# Presentation: 515514

## The importance of the initial geometry in relativistic nuclear collisions 

- Richard Hollis
- for the PHOBOS collaboration

## Outline

- Flow measurements from PHOBOS
- Fluctuations in the collision geometry
- Fluctuations of elliptic flow
- Summary

## 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(********R ****) = N****0 ****(1 + 2v****1****cos (********R****) + 2v****2****cos (2(********R****)) + ... ) **

## PHOBOS detector

## data: v2 vs elliptic flow measurements from PHOBOS

- Elliptic flow for **Au+Au** collisions
- grows with energy
- declines with centrality (small eccentricity)
- non-zero for central data (where ~0)

**Centrality: 0-40%**

******: PRL 94, 122303 (2005)**

**N****part****: nucl-ex/0610037, PRC 72, 051901 (2005)**

## In Cu+Cu data, larger elliptic flow signal observed for central (small eccentricity) data
Understand this from a more detailed geometrical description

- Understand this from a *more* detailed geometrical description

- data: v2 vs elliptic flow measurements from PHOBOS

**Cu+Cu: nucl-ex/0610037**

**Centrality: 0-40%**

- defining eccentricity
- standard and participant

## Defining eccentricity

- Reaction plane: plane intersecting the centers of the two nuclei along beam axis
- std: defined from the positions of the ***interaction*** nucleons in the (***x***,***y***) frame

**Eccentricity: characterizes the almond shape of the collision zone**

**y**

**x**

## Defining eccentricity

** ****Au+Au**
**200 GeV**

** ****Cu+Cu**
**200 GeV**

**Statistical errors only**

- takes into account the rotation
- of the participant plane, relative
- to the reaction plane of the nuclei

**Cu+Cu: nucl-ex/0610037**

**Au+Au: PRL 94, 122303 (2005)**

## Eccentricity vs Npart

** ****Au+Au**
**200 GeV**

** ****Cu+Cu**
**200 GeV**

**Statistical errors only**

**Cu+Cu: nucl-ex/0610037**

- Scale v2 by eccentricity

******std**

******part**

**ecc: nucl-ex/0610037**

**Au+Au: PRL 94, 122303 (2005)**

## Scaling by eccentricity

** ****Au+Au**
**200 GeV**

** ****Cu+Cu**
**200 GeV**

**Statistical errors only**

- Detailed geometrical description unifies Au+Au and Cu+Cu results

**Cu+Cu: nucl-ex/0610037**

**ecc: nucl-ex/0610037**

**Au+Au: PRL 94, 122303 (2005)**

- fluctuations in the initial geometry
- ... and in the elliptic flow

## Glauber Model  fluctuations

- Fluctuations in the eccentricity are calculated from a MC Glauber model

## Glauber Model  fluctuations

- Fluctuations in the eccentricity are calculated from a MC Glauber model

## Data v2 fluctuations

- Check:
- v2 from this analysis matches the existing results

**<v****2****>**

**Number of participants**

**|η|<1**

**Track: PRC 72, 051901 (2005) **

**Hit: PRL 94, 122303 (2005)**

## fluctuation comparison

- Data results show significant dynamical fluctuations
- Comparison of data with a MC which has no fluctuations

**nucl-ex/0702036**

## fluctuation comparison

- Magnitude of v2 fluctuations is in agreement with part fluctuations
- The detailed description of the initial geometry appears to be imprinted on the final particle distribution.

**nucl-ex/0702036**

## summary

- 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 part are also imprinted on the final distribution of particles (v2)

**v****2****: nucl-ex/0610037**

******(v****2****)/v****2****: nucl-ex/0702036**

##                   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

- auxiliary slides

## PHOBOS:flow analysis

- PHOBOS:flow analysis

- “Sub-event” method
- Used for Hit and Track based analyses
- Assumes that RP()=RP(’)