# Presentation: 183764

## System size, energy and  dependence of directed and elliptic flow

**Steven Manly   (Univ. of Rochester) ****For the PHOBOS Collaboration**

- S.Manly (PHOBOS) - QM2005

## Collaboration meeting in Maryland, 2003

***Collaboration meeting, BNL October 2002***

**Burak Alver****, Birger Back,**** ****Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, ****Richard Bindel****,**
** ****Wit**** Busza (Spokesperson), Zhengwei Chai, ****Vasundhara Chetluru****, Edmundo Garc****í****a, ****Tomasz Gburek****, Kristjan Gulbrandsen, Clive Halliwell, ****Joshua Hamblen****, ****Ian Harnarine****, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Jay Kane,Piotr Kulinich, Chia Ming Kuo, ****Wei Li****, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, **
**Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, ****Corey Reed****, **
**Eric Richardson****, Christof Roland, Gunther Roland, ****Joe Sagerer****, Iouri Sedykh, Chadd Smith, **
**Maciej Stankiewicz****, Peter Steinberg, George Stephans, Andrei Sukhanov, ****Artur Szostak****, **
**Marguerite Belt Tonjes, Adam Trzupek, ****Sergei Vaurynovich****, Robin Verdier, Gábor Veres, **
**Peter Walters****, ****Edward Wenger****, ****Donald Willhelm****, Frank Wolfs,  Barbara Wosiek, Krzysztof Woźniak,   ****Shaun Wyngaardt****, 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**

***Collaboration meeting in Maryland, 2003***

- S.Manly (PHOBOS) - QM2005

## Flow in PHOBOS

- S.Manly (PHOBOS) - QM2005

## Flow in PHOBOS

**Correlate reaction plane determined from azimuthal pattern of hits in one part of detector**

**Flow in PHOBOS**

**Subevent A**

- S.Manly (PHOBOS) - QM2005

## Flow in PHOBOS

**with azimuthal pattern of hits in another part of the detector **

**Flow in PHOBOS**

**Subevent B**

- S.Manly (PHOBOS) - QM2005

## Flow in PHOBOS

**Or with tracks identified in the spectrometer arms**

**Flow in PHOBOS**

**Tracks**

- S.Manly (PHOBOS) - QM2005

## Flow in PHOBOS

**Separation of correlated subevents typically large in ******

**Flow in PHOBOS**

- S.Manly (PHOBOS) - QM2005

## Flow in PHOBOS

**For directed flow we use subevents that are symmetric about ********=0**

**Flow in PHOBOS**

**Subevent B**

**Subevent A**

- S.Manly (PHOBOS) - QM2005

## Probing collisions with flow

**Centrality**
**p****T**
**Pseudorapidity**
**Energy**
**System size**
**Species**

**Probing collisions with flow**

- S.Manly (PHOBOS) - QM2005

## Au-Au – directed flow

***Au-Au  19.6 GeV h******±***

***Au-Au  62.4 GeV h******±***

***Au-Au  130 GeV h******±***

***Au-Au  200 GeV h******±***

**Update of directed flow result first shown at QM2004**
**Similar (2-subevent) technique**
**Added 62.4 GeV data**
**Confirmed with mixed harmonic analysis**

***See poster by A. Mignerey in Poster 1, section 2, number 47***

***PHOBOS preliminary***

***PHOBOS preliminary***

***PHOBOS preliminary***

***PHOBOS preliminary***

***0-40% centrality***

***0-40% centrality***

***0-40% centrality***

***0-40% centrality***

- S.Manly (PHOBOS) - QM2005

## Au-Au – elliptic flow

***PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303***

***PHOBOS Au-Au, h******±***

***PHOBOS Au-Au, h******±***

***PHOBOS Au-Au, h******±***

***PHOBOS Au-Au, h******±***

***0-40% centrality***

***0-40% centrality***

***0-40% centrality***

***0-40% centrality***

**Au-Au – elliptic flow**

- S.Manly (PHOBOS) - QM2005

## Au-Au – elliptic flow

***PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303***

***PHOBOS Au-Au, h******±***

***PHOBOS Au-Au, h******±***

***PHOBOS Au-Au, h******±***

***PHOBOS Au-Au, h******±***

***0-40% centrality***

***0-40% centrality***

***0-40% centrality***

***0-40% centrality***

**Au-Au – elliptic flow**

- S.Manly (PHOBOS) - QM2005

## Directed flow – extended longitudinal scaling

**Directed flow exhibits extended longitudinal scaling, i.e., approximate rest frame of nucleus.**

**Directed flow – extended longitudinal scaling**

***Systematic errors only***

***PHOBOS preliminary h******±******, ******Au-Au***

***0-40% centrality***

******'****=|********|-y****beam**

**v****1**

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – extended longitudinal scaling

***Au-Au data, h******±***

***0-40% centrality***

******'****=|********|-y****beam**

**Elliptic flow exhibits striking extended longitudinal scaling**

***PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303***

**v****2**

**Elliptic flow – extended longitudinal scaling**

***Systematic errors only***

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – extended longitudinal scaling

**Elliptic flow exhibits striking extended longitudinal scaling**

***PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303***

***If so, it is an unfortunate coincidence that we saturate *****v*****2****** right at the highest energy density we can achieve:  no break in slope***

**Mid-rapidity, 200 GeV, Au-Au Reached the hydro limit?**

******'****=|********|-y****beam**

**v****2**

**Elliptic flow – extended longitudinal scaling**

***Au-Au data, h******±***

***0-40% centrality***

***Systematic errors only***

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – Cu-Cu results

**Differential flow has proven to be a useful probe of heavy ion collisions:**
**Centrality**
**p****T**
**Pseudorapidity**
**Energy**
**System size**
**Species**

**Elliptic flow – Cu-Cu results**

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – Cu-Cu results

**Elliptic flow – Cu-Cu results**

** ****Cu flow is large**
** ****Track- and hit-based results agree (200 GeV)**
**~20-30% rise in v****2**** from 62.4 to 200 GeV**

***PHOBOS preliminary Cu-Cu, h******±***

***PHOBOS preliminary Cu-Cu, h******±***

***Hit based 62.4 GeV***

***Hit based 200 GeV***

***Track based 200 GeV***

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – Cu-Cu results

**Elliptic flow – Cu-Cu results**

**Cu-Cu v****2****(****η****) ****shape reminiscent of Au-Au**

***PHOBOS preliminary Cu-Cu, 62.4 GeV, h******± 0-40% centrality***

***PHOBOS preliminary Cu-Cu, 200 GeV, h******± 0-40% centrality***

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – Cu-Cu results

**Longitudinal scaling reminiscent of Au-Au**

**Cu-Cu collisions also exhibit extended longitudinal scaling**

***statistical errors only***

- S.Manly (PHOBOS) - QM2005

## System size and eccentricity

**System size and eccentricity**

**Expect the geometry, i.e., the eccentricity, of the collision to be important in comparing flow in the Au-Au and Cu-Cu systems**

**Centrality measure ******** N****part**** ******** ******

***Paddle signal, ZDC, etc.***

**MC simulations**

*** ******What is the relevant eccentricity for driving the azimuthal asymmetry?***

- S.Manly (PHOBOS) - QM2005

## System size and eccentricity

**System size and eccentricity**

**Participant eccentricity (********part****)**

**Standard eccentricity (********standard****)**

**Two possibilities**

- S.Manly (PHOBOS) - QM2005

## System size and eccentricity

**Fluctuations in eccentricity are important for the Cu-Cu system.  **

**System size and eccentricity**

***Must use care in doing Au-Au to Cu-Cu flow comparisons.  Eccentricity scaling depends on definition of eccentricity. ***

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – v2 scaling

**Elliptic flow – v****2**** scaling**

** ****Expect <v****2****>/<********> ****~ ****constant for system at hydro limit. **
** ****Note the importance of the eccentricity choice. **

** ****h****±**

***1************ statistical and systematic errors added in quadrature***

** ****h****±**

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – v2 scaling

**Elliptic flow – v****2**** scaling**

** ****h****±**

***1************ statistical and systematic errors added in quadrature***

** ****h****±**

**Given other similarities between Au-Au and Cu-Cu flow, perhaps this is evidence that ********part**** is (close to) the relevant eccentricity for driving the azimuthal asymmetry**

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – v2 scaling

**Expect**

**in “low density limit”.  **

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – v2 scaling

**Approximate “LDL” scaling observed.  **

** ****Caution:****  we used ********part**** for PHOBOS data.  Important for Cu-Cu, less critical for Au-Au.**
** ****Scale v****2****(********) to  ~v****2****(y) (10% lower)**
** ****Scale dN/d******** to be ~dN/dy (15% higher)**

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – v2 scaling

**Approximate “LDL” scaling observed.  **

***Points for STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments***

** ****Caution:****  we used ********part**** for PHOBOS data.  Important for Cu-Cu, less critical for Au-Au.**
** ****Scale v****2****(********) to  ~v****2****(y) (10% lower)**
** ****Scale dN/d******** to be ~dN/dy (15% higher)**

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – system dependence

**Elliptic flow – system dependence**

**Eccentricity difference is important for same centrality selection. **
**V****2****(p****T****) for Cu-Cu is similar v****2****(p****T****) for Au-Au when scaled by ********part**

***PHOBOS preliminary h******±***

***0-50% centrality***

***PHOBOS preliminary h******±***

***0-50% centrality***

***PHOBOS preliminary h******±***

***0-50% centrality***

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – system dependence

**v****2**** for Cu-Cu is ~20% smaller than v****2**** for Au-Au plotted 0-40% centrality.  Drops another ~20% if scaled by ratio**

***PHOBOS 62.4 GeV  h******±****** 0-40% centrality***

**Elliptic flow – system dependence**

***preliminary***

***preliminary***

***PHOBOS 200 GeV  h******±****** 0-40-% centrality***

***Statistical errors only***

***Statistical errors only***

- S.Manly (PHOBOS) - QM2005

**Notes:**
Initial energy density and spatial elliptic deformation

## Elliptic flow – system dependence

**This data shows v****2**** does not scale linearly with A as expected by AMPT (factor of 3)**

***AMPT multi-phase transport model (Chen and Ko, nucl-th/0505044)***

***PHOBOS 62.4 GeV  h******±****** 0-40% centrality***

**Elliptic flow – system dependence**

***preliminary***

***preliminary***

***PHOBOS 200 GeV  h******±****** 0-40-% centrality***

***Statistical errors only***

***Statistical errors only***

- S.Manly (PHOBOS) - QM2005

**Notes:**
Initial energy density and spatial elliptic deformation

## Conclusions

** ****Au-Au directed flow including the new 62.4 GeV data.**

- S.Manly (PHOBOS) - QM2005

## Conclusions

** ****Cu-Cu elliptic flow large.  Similar in shape to Au-Au.**

***PHOBOS preliminary Cu-Cu, 62.4 GeV, h******± 0-40% centrality***

***PHOBOS preliminary Cu-Cu, 200 GeV, h******± 0-40% centrality***

- S.Manly (PHOBOS) - QM2005

## Conclusions

** ****Au-Au and Cu-Cu systems exhibit extended longitudinal scaling.  No break in evolution as function of ****η**** ****due to reaching hydro limit****.**

***statistical errors only***

- S.Manly (PHOBOS) - QM2005

## Conclusions

** ****Eccentricity definition very important for small systems.**

** ****h****±**

***1************ statistical and systematic errors added in quadrature***

** ****h****±**

- S.Manly (PHOBOS) - QM2005

## Conclusions

** ****Similarity of Au-Au to Cu-Cu flow and the fact that scaling seems to work for ********part**** may imply that ********part**** (or something close to it) is the relevant geometric quantity for generating the azimuthal asymmetry. **

- S.Manly (PHOBOS) - QM2005

## Conclusions

** ****Au-Au directed flow results updated.**

** ****Au-Au and Cu-Cu systems exhibit extended longitudinal scaling.  No break in evolution as function of ****η**** ****due to reaching hydro limit****.**

** ****Eccentricity definition very important for small systems.**

** ****Cu-Cu elliptic flow large.  Similar in shape to Au-Au.**

** ****v****2****(p****T****) is similar in Au-Au and Cu-Cu systems when ********part**** is used.**

** ****Similarity of Au-Au to Cu-Cu flow and the fact that scaling seems to work for ********part**** may imply that ********part**** (or something close to it) is the relevant geometric quantity for generating the azimuthal asymmetry. **

- S.Manly (PHOBOS) - QM2005

## Backup Slides

- S.Manly (PHOBOS) - QM2005

## Elliptic flow subevent regions

**Elliptic flow subevent regions**

- Cu-Cu, 200 and 62.4 GeV and Au-Au, 19.6, 62.4, 130 and 200 GeV:  0.1<|η|<3.0
- (use 0.5<|η|<3.0 and 1.0<|η|<3.0 for systematic studies)

***Regions used to determine reaction plane and resolution.***

- S.Manly (PHOBOS) - QM2005

## Directed flow subevent regions

***Regions used to determine reaction plane and resolution.***

- v1 baseline Au-Au, 19.6, 62.4, 130 and 200 GeV:  1.5<|η|<3.0 and 3.0<|η|<5.0
- (use 1.5<|η|<2.5 and 3.5<|η|<5.0 for systematic studies)

- v1 mixed harmonic Au-Au, 19.6, 62.4, 130 and 200 GeV: 1.5<|η|<3.0 and 3.0<|η|<5.0 for the first harmonic part and 0.1<|η|<3.0 for the second harmonic part

- S.Manly (PHOBOS) - QM2005

## Au-Au update – directed flow

**Shows non-flow correlations small**

***Mixed harmonic method:  STAR collaboration, Phys. Rev. C 72 (2005) 014904**** *

***PHOBOS preliminary h******±****** Au-Au***

**Au-Au update – directed flow**

***PHOBOS preliminary h******±****** Au-Au***

***PHOBOS preliminary h******±****** Au-Au***

***PHOBOS preliminary h******±****** Au-Au***

- S.Manly (PHOBOS) - QM2005

## Au-Au update – directed flow

**Au-Au update – directed flow**

**62.4 GeV results are particularly good due to: **
** ****large directed flow**
** ****large number of tracks/event **
** ****large elliptic flow (for    mixed harmonic)**

***STAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/0409029***

**Preliminary PHOBOS and STAR results agree well at 62.4 GeV except at highest |********|**

***62.4 GeV Au-Au, h******±***

- S.Manly (PHOBOS) - QM2005

## Au-Au update – directed flow

- 62.4 GeV directed flow comparison

***STAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/0409029***

- S.Manly (PHOBOS) - QM2005

## Au-Au update – directed flow

**Au-Au update – directed flow**

**Comparison of directed flow results at 62.4 GeV**

***Estimated by PHOBOS from weighted average of STAR data in multiple centrality bins***

**We used the centrality dependence of STAR’s results to estimate the STAR results in the 10-50% centrality bin **

***62.4 GeV Au-Au, h******±***

**Discrepancy at high ****η**** possibly due to differences in low momentum cutoff?**

- S.Manly (PHOBOS) - QM2005

## Au-Au update – directed flow

**Au-Au update – directed flow**

***STAR 200 GeV results from Phys. Rev. C 72 (2005) 014904***

- S.Manly (PHOBOS) - QM2005

## Au-Au update – elliptic flow

**Only statistical errors shown**

**Au+Au data**

**(0-40% central)**

**Au-Au update – elliptic flow**

***PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303***

- S.Manly (PHOBOS) - QM2005

## Elliptic flow – Cu-Cu results 

***Models from Hirano et al., nucl-th/0506058, probably see more later this session***

**Cu-Cu more like Hydro than JAM hadron string cascade model**

***Here JAM uses a 1 fm/c formation time.  Hydro (160) has kinetic freezeout temperature at 160 MeV***

*** ******preliminary 200 GeV Cu-Cu***

*** ******preliminary 200 GeV 15-25% Cu-Cu***

***Statistical errors only***

***Statistical errors only***

- S.Manly (PHOBOS) - QM2005

## System size and eccentricity

**System size and eccentricity**

***Au-Au***

***Au-Au***

***Cu-Cu***

***Cu-Cu***

***PHOBOS-Glauber MC preliminary***

***PHOBOS-Glauber MC preliminary***

***PHOBOS-Glauber MC preliminary***

***PHOBOS-Glauber MC preliminary***

***Mean eccentricity shown in black***

- S.Manly (PHOBOS) - QM2005