Flow Vorticity and Rotation in Peripheral HIC

1. Flow Vorticity and Rotation in Peripheral HIC Dujuan Wang University of Bergen, Norway 2014 CBCOS, Wuhan, 11/05/2014

2. Outline • Introduction • Vorticity for LHC, FAIR & NICA • Rotation in an exact hydro model • Summary

3. Introduction • Pre-equilibrium stage  Initial state • Quark Gluon Plasma  FD/hydrodynamics Particle In Cell (PIC) code • Freeze out, and simultaneously “hadronization” Phase transition on hyper-surface  Partons/hadrons

4. For perfect fluid: In Local Rest (LR) frame= (e, P, P, P); Relativistic Fluid dynamics model Relativistic fluid dynamics (FD) is based on the conservation laws and the assumption of local equilibrium ( EoS) 4-flow: energy-momentum tensor:

5. tilted initial state, big initial angular momentum Flow velocity Pressure gradient Structure and asymmetries of I.S. are maintained in nearly perfect expansion. [L.P.Csernai, V.K.Magas,H.Stoecker,D.D.Strottman, PRC 84,024914(2011)]

6. The rotation and Kelvin Helmholtz Instability (KHI) More details in Laszlo’ talk Straight line  Sinusoidal wave for peripheral collisions [L.P.Csernai, D.D.Strottman, Cs.Anderlik, PRC 85, 054901(2012)]

7. 2. Vorticity Definitions: [L.P. Csernai, V.K. Magas, D.J. Wang, PRC 87, 034906(2013)] Classical flow: Relativistic flow: The vorticity in [x,z] plane is considered.

8. +0 More details: +- ++ Weights: 0+ Etot: total energy in a y layer Ncell: total num. ptcls. In this y layer In [x,z] plane: Corner cells

9. Vorticity @ LHC energy: In Reaction Plane t=0.17 fm/c

10. In Reaction Plane t=3.56 fm/c

11. In Reaction Plane t=6.94 fm/c

12. b5 All y layer added up at t=0.17 fm/c

13. b5 All y layer added up at t=3.56 fm/c

14. Average Vorticity in summary Decrease with time Bigger for more peripheral collision Viscosity damps the vorticity

15. Circulation:

16. Vorticity @ NICA , 9.3GeV:

17. Vorticity @ FAIR, 8 GeV

18. 3, Rotation in an exact hydro model Hydrodynamic basic equations

19. The variables: Scaling variable: Csorgo, arxiv: 1309.4390[nucl.-th]

20. More details: rhs: y cylindrical coordinates:

21. lhs:

22. Kinetic energy: Expansion energy at the surface Rotational energy at the surface Expansion energy at the longitudinal direction sρM & syM: Boundary of spatial integral (α and β are independent of time) For infinity case:

23. Internal energy:

24. Solutions: The solution: Runge-Kutta method: Solve first order DE initial condition for R and Y is needed, and the constants Q and W

25. Table 1 : data extracted from L.P. Csernai, D.D Strottman and Cs Anderlik, PRC 85, 054901 (2012) R : average transverse radius Y: the length of the system in the direction of the rotation axis θ : polar angle of rotation ω :anglar velocity

26. Energy time dependence: Energy conserved ! decreasing internal energy and rotational energy leads the increasing of kinetic energy .

27. Spatial expanding: Smaller initial radius parameter overestimates the radial expansion velocity due to the lack of dissipation

28. Expansion Velocity: In both cases the expansion in the radial direction is large. Radial expansion increases faster, due to the centrifugal force from the rotation. It increases by near to 10 percent due to the rotation. the expansion in the direction of the axis of rotation is less.

29. Summary • High initial angular momentum exist for peripheral collisions and the presence of KHI is essential to generate rotation. • Vorticity is significant even for NICA and FAIR energy. • The exact model can be well realized with parameters extracted from our PICR FD model Thank you for your attention!

31. Table 2 : Time dependence of characteristic parameters of the exact fuid dynamical model. Large extension in the beam direction is neglected.

32. αand β