Neutrino process es in dense quark matter: e missivity and bulk viscosity

1. Neutrino processes in dense quarkmatter:emissivity and bulk viscosity • Introduction • Neutrino emissivity in dense quark matter • Bulk viscosity in strange quark matter • Discussions and outlooks Qun Wang University of Science and Technology of China • 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) 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 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, 014021 (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～5-100 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, 034012(2006) Asymptotic form At the limit

15. Neutrino emission in pion-condensed quark matter Pion-condensed quark matter: Son, Stephanov, PRL 82,592(2001) He, Jin, Zhuang, PRD 71, 116001(2005) …… …… X.G. Huang, QW, P.F. Zhuang PRD 76, 094008(2006)

16. Anisotropy in neutrino emission in A-phase Schmitt, Shovkovy, QW, PRL 94, 211101(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. Dissipation 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 lagbetween density and pressure perturbation

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 Baryon number conservation & charge conservation 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, 074016 (2007)

27. Positivity of bulk viscosity in multi-component fluids Multi-component fluids as an open system locally, with particle exchange Internal energywork 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