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