中性子星が問いかける核物理の新たな問題

New nuclear-physics-problems addressed by neutron stars

2009.12.14 （ RIKEN ）

T. Takatsuka (Iwate Univ.)

Based on the works with S. Nishizaki (Iwate Univ.) Y. Yamamoto (Tsuru Univ.) R. Tamagaki (Prof. Emeritus of Kyoto Univ.)

In this talk, I discuss following problems:

□ E_{sym} is gathering much attention

(A) Density dependence of E_{sym} and possible consequences on neutron stars.

□ Hyperon, surely participate in neutron star (NS) cores. Then, what happens?

(B) Dramatic softening of NS equation of state ( ← Mass observation)

(C) Dramatically accelerated ν-emission due to “Hyperon direct URCA” processes, namely, “Hyperon Cooling” ( ← Surface temperature observation)

(EOS)

Topic (A)

（ A) 　 Nuclear 　 Symmetry Energy (E_{sym})

□ Linking the nuclear physics and astrophysics

① Large E_{sym} ⇔ 　 high p fraction in NSs (*) small E_{sym} ⇔ 　 low p fraction in NSs (*) acceleration of neutron star (NS) cooling (direct URCA)

② Super-soft (density-dependence of ) E_{sym}

→ Too soft neutron star (NS) EOS → contradicting NS-mass observation → New effects to solve the problem

Symmetry energy is given by the energy difference between neutron matter and symmetric nuclear matter

□ Suggestion of super-soft E_{sym}

○ Very recently, Z. Xiao et al [1] suggested that the super-soft E_{sym } (which increases with ρ and then decreases, going down to negative values at around ^3ρ_0) is preferred by the analysis of π^-/π^+ FOPI/GSI data [2].

○ D. Wen et al [3] discussed that, the super-soft E_{sym} causes a very soft EOS and cannot keep neutron stars (NSs) stable.

[1] Z. Xiao, B.-A.. Li, L-W. Chen, G.-C. Yong, and M. Zhang, PRL 102 (2009) 062502. [2] W. Reisdorf et al., NP A781(2007) 459. [3] D.-H. Wen, B.-A. Li and L.-W. Chen, arXiv: 0908.1922 v2 [nucl-th] 4 Nov. 2009.

○ To save the situation, they introduced a non-Newtonian gravity leading to an additional pressure P_{UB} to make the EOS stiffer (P_{UB}=1/2(g/μ)^2ρ^2 with μ the U-boson mass and g the coupling constant between U-boson and baryons) and made the EOS with super-soft E_{sym} compatible with NS mass observed (the Mass from theory should exceed at least the 1.44 Solar mass of PSR1913+16).

In the work by D. Wen et al, the energy expressions are given as

Fig.A Fig.B

□ Careful investigations are required!

○ However, from a view of realistic nucleon matter calculations so far made (i.e., G-matrix or variational approach with realistic NN interactions) the super-soft E_{sym} proposed is extraordinary, as seen from Figs. A and B (x=1 case corresponds to the super-soft E_{sym}).

○ The situation is made clearer when the EOSs of neutron matter are compared. Although EOSs for symmetric nuclear matter are very similar (Fig. C), those for neutron matter are very different (Fig. D). The EOS for x=1 case (with the super-soft E_{sym}) is extremely soft and leads to a negative pressure even at around 3ρ_0. This aspect is very particular and has not been encountered in nucleon matter calculations without phase transitions.

○ More careful investigations, as well as further experimental confirmations, are needed in nuclear physics side, before going to the introduction of the non-Newtonian gravity.

Fig.C Fig.D

□ Density-dependence of E_{sym} is not so different for the realistic calculations

□ Behavior of E_{sym} (ρ) (ρ>ρ_0) suggested by the analysis of π^-/π^+ ratios is super-soft, i.e., E_{sym}(ρ) going down to negative values for ρ>3ρ_0

→ too soft EOS of NSs to be compatible with NS-mass observed → some new effects, e.g. non-Newtonian gravity?

□ 　 However, Neutron matter EOS corresponding to the super-soft E_{sym} (ρ) is very particular,

→ Needs more careful investigations.

Summary

　Mechanism for Y-mixing

１）

２）

３）

1)　P.R.　C38　(1988)　10102)　N.P.　A361　(1981)　5023)　P.R.　C58　(1998)　1804

Topic (B): Dramatically softened EOS due to Y-mixing

→ Contradicts NS masses observed → Necessity of some “Extra Repulsion”→ Introduction of 3-body force repulsion acting universally (i.e., YN, YY as well as NN)→ nicely consistent results

Dramatic softening of EOS Necessity of “Extra Repulsion”

TNI3 TNI3u: Universal inclusion of TNI3 repulsion

L-Vidana et al, P.R. C62 (2000) 035801M. Baldo et al, P.R. C61 (2000) 055801

Dramatic Softening of EOS

・ Strongly softened EOS due to Y-mixing → inconsistency with observations (M_{max} from theory cannot exceed 1.44 Solar mass from observation) →This problem cannot be resolved by enhancing the 2-body force repulsion and is very serious (we fall into the dilemma that the use of stronger 2-body repulsion leads to a more developed Y-mixed phase with softer EOS). →NSs teach us that some “Extra Repulsion” is missing in hypernuclear systems (i.e., YN, YY parts)

Three-body force as a test of “Extra Repulsion”

Test 1: Fujita-Miyazawa type ---2π exch. via Δ excitation (2πΔ)　　　→ Extension from NNN to BBB (B=N, Y) systems.　　　・ Short-range correlation is duly taken into account　　　・ Coupling constants for BBπ are estimated from 　　　　　 quark model of baryons.　　　・ Note: No ΛΛπ direct coupling.

　　　　　　　　 ・ 2πΔ-type cannot substitute the “Extra Repulsion”, because it does not act on Λ → Necessity of “Universal” nature (i.e., acts independently on baryon species)

2π-exchange with Δexcitation3-body force

Ｎ Ｎ Ｎ

π

π

Δ

f(r)

f(r)

With s.r.c. f(r)

目的： Origin の１つとして、 2π-exch,withΔ(1232)　　　　　　励起型の３体力を（Ｎ＋Ｙ）系に拡張し、これがどこまで“ Extra Repulsion” を担えるかを

検討する

π

π

Δ

N N N

N N N

N N

NN

N N

NN

N

N

N

N

N N

N N

N

N

Σ

ΣΛ

Λ

Λ

ΛΛ

Λ

Σ

Σ

Σ Σ

Δ

ΣΣ ΣΣ

ΣΣ

Σ

ΣΣΣ

Σ

Σ

Σ

Σ

Σ

Σ

Σ

Σ ＊

Σ ＊

Σ ＊

Σ ＊

Σ ＊

Σ ＊Δ

Σ

3-body force in Y-mixed matter

Three-body force repulsion from String-Junction Model (SJM) for quark structure of baryons* 　　　・ SJM (relevant to a confinement mechanism) is flavor-independent → does not depend on baryon species → “Universality” is okay　　　・　 According to the treatment by Hokudai group** (NNN → effective two-body NN), three-baryon force from SJM is expressed as two-baryon effective force

→ SJM 3-body repulsion plays a role of “universal” repulsion for Hypernuclear systems

* R. Tamagaki, PTP. 119(2008) 965;Soryushiron-kenkyu (kyoto) 115 (2007) 27.

** K. Kasahara, Y. Akaishi and H. Tanaka, Prog. Theor. Phys. Suppl. No.56 (1974) 96.

Test 2:

(a) 2B come in short distance (b) Deformation (resistance)(c) Fusion into 6-quark state

(by R. Tamagaki)

TO SUMMARIZE

Neutron Star Mass v.s. Central Density

Symmetric Nuclear Matter

Model: 2-body (RSC pot. ) +3-body (2πΔ, SJM)

Exp.

1) Hyperon-Mixed NSs teach us the missing of some “Extra Repulsion” in Hypernuclear systems (i.e., YN and YY parts)2) 2πΔ(Fujita-Miyazawa)-type 3-nucleon force extended to 3-baryon (N,Y) force, gives rise to an increasing repulsion with increasing ρ, but cannot play a role of “Extra Repulsion” needed for Y-mixed NSs, because it does not work on Λ.3) 3-baryon force repulsion for SJM acts “universally” due to the flavor-independence 4) Cmbined two important 3-body force process, i.e., {2πΔ+SJM} three-body force generates an important candidate for “Extra Repulsion”.5) In addition, {2πΔ+SJM} effects act for meeting the saturation condition of symmetric nuclear matter.

Summary

Topic (C): Hyperon cooling

・ Usual β-decay (n → p+e^- + ν, p+e^- → n+ ν , so 　　 on) is not allowed

・ Standard cooling mechanism　 　　　 n+n → n+p+e^- + ν 　 (the inverse process and so on)

・ When Y participates β-decay with Y is made possible! Λ → p+e^- + ν , Σ^- → Λ+e^- + ν , so on

→ NS cooling is dramatically accelerated → but “too rapid” (inconsistent with observations) → Necessity of Y-superfluidity to suppress “too rapid” cooling

-

--

-

With or without Y-mixed core depends on M

CASE: TNI6u Critical Temperature T_c

versus Density ρ

□Pairing type: n → ^3P_2 p, Λ, Σ^- → ^1S_0

□Pairing interactions: n, p → OPEG-A pot. Λ, Σ^- → ND-Soft for solid lines

□ 　 Hyperon cooling scenario combined with Y- superfluidity nicely explain the cooling of colder class NSs

□ 　 However, less attractive ΛΛ interaction (suggested by the “NAGARA event”) denies the Λ-superfluidity, and thereby hyperon cooling scenario breaks down.

□ 　 We need further investigations.

Summary

　ハイペロン冷却と成立条件

① 　 Y 混在ーーー必ず起こる

② 　 Y 超流動の発現必要（何故なら「冷え過ぎ」の抑制機構）

　 　＊ Λ は NO （ by 　 NAGARA), 　∑ ^- は OK とすること可

③ 　運動量三角形の成立ーーー要着目

　　 ＊ 3 種バリオンのフェルミ運動量　　　 　 Large (k_n), Small (k_p), Small (k_e),

　　　　 Small (k_{Λ} ), Small (k_{Σ^-})

　　 ＊ Large component が加わるとダメ

　　　 n ⇔ p + l , ( l = e^-, μ^-), Σ^- ⇔ n + e^- は難　　　　　　　　　 Λ ⇔ p + l , Σ^- ⇔ Λ + l は可

□ 打開の可能性

　　　　 ρ_t （ Σ^- ）～ ρ_t （ Λ ）～４ ρ_0

　　→ ρ_t （ Σ^- ）＜ ρ_t （ Λ ） と

Σ^- が Λ より先行するケースを考える

→ NO 　 Λ-Super, 　 but Σ^- -Super survives,

　　　　 Σ^- → Λ ＋ l ＋ ν_l （ l ＝ e^-, μ^- ）は OK,

Λ→ ｐ＋ l ＋ ν_l は NO の領域があればよい

ー

-

-

E_sym　(Symmetry　Energy ）依存性

□ 現状のまとめ

　 ① 運動量保存則（ Mom.-Triangle ）に着目 ② Σ^- が Λ より先行して出現するケースでは 「ハイペロン冷却シナリオ」復活の可能性　　　　　　　　　　 あり ③ → 更につめる必要（グザイも含めて）