Collective Flow in Heavy-Ion Collisions

Kirill Filimonov (LBNL)

What is Flow in Heavy-Ion Collisions?

• Collective motion characterized by space-momentum correlation of dynamic origin

• Concept from Hydrodynamics: - hot and compressed matter

behaves like a compressible fluid

• axially symmetric radial flow• azimuthally anisotropic transverse flow

Types of Flow:

Collective Behavior in non-central Heavy Ion Collisions

b – impact parameter

Low energy heavy-ion collisions: E/A=25 MeV

Collective Behavior in non-central Heavy Ion Collisions

Relativistic heavy-ion collisions: E/A~0.4-10 GeV

b – impact parameter

“spectators”

“spectators”

“participants”

Collective Behavior in non-central Heavy Ion Collisions

Passage time: 2R/(βcmγcm)

“spectators”

“spectators”

“participants”

REACTION PLANE

• 15 fm/c at 1 GeV/nucleon• 5.4 fm/c at 10 GeV/nucleon• 1.4 fm/c at 160 GeV/nucleon

View in transverse plane

TARGET PROJECTILE

Spectator blocking

x

y

Azimuthal anisotropy in momentum space (directed flow)

px

py

Directed (sideward) FlowExample: E877 (AGS, 11 AGeV)

<px> ≠0

px

py protons deuterons

Out-of-plane squeeze-out (spectator blocking)

x

y

Azimuthal anisotropy in momentum space (elliptic flow)

px

py

dN/d

-/2 0 /2

In-plane elliptic flow (due to pressure gradient)

x

y

Azimuthal anisotropy in momentum space (elliptic flow)

px

py

dN/d

-/2 0 /2

Interplay of passage/expansion times

Passage time: 2R/(βcmγcm)Expansion time: R/cs cs=c√dp/dε - speed of sound

Sensitivity to nuclear EOSScience, Vol 298, Issue 5598, 1592-1596, 22 November 2002Determination of the Equation of State of Dense Matter Pawel Danielewicz, Roy Lacey, William G. Lynch

Directed Flow: Elliptic flow:

Elliptic flow at RHIC

b – impact parameter

“spectators”

“spectators”

Longitudinal and transverse expansion => no influence of spectator matter at midrapidity

Elliptic flow at RHIC

Reactionplane

In-planeOu

t-o

f-p

lan

e

Y

X

Re-interactions FLOW Re-interactions among what? Hadrons, partons or both?

In other words, what equation of state?

Flow

Flow

Azimuthal distributions at RHIC

STAR, PRL90 032301 (2003)

b ≈ 4 fm

“central” collisions

b ≈ 6.5 fm

midcentral collisions

Azimuthal distributions at RHIC

STAR, PRL90 032301 (2003)

b ≈ 4 fmb ≈ 6.5 fmb ≈ 10 fm

peripheral collisions

“v2”

v2 Excitation Function

Rich structure

Transition from in-plane to out-of-plane and back to in-plane emission

Geometry effect in addition to (smooth?) change in pressure

v2 vs Energy Density

Steady increase with energy density

Close to hydrodynamic limit for most central collisions at RHIC

Elliptic flow => sensitivity to early system

“Elliptic flow”

• evidence ofcollective motion

• sensitive to early pressure

• evidence for• early thermalization

• QGP in early stage

Hydrodynamiccalculation ofsystem evolution

Quark-number scaling

At intermediate pT v2 appears to depend on quark-number

For pT/n > 0.6 GeV/c, v2 scales with the number of quarks n, as predicted for hadron formation by quark coalescence

v2hadron (pT

hadron ) nv2quark (pT

quark )

pThadron npT

quark

Pions deviate: perhaps because they are goldstone bosons but also because of resonance decay contributions.

Conclusions and Outlook

• Elliptic flow at RHIC => Evidence for early pressure

• First time hydro works in heavy ion collisions!

• Indications of re-interaction between constituent quarks

• Will charm flow at RHIC?