原子核物理学連続講義・コースХ－3

Baryonic Matter and Neutron Stars（第3回）

T. Takatsuka (Prof. Emeritus of Iwate Univ.)□ Hyperons in NSs --- Earlier works○ Suggestion for Y-mixing in NSs
・A.G.W. Cameron,
Astrophys. J., 130 (1959) 884.

○ Attempts for Y-mixing calculation
・S. Tsuruta and A.G.W. Cameeron,Canadian Journal of Physics, 44 (1966) 1895.
・W.D. Langer and L.C. Rosen,
Astrophysics and Space Science, 6 (1970)
217.
・V.R. Pandharipande,
Nucl. Phys. A178 (1971) 123.
・N.K. Glendenning,
Nucl. Phys. A493 (1989) 521.

○ From ～1995, many works stimulated
by a progress of hypernuclear physics
in laboratories and observations forNSs --- e.g. see references cited in a review;
・T. Takatsuka, Prog. Theor. Phys. Suppl. No.156 (2004) 84.

3 5 10 20

S. Tsuruta and A.G.W. Cameron,Canadian Journal of Phys., 44 (1966) 1895.

12 35W.D. Langer and L.C. Rosen,
Astrophysics and Space Science, 6(1970) 217.

1 2 5 10

1 2 3 4V.R. Pandharipande, Nucl.Phys. A178 (1971)125.

56N.K. Glendenning, Nucl. Phys. A493 (1989) 521.

6. Hyperons mixing and consequences onneutron stars (NSs)
6-1. Hyperons as new constituents of NSs

Hyperons (Ys) are sure to appear !

Mechanism of Y-mixing

Fermi energies
300

10% mixing
5%200(MeV)

pure n-matter
100n1

2

3

456

[3] M.Baldo, G.F. Burgio and H.-J. Schulze, Phys. Rev. C61 (2000)
055801[4] I. Vidaña, A. Polls, A. Ramos, L. Engvik and M. Hjorth-Jensen,
Phys. Rev. C62 (2000) 035801

Y-mixing,Then□ What happens ?
⇓6-2. Two serious problems2TNI3(1)

NO Y
TNI2
1.5Y-mixing

1with Y×●×●
51015

Strong Softeningof the EOS

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

○ Hyperons are always present→ profound consequence for NS-mass●●

H. Dapo, B-J. Schaefer and J. Wambach, Phys. Rev. C81 (2010)
035803

G-matrix with nucleonic
3-body force●

Z.H. Li and H.-J. Schulze, PR C78 (2008)028801.

Chiral SU(3) RMF●K. Tsubakihara, H. Maekawa, H.
Matsumiya and A. Ohnishi, PR C81(2010) 065206.

Even Λ-only mixing, situation is the same!

(2) Too rapid cooling
NS cooling due to ν-emission（Ｊ．Ｍ．Ｌａｔｔｉｍｅｒ ｅｔ ａｌ．，ＰＲＬ６６（１９９１）２７０１）

Y-coolingThermal Evolution of NSs

Tsuruta et al
Ap. J. 691(2009) 621

Log Time (years)

7. Possible solution for the problem

Too soft EOS (Problem 1)
Dramatic softening of EOS→

Universal 3-body force
The contradiction between theory and observation(M_max < M_obs) strongly suggests the necessityof some extra repulsion in dense hypernuclearsystems→ 3-body force repulsion acting “universaly” onNN,YNand YY parts (universal 3-body force) is apromising candidate [1][2]Dramatic softening of EOS

MassEOS

1500

Necessity of “Extra Repulsion”
2TNI3(NO Y)P

TNI3(NO Y)

1000

TNI3u(Y)TNI3u(Y)
1.5

Y-mixing

Universal3bodyforce

500

1TNI3(Y)5

TNI3

TNI3(Y)

05

1015

10

TNI3u: Universal inclusion of TNI3 repulsion

Too rapid cooling (Problem 2)
Too -rapid cooling → Hyperon superfluidity
NSs with M> 1.35 Msun have a Y-mixed core. If Ysuperfluidity is realized, it suppresses the efficient νemmision by Y-Durca (exp (-Δ/T))→ moderate cooling consistent with colder class NSs

That is, a new scenario isLighter NSs → Warm (standard slow cooling of Murca)
Heavier NSs → Cool (nonstandard fast cooling ofYDurca (“hyperon cooling”) + Y-super)
Massive NSs → Very Cold (“hyperon cooling”)

１）
２）

３）

1) P.R. C38 (1988) 1010
2) N.P. A361 (1981) 502
3) P.R. C58 (1998) 1804

With or without Y-mixed core depends on M

CASE:TNI6uSuppression by
Λ-Superfluidity24

Λ-Durca20○ ε: ν-emissivity due toΛ-Durca (Red)
Murca (Green)
16
dashed line: No suppression
Murca○ T: internal temperature ofNSs

12---------------T.Takatsuka,S.Nishizaki,Y.Yamamoto
and R.Tamagaki,
Prog.Theor.Phys.115(2006)355

83456

NAGARA event

F-G A Pot.
Solid lines: Original
Dashed lines: Modified
due to “NAGARA”

V(ND-soft)→ 0.5V(ND-soft) ; Hiyama

Takahashi et al., PRL 87 (2001) 212502

Nijmegen-D ΛΛ-pot.

○Λα○ Λ

* How about the rearrangement effects?

4.44 GeV Core150 1.98
1.92

ND-Soft100(MeV)

ND-Soft Pot.

50

01.

2. r(fm)

3.

NAGARA-50(0.45, 0.6)4-10056

present status of NS cooling□ Cooling processes:• Murca (modified URCA)• cooper-pair (pair breaking-formation)• N-Durca (direct URCA)• Exotic (Y,π,K,q, etc.) (Durca)□Observations:detection---about 10, upper limmit---about 16*hotter NSs(Puppis,CAS-A,RX J002+6246,PSR 0656+14, ---)
*colder NSs(Vela, PSR1706-44, 3C58, CTA-1, Vela-twin --- )□ Cooling Model○ NO exiotics(minimal) verusus exisotics(non-standard)○ Obs. Cold-class NSs  necessity of exotics○ Vela (3C58)  exotic cooling(Y) + superfluidity(Y)○ CAS-A evidence of 3P2-super !

← Critical temperature of
3P2-Superfluid○ nt1 from Gusakov, et al.,A&A, 423 (2004) 1063.
○ Extraordinal density
dependence of 3P2-gap

R.B. Wiringa, V. Fiks and A. Fabrocini,
PR C38 (1988) 1010.

A. Akmal, V.R. Pandharipande and D.G.
Ravenhall, PR C58 (1998) 1804.

8-1. Universal 3-body force□ {2πΔ-type + SJM} schemeAn origin of “universal 3-body force”• “3-body force of extended 2πΔ-type”(atlong and intermwdiate ranges) + “3-bodyforce based on the string-junction quarkmodel(SJM;at short distance) has beenstudied [5]-------------[5] T.Takatsuka,S.Nishizaki and R.Tamagaki,
Proc.Int.Symp.”FM50”(AIP Conference proceedings,2008)209

Extended 2πΔ-Type 3-body Force; not universal

B*;T.Kasahara,Y.Akaishi and H.Tanaka,PTP Suppl.No.56(1974)96

Extension to N+Y system

EOS of Neutron Star Matter
400

Effects of 2𝜋Δ-type
3-body force (𝑈 2𝜋Δ )300(MeV)Y-mixing+𝑈 2𝜋∆200

NO Y(2-body 𝑉)

100

05

𝜌/𝜌010Repulsion from SJM-----flavor independent(a) 2B come in short distance(b) Deformation (resistance)(c) Fusion into 6-quark state(by R. Tamagaki)
Prog. Theor. Phys. 119(2008) 965.

○ Energy barrier (～2GeV) corresponds to repulsive coreof BB interactions

R. Tamagaki, Prog. Theor. Phys. 119 (2008) 965.

Fraction of constituents in Y-mixed NSs

Mass v.s. Central Density

8-2. Hybrid stars with quark
degrees of freedom

Introduction
ESoftendwith exotics (e.g. Ymixing, quark matter)ρ□ Possibility of quark matter in NSs *)A way of approach
H-phaseH-Q trans. Q-phase<Matching>□ Q: q-matter + asymptotic
freedom?
uncertain□ H: point particle+ interaction→ G-Matrix, Variational

uncertain□ HQ Phase transition
Cross point (Maxwell,Gibbs) → notnecessarily reliable□ Need new strategy------------・ T. Takatsuka, T. Hatsuda and K. Masuda, AIP Conference Proceedings 1484
(Melvile, N.Y. 2012) 406.
・ K. Masuda, T. Hatsuda and T. Takatsuka, ApJ 794 (2013) 12.

(1) “3-window model”“known”H(G-matrix)

unknown“known”

HQQ(NJL)

not by Gibbs condition,
but by phenomenologicalinterpolation-----------------・ T. Takatsuka, “Genshikaku Kenkyu”
Vol.57 (2013) 270.

Some results for NS models

Dependence on (m, n)

3.0
0.5
2.0

PSR J1614-2230

0.0

PSR1913+16
1.0

10

R (km)

15

1.5

31.0

2100.0

TNI2u

5678

1500

P1000
TNI3u
0.5

500

0123456789Stiffening of EOS due to H-Q transition
1500

P
1000

TNI3u
1.0500TNI2u0ε500

1000

1500

2000

2500

Sound Velocity
1.02.530.5

HH-QQ

TNI2u012345678x

(2) “H-Q crossover model”

・K. Masuda, T. Hatsuda and T. Takatsuka, ApJ. 794 (2013) 12; PTEP 073D01 (2013).

○○/○○

Pressure v.s.
density

Remarks

densitydensity

Short summary□ Two-solar mass problem with hyperons(A) pure hadron framework“universal 3-body force” is one of the solution* study on the origin is the next important subject(B) “hadron + quark” framework
Introduction of Q-degrees of freedom from a view of “3-windowmodel” and “H-Q crossover model” is another promising solution□ Too-rapid cooling problem with hyperons
necessity of hyperon superfluidity yes?, no?
 more careful investigation; ΛΛ interaction from NGARA,
effects to enhance the attraction
 other possibilities□ We have to solve the two problems challenged by NSs
at the same time9. Hot NSs at birth withhyperon mixing□ Effective Interaction Approach (EIA)at Finite-Temperature (T>0) [1]Weak T-dep. of G(T)At most, ～5% difference even for T=40MeV!

Single and bulk quantities□ Hyperon-Mixed Supernova Matter (SM)CompositionandPopulation○ Red (black) linesfor SM (NSM)

Internalenergy○ HOT: SM with Y
COLD: NSM with Y○ TNI3u casePressure○ TNI3u caseMaximum-mass NSs(TNI3u)Density profile of composition(TNI3u)HOTCOLDThermal evolution and maximum mass
(TNI3u)Short summary