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S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 1
System size, energy and dependence of directed and elliptic flow
Steven Manly (Univ. of Rochester)
For the PHOBOS Collaboration
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 2
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 García,
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 LABORATORYINSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY
NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGOUNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER
Collaboration meeting in Maryland, 2003
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 3
Flow in PHOBOS
Ring counter
Octagon
Spectrometer arm
Paddle trigger
Vertex detector
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 4
Correlate reaction plane determined from azimuthal pattern of hits in one part of detector
Flow in PHOBOS
Subevent A
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 5
with azimuthal pattern of hits in another part of the detector
Flow in PHOBOS
Subevent B
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 6
Or with tracks identified in the spectrometer arms
Flow in PHOBOS
Tracks
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 7
Separation of correlated subevents typically large in
Flow in PHOBOS
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 8
For directed flow we use subevents that are symmetric about =0
Flow in PHOBOS
Subevent B
Subevent A
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 9
Differential flow has proven to be a useful probe of heavy ion collisions:
CentralitypT
PseudorapidityEnergySystem sizeSpecies
Probing collisions with flow
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 10
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% centrality0-40% centrality
0-40% centrality
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 11
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 12
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
ó
Recent theoretical progress in understanding v2(η). See, for example:
M.Csanád, T.Csörgó, B.Lörstad, Nucl. Phys. A742 (2004) 80 [nucl-th/0310040]
U.Heinz, P.F.Kolb, J.Phys. G30 (2004) S1229 [nucl-th/0403044]
T.Hirano, M.Isse, Y.Nara, AOhnishi, and K Yoshino, nucl-th/0506058
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 13
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
'=||-ybeam
v 1
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 14
Au-Au data, h±
0-40% centrality
'=||-ybeam
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 15
’=||-ybeam
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 v2 right at the highest energy
density we can achieve: no break
in slope
Mid-rapidity, 200 GeV, Au-Au Reached the hydro limit?
'=||-ybeam
v 2
Elliptic flow – extended longitudinal scaling
Au-Au data, h±
0-40% centralitySystematic errors only
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 16
Differential flow has proven to be a useful probe of heavy ion collisions:
CentralitypT
PseudorapidityEnergySystem sizeSpecies
Elliptic flow – Cu-Cu results
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 17
Elliptic flow – Cu-Cu results
Cu flow is large
Track- and hit-based results agree (200 GeV)
~20-30% rise in v2 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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 18
Elliptic flow – Cu-Cu results
Cu-Cu v2(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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 19
Elliptic flow – Cu-Cu results
Longitudinal scaling reminiscent of Au-Au
PHOBOS preliminary Cu-Cu, h±
v 2
'=||-ybeam
Cu-Cu collisions also exhibit extended longitudinal scaling statistical errors only
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 20
22
22
xy
xy
Standard eccentricity (standard)
x
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 Npart
Paddle signal, ZDC, etc.
MC simulations
What is the relevant eccentricity for driving the azimuthal asymmetry?
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 21
Fluctuations in eccentricity are important for small A.
22
22
xy
xy
System size and eccentricity
Participant eccentricity (part)
x
Standard eccentricity (standard)
x
Two possibilities
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 22
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 23
Elliptic flow – v2 scaling
Expect <v2>/<> ~ 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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 24
Elliptic flow – v2 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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 25
Elliptic flow – v2 scaling
dy
dN
s
1v2 Expect in “low density limit”.
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 26
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 v2() to ~v2(y) (10% lower)
Scale dN/d to be ~dN/dy (15% higher)
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 27
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 v2() to ~v2(y) (10% lower)
Scale dN/d to be ~dN/dy (15% higher)
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 28
Elliptic flow – system dependence
Eccentricity difference is important for same centrality selection.
V2(pT) for Cu-Cu is similar v2(pT) for Au-Au when scaled by part
PHOBOS preliminary h±
0-50% centralityPHOBOS preliminary h±
0-50% centrality
PHOBOS preliminary h±
0-50% centrality
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 29
v2 for Cu-Cu is ~20% smaller than v2 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
preliminarypreliminary
PHOBOS 200 GeV h± 0-40-% centrality
Statistical errors onlyStatistical errors only
Cupart
Aupart
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 30
This data shows v2 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
preliminarypreliminary
PHOBOS 200 GeV h± 0-40-% centrality
Statistical errors onlyStatistical errors only
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 31
Conclusions
Au-Au directed flow including the new 62.4 GeV data.
PHOBOS preliminary
Au-Au 19.6 GeV Au-Au 62.4 GeV
Au-Au 130 GeV Au-Au 200 GeV
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 32
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 33
Conclusions
Au-Au and Cu-Cu systems exhibit extended longitudinal scaling. No break in evolution as function of η due to
reaching hydro limit.
PHOBOS Au-Au, h± PHOBOS preliminary Cu-Cu, h±
v 2
'=||-ybeam'=||-ybeam
v 2
statistical errors only
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 34
Conclusions
Eccentricity definition very important for small systems.
h±
1 statistical and systematic errors added in quadrature
h±
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 35
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 36
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.
v2(pT) 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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 38
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 39
Directed flow subevent regionsRegions 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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 40
Baseline analysis overlaid with new PHOBOS mixed
harmonic analysis
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 41
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 42
Au-Au update – directed flow
62.4 GeV directed flow comparisonSTAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/0409029
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 43
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 44
Comparison of preliminary PHOBOS 200 GeV v1 with published STAR results. Plots identical
except for STAR centrality selection.
Au-Au update – directed flow
STAR 200 GeV results from Phys. Rev. C 72 (2005) 014904
S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 45
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 – U. Rochester Quark Matter, Budapest, Hungary - August 2005 46
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-CuStatistical errors only
Statistical errors only