WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 1 Observables and initial conditions for rotating and expanding fireballs T. Csörgő 1,2, I.Barna 1.

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Presentation transcript:

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 1 Observables and initial conditions for rotating and expanding fireballs T. Csörgő 1,2, I.Barna 1 and M. I. Nagy 3 1 Wigner Research Center for Physics, Budapest, Hungary 2 KRF, Gyöngyös, Hungary 3 ELTE, Budapest, Hungary Introduction Introduction Non-relativistic hydro equations Rotating and expanding fireball solutions Dynamics Observables and initial conditions: Single particle spectra, elliptic flow, HBT radii Summary arXiv: arXiv: in preparation

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 2 Motivation: initial angular momentum Motivation: initial angular momentum Conserved quantities: important in heavy ion collisions also. L. Cifarelli, L.P. Csernai, H. Stöcker, EPN 43/22 (2012) p. 91 M. I. Nagy, Phys. Rev. C83 (2011) Phys. Rev. C83 (2011) T. Csörgő and M. I. Nagy, Phys.Rev. C89 (2014) 4, Phys.Rev. C89 (2014) 4,

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 3 Hydrodynamics: basic equations Hydrodynamics: basic equations Basic equations of non-rel hydrodynamics: Euler equation needs to be modified for lattice QCD EoS: no „n”. Use basic thermodynamical relations for lack of conserved charge (baryon free region)

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 4 Rewrite for v, T and (n, or  ) Rewrite for v, T and (n, or  ) lattice QCD EoS: modification of the dynamical equations:

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 5 Ansatz for rotation and scaling Ansatz for rotation and scaling The case without rotation: known self-similar solutions T. Cs, hep-ph/ S. V. Akkelin, T. Cs et al, hep-ph/ … Let’s add ω ≠0, let’s rotate! First good news: scaling variable remains good → a hope to find ellipsoidal rotating solutions!

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 6 Cs. T and M. I. Nagy, arXiv: , PRC89 (2014) 4, arXiv: From self-similarity Ellipsoidal ->spheroidal time dependence of R and  coupled Conservation law! Common properties of solutions Common properties of solutions

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 7 Solutions for conserved particle n Solutions for conserved particle n T. Cs. and M.I. Nagy, arXiv: , PRC89 (2014) 4, arXiv: Similar to irrotational case: Family of self-similar solutions, T profile free T. Cs, hep-ph/ hep-ph/ but: rotation leads to increased transverse acceleration!

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 8 Role of temperature profiles Role of temperature profiles Expanding shells of fire: large temperature gradient, but small radial flow T. Cs, hep-ph/ , APPBhep-ph/ Typical: h+p (NA22) p+p (STAR, ALICE) See: A. Bialas and W. Florkowski

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 9 1B: conserved n, T dependent e/p 1B: conserved n, T dependent e/p Rotation: increases the transverse acceleration. Only if T is T(t): Gaussian density profiles! But, a more general EoS, similar to T. Cs. et al, hep-ph/

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 10 n=0, lattice QCD type EoS n=0, lattice QCD type EoS Two different class of solutions: p/e = const  arbitrary  profile or p/e = f(T)  Gaussian  profile only Notes: increased acceleration (no „n” vs conserved „n”)

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 11 Observables from rotating solutions Observables from rotating solutions Note: (r’, k’) in fireball frame rotated wrt lab frame (r,k) Note: from now on, rotation in the (X,Z) impact parameter plane !

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 12 Role of EoS on acceleration Role of EoS on acceleration Lattice QCD type Eos is explosive Tilt angle  integrates rotation in (X,Z) plane: sensitive to EoS!

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 13 Spherical intital conditions Spherical intital conditions X 0 = Y 0 = Z 0 = 5 fm... X 0 = Y 0 = Z 0 = 0 T 0 = 350 MeV  0 increases from 0 to 0.1 c/fm Spheroidal symmetry, With rotation around y axis X = Z = R >< Y

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 14 Dynamics of evolution: Sizes Dynamics of evolution: Sizes

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 15 Dynamics of evolution: T, vorticity Dynamics of evolution: T, vorticity Temperature decreases faster due to rotation Angular velocity  decreases quickly Vorticity ~ angular velocity

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 16 Single particle spectra 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 lQCD EoS: observables calculable if ~ n (Landau freeze-out)

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 17 Directed, elliptic and other flows 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 at y=0 For fluctuations, see: M. Csanád and A. Szabó, Phys.Rev. C90 (2014) 5, From particle spectra → flow coefficents v n

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 18 Dynamics of elliptic flow Dynamics of elliptic flow

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 19 Reminder: Universal w scaling of v 2 Reminder: Universal w scaling of v 2 Rotation does not change v2 scaling, but it modifies radial flow Black line: Buda-Lund prediction from 2003 nucl-th/ Comparision with data: nucl-th/ v 2 data depend on: particle mass m, centrality %, energy √s, rapidity y, p t

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 20 Details of universal w scaling of v 2 nucl-th/

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 21 HBT radii for rotating spheroids HBT radii for rotating spheroids Rotation terms add to radial flow, same m dependence → Rotation decreases HBT radii similarly to Hubble flow. Diagonal Gaussians in natural frame Same effect found numerically: S. Velle, S. Mehrabi Pari, L.P. Csernai, arxiv: arxiv:

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 22 HBT radii in the lab frame HBT radii in the lab frame HBT radii without ω: But spheriodal symmetry of the solution Makes several cross terms vanish → need for ellipsoidal solutions

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 23 HBT radii in the lab frame HBT radii in the lab frame HBT radii without ω: But spheriodal symmetry of the solution Makes several cross terms vanish → need for ellipsoidal solutions HBT for ω, X=Y=R:

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 24 Dynamics of HBT radii Dynamics of HBT radii

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 25 Observables calculated Effects of rotation and flow have same mass dependence Spectra: slope increases v 2 : universal w scaling remains valid HBT radii: Decrease with mass intensifies Even for spherical expansions: v 2 from rotation. Picture: vulcano How to detect the rotation? Summary for hydro solutions

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 26 Observables calculated Effects of rotation and flow have same mass dependence Spectra: slope increases v 2 : universal w scaling remains valid HBT radii: Decrease with mass intensifies Even for spherical expansions: v 2 from rotation. Picture: vulcano How to detect the rotation? Summary for hydro solutions

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 27 Thank you for your attention! Thank you for your attention! Questions? Questions?

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 28 Backup slides – Discussion Backup slides – Discussion

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 29 First integrals: Hamiltonian motion First integrals: Hamiltonian motion 1A: n is conserved 2A: n is not conseerved Angular momentum conserved Energy in rotation → 0

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 30 Rotating 3d ellipsoid X Y Z Rotating 3d ellipsoid X ≠ Y ≠ Z

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 31 Scaling variables for X Y Z Scaling variables for X ≠ Y ≠ Z First good news: scaling variable remains good, Ds = 0: → a hope to find rotating 3d ellipsoidal solutions, too!

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 32 Solution for X Y Z Solution for X ≠ Y ≠ Z First 3d ellipsoidal exact hydro solution: lQCD EoS can be co-variad with the initial condition → hadronic final state may be the same

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 33 Single particle spectra Single particle spectra Expectation for tilted sources: tilted elliptical specra ~ OK, but:

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 34 Directed, elliptic and other flows Directed, elliptic and other flows From the single particle spectra → flow coefficents v n

WPCF 2015, Warsaw, 2015/11/06 Csörgő, T. for Nagy, M 35 HBT radii in the lab frame HBT radii in the lab frame HBT radii without ω: spheriodal symmetry of the hydro solution  several cross terms vanish  need for ellipsoidal solutions HBT for ω, X=Y=R: