Structure and propermes of nuclear ma3er in compact stars

Transcription

1 Structure and propermes of nuclear ma3er in compact stars Toshiki Maruyama (JAEA) Nobutoshi Yasutake (Chiba Inst. of Tech.) Minoru Okamoto (Univ. of Tsukuba & JAEA) Toshitaka Tatsumi (Kyoto Univ.) Low- density nuclear ma3er in the crust of neutron stars or core of supernovae High- density ma3er in the core of neutron stars

2 Low- density nuclear ma3er Inhomogeneous structures. There are two ways of understanding inhomogeneous ma3er. 1. From inhomogeneous to uniform Compression of low- density ma3er. crystal of atoms in degenerate electrons. crystal of nuclei in degenerate neutrons. uniform nuclear ma3er. 2. From uniform to inhomogeneous Instability of uniform ma3er below the saturamon density. phase transimon & mixed phase (clustering).

3 1. From inhomogeneous to uniform Neutron- rich nuclei in electron sea compression Neutron- rich nuclei in neutron sea uniform

4 2. From uniform to inhomogeneous 4

5 RMF + Thomas- Fermi model

6 Choice of parameters ProperMes of nuclei Ma3er propermes Bulk properties of nuclei, such as binding energies, proton fractions, and density profiles, are well reproduced.

7 Pressure of uniform nuclear ma3er Total pressure is positive. Monotonically increases with density and temperature.

8 EOS of mixed phase Single component congruent (e.g. water) Maxwell construction satisfies the Gibbs cond. T I =T II, P I =P II, µ I =µ II. Many components non-congruent (e.g. water+ethanol) Gibbs cond.t I =T II, P ii =P i II, µ ii =µ i II. No Maxwell construction! Many charged components (nuclear matter) Gibbs cond. T I =T II, µ ii =µ i II. No Maxwell construction! No constant pressure!

9 EOS of mixed phase What is necessary? SaMsfying the Gibbs condimons, we have to look for inhomogeneous density distribumon of nucleons and electrons, which minimize the free- energy density.

10 Numerical calculamon of mixed- phase structure WS-cell 10

11 Nuclear pasta structures Baym, Bethe, Pethick, 1971 Nuclei inside- out uniform Ravenhall et al 1983 & Hashimoto et al 1984 Concept of pasta structures. Minimizing free- energy of the inhomogeneous structure, i.e., achieving the balance between surface tension and the Coulomb repulsion nuclear pasta uniform Figure from K. Oyamatsu, NPA561, 431 (1993)

12 Pasta structures in ma3er (case of fixed Y p ) Density profiles in WS cells T=0 Y p =0.5 T=0 Y p =0.1

13 Symmetric matter Y p =0.5 Asymmetric matter Y p =0.3

14 More realismc case for supernova core: Neutrino- trapped ma3er

15 Neutrino degenerate and inhomogeneous ma3er. Preceding studies: Ogasawara & Sato PTP68(1982)222 EffecMve interacmon + Thomas- Fermi, T = 0, Y l = fixed Ogasawara & Sato PTP70(1983)1569 EffecMve interacmon + Thomas- Fermi, T > 0, Y l = fixed Enhancement of inhomogeneous structures (droplet & bubble) Watanabe, Iida, Sato NPA687(2001)512 EffecMve interacmon + flat density, T = 0, Y l = fixed Enhancement of pasta phases. Our present study: RelaMvisMc mean field + Thomas- Fermi, T > 0, Y l = fixed Fully consistent density distribumon.

16 EquaMons to be solved

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19 EOS (pressure) of nuclear ma3er at finite temperature with a fixed proton fracmon Y p =0.3 (below) and a fixed lepton fracmon Y l =0.3 (right panels). The appearance of inhomogeneous structure sonens the EOS for both cases. They show similar dependence on the density. 4 MeV T=0 8 MeV T=5 MeV 3 MeV 0.1 MeV

20 Fully 3 dimensional (3D) calculamon Use of the Wigner- Seitz cell 3D 1D 2D LimitaMon of emerging structures. Complex structures were missing dumbbell Gyroid Crystalline structures could not be discussed. network doublediamond droplet bubble bcc la<ce rod tube Honeycomb

21 Results of our 3D RMF calculamons proton Y p = Z/A = 0.5 electron Droplet [fcc] ρ B = fm -3 Rod [honeycomb] fm -3 Slab 0.05 fm -3 Tube [honeyc omb] 0.08 fm -3 Bubble [fcc] fm -3

22 Y p = Z/A = 0.5 EOS has a similar behavior to that of the convenmonal studies. Novelty: fcc laoce of droplets can be the ground state at some density. Not the Coulomb interacmon among point parmcles but the change of the droplet size is relevant.

23 proton neutron droplet rod [fcc] [simple] -3 ρb = fm fm-3 slab 0.05 fm-3 tube [simple] fm-3 bubble [fcc] fm-3 proton neutron droplet [fcc] ρb=0.020 fm-3 rod [simple] 0.040fm-3 slab 0.05 fm-3 tube bubble [simple] [fcc] fm fm-3

24 Some complex metastable states in our 3D RMF calc. Mixture of Droplet and Rod Mixture of Slab and Tube Dumbbell Network

25 Structure of compact stars TOV equamon Pressure (EOS the input) total mass and radius. Mass radius relagon and the maximum mass is determined by the EOS of ma3er. 25

26 Sonening of EOS by hyperon nucleon }hyperon included Improve the maximum mass by introducing transimon into quark ma3er (?) Schulze et al, PRC73 (2006) [Maieron et al, PRD70 (2004) ]. However, mixed phase may sonen the EOS. A bulk calculamon suggests wide region of mixed phase. [Glendenning, PRD46,1274]. 26

27 Hadron- Quark mixed- phase structure and EOS (T=0) Assume regularity in structure: divide whole space into equivalent neutral cells with a geometrical symmetry (3D: sphere, 2D : cylinder, 1D: plate). Wigner- Seitz approx. Give a sharp boundary between H and Q phases and a geometry (Unif/Dropl/...). Solve the field equagons numerically and get density profiles. OpMmize the cell size and H- Q boundary posimon (choose the energy- minimum). Choose energy- min geometry (Unif H, droplet, rod, slab, tube, bubble, Unif Q). Hadron phase Brueckner Hartree Fock model Quark phase MIT bag model 27

28 EOS of ma3er Full calculamon is close to the Maxwell construcmon (local charge neutral). Far from the bulk Gibbs calculamon (neglects the surface and Coulomb).

29 Mass- radius relamon of a cold neutron star τ surf =40 29

30 Summary RMF + Thomas Fermi calculation for low-density nuclear matter Pasta structure appears and affects on the EOS. For neutrino-trapped matter, pasta structures are enhanced by neutrinos The EOS depends largely on the structure and the existence of neutrinos. Fully 3D calculation Okamoto et al is developing. Hadron-quark mixed phase is important for structure and mass of compact stars. We have developed a method to calculate EOS of mixed phase. But each EOS should be improved to sustain neutron stars Thank you for your a3enmon! END

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32 Finite- size effects Strong surface tension and weak Coulomb large R extreme case no minimum. (pasta unstable) [Voskresensky et al, PLB541(2002)93; NPA723(2003)291; amorphous PRD(2012)] Dependence of E/A on R. 32

33 TOV equamon Structure of compact stars Pressure (input of TOV eq.) total mass and radius. Bulk Gbbs Full calc τ surf =40 MeV/fm 2 Maxwell const. 33

34 Hadron- Quark mixed- phase structure and EOS (T=0) Assume regularity in structure: divide whole space into equivalent and neutral cells with a geometrical symmetry (3D: sphere, 2D : cylinder, 1D: plate). Wigner- Seitz cell approx. WS-cell Divide a cell into hadron phase and quark phases. Give a geometry (Unif/Dropl/Rod/...) and a baryon density ρ B. Solve the field equamons numerically. OpMmize the cell size and H- Q boundary posimon (choose the energy- minimum). Choose an energy- minimum geometry among 7 cases (Unif H, droplet, rod, slab, tube, bubble, Unif Q). 34

35 2-3 ρ 0 EOS < 1.4M sol >1.5 M sol } (?) [Maieron et al, PRD70 (2004) etc]. Schulze et al, PRC73 (2006) Gibbs [Glendenning, PRD46,1274]. 35

36 Beta- equilibrium case T=0 Beta equil. Only droplet structure appears. The change of EOS due to the non-uniform structure is small.

37 Instability of uniform ma3er at finite T mechanical instability formation of pasta phase coexistence Due to the surface tension and the Coulomb interacmon, the region of inhomogeneous ma3er is limited ( pasta < coexistence ). But Mechanical instability is not crucial for pasta formamon!

38 Y p = Z/A = 0.5 EOS has a similar behavior to that of the convenmonal studies. Novelty: fcc laoce of droplets can be the ground state at some density. Not the Coulomb interacmon among point parmcles but the change of the droplet size is relevant.

39 Kaonic pasta structure

40 ( Gibbs ) ρ th =0.34 fm 3 ρ th =1.15 fm 3 Neutral matter Charged matter 40

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