Causal Viscous Hydrodynamic Response to High-

Momentum Jets

DNP Fall 2010

Cristina I. Moody

Denes Molnar

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MotivationFrom Hydro Expect

– Triangular Flow?

– Viscous Effects?– Sheer Stress

– Relaxation Time

Casalderrey-olana et al. Phys. Conf. Ser. 27, 22 (2005)v

F. Wang Strangeness Quark Matter 2009

Mach Cone Like Structures in Data

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Hydrodynamics

• Ideal Hydrodynamic Model - No Viscosity

• Navier-Stokes Hydrodynamic Model – with Viscosity (but acausal)

• Israel-Stewart Hydrodynamic Model – Viscosity and Relation Time

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Response to a Gaussian Source

• Very Simple Jet Model

• Temperature ~ 300 MeV

• Spherically Symmetric Ideal

• Spherically Symmetric (Linearized) Navier-Stokes (small k)

For QGP:

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Comparison of Ideal, NS, & IS for Static Source

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Comparison of Ideal, NS, & IS for Static Source

t=0.4 fm

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Comparison of Ideal, NS, & IS for Static Source

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Comparison of Ideal, NS, & IS for Static Source

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Comparison of Ideal, NS, & IS for Static Source

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• in &

• Jet velocity:

• Source:

• For more realistic source: Neufeld & Renk

• Parameters:– Gaussian Width = 0.35 fm– T ~ 300 MeV

Comparison of Ideal, NS, & IS Jets Moving Through the Fluid

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Comparison of Ideal, NS, & ISJets Moving Through the Fluid

t = 1. fm

t = 5 fm

0 1/2 1 2

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Comparison of Ideal, NS, & ISJets Moving Through the Fluid

Tau = 4 fm

t = 1. fm

t = 5 fm

Tau = 1 fmTau = 1/4 fm Tau = 2 fm

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Momentum Flow

• Isochronous “bulk flow” freezeout -> azimuthal momentum distribution

• Assumptions: All particles are emitted locally in direction of momentum density

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Momentum Flow

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Momentum Flow

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Summary & Future WorkSummary

Studied jet propagation in a static viscous medium using a simple Gaussian model• Relaxation time effects in Israel-Stewart hydro:

• Large effect at small times• Modest effect at later times• Waves for larger relaxation times appear more ideal

Future Work• Inhomogeneous evolving medium• More realistic jet source• Freezeout

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