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Observables and initial conditions from exact rotational hydro solutions. T . Csörgő 1 , I. Barna 1 and M.I . N agy 1, 3 1 MTA Wigner Research Center for Physics , RMKI 3 ELTE University, Budapest, Hungary New exact rotating hydro solutions Two different family of equations of state

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Observables and initial conditions from exact rotational hydro solutions

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Observables and initial conditions from exact rotational hydro solutions

Observables and initial conditions from exact rotational hydro solutions

T. Csörgő1 , I. Barna 1 and M.I. Nagy1,3

1 MTA Wigner Research Center for Physics, RMKI

3ELTE University, Budapest, Hungary

New exact rotating hydro solutions

Two different family of equations of state

Summary: new rotating exact hydro solutions

arXiv:1309.4390v2PRC 89, 044901 (2014)

Comparison with a 3d rotating relativisitic hydro solution

L.P. Csernai, D.-J. Wang and T. Cs, arXiv:1406.1017

Single particle spectra

Elliptic and higher order flows

Oscillations of HBT radii

Summary: effects on observables

+ manuscript in preparation


Observables and initial conditions from exact rotational hydro solutions

Motivation: initial angular momentum

Observation of conserved quantities: important

Example from L. Cifarelli, L.P. Csernai, H. Stöcker,

EPN 43/22 (2012) p. 91


Observables and initial conditions from exact rotational hydro solutions

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)


Observables and initial conditions from exact rotational hydro solutions

Rewrite for v, T and (n, or s)

lattice QCD EoS: modification of the dynamical equations:


Observables and initial conditions from exact rotational hydro solutions

Ansatz for rotation and scaling

The case without rotation:

known self-similar solution

T. Cs, hep-ph/00111139

S. 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!


Observables and initial conditions from exact rotational hydro solutions

Common properties of solutions

  • From self-similarity

  • Ellipsoidal ->spheroidal

  • time dependence of

  • R and w coupled

  • Conservation law!

For details, see arXiv:1309.4390


Observables and initial conditions from exact rotational hydro solutions

Solutions for conserved particle n

Similar to irrotational case:

Family of self-similar solutions, T profile free

T. Cs, hep-ph/00111139

Rotation leads to increased transverse acceleration!

For details, see arXiv:1309.4390


Observables and initial conditions from exact rotational hydro solutions

Role of temperature profiles


Observables and initial conditions from exact rotational hydro solutions

1B: conserved n, T dependent e/p

Works only if T is T(t) only

But more general EoS

Similar to

T. Cs. et al,

hep-ph/0108067

Rotation: increases transverse acceleration


Observables and initial conditions from exact rotational hydro solutions

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)


Observables and initial conditions from exact rotational hydro solutions

First integrals: Hamiltonian motion

1A: n is conserved

2A: n is not conseerved

Angular momentum conserved

Energy in rotation → 0


Observables and initial conditions from exact rotational hydro solutions

Summary so far: rotating solutions

New and rotating

exact solutions of fireball hydro

Also for lattice QCD family of EoS

Now analyzed in detail

(after 53 years)

Important observation:

Rotation leads to stronger radial expansion

lQCD EoS leads to stronger radial expansion

  • Perhaps connected to large radial flows

  • in RHIC and LHC data

  • Observables:

  • Next slides

arXiv:1309.4390 (v2)


Observables and initial conditions from exact rotational hydro solutions

Comparison with 3d relativistic hydro

3d numeric

hydro solution

Analytic solution

Recent result from:

L. P. Csernai, D.-J. Wang and T.Cs.

  • arXiv:1406.1017

1) Rotation boosts radial flow

2) Hadronic observables similar, but penetrating probes will differ!


Observables and initial conditions from exact rotational hydro solutions

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 !


Observables and initial conditions from exact rotational hydro solutions

Role of EoS on acceleration

Lattice QCD type Eos is explosive

Tilt angle q integrates rotation in (X,Z) plane: sensitive to EoS!


Observables and initial conditions from exact rotational hydro solutions

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


Observables and initial conditions from exact rotational hydro solutions

Directed, elliptic and other flows

  • From the single particle spectra

  • → flow coefficents vn

  • Note: model is fully analytic

  • As of now, only X = Z = R(t)

  • spheroidal solutions are found

  • → vanishing odd order flows or

  • odd order flows signalfluctuations

  • see also M. Csanád and A. Szabó,

  • arXiv:1405.3877


Observables and initial conditions from exact rotational hydro solutions

Reminder: Universal w scaling of v2

  • Rotation does not change v2 scaling, but it modifies radial flow

  • Black line: Buda-Lund prediction from 2003

  • nucl-th/0310040

  • Comparision with data:

  • nucl-th/0512078

  • Note: v2 data depend on particle type, centrality, colliding energy, rapidity, pt


Observables and initial conditions from exact rotational hydro solutions

Details of universal w scaling of v2

nucl-th/0512078


Observables and initial conditions from exact rotational hydro solutions

HBT radii for rotating spheroids

Diagonal Gaussians in natural frame

New terms with blue

→ Rotation decreases HBT radii similarly to Hubble flow.


Observables and initial conditions from exact rotational hydro solutions

HBT radii in the lab frame

  • HBT radii without flow

But spheriodal symmetry of the solution

Makes several cross terms vanish → need for ellipsoidal solutions


Observables and initial conditions from exact rotational hydro solutions

HBT radii in the lab frame

  • HBT radii without flow

But spheriodal symmetry of the solution

Makes several cross terms vanish → need for ellipsoidal solutions


Observables and initial conditions from exact rotational hydro solutions

HBT radii in the lab frame

  • Now using axial symmetry around y

Axialsymmetry of the solution: only out-side oscillations remain

→ need for ellipsoidal solutions


Observables and initial conditions from exact rotational hydro solutions

Qualitatively rotation and flow similar

But need more time to do time dependent calculations

note: side-long oscillations

expected for non-axial solutions

and for less academic studies

(relativistic solutions)


Observables and initial conditions from exact rotational hydro solutions

New directions: Multipole solutions

note: multipolemodes

~ indepenent

and fit v3 … data

M. Csanád, A. Szabó arXiv:1405.3877

New viscous relativistic solutions:

Y. Hatta, J. Noronha, B.-W. Xiao

  • arXiv:1403.7693, arXiv:1405.1984


Observables and initial conditions from exact rotational hydro solutions

Summary

Observables calculated

Effects of rotation and flow

Combine and have same mass dependence

Spectra: slope increases

v2: universal w scaling remains valid

HBT radii:

Decrease with mass intensifies

Even for spherical expansions:

v2 from rotation.

  • Picture: vulcano

  • How to detect the rotation?

  • Next steps: penetrating probes

  • observables from solutions

  • detailed comparisons with data


Observables and initial conditions from exact rotational hydro solutions

Summary

Observables calculated

Effects of rotation and flow

Combine and have same mass dependence

Spectra: slope increases

v2: universal w scaling remains valid

HBT radii:

Decrease with mass intensifies

Even for spherical expansions:

v2 from rotation.

  • Picture: vulcano

  • How to detect the rotation?

  • Next steps: observables from solutions

  • detailed comparisons with data

  • penetrating probes …


Observables and initial conditions from exact rotational hydro solutions

Thank you!


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