Realization of Λ-Superfluidity in Neutron Stars by ΛΛ interaction taking account of

Pauli-Blocking effects

T. Takatsuka ( RIKEN ; Iwate Univ.)

S. Nishizaki (Fac. Sci & Eng. Iwate Univ.)

Y. Akaishi (RIKEN)

NSMAT2016 (Nov.22, Sendai, Japan

1. Background and the aim here

2. Approach to Λ-superfluid problem

3. Results and concluding summary

Dramatic softening of EOS Necessity of “Extra Repulsion”

As a review T.Takatsuka, Prog.Theor.Phys.Suppl.No.156 (2004) 84.

5 10

Universal

3body

force Y-mixing

EOS

TNI3

(NO Y)

1500

1000

500

P

TNI3u

(Y)

0 5 10 15

Mass

TNI3(NO Y)

TNI3u(Y)

TNI3(Y)

2

1.5

1

In the earlier works, U was introduced quite phenomenologically.,

but ,in 2008, U(SJM) from the Strihg-Junction Model for quark structure

of baryons was constructed by R.Tamagaki,

[1], which is spin- and flavor-Independent

and hence gives the universality to the

3-baryon force .

Actually it has been shown that

the SJM 3-body force generates

a EOS stiff enough to sustain

the 2-solar-mass NSs, even under

the Y-mixing [2].

2–solar- mass NSs with Y core

are possible !

(it was before the observations) ------------------------------------------------------- [1] R.Tamagaki, Prog.Theor.Phys.119 (2008) 963.

[2] T.Takatsuka ,S.Nishizaki and R.Tamagaki, AIP.Cof.Proc. 1011(2008) 209.

Thermal Evolution of NSs

Log Time (years)

Tsuruta et al

Ap. J. 691

(2009) 621

(𝑀 > 0.8𝑀𝑠𝑢𝑛）

NO Λ-super due to “NAGARA”

A-dependence ?

1. Background and the aim here 1)Y-mixing causes 2 serious problems ① Too softened EOS ! eg. 𝑀𝑚𝑎𝑥=｛1,88(NO Y)→ 1.1(with Y)｝𝑀𝑠𝑢𝑛→ clearly contradicts 2𝑀𝑠𝑢𝑛 -NS obs. → suggests the necessity of some extra repulsion . “Universal 3-body force U(BBB) has been found to be a solution [1] ② Too-rapid cooling! Some NSs need more efficient ν-emission than standard Murca process (n+N →p+N+𝑒−+ν, and the inverse) → YDurca (Λ→p+𝑒_ and the inverse, and so on) called “Y-cooling” is a candidate because ∈𝑌𝐷𝑢𝑟𝑐𝑎 ~105−6 ∈𝑀𝑢𝑟𝑐𝑎 . But when directly applied , it leads to “too-rapid cooling” → then the existence of Λ-superfluidity is a possible solution. 2) Λ-super is OK or not ? [2] Realization of Λ-super is okay for old ΛΛ int, but is hard when less attractive ΛΛ

int. suggested by the “NAGARA events 𝐻𝑒ΛΛ6 “ [3]→ Inclusion of Pauli-blocking

effects in ΛΛーΞN coupling channel to enhance the ΛΛ int. might be a solution. --------------------- [1]S.Nishizaki , Y.Yamamoto and T.Takatsuka, PTP. 105(2001)607;108(2002)703. [2]T.Takatsuka,PTP. Suppl.No.156(2004)84. [3T.Takahashi et al., ]

The aim here is to investigate the possibility of Λ-superfluid by taking account of the attractive effect on ΛΛ int. from the Pauli – blocking in ΛΛーΞN , by using single-particle properties under the EOS compatible with 2-𝑀𝑠𝑢𝑛 NSs recently observed

2. Approach to superfluid problem (1) EOS with Y-mixing consistent to massive NSs

○Effective interaction approach 𝑉 = 𝑣 (BB) + 𝑈 (BBB) ○ 𝑣 (BB) is based on the G-matrix calculations (RSC for NN, Nijmegen D pot. For YN and YY) ○3-body force 𝑼 (BBB) = 𝑼 (SJM) + = 𝑼 (TNA) ; Universal 𝑼 (SJM) from String-Junction Model for quark structure of baryons, proposed by R.Tamagaki[3] and has been shown to generate 2𝑀𝑠𝑢𝑛 NSs.[4]. ○𝑈 (TNA) from the attractive part of a phenomenological TNI of FP[5] is introduced so as to reproduce the saturation property of symmetric nuclear matter. (2) Free space ΛΛ interaction VF3 from Akaishi et al [6]which takes account of the Pauli-blocking effects in medium, keeping the consistency with NAGARA data. (3) Solve the gap equation for ΛΛ pairing by using the Single-particle properties such as the effective mass 𝑚Λ* and Fermi momentum 𝑘𝐹Λ under the EOS (1)。 [3]R.Tamagaki, PTP. 119(2008) 865 {4}T.Takatsuka,S.Nishizaki and R.Tamagaki, AIP Conf.Proc. 1011 (2008) 209. [5]B. Friedmann and V. R. Pandharipande, Nucl. Phys. A361 (1981) 502. [6] K. S. Myint, S. Shinmura and Y. Akaishi, Eur. Phys. J. A16 (2003) 21

(a) 2B come in short distance

(b) Deformation (resistance)

(c) Fusion into 6-quark state

(by R. Tamagaki)

Repulsion from SJM-----flavor independent

Prog. Theor. Phys. 119

(2008) 965.

○ Energy barrier (～2GeV) corresponds to repulsive core

of BB interactions

BBB interactions Additionally 2GeV excitation Height of 3-body pot.

Λ 𝚺−

Fraction (%)

M-R relation

ΛΛ―ΞN coupling

Pauli-

blocking

Ξ N Ξ N

Λ Λ Λ Λ

In free space in medium

Λ Λ Λ Λ

is

1 2 3 r(fm)

50

0

100

-50

-100

(MeV)

13.4GeV core

4.4GeV

2.0GeV

With NAGARA

ND-Soft original

Pauli-Blocking

VF3 {3}K.S.Myint,S.Shinmura

And Y.Akaishi ,

Eur.Phys.J.A16(2003)21

ΛΛ Pot.

○ Here, we note the 3-elements (Fermi momentum

k , effective mass m* and pairing interaction) to

control the energy gap.

#) For 3P2 NN pairing, the situation is similar, although the gap

equation becomes complex due to the 3P2-3F2 tensor-coupling.

FB B

２．Ｒｅｓｕｌｔｓ ａｎｄ ｃｏｎｃｌｕｄｉｎｇ ｓｕｍｍａｒｙ

Critical Temperature of Λ-Superfluid

ND-Soft original

Taking account

of Pauli Blocking

Effects (VF3)

(VF2)

SJM2+TNA EOS

4 5

Tin ~

6

(K)

2.03

( 𝜌𝑐 = 7.4 𝜌0 )

NAGARA

Concludig summary

Due to the Y-mixing in NS cores, we are faced to two

serious problems ; too-softened EOS and too-rapid

cooling . Both of which contradict observations.

These two problems have to be solved at the same time

.

In the case of pure hadronic framework . the universal

3-body force is a solution for the former problem.

For the problem of too-rapid Y-cooling, a central concern

is how to revive the Λ-superfluidity , consistently with

NAGARA event. .We find a possibility to have the Λ-

superfluid in NSs, by taking account of the Pauli-

Blocking effects in medium for ΛΛ-ΞＮ coupling.