The importance of the initial geometry in relativistic nuclear collisions

1. The importance of the initial geometry in relativistic nuclear collisions Richard Hollis for the PHOBOS collaboration

2. Outline • Flow measurements from PHOBOS • Fluctuations in the collision geometry • Fluctuations of elliptic flow • Summary Richard Hollis University of Illinois at Chicago

3. z Reaction plane M. Kaneta y x What is flow? • Azimuthal anisotropy resulting from pressure gradient • Elliptic flow is the second harmonic in the Fourier expansion of azimuthal particle distributions dN/d(f -YR ) = N0 (1 + 2v1cos (f-YR) + 2v2cos (2(f-YR)) + ... ) Richard Hollis University of Illinois at Chicago

4. Spectrometer Large coverage: |h| < 5.4 Octagon Ring counters Ring counter Vertex detector PHOBOS detector Richard Hollis University of Illinois at Chicago

5. h: PRL 94, 122303 (2005) (|h|<1) Npart: nucl-ex/0610037, PRC 72, 051901 (2005) data: v2 vs helliptic flow measurements from PHOBOS • Elliptic flow for Au+Au collisions • grows with energy • declines with centrality (small eccentricity) • non-zero for central data (where e~0) Centrality: 0-40% Richard Hollis University of Illinois at Chicago

6. Cu+Cu: nucl-ex/0610037 (|h|<1) data: v2 vs helliptic flow measurements from PHOBOS • In Cu+Cu data, larger elliptic flow signal observed for central (small eccentricity) data • Understand this from a more detailed geometrical description Centrality: 0-40% Richard Hollis University of Illinois at Chicago

7. defining eccentricity standard and participant Richard Hollis University of Illinois at Chicago

8. YR Defining eccentricity Eccentricity: characterizes the almond shape of the collision zone y x Reaction plane: plane intersecting the centers of the two nuclei along beam axis estd: defined from the positions of the interaction nucleons in the (x,y) frame Richard Hollis University of Illinois at Chicago

9. Cu+Cu: nucl-ex/0610037 Y0 Y0 Defining eccentricity Au+Au: PRL 94, 122303 (2005) Statistical errors only Cu+Cu 200 GeV Au+Au 200 GeV takes into account the rotation of the participant plane, relative to the reaction plane of the nuclei Richard Hollis University of Illinois at Chicago

10. Cu+Cu: nucl-ex/0610037 Y0 Y0 Eccentricity vs Npart Au+Au: PRL 94, 122303 (2005) ecc: nucl-ex/0610037 Statistical errors only Cu+Cu 200 GeV Au+Au 200 GeV estd epart Scale v2 by eccentricity Richard Hollis University of Illinois at Chicago

11. Cu+Cu: nucl-ex/0610037 Y0 Y0 Scaling by eccentricity Au+Au: PRL 94, 122303 (2005) ecc: nucl-ex/0610037 Statistical errors only Cu+Cu 200 GeV Au+Au 200 GeV Detailed geometrical description unifies Au+Au and Cu+Cu results Richard Hollis University of Illinois at Chicago

12. fluctuations in the initial geometry … and in the elliptic flow Richard Hollis University of Illinois at Chicago

13. Glauber Model e fluctuations • Fluctuations in the eccentricity are calculated from a MC Glauber model Richard Hollis University of Illinois at Chicago

14. Glauber Model e fluctuations • Fluctuations in the eccentricity are calculated from a MC Glauber model Richard Hollis University of Illinois at Chicago

15. Track: PRC 72, 051901 (2005) Data v2 fluctuations Hit: PRL 94, 122303 (2005) • Check: • v2 from this analysis matches the existing results <v2> |η|<1 Number of participants Richard Hollis University of Illinois at Chicago

16. nucl-ex/0702036 |η|<1 PHOBOS Number of participants fluctuation comparison • Data results show significant dynamical fluctuations • Comparison of data with a MC which has no fluctuations Richard Hollis University of Illinois at Chicago

17. nucl-ex/0702036 |η|<1 |η|<1 s(epart)/<epart> PHOBOS Number of participants Number of participants fluctuation comparison • Magnitude of v2 fluctuations is in agreement with epart fluctuations • The detailed description of the initial geometry appears to be imprinted on the final particle distribution. Richard Hollis University of Illinois at Chicago

18. v2: nucl-ex/0610037 |η|<1 Number of participants |η|<1 PHOBOS Number of participants summary s(v2)/v2: nucl-ex/0702036 • Initial geometrical configuration plays an important role in the detailed particle production distributions • The azimuthal anisotropy (v2) is strongly related to the detailed eccentricity of the collisions • The fluctuations of epart are also imprinted on the final distribution of particles (v2) Richard Hollis University of Illinois at Chicago

19. Collaboration Burak Alver, Birger Back,Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Joshua Hamblen, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Christof Roland, Gunther Roland, Joe Sagerer, Peter Steinberg, George Stephans, Andrei Sukhanov, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, Bolek Wysłouch ARGONNE NATIONAL LABORATORY BROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER Richard Hollis University of Illinois at Chicago

20. auxiliary slides Richard Hollis University of Illinois at Chicago

21. Rings Only Hit-based method Track-based method PHOBOS: PRL 89, 222301 (2002) PHOBOS: PRC C72, 051901R (2005) Octagon Only Octagon and Rings PHOBOS:flow analysis • “Sub-event” method • Used for Hit and Track based analyses • Assumes that RP(h)=RP(h’) Richard Hollis University of Illinois at Chicago