Nuclear Matter EOS for Supernova Simulations

1. Nuclear Matter EOS for Supernova Simulations Chikako ISHIZUKA(Hokkaido Univ.) Akira OHNISHI(Hokkaido Univ.) Kohsuke SUMIYOSHI(Numazu CT) Shoichi YAMADA(Waseda Univ.) As we make physics inputs more realistic, why does SNe in numerical simulation become difficult? Aim : To attack this problem from nuclear hadron physics side.

2. Successful hydro. simulation of core collapse SNe  Long standing problem Pure hydrodynamics (Success!) 1-dim. calc. with dynamical neutrino transport (Failure!) Various hydrodynamical mechanisms (In progress!) (e.g.)2-dim. effects – convection, rotation, magnetic field What is a clue to solve this problem? Nuclear physics inputs (e.g.)EOS, neutrino production rate, neutrino transport Let’s examine whether these inputs are proper, or not!

3. Nuclear matter properties related to supernova simulations Stable nuclei Unstable nuclei Hyperon matter Meson condensation Which information is necessary for SN simulations? Nuclear Pasta Updated Exp. Data!

4. Why Are Hyperons Important in Dense Matter ? EF ML-Mn n L n Nucleon has large Fermi momentum and small mass. Hyperon has small Fermi momentum and large mass. Negative charged baryon and neutral baryon is favored under high density circumstances.

5. Possible Role of Hyperons in Supernova Hyperons would exist in Neutron Star Core - Should appear during the cooling stage Density and Temperature are High in the Collapse and Bounce Stage (e.g. ~2r0 in a calculation of rotational core with strong magnetic field (Kotake et al.)) - May appear even in the Early (Bounce) Stage Hyperons Soften EOS - May Increase the Explosion Energy Let's Check it Out !

6. Method : Relativistic Mean Field + Local-Density Approx. • Shen, Toki, Oyamatsu, & Sumiyoshi, 1998, NPA, PTP • Based on relativistic Bruckner Hartree-Fock • Checked by exp. data of unstable nuclei • Nuclear structure: mass, charge radius, neutron skin, …

7. Extension from SU(2) to SU(3) Lagrangian (Shaffner et al.1996) How to decide YN interaction • Old conjecture RMF using Lagrangian derived from SCL of lattice QCD (Kawamoto et al., Tsubakihara & Ohnishi) DWIA with Optimal momentum approximation (Maekawa & Ohnishi)

8. Pairng energy better fit (Tubakihara 2004) Analysis of single L hyper nuclei spectroscopy UL shallower than -30MeV  favorable Lagrangian derived from SCL of lattice QCD • Less parameter model than TM1 • More reliable analysis of hyper nuclear data

9. DWIA with optimal momentum approximation K Optimal momentum π :Pπ θ q On shell equation Y N :PN Ref. Gurvitz “Optimal elementary cross section”

10. 28Si(π-,K+),Σ-quasi-free peak (KEK E438) Im. Ｗ０＝-50,-30,-10 (MeV) Maekawa 2004 +30MeV 0MeV Best fit! Attractive S  Bad… +10MeV -30MeV

11. Σ Potential Effects in Neutron Star (RMF: Sahu, Ohnishi Nucl. Phys. A691 (2001), 439.) Repulsive Potential for∑ → ∑ does not appear Attractive Potential for∑ → ∑ appears at aroundr=2r0 Max. Mass and Compositions are SENSITIVE to Interaction !! e.g. Nishizaki-Takatsuka-Yamamoto, PTP 108 (02) 703. • UL=-30MeV  UL=-28MeV • US=-30MeV  US=+30~+90MeV • UX=-30MeV  UX=-15MeV

12. Neutron star matter Thermal pions: Interaction with nucleon NO! EOS keep the stiffness 1.44 Max. neutron star mass 1.44Msolar  OK!

13. Hyperon, pion  Softening EOS at high densities (Pauli principle, pion condensation) Muon  Softening EOS at low densities Neutrino Making EOS Stiff at low densities 1dim. Spherical hydro. calc. (Sumiyoshi 2004) adiabatic expansion (without neutrino transport) Initial model = WW95 Small difference of EOS change the result!

14. SN explosion energy gain due to EOSs Explosion energy Hyperons, pions increase Eexp by (0.1-0.5), respectively Muon suppress the explosion (In the present hydro. model, rmax~1.3r0. In more realistic model, rmax~2r0  More energy gain due to EOS are expected!

15. Summery of this talk • Relativistic EOS table containing nuclear matter properties • from low densities (various nuclei in bubble phase) • to high densities (hyperon matter or meson condensation) • within an ambiguity of YN interaction at present. • -Hyperon-nucleon interactions suggested by • DWIA with optical momentum approx. analysis • and RMF based on strong coupling limit of lattice QCD. • Supernova phenomena based on the consistent picture • with the recent progress in strangeness nuclear physics. • Percent order explosion energy gain is obtained • due to softening of EOS by hyperons and pions • in 1-dim. spherical core collapse and bounce simulations. • Hyperon contribution can not be neglected in more realistic supernova simulations including black hole formation.

16. Current study and interest • Pion contribution can not be included in • a usual framework of RMF • - Correlation between nucleons and pion • in a new framework of RMF+pi •  may make EOS softer than thermal pions do. • Improvement of low density part is needed! • Statistical feature becomes strong • under finite T and low density conditions. • -Thomas-Fermi approx. works well near T~0MeV. •  NSE+RMF EOS table may be clued to successful SNe! • - closely related with electron capture….