotation in the (X,Z) impact parameter plane !
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Csörgő, T.14
Role of EoS on acceleration
Lattice QCD type Eos is explosive
Tilt angle q integrates rotation in (X,Z) plane: sensitive to EoS!
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Csörgő, T.15
Single particle spectra
In the rest frame of the fireball:
Rotation increases effective temperatures both in the
longitudinal and impact parameter direction
in addition to Hubble flows
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Csörgő, T.16
Directed, elliptic and other flows
Note: model is fully analytic
As of now, only X = Z = R(t)spheroidal solutions are found
→ vanishing odd order flows
See next talk for fluctuations
From the single particle spectra→ flow coefficents vn
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Csörgő, T.17
Reminder: Universal w scaling of v2
Rotation does not change v2 scaling, but it modifies radial flow
Black line: Buda-Lund prediction from 2003nucl-th/0310040
Comparision with data:nucl-th/0512078Note: v2 data depend on particle type, centrality, colliding energy, rapidity, pt
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Csörgő, T.18
Details of universal w scaling of v2
nucl-th/0512078
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Csörgő, T.19
HBT radii for rotating spheroids
New terms with blue → Rotation decreases HBT radii similarly to Hubble flow.
Diagonal Gaussians in natural frame
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Csörgő, T.20
HBT radii in the lab frame
HBT radii without flow
But spheriodal symmetry of the solutionMakes several cross terms vanish → need for ellipsoidal solutions
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Csörgő, T.21
HBT radii in the lab frame
HBT radii without flow
But spheriodal symmetry of the solutionMakes several cross terms vanish → need for ellipsoidal solutions
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Csörgő, T.22
Qualitatively rotation and flow similar
But need more time dependent calculations
and less academic studies(relativistic solutions)
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Csörgő, T.23
Summary
Observables calculated
Effects of rotation and flowCombine and have same mass dependence
Spectra: slope increasesv2: universal w scaling remains valid
HBT radii:Decrease with mass intensifies
Even for spherical expansions:v2 from rotation.
Picture: vulcanoHow to detect the rotation?
Next step: penetrating probes
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Csörgő, T.24
Summary
Observables calculated
Effects of rotation and flowCombine and have same mass dependence
Spectra: slope increasesv2: universal w scaling remains valid
HBT radii:Decrease with mass intensifies
Even for spherical expansions:v2 from rotation.
Picture: vulcanoHow to detect the rotation?
Next step: penetrating probes