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Variational study of hyperon mixing in neutron stars and supernova - - PowerPoint PPT Presentation

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Variational study of hyperon mixing in neutron stars and supernova cores H. Togashi (RIKEN) Outline 1 Introduction 2 Nuclear EOS for non-uniform matter 3 Nuclear EOS with hyperons 4 Summary NSMAT 2016 @ Sendai, Japan, November

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Variational study of hyperon mixing in neutron stars and supernova cores

  • H. Togashi (RIKEN)

NSMAT 2016 @ Sendai, Japan, November 21th, 2016

1：Introduction 2：Nuclear EOS for non-uniform matter 3：Nuclear EOS with Λ hyperons 4：Summary

Outline

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SLIDE 2

SN-EOS list by M. Hempel

There are no supernova EOSs based on the microscopic many-body theory.

  • 1. Lattimer-Swesty EOS : The Skyrme-type interaction (NPA 535 (1991) 331)

(NPA 637 (1998) 435)

  • 2. Shen EOS : The Relativistic Mean Field Theory

Hyperon EOS

1: Introduction

Nuclear equation of state (EOS) for core-collapse supernova (SN) simulations

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Our Plan to Construct the SN-EOS

(NPA902 (2013) 53)

Nuclear EOS for Uniform Matter

  • Nuclear Potential : Argonne v18 (AV18) + Urbana IX (UIX)
  • Wave Function : Jastrow wave function
  • Method : Cluster variational method

Nuclear EOS for Non-uniform Matter

  • M. Takano (Waseda Univ.) , K. Nakazato (Kyushu Univ.),
  • Y. Takehara, S. Yamamuro, H. Suzuki (Tokyo Univ. of Science)

with the Thomas-Fermi calculation

High-density region Low-density region

Nuclear EOS with Λ Hyperons

  • M. Takano (Waseda Univ.) , E. Hiyama (RIKEN)

using an extension of the cluster variational method

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Bulk energy Gradient energy Coulomb energy

Free energy of a Wigner-Seitz cell f : Free energy density of uniform nuclear matter

We use the Thomas-Fermi method by Shen et al.

(PTP 100 (1998) 1013, APJS 197(2011) 20)

2: Nuclear EOS for Non-uniform Matter

Particle number density distributions

Protons and neutrons (i = p, n) Alpha-particles

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Phase Diagram of Hot Nuclear Matter

  • H. T. et al., submitted to Nucl. Phys. A
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Heavy Nuclei in Supernova Matter

  • H. T. et al., submitted to Nucl. Phys. A

More by K. Nakazato on Wed.

→ The density derivative coefficient of the symmetry energy L (Our EOS: L = 35 MeV Shen EOS: L = 111 MeV) Details are discussed by Oyamatsu & Iida in PRC 75 (2007) 015801

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Free Energy & Pressure

  • H. T. et al., submitted to Nucl. Phys. A
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Hamiltonian of hyperon matter

HN: Nuclear Hamiltonian (AV18+UIX)

(E. Hiyama et al., PRC 74 (2006) 054312, PRC 66 (2002) 024007)

Hyperon interactions are determined so as to reproduce the experimental data on single-and double-Λ hypernuclei.

3: Nuclear EOS with Λ Hyperons

The expectation value of H is calculated with the Jastrow wave function in the two-body cluster approximation

ΦF: Fermi-gas wave function

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Energy of Hyperon Matter

Baryon number density: nB = np + nn + nΛ ni : Particle number density xi = ni /nB : Particle fraction (i = p, n, Λ)

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(K. E. Schmidt et al., Phys. Lett. 87B(1979) 11) (A. Mukherjee et al., PRC 75(2007) 035802)

Free energy F is expressed by the average occupation probabilities.

We follow the prescription proposed by Schmidt and Pandharipande.

(i = p, n, Λ)

Free energy is minimized with respect to mi*

mi*: Effective mass of baryons εi(k): Single particle energy

Free energy of hyperonic nuclear matter

Free Energy of Hyperon Matter

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SLIDE 11

Mass-radius relations of neutron stars J1614-2230: Nature 467 (2010) 1081 J0348+0432: Science 340 (2013) 1233232 Shaded region is the observationally suggested region by Steiner et al. (Astrophys. J. 722 (2010) 33)

Application to Neutron Stars

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Fractions of Λ hyperons XΛ in supernova matter

Application to Supernova Cores

  • 3. Fixed electron fraction : Ye = 0, 0.3, 0.5
  • 2. β-stable matter with trapped neutrinos
  • 1. Isothermal matter (T = 10, 20, and 30 MeV)

We construct the EOS of supernova matter with the following conditions.

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We consider a simplified hyperon three-body repulsive force (TBF) for ΛNN, ΛΛ ΛΛN, and ΛΛΛ ΛΛΛ systems.

(Y. Yamamoto et al., PRC 90 (2014) 045805)

P r e l i m i n a r y

Shen EOS Variational

(H. T. et al., PRC 93 (2016) 035808)

Mass-radius relations of neutron stars XΛ in supernova matter

Hyperon Three-Body Force

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Summary

  • 1. New nuclear EOS for SN simulations is constructed

with realistic nuclear forces (AV18 + UIX).

Our complete SN-EOS table will be available soon!

  • The effect of Λ hyperons on supernova matter becomes larger

at higher temperatures and lower proton fractions.

  • 2. Our SN-EOS table is extended to consider

Λ hyperon mixing at zero and finite temperatures.

  • EOS of uniform nuclear matter is constructed

with the cluster variational method.

  • EOS of non-uniform nuclear matter is constructed

with the Thomas-Fermi calculation.