viscous hydrodynamics
DESCRIPTION
Viscous hydrodynamics. with shear and bulk viscosity . Huichao Song and Ulrich Heinz . The Ohio State University. Supported by DOE. Quark Matter 2009 . March 30-April 4, Knoxville, TN. 04 /02/2009. Glauber. Luzum & Romatschke , PRC 2008. CGC. - PowerPoint PPT PresentationTRANSCRIPT
Viscous hydrodynamics
Quark Matter 2009
Huichao Song and Ulrich Heinz
The Ohio State UniversitySupported by DOE
04/02/2009
March 30-April 4, Knoxville, TN
with shear and bulk viscosity
Luzum & Romatschke, PRC 2008 Glauber CGC
-Glauber vs.CGC ~100% effect on the extracted value of-A detailed extraction of shear viscosity entropy ratio also requires:
)41(/ s
s/
-viscous late hadronic stage -non-equilibrium chemistry in HG has been studied in ideal hydro
-bulk viscosity ? -Present conservative upper limit:
5
shear viscosity bulk viscosity Viscous hydro with shear & bulk viscosity
(2nd order shear-bulk -mixing term (Muronga, Rischke) not included.)
0)( xT
Conservation laws:
gpuupeT )()(
u
TT
212
Evolution equations for shear pressure tensor and bulk presurre:
uT
Tu
21)(
Numerical Results
Bulk viscosity:
Shear viscosity: ,4/108.0/ s 0/or s
Relaxation times: (see later)
QGPHRG
Min. AdS/CFT prediction
Shear viscosity vs. bulk viscosity (I)
-Shear viscosity: decelerate cooling process in early stage accelerate cooling process in middle and late stages-Bulk viscosity: decelerate cooling process
Same initial & final conditionsideal hydro viscous hydro-shear only viscous hydro-bulk only
Local temperature
Shear viscosity vs. bulk viscosity (II)
-shear viscosity: increases radial flow, results in flatter spectra -bulk viscosity: decreases radial flow, results in steeper spectra
radial flow spectra
Same Initial & final conditionsideal hydro viscous hydro-shear only viscous hydro-bulk only
0,4/1 c1,0 c
0,0 c
ss //
Shear viscosity vs. bulk viscosity (III)
-v2 is sensitive to both shear and bulk viscosity
Elliptical flow v2
Same Initial & final conditionsideal hydro viscous hydro-shear only viscous hydro-bulk only
Viscous v2 suppression: shear and bulk viscosity ideal hydro visc. hydro:
-at RHIC, 2 x min. bulk viscosity could result in ~50% additional v2 suppression
-when extracting the from RHIC data, bulk viscous effects cannot be neglected s/
20%30%
ss //
1,4/1 c0,4/1 c
2,4/1 c
Viscous v2 suppression: shear and bulk viscosity ideal hydro visc. hydro:
-at RHIC, 2 x min. bulk viscosity could result in ~50% additional v2 suppression
-when extracting the from RHIC data, bulk viscous effects cannot be neglected s/
20%30%
ss //
1,4/1 c0,4/1 c
2,4/1 c
0
)0( bulk viscosity effects:
(a) Change the flow profile during hydro evolution (b) Additional spectra correction along freeze-out surfacef
Song & Heinz: v2 will decrease, flow corrections only (a), , at freeze-out Monnai & Hirano: v2 will increase, spectra corrections only(b), ideal hydro for evolution
-relaxation time effects Bulk Viscosity
Bulk viscous v2 suppression:-- Smaller vs. larger relaxation time
-viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure
Effects from initialization of (I)Smaller relaxation time
-after (several relaxation times), viscous pressure loses memory of initial cond.
fm/c)5.0( is insensitive to different initializations of 2v-When is small ,
Effects from initialization of (II)
-after (several relaxation times), viscous pressure loses memory of initial cond.
larger relaxation time
fm/c)5( is sensitive to different initializations of 2v-When is larger ,
Effects from initialization of (III)
-viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure
Smaller vs. larger relaxation time
A Short Summary
-When extracting QGP viscosity from experimental data, bulk viscosity effects should not be neglected
-first attempts to constrain from RHIC data indicate )41(5/ s
a realistic EOS, initialization, bulk viscosity, highly viscous hadronic stage
s/
-More theoretical inputs are needed for bulk viscosity:
No consistent simultaneous treatment yet of:
- relaxation time- initialization for bulk pressure - bulk viscosity of hadronic phase, etc
16
Thank You
Viscous hydro: a short summary for shear viscosity --shear viscosity only -2+1-d viscous hydro code individually developed by
different groups:-v2 at RHIC is sensitive to even the minimum shear viscosity entropy ratio -v2 suppression from different groups ranges from 20% to 70% -the above discrepancy was largely resolved by investigating effects
from system size, EoS and different forms of I-S eqns. used
-Code checking within the TECHQM collaboration:
-The first attempt to extract QGP shear viscosity from RHIC data: Luzum & Romatschke, PRC 78 (2008)
TECHQM webpage
Song & Heinz, PRC 78 (2008)
Romatsche & Romatschke (INT), Song & Heinz (OSU), Dusling & Teaney (Stony) Huovinen & Molnar (Purdue), Chaudhuri (Kolkata, India)
70% 20%
Viscous hydro in 2+1-dimension
)())(())(()(1pvTvTT yy
yyx
yx
y
xyxy y yy
xx xyy)())(())(()(1
pvTvTT xyx
yxx
xx
x x
p
TTT yy
xx )()()(1 2
3+1 2+1coordinates),,,( yx--the transport equations for energy momentum tensor are explicit written as:
u
TT
D2121
gpuupeT )()( 0)( xT
u
TT
uD21)(1
Bjorken approximation:
-shear tensor decelerate longitudinal expansion, but accelerate transverse expansion -bulk pressure decelerates both longitudinal & transverse expansion (bulk pressure effectively softens the EoS near the QCD phase transition)
Shear viscosity vs. bulk viscosity (I)
-Shear viscosity: slowing down of cooling process due to decelerated longitudinal expansion initially, but faster cooling in middle and late stages due to stronger transverse expansion-Bulk viscosity: slowing down of cooling process, since it decelerate longitudinal and transverse expansion; most of the effects in mixed phase region
The same Initial & final conditions:ideal hydro viscous hydro-shear only viscous hydro-bulk only
Local temperature Local temperature
0,4/1 c1,0 c
0,0 css //
Effects from initialization of mn
- is insensitive to different initializations of mn2v
yyxx
-after ~1fm/c (several relaxation times), viscous pressure loses memory of initial cond.
Song & Heinz, PLB08 & PRC 77(2008)
mnmn 2 0mnvs.
-Effects on entropy production: ~20%
sT/3
EOS
EOS