1. Qun Wang University of Science and Technology of China
Neutrino processes in dense quark matter: emissivity and bulk viscosity
Qun Wang
University of Science and Technology of China
Introduction
Neutrino emissivity in dense quark matter
Bulk viscosity in strange quark matter
Discussions and outlooks
A. Schmitt, I. Shovkovy, QW, PRL 94, (2005) [Erratum: PRL 95, (2005)]
A. Schmitt, I. Shovkovy, QW, PRD 73, (2006)
QW, Z. Wang, J. Wu, PRD 74, (2006)
X. Huang, QW, P. Zhuang, PRD 76, (2007)
H. Dong, N. Su, QW, 75, (2007)
Strange Quark Matter, Beijing, Oct 6-10, 2008

2. Compact Star as Lab Mass: 1.25M  M  2M Radius: R10 km Period:
1.6 ms  P  12 s
Core temperature:
10 keV  T  10 MeV
Surface magnetic field:
108 G  B  1014 G
Overview about neutron stars:
Schaffner-Bielich’s talk
Blaschke’s talk
Xu’s talk

3. Freezeout temperature and chemical potential in Heavy Ion Collisions
Andronic, Braun-Munzinger, Stachel, 2006
Braun-Munzinger,Magestro,Redlich,Stachel, 2001
Cold baryonic matter

4. Neutrino emission in supernova explosion
Overview about
SN explosion:
Schaffner-Bielich’s
talk

5. Cooling of neutron star
Overview about
neutron stars:
Schaffner-Bielich’s talk
Blaschke’s talk
Xu’s talk

6. Neutrino emissivity
in dense quark matter

7. Major neutrino processes in normal state
Urca: fast, ~T6
Bremstrahlung:
slow, ~T8
Modified Urca: slow, ~T8

8. What’s inside neutrino emissivity
How to derive it

9. Kadanoff-Baym equation
closed time path: solution
to non−equilibrium problems
Self-energy

10. Neutrino emissivity
W-boson self-energy
W-boson self-energy

11. Phase space Fermi liquid behavior open up phase space:
Valid for normal and CSC phase
QW, Wang, Wu, PRD 74, (2006)

12. Neutrino emission in spin-1 CSC
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 ～ KeV → fit data
Spin-1 phases

13. Simplify collisional integral

14. Neutrino emission in spin-1 CSC
Energy emissivity for spin-1 CSC
Schmitt, Shovkovy, QW,
PRD 73, (2006)
Asymptotic form
At the limit

15. Neutrino emission in pion-condensed quark matter
Son, Stephanov, PRL 82,592(2001)
He, Jin, Zhuang, PRD 71, (2005)
…… ……
X.G. Huang, QW, P.F. Zhuang
PRD 76, (2006)

16. Anisotropy in neutrino emission in A-phase
Schmitt, Shovkovy, QW,
PRL 94, (2005)
[Erratum: PRL 95,
159902(2005)]

17. Bulk viscosity in strange quark matter at high density

18. 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, ‘98
Friedman & Morsink, ‘98
Andersson, Kokkotas, Schutz, ’99
Andersson, Kokkotas, Stergioulas, ’99
Andersson, Comer, ‘01
Alford, Schmitt, Rajagopal,
Schafer, ’07
Dong, Su, QW, 07’

19. What is bulk viscosity
Definition 1
Definition 2

20. Nature of chemical reaction driven bulk viscosity
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.
weak interaction
A phase lag between density and pressure perturbation
Dissipation

21. Weak processes in bulk viscosity
Volume oscillation → Chemical non-equilibrium
Re-equilibration via
2 time scales:
external oscillation frequency ω
microscopic relaxation time τ

22. Weak processes in bulk viscosity

23. Constraints in strange quark matter
Electric charge neutrality
Equation of state
Fluid oscillation
Chemical equilibrium
Choose
as independent variables
Two additional equations are needed

24. Continuity equation Baryon number conservation People normally use
Continuity equation for particle-j
Implies
Sawyer, ’89
Madsen, ’92
Dai, Lu, ’96
Alford, Schmitt, ’07
Alford, Braby, Reddy, Schaefer, ’07
Sa’d, Shovkovy, Rischke, ’07
Reaction rate

25. Baryon number conservation
& charge
new constraints
New solution respecting new constraints: an extreme case

26. Numerical results New solution Conventional solution
H.Dong, N.Su, Q.Wang PRD 75, (2007)

27. Positivity 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
Change of internal energy during a period
(heat and particle exchange in current problem are negligible)
period
the i-th cell
Chen, Dong, QW, in preparation

28. Positivity of bulk viscosity in multi-component fluids
Chen, Dong, QW, in preparation

29. Positivity of bulk viscosity in multi-component fluids
Israel, Stewart, 1976
reproduce coventional
results for simple fluid
Chen, Dong, QW, in preparation

30. Summary 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