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Causal Viscous Hydrodynamic Response to High-Momentum Jets DNP Fall 2010 Cristina I. Moody Denes Molnar
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Moody DNP 5 Nov 20102 Motivation From 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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Moody DNP 5 Nov 20103 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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Moody DNP 5 Nov 20104 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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Moody DNP 5 Nov 20105 Comparison of Ideal, NS, & IS for Static Source
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Moody DNP 5 Nov 20106 Comparison of Ideal, NS, & IS for Static Source t=0.4 fm
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Moody DNP 5 Nov 20107 Comparison of Ideal, NS, & IS for Static Source
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Moody DNP 5 Nov 20108 Comparison of Ideal, NS, & IS for Static Source
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Moody DNP 5 Nov 20109 Comparison of Ideal, NS, & IS for Static Source
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Moody DNP 5 Nov 201010 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 for more realistic source: Neufeld & Renk
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Moody DNP 5 Nov 201011 Comparison of Ideal, NS, & IS Jets Moving Through the Fluid t = 1. fm t = 5 fm 0 1/2 1 2
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Moody DNP 5 Nov 201012 Comparison of Ideal, NS, & IS Jets Moving Through the Fluid Tau = 4 fm t = 1. fm t = 5 fm Tau = 1 fmTau = 1/4 fmTau = 2 fm
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Moody DNP 5 Nov 201013 Momentum Flow Isochronous “bulk flow” freezeout -> azimuthal momentum distribution Assumptions: All particles are emitted locally in direction of momentum density
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Moody DNP 5 Nov 201014 Momentum Flow
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Moody DNP 5 Nov 201015 Momentum Flow
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Moody DNP 5 Nov 201016 Summary & Future Work Summary 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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Moody DNP 5 Nov 201017
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