Nuclear equation of state with realistic nuclear forces

Transcription

1 Nuclear equation of state with realistic nuclear forces Hajime Togashi (RIKEN) Collaborators: M. Takano, K. Nakazato, Y. Takehara, S. Yamamuro, K. Sumiyoshi, H. Suzuki, E. Hiyama 1:Introduction Outline 2:Supernova EOS with realistic nuclear forces 3:Application to astrophysical objects 4:Hyperon mixing in dense matter New perspectives on Neutron Star ECT*, Oct. 11th, 2017

2 1. Introduction Nuclear Equation of State (EOS) : F/N = F(n B, Y p, T)/N Pure neutron matter (Proton fraction Y p = 0) E sym + E 0 L n 0 E 0 K 0 Symmetric nuclear matter (Y p =1/2) Phenomenological model Skyrme-Hartree-Fock Relativistic mean field (RMF) Density functional theory Many-body theory with bare forces Brueckner-Hartree-Fock Variational method Quantum Monte Carlo 2/22

3 Nuclear EOS and Core-Collapse Supernovae Nuclear EOS at finite temperature is one of the crucial ingredients for the numerical simulations of Core-Collapse Supernovae. Scenario of the Core-Collapse Supernovae (SNe) K. NUFRA /22

4 Nuclear EOS and Core-Collapse Supernovae Nuclear EOS at finite temperature is one of the crucial ingredients for the numerical simulations of Core-Collapse Supernovae. Scenario of the Core-Collapse Supernovae (SNe) - The stiffness of high-density nuclear matter - Species of nuclides in hot matter Nuclear EOS K. NUFRA /22

5 Nuclear EOS for SN simulations - SN-EOS should provide thermodynamic quantities in the wide ranges. Temperature T : 0 T 400 MeV Density ρ : ρ B g/cm 3 Proton fraction Y p : 0 Y p SN matter contains uniform and non-uniform phases. Uniform Non-uniform Phase diagram of nuclear matter [based on HT et al., NPA 961 (2017) 78] 4/22

6 Current status of SN-EOS 5/22 Skyrme-type effective interaction Relativistic Mean Field Theory (M. Oertel et al., Rev. Mod. Phys. 89 (2017) ) There is no SN-EOSs based on the microscopic many-body theory. We aim to construct a new SN-EOS with the variational method starting from bare nuclear forces.

7 EOS with Variational Method 6/22 Fermi Hypernetted Chain (FHNC) method Uniform matter at zero temperature: APR (A. Akmal, V. R. Pandharipande, D. G. Ravenhall, PRC 58 (1998) 1804) Potential: AV18+UIX Wave function: Jastrow wave function Uniform matter at finite temperature: A. Mukherjee, PRC 79(2009) Extension of the APR EOS to finite temperature with the variational method proposed by Schmidt and Pandharipande. (Phys. Lett. 87B(1979) 11, PRC 75(2007) ) Those calculations are performed only for Symmetric Nuclear Matter and Pure Neutron Matter.

8 7/22 Our procedure to construct the SN-EOS 1: Cluster variational method with AV18 + UIX Uniform Non-uniform 2: Tuning of the parameters with the Thomas-Fermi calculation for atomic nuclei 3: Thomas-Fermi calculation for non-uniform matter

9 2. Supernova EOS with realistic nuclear forces 8/22 Nuclear Hamiltonian Argonne v18 (AV18) two-body potential Urbana IX (UIX) three-body potential AV18 potential: (PRC 51 (1995) 38) UIX potential: (PRL 74 (1995) 4396)

10 Expectation value of the Hamiltonian 9/22 Jastrow wave function Φ F : The Fermi-gas wave function Correlation function: Cluster-expansion E 2 /N is the expectation value of H 2 in the two-body cluster approximation. Modified expectation value of H 3 with Φ F Correction term Total energy per nucleon E/N = E 2 /N + E 3 /N

11 Nuclear EOS for uniform matter Free energy at finite temperature F/N is calculated with the variational method proposed by Schmidt and Pandharipande. (Phys. Lett. 87B(1979) 11, PRC 75(2007) ) n 0 [fm -3 ] 0.16 E 0 [MeV] K [MeV] E sym [MeV] Our EOS : HT and M. Takano, NPA 902 (2013) 53 APR : A. Akmal, V. R. Pandharipande, D. G. Ravenhall, PRC 58 (1998) 1804 FHNC : A. Mukherjee, PRC 79(2009) /22

12 11/22 Nuclear EOS for non-uniform matter Free energy of a Wigner-Seitz cell Bulk energy We use the Thomas-Fermi method by Shen et al. (PTP 100 (1998) 1013, APJS 197(2011) 20) Gradient energy Coulomb energy Free energy density of uniform matter: f = f N + f α Particle number density distributions Protons and neutrons (i = p, n) Alpha-particles

13 Thomas-Fermi calculation for isolated atomic nuclei M = M TF -M exp M TF : Mass by the Thomas-Fermi calculation M exp : Experimental data (G. Audi et al., NPA 729 (2003) 337) RMS deviation (for 2226 nuclei) 2.99 MeV (Variational EOS) 42.9 MeV (Shen EOS) 12/22

14 Thomas-Fermi calculation for non-uniform matter Due to the smaller value of L K. Oyamatsu & K. Iida PRC 75 (2007) Our EOS: L = 35 MeV HT et al., NPA 961 (2017) 78 Shen EOS: L = 111 MeV 13/22

15 Thermodynamic Quantities Free energy per nucleon Pressure Entropy HT et al., NPA 961 (2017) 78 14/22

16 Home Page of Variational EOS table 15/22 (HT et al., NPA961 (2017) 78)

17 3. Application to astrophysical objects Cold Neutron Star: charge neutral, β-stable mixture of n, p, e -, µ - at T = 0 MeV Radius of a 1.4 M neutron star: R 1.4 = km (Variational) R 1.4 = km (SFHo) Figure by M. Hempel J : Science 340 (2013) J : Nature 467 (2010) 1081 Shaded region is the observationally suggested region by Steiner et al. (Astrophys. J. 722 (2010) 33) 16/22

18 Inner Structure of Neutron Stars 17/ fm -3 (Variational) fm -3 (BPS) BPS: G. Baym, C. Pethick, P. Sutherland, APJ 170 (1971) 299 NV: J. W. Negele and D. Vautherin, NPA 207 (1973) 298 Neutron Drip

19 18/22 Application to Core-Collapse Supernovae 1D neutrino-radiation hydrodynamics simulations Progenitor: Woosley Weaver 1995, 15M Astrophys. J. Suppl. 101 (1995) 181 SN simulation numerical code: K. Sumiyoshi, et al., NPA 730 (2004) 227 Radial trajectories of mass elements

20 19/22 4. Hyperon mixing in dense matter Hamiltonian of Λ hyperon matter H N : Nuclear Hamiltonian (AV18+UIX) ΛN V ij : Λ-Nucleon (N) potential (E. Hiyama et al., PRC 74 (2006) ) - Constructed so as to reproduce the experimental binding energies of light Λ hypernuclei with the Gaussian expansion method. ΛΛ V ij : Λ-Λ potential v ij TBF Two-Body Central Potentials (E. Hiyama et al., PRC 66 (2002) ) - the experimental double-λ binding energy from 6 He (NAGARA event) ΛΛ : Effective potential based on Three-Baryon Force (TBF) for ΛNN, ΛΛN, ΛΛΛ systems (Y. Yamamoto et al., PRC 90 (2014) , HT et al., PRC 93 (2016) )

21 Neutron star matter with Λ hyperon Variational Shen EOS Mass-radius relations of neutron stars Particle fractions in neutron star matter 20/22

22 Supernova matter with Λ hyperon 21/22 Supernova matter - Charge neutral and Isentropic matter (The entropy per baryon S ~ 1-2) - Neutrino-free or neutrino-trapped (Y l = Y e + Y νe = 0.3) β-stable matter X Λ in neutrino-trapped supernova matter (Y p ~ 0.25) X Λ in neutrino-free supernova matter (Y p ~ 0.1)

23 Summary Nuclear EOS for SN simulations is constructed with realistic nuclear forces (AV18 + UIX). Our SN-EOS is available at CompOSE online service also provides our EOS table. Variational EOS table is being extended to consider Λ hyperon mixing in nuclear matter. Does the three-baryon force play key role to understand the inner structure of compact stars? Need further discussions (Hypernuclei, Quark phase, Lattice QCD ) 22/22