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, 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

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

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

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

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

Neutrino emissivity in dense quark matter

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

What’s inside neutrino emissivity How to derive it

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

Neutrino emissivity W-boson self-energy W-boson self-energy

Phase space Fermi liquid behavior open up phase space: Valid for normal and CSC phase QW, Wang, Wu, PRD 74, 014021 (2006)

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

Simplify collisional integral

Neutrino emission in spin-1 CSC Energy emissivity for spin-1 CSC Schmitt, Shovkovy, QW, PRD 73, 034012(2006) Asymptotic form At the limit

Neutrino emission in 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)

Anisotropy in neutrino emission in A-phase Schmitt, Shovkovy, QW, PRL 94, 211101(2005) [Erratum: PRL 95, 159902(2005)]

Bulk viscosity in strange quark matter at high density

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’

What is bulk viscosity Definition 1 Definition 2

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

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

Weak processes in bulk viscosity

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

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

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

Numerical results New solution Conventional solution H.Dong, N.Su, Q.Wang PRD 75, 074016 (2007)

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

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

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

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