1 11/20/ /10/2014 Jinniu Hu Stellar neutrino emission at finite temperature in relativistic mean field theory Jinniu Hu School of Physics, Nankai University Quarks and Compact Stars 2014, October, 20-22, 2014, Beijing, China

20/10/2014 Jinniu Hu Outline  Introduction  Theoretical framework  Numerical results  Summary and perspective

20/10/2014 Jinniu Hu The origin of neutron star

20/10/2014 Jinniu Hu Neutron star cooling Direct Urca process Modified Urca process NN bremsstrahlung process D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, P. Haensel, Phys. Rep. 354(2001)1

20/10/2014 Jinniu Hu The research status: from the point of neutron star matter  Fermi gas model ： J. M. Lattimer, C. J. Pethick, M. Prakash, and P. Haensel, Phys. Rev. Lett. 66(1991)2701  Relativistic mean field theory (σ,ω,ρ) ： L. B. Leinson, and A. Pérez, Phys. Lett. B 518(2001)15 L. B. Leinson, Nucl. Phys. A 707(2002)543 G. Shen, J. Meng and, G. C. Hillhouse G. C. HEP&NP, Supp. 28(2004)99 W. B. Ding, G. Z. Liu, M. F. Zhu, Z. Yu, and E. G. Zhao, A&A 506 (2009) L13  Relativistic mean field theory (σ,ω,ρ,δ) ： Y. Xu, G. Z. Liu, C. Z. Liu, C. B. Fan, H. Y. Wang, M. F. Zhu and, E. G. Zhao, Chin. Phys. Lett. 30(2013)  Brueckner-Hartree-Fock theory ： M. Baldo, G. F. Burgio, H.-J. Schulze, and G. Taranto, Phys. Rev. C 89(2014)048801

20/10/2014 Jinniu Hu Proton-neutron effective mass splitting in relativistic mean field (RMF) theory ✓ Scalar isovector meson in Hartree approximation ✓ Relativistic Hartree-Fock approximation X. Roca-Maza, X. Vinas, M. Centelles, P. Ring, and P. Schuck, Phys. Rev. C 84(2011) σ,ω,ρ,π W. L. Long, N. Van Giai, J. Meng, Phys. Lett. B 604(2006) 150

20/10/2014 Jinniu Hu Outline  Introduction  Theoretical framework  Numerical results  Summary and perspective

20/10/2014 Jinniu Hu Direct Urca process ✓ Neutrino emissivity Q (D) ✓ The matrix element of the neutron beta decay G F, C, C V, C M, C A are the coupling constants in weak interaction and F q is the form factor D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, P. Haensel, Phys. Rep. 354(2001)1

20/10/2014 Jinniu Hu Direct Urca process ✓ Fermi–Dirac distribution ✓ The Neutrino emissivity in non-relativistic limit where, and

20/10/2014 Jinniu Hu The neutrino emissivity in other processes The modified Urca (MU) processes The NN bremsstrahlung (BNN) processes

20/10/2014 Jinniu Hu ✓ Lagrangian RMF theory in finite temperature ✓ Effective nucleon mass in RMF theory ✓ Pressure density ✓ Energy density ✓ Fermion and antifermion distribution functions B. Liu, V. Greco, and V. Baran Phys. Rev. C 65(2002)045201

20/10/2014 Jinniu Hu Outline  Introduction  Theoretical framework  Numerical results  Summary and perspective

20/10/2014 Jinniu Hu The properties of nuclear matter Nuclear matter Yp: proton fraction npe neutron star matter T=0 NLδ : B. Liu, V. Greco, and V. Baran Phys. Rev. C 65(2002) DD-MEδ : X. Roca-Maza, X. Vinas, M. Centelles, P. Ring, and P. Schuck, Phys. Rev. C 84(2011) ρ 0 (fm -3 )E/A (MeV)a asym (MeV)K (MeV)M * /M NLδ0.160− DD-MEδ0.152−

20/10/2014 Jinniu Hu The critical density of Direct Urca process at T=0

20/10/2014 Jinniu Hu Reduction factors M ij at finite temperature NLδ

20/10/2014 Jinniu Hu DD-MEδ Reduction factors M ij at finite temperature

20/10/2014 Jinniu Hu Proton fractions at npe neutron matter L. W. Chen, F. S. Zhang, Z. H. Lu, W. F. Li, Z. Y. Zhu, and H. R. Ma, Jour. Phys. G 27 (2001)1799 A. Li, X. R. Zhou, G. F. Burgio, and H. –J Schulze, Phys. Rev. C 81(2010)025806

20/10/2014 Jinniu Hu Reduction factors: NLδ VS DD-Meδ T=0

20/10/2014 Jinniu Hu Reduction factors: δ meson effect DD-ME2: G. A. Lalazissis, T. Niksi´, D. Vretenar, and P. Ring, Phys. Rev.C 71 (2005) DD-MEδ: X. Roca-Maza, X. Vinas, M. Centelles, P. Ring, and P. Schuck, Phys. Rev. C 84(2011) M 11 M 31 M 13 M 22 M 40 M 04

20/10/2014 Jinniu Hu The effective proton and neutron masses: DD-ME2 VS DD-MEδ npe NM

20/10/2014 Jinniu Hu Outline  Introduction  Theoretical framework  Numerical results  Summary and perspective

20/10/2014 Jinniu Hu Summary 1. We study the neutrino emissivity at finite temperature in relativistic mean field theory. 2. The neutrino emissivity in non-relativistic limit is mainly determined by the nucleon effective masses. 3. The neutrino emissivity becomes larger at high temperature and suppressed at large density. 4. The isovector meson is very important in neutrino emission, which generates the proton-neutron mass splitting. Perspectives 1. The relativistic beta decay matrix elements 2. The effective mass splitting from Fock term 3. The neutrino emissivity in strangeness freedom ……

20/10/2014 Jinniu Hu Thank you very much for your attention !