neutrino processes in dense quark matter: emissivity and bulk viscosity qun wang university of...
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Neutrino processNeutrino processeses in dense quark in dense quark matter:matter:eemissivity and bulk viscositymissivity and bulk viscosity
Qun WangUniversity of Science and Technology of China
Introduction Neutrino emissivity in dense quark matter Bulk viscosity in strange quark matter Discussions and outlooks
Strange Quark Matter, Beijing, Oct 6-10, 2008
• A. Schmitt, I. Shovkovy, QW, PRL 94, 211101(2005) [Erratum: PRL 95, 159902(2005)]• A. Schmitt, I. Shovkovy, QW, PRD 73, 034012(2006)• QW, Z. Wang, J. Wu, PRD 74, 014021 (2006)• X. Huang, QW, P. Zhuang, PRD 76, 094008 (2007)• H. Dong, N. Su, QW, 75, 074016 (2007)
Compact Star as LabCompact Star as Lab Mass:Mass:
1.25M1.25M M M 2M 2M
Radius:Radius:RR10 km10 km
Period:Period:1.6 ms1.6 ms P P 12 s 12 s
Core temperature:Core temperature:10 keV10 keV T T 10 MeV 10 MeV
Surface magnetic field:Surface magnetic field:101088 G G B B 10 101414 G G
Overview about neutron stars: Schaffner-Bielich’s talkBlaschke’s talkXu’s talk
Freezeout temperature and chemical potential iFreezeout temperature and chemical potential in n HHeavy eavy IIon on CCollisionsollisions
Andronic, Braun-Munzinger, Stachel, 2006Braun-Munzinger,Magestro,Redlich,Stachel, 2001 Cold baryonic matter
Neutrino emission in supernova Neutrino emission in supernova explosionexplosion
Overview about SN explosion:
Schaffner-Bielich’s talk
Cooling of neutron starCooling of neutron star
Overview about neutron stars:
Schaffner-Bielich’s talkBlaschke’s talkXu’s talk
Neutrino emissivity Neutrino emissivity in dense quark matterin dense quark matter
Major neutrino processes in normal Major neutrino processes in normal statestate
Urca: fast, ~T6
Modified Urca: slow, ~T8
Bremstrahlung: slow, ~T8
What’s inside neutrino emissivityWhat’s inside neutrino emissivity
How to derive itHow to derive it
What’s inside What’s inside neutrino emissivityneutrino emissivity
Kadanoff-Baym equationKadanoff-Baym equation
Self-energySelf-energy
closed time path: solution to non−equilibrium problems
Neutrino emissivityNeutrino emissivity
W-boson self-energyW-boson self-energy
W-boson self-energyW-boson self-energy
Phase spacePhase space
Fermi liquid behavior open up phase space:Fermi liquid behavior open up phase space:Valid for normal and CSC phaseValid for normal and CSC phase
QW, Wang, Wu, PRD 74, 014021 (2006)
Neutrino emission in spin-1 Neutrino emission in spin-1 CSCCSC
Why spin-1 CSC
• Spin-0 phases φ ~ 100 MeV too large → too slow cooling• Normal quark matter → too fast cooling• Spin-1 phases φ ~ 5-100 KeV → fit data
Spin-1 phases
Simplify collisional integralSimplify collisional integral
Neutrino emission in spin-1 CSCNeutrino emission in spin-1 CSC
Energy emissivity for spin-1 CSC
Asymptotic form
At the limit
Schmitt, Shovkovy, QW, PRD 73, 034012(2006)
Neutrino emission in pion-condensed quark matterNeutrino emission in pion-condensed quark matter
X.G. Huang, QW, P.F. ZhuangPRD 76, 094008(2006)
Pion-condensed quark matter:
Son, Stephanov, PRL 82,592(2001)He, Jin, Zhuang, PRD 71, 116001(2005)…… ……
Anisotropy in neutrino emission in A-phaseAnisotropy in neutrino emission in A-phase
Schmitt, Shovkovy, QW, PRL 94, 211101(2005) [Erratum: PRL 95, 159902(2005)]
Bulk viscosity in strange Bulk viscosity in strange quark matter at high densityquark matter at high density
Why bulk viscosity?Why bulk viscosity?• r-mode: non-radial pulsation modes• unstable in rotating stars of perfect fluid → emission of gravitational waves
• fast rotating stars are observed: τ ~ 1 ms• damping effect from bulk/shear viscosity• deduce the upper limit for rotation frequency
Andersson, ‘98Friedman & Morsink, ‘98Andersson, Kokkotas, Schutz, ’99Andersson, Kokkotas, Stergioulas, ’99Andersson, Comer, ‘01Alford, Schmitt, Rajagopal, Schafer, ’07Dong, Su, QW, 07’
What is bulk viscosityWhat is bulk viscosity
Definition 1
Definition 2
Physically, bulk viscosity arises from re-equilibration processes. If some quantity goes out of equilibrium on compression, and re-equilibrates on a timescale , then pressure gets out of phase with volume and energy is consumed.
DissipationDissipationA phase lag between density and pressure perturbation
weak interaction
Nature of chemical reaction driven Nature of chemical reaction driven bulk viscositybulk viscosity
Weak processes in bulk viscosityWeak processes in bulk viscosity
• Re-equilibration via
• 2 time scales: external oscillation frequency ω microscopic relaxation time τ
• Volume oscillation → Chemical non-equilibrium
Weak processes in bulk viscosityWeak processes in bulk viscosity
/ ( 0)
d s
u e d
u e s
Chemical equilibrium
Electric charge neutralityEquation of state
3
2 2 322 2
( , ,0
1 1,
)
3
1
3
i i ei
i i i e e
i Bi
Q n n
n m n
n
i u d s
n
Constraints in strange quark matterConstraints in strange quark matter
Fluid oscillation
0 0 0
0 0 0
( , , , )
i tB B B B B
i tj j j j j
n n n n n e
n n n n n e
j u d s e
2B e
B s
u
d e
n n
n n
n
n n
R e EOSi Pn
Choose as independent variables
, ,B s en n n
Two additional equations are needed
-
( )
j kj k kj kk
k
J c c
T
0BB B
dnn
dt v
Baryon number conservation
jj j j
dnn J
dt v
Continuity equationContinuity equation
Continuity equation for particle-j
( / )
sB s
e
ie
i B
B
dXn J
dtdX
n J
X n
dt
n
People normally use
Implies
i B v v
Reaction rate
Sawyer, ’89Madsen, ’92Dai, Lu, ’96Alford, Schmitt, ’07Alford, Braby, Reddy, Schaefer, ’07Sa’d, Shovkovy, Rischke, ’07
Baryon number conservation& charge conservation
10
3
0
i Bi
i i ei
J J
Q J J
1
3B B i ii
e e i i ii
n n
n Q n
v v
v v
Baryon number conservationBaryon number conservation
0s
u d
v
v v
New solution respecting new constraints: an extreme case
new constraints
(2 )
( )
3
B u de B
e u d
Bu B
u d
n n n
n n n
n
n n
v v
v v
New solution
Conventional solution
H.Dong, N.Su, Q.Wang PRD 75, 074016 (2007)
Numerical resultsNumerical results
Change of internal energy during a period (heat and particle exchange in current problem are negligible)
Positivity of bulk viscosity in multi-component fluidsPositivity of bulk viscosity in multi-component fluids
Multi-component fluids as an open system locally, with particle exchange
Internal energy work done on system heat transfer particle exchange
period
the i-th cellChen, Dong, QW, in preparation
Positivity of bulk viscosity in multi-component fluidsPositivity of bulk viscosity in multi-component fluids
Chen, Dong, QW, in preparation
Positivity of bulk viscosity in multi-component fluidsPositivity of bulk viscosity in multi-component fluids
Chen, Dong, QW, in preparation
Israel, Stewart, 1976
reproduce coventional results for simple fluid
Summary and conclusionSummary and conclusion
• We have studied neutrino emissions in spin-1 CSC phases and pion condensed quark matter
• Anisotropy in neutrino emission is found in the A-phase of spin-1 CSC
• General constraints on fluid velocity divergences for particles in quark matter are derived from baryon number conservation and enforced electric charge neutrality. A new oscillation pattern in strange quark matter satisfying these conditions is found and its bulk viscosity is calculated
• Positivity of bulk viscosity is proved for multi-component fluid, and a new method for bulk viscosity based on entropy is proposed, which can reproduce coventional results for simple fluid