Nuclear Matter in Neutron Stars
by Experiments and Astronomical
Observations	Takashi Nakamura
Tokyo Institute of Technology	

Hadrons and Hadron Interactions in QCD 2015, @YITP, Kyoto Univ. Mar. 2015

Mysteries of Neutron Star	
l Final form of “matter” evolution in the universel Highest dense “matter” in the universe (Gigantic Nuclei)	
Crust:
Mass: 1~2 Msun , Radius：~10-15 km , ρ(r=0) =3∼10ρ0	

Nuclear Pasta ?
l Various form of “matter” made of hadrons/quarks

p
n

s
d

Outer Core:

n
Λ	

u

Neutron Matter	Ξ	Superfluid?	

s

s

u

Inner Core:NASA	

Center:Strangeness Hadronic matter	?

•Quark matter ?

High dense nuclear matterwith Hyperons 	

Deconfined quarks
Color superconductivity	2012-2016 新学術領域「実験と観測で解き明かす中性子星の核物質」
Grant-in-aid for innovative area:“ Nuclear Matter in neutron Stars
investigated by experiments andastronomical observations”
H. Tamura (Tohoku U.)
T.Takahashi (KEK), T.Murakami(Kyoto U.),
T.Nakamura(Tokyo Tech), S.Horikoshi(U.Tokyo),
T. Takahashi(JAXA),A.Onishi(YITP)	Joint project among Experiments, Observations, Theories 	
“Science of Matter basedon quarks”

Ｘ-ray observatory

ASTRO-H

Understand structure of n-star	
Theories	

World-leading
two accelerators and
X-ray satellite	

RIKEN RI Beam Factory

RIBF

Nuclear matter EOS	r

X-ray astronomy	

⇒ n-star radius	
n-rich nuclei	
High Int. Proton
Acc. J-PARC

Strangeness nuclear
physics

Cold atoms	
⇒ properties ofneutron matter⇒ Interaction of hyperons	Contents	• Introduction –Nuclear matter in Neutron Stars• EOS of Neutron-rich matterprobed by RI-Beam Experiments (My expertise)• EOS for Low-density Neutron-rich Nuclear
Matter Studied by Cold Atoms• Hadronic Matter with Strangeness in NeutronStars Explored by Experiments• New development of Research on Neutron Stars
by X- and Gamma-Rays Observatory• Theoretical studies of neutron star and nuclear
matter• Summary and Outlook

EOS	
Equation of State of Nuclear Matter

E=E(ρ) 	

P = ρ2

Energy/Baryon	

∂E∂ρHydrostatic Equilibrium (General Relativity: T.O.V. Eq.) + EOS

à Radius, Maximum Mass, Mass-Radius Relation of N Star
Pressure (Nuclear/Hadronic Interactions,+ Fermi motion)	
Stiffer(Softer) EOSà Pressure is high(low)à Larger(Smaller) mass
is sustainable	Self-Gravity(Attractive)• Composition of N Star
• Cooling Mechanism (URCA)• Glitch (Sudden jump in Rotation)	
 J.M. Lattimer, Annu. Rev. Nucl. Part. Sci.
62, 485 (2012).	

Experiments to explore EOSn Inner Core (ρ > 2ρ0)

How EOS changes with N/Z ratio?

Hyperons Exist in N-Star?
If so, How?

Properties of
N-rich Nuclei

E (energy/baryon)n Outer Core (ρ < 2ρ0)	NeutronMatter(A=N)	

stiff	
+Strange Hadronic
Matter(Λ,Ξ,Κ…)	
soft	

2ρ0	
ρ0	

ρ (density)	

Symmetric
Nuclear Matter(N=Z)	

Properties
of Ultra-cold
Fermionic
Heavy ion
Stable Nuclei
Gas	
Collisions of
n-rich Nuclei	

Λ	

p	

K-	
p	

Properties ofHypernuclei
and Kaonic Nuclei	Collaboration among Experiments/Astrophysical Observations/ Theories
EOS of Nuclear Matter	

Uniquely
Determined

Demorest et al., Nature 467, 1081 (2010)
1.97(4) ​𝑴↓⨀ (Shapiro Delay)	

Experiments at
RIBF/J-PARC/Ultra-cold Fermions	+Theories	

M

Mass-Radius Curve

EOS Puzzle !

N-Star Mass	

Observations ofRadius of
N-StarDetermine
EOS	＋	

Confirm
EOS	

The EOS	
Radius (km)(Not yet determidirectly
by observations)

Constrain
on Hadronic/Nuclear Theories,
Existence of Quark StarEOS of neutron-rich matterprobed by RI-BeamExperiments
	Properties of Medium and Low-density Neutron-rich
Nuclear Matter (ρ ~ ρ0, ρ < ρ0)T.Nakamura(Tokyo Tech), S.Shimoura(CNS,U-Tokyo),
Y.Togano(Tokyo Tech), Y.Kondo(Tokyo Tech), T.Teranishi(Kyushu)

EOS for High-Density Neutron-rich Nuclear Matter(ρ ~2ρ0)

T. Murakami(Kyoto), K. Ieki(Rikkyo), T. Isobe(RIKEN), A.Taketani(RIKEN),
K.Kurita(Rikkyo), H.Baba(RIKEN)EOS (Nucleonic Degree of Freedom)	
Difference of n and p densities	
EOS of Nuclear Matter	
E(ρ,δ)	

ρn − ρ p N − Z
≈
ρ0
A

A=N	

E ( ρ , δ ) = E ( ρ ,0) + S ( ρ )δ 2 + ... δ =N=Z	⎛ ρ − ρ 0 ⎞ K sym ⎛ ρ − ρ 0 ⎞⎟⎟ +⎜⎜⎟⎟ + ...
S ( ρ ) = J + L⎜⎜⎝ 3ρ 0 ⎠ 18 ⎝ ρ 0 ⎠

2

J	
S(ρ)	

Symmetry Energy: S(ρ)

EOS of nuclear matter within nucleonic D.O.F 	p Provide Basis of EOS with non-nucleonic D.O.F
à Maximum densityà Compositionà Maximum Mass/Radii of N-Starp Direct determination of EOS (within nucleonic D.O.F)
can be possible using a variety of observablesp Most important but unknown term: Symmetry Energy S(ρ)
Neutron-rich Nuclei àMicroscopic Laboratory for Neutron-Star Physics	

How to determine the EOS?	
p S(ρ) : J, L(pressure), Ksym(Incompressibility)ß Collective Motion of Neutron-rich Nuclei	
n-skinPygmy Dipole Resonance (E1)	

Core

Breathing Mode (E0)	
Y.Togano, M. Shikata, CATANAà PDR of 52Ca,

PDR

p Superfluidity ßDineutron correlation in low-dense matternn

Coulomb Breakup of 2n Halo 22C and 19B	Deformed Driven Halos: 31Ne,37Mg
TN et al., PRL112,142501(2014).
N.Kobayashi, TN et al.,PRL112, 242501(2014).	

p S(ρ)ßNuclear force(density dependence, isospin dependence, 3N/4N force)ß tetra neutron, exotic nucleonic system4n26, 28O	
S.Shimoura 4n exp at SHARAQ Done, Next-generation N-array
Kondo: 26O, Done at SAMURAI, 2012, 28O Approved experiment (Grade-S)
Sekiguchi 3N force 	

p S(ρ)ßBulk Propertyß neutron skin thickness(Tamii,Togano),masses (Yamaguchi)

RIKEN RI Beam Factory (RIBF)
Completed in 2007
New-Generation RI-beam facility

SCRIT	
2013	

2008	

ZDS	

SAMURAI	
2012	

SRC	

BigRIPS 2007	

Rare RI
RING	
2014	
SHARAQ	
2009	

SRC: World Largest Cyclotron (K=2500 MeV)
Heavy Ion Beams up to 238U at 345MeV/u (Light Ions up to 440MeV/u)
BigRIPS: Large Acceptance Fragment Separator (80mradx100mrad, dP/P:6%)
ü 3-5 Orders Gain in the Yield of Neutron-rich Nuclei
ü >1000 New Species in neutron-rich nuclei	SAMURAI--Large Acceptance Spectrometer in RIBF --	

Superconducting Analyzer for MUltiparticle from RAdio Isotope Beam with
7Tm of bending power	

Superconducting
Magnet (3T)	

KinematicallyNeutron(s)	
completemeasurements by detecting
superconducting
multiple particles in coincidence
coilpole(2m dia.)

RI beamfrom BigRIPS	
RI
Beamvacuum chamber

NeutrontargetØ Superconducting Magnet

3T with 2m dia. pole(designed resolution 1/700)

Heavy
80cm gap (vertical)
Fragment	Ø Heavy Ion Detectors

Ø Proton DetectorsØ Neutron Detectors
Ø Large Vacuum ChamberrotateØ Rotational Stage

ProtonHeavy Ion

Invariant Mass Measurement
Missing Mass
Measurement
March,
2012	
Slide: K. Yoneda	

Approach to EOS of Neutron matter/Neutron-rich Matter	Neutron Skin Nuclei	ρ

Neutron-Skin Nuclei "Normal Nuclei	 (Neutron-rich Nuclei)"

n
p

r

V
Sp	
 ~Sn~8MeV	ρ coren
NeutronSkinpr

N-richà Larger neutron Fermi energy	
2/3!2⎛ 2 N ⎞
(n)
(0)
2
2/3
εF =
(3π ρ n ) = ⎜⎟ ε F
2mn⎝ A ⎠

δRnp=<r2>n1/2-<r2>p1/2	

for N=2Z à 1.2εF(0) (without n-skin)	

ρρ Larger L favorsnp

Smaller <ρn>

r p

V

n

r

EOS of Nuclear Matter	

p n

p

n

E(ρ,δ)	

A=N	
N=Z	

Neutron Skin : Formed due to S(ρ)δRnp(or Rn)-- Depends on EOS 1/4
1/4	
P
R
∝
∝L
0
as in NS radius 	
 NS

J	
S(ρ)	

Pygmy Dipole Resonance of Neutron Skin Nuclei--- Also Sensitive to EOS	GDR(Giant
B(E1)NormalE1Strength	

Nuclei	GDR

Dipole Resonance)~20MeV

core

Ex
Photon(γ)B(E1)

Neutron Skin Nuclei	PDR (Pygmy
Dipole Resonance) GDRn-skinCore

5~10MeV ~20MeV
PDR

Ex
Stiff EOSàThicker Neutron Skin à Larger Pygmy Mode

PDR and skin thickness
T. Inakura et al.,
PRC84, 021302 (2011)
T. Inakura et al.,arXiv:1306.3089

skin thickness [fm]B(E1)
PDR strength [e2fm2](Calc.Inakura)	
PDR	

PDR	

S4n
S4n
S4n

52Ca	

50Ca	

48Ca	

PDR of neutron-skin nuclei
	

CATANA

Target	n	

(CsI(Na) Array) 	

51Ca	

52Ca
200MeV/nucleon
Y. Togano: Approved experiment at RIBF
Planned in 2016	

Production of Unbound 26O States: Y.Kondo et al.
	

23F	
 24F	
 25F	
 26F	
 27F	
 28F	
 29F	
 30F	
 31F	
22O	
 23O	
24
O	
25O	
26O	
 27O	
28O	

Z=8	

N=20	
 2015	
Ground state	
 Planned

21N	
 22N	
 23N	

Counts /100keV	

19B	

Oxygen Anomaly	

F+Cà26Oà24O+2n
N=16(preliminary)	

22C	
20C	
21C	
 27

(New magic number)	

Excited state（new）	

Energy(MeV)	

26Ne	
27
24Ne	
25Ne	
Ne	
28Ne	
29Ne	
30Ne	
31Ne	
32Ne	

T. Otsuka
et al., PRL105,A.Schwenk
032501 (2010)	
C.Caesar
et al.(GSI,Data),(Theory)PRC88,034313 (2013)	
Theory: NN+3N(chiral) +residual 3N
2+	
 line	
Drip line	
Drip
1.5

2	

0+	
0+	
0	
 Conventional models:à26O bound3N interaction (repulsive) ? 	
24O	
26O	
25O	
Experimental Result:	
~1.3MeV	 +(2 )	
0.75MeV	

Decay energy (MeV)	

24O+2n	25O+n	

<50keV	
 +	
0gs
26O	

π-/π+ ratio in Heavy ion collisions	T.Murakami, T. Isobe et al.	
124
50Sn82 (n-rich)@200~300 MeV	132

50Sn74

RIBF
MSU
ρ0	

GSI
2ρ0	

Bao-An Li et al.,Phys. Rep. 464, 113 (2008).	

π-/π+	

High-density(participant region)	

(π-/π+)~ (N/Z)2 of participant
region of heavy ion collisions(Δ resonance model)-- sensitive to S(ρ)	

softer	

stiffer	

124Sn+124Sn	
112Sn+112Sn	

(N/Z)system	

Ebeam/A (GeV)	

RIBF

SπRIT Collaboration

SAMURAI Pion Reconstruction and Ion-Tracker	
132Sn @ 200 A MeV
108Sn @ 300 A MeV	π+	Target(124Sn,112Sn)	

π-	
TPC(Time projection
Chamber)	

SAMURAI at RIBF (200A-300A MeV)	
132

π+/π-+X	
π+/π-+X	

112+ 124 Sn50Sn62 +50
74 à π /π +X	

124 Sn à
50Sn82 +50
74
124 Sn112 Sn
50
74 +
50
62 à

108

50Sn58 +112

50Sn74 à

π+/π-+X	

NEBULA
NeuLAND(Neutron
Detectors)

To constrain symmetry energy
Y(n)/Y(p), Y(π-)/Y(π+) etc.	

δ=(ρn-ρp)/ρ0 : 0.09--0.22	

Installation Test of TPC into SAMURAI in July 2014	Symmetry Energy (ρ~ρ0) ---Current Status
M.B. Tsang et al.,
PRC86, 015803 (2012).
I. Tews et al.,PRL110,032504(2013).
DP: Dipole Polarizability(A. Tamii PRL107, 062502 (2011)).
HIC: Heavy Ion Collision
PDR: Pygmy Dipole Resonance
IAS: Isobaric Analogue State
FRDM: Finite Range Droplet
Model (nuclear mass analysis)n-star: Neutron Star Observation
χEFT: Chiral Effective Field Theory

DP: L=45±18 MeV
J=30.9±1.5 MeV

K symL(ρ − ρ0 ) + 2 (ρ − ρ0 )2 + ...
S (ρ ) = J +3ρ 0
18 ρ 0EOS for Low-density Neutronrich Nuclear Matter Studied
by Cold Atoms	
M. Horikoshi (U.Tokyo), T. Mukaiyama (UEC),
T.Nakatsukasa(Tsukuba U), K. Mizushima (Okayama U.)

From ultracold atom to the neutron star M-R curve

Neutron Star	

Cold Fermi atoms
𝑬=𝒇(𝝆  )	E( ρ, δ = 1)

𝑬	
	

TOV	

ρ0	

Constrain in these regions	

2ρ0	

𝝆	
  

Superfluid transition at the unitarity
Momentum distribution ofpaired fermions	Trap cold
atoms in an
optical trap	

100	

Evaporative cooling	

​𝑻T/T
/𝑻↓𝑭
F	
Fermi Liquid	
Molecules	

​Tc↓𝒄
Molecular-BEC	 𝑻	 	SuperFluid	
BEC
Limit
(Strong
Coupling)	

Inner crust	
Unitary limit	

BCS
Limit
−​𝟏/​𝒌↓𝑭
1 𝒂 (Weak−k F a Coupling)	

M.Horikoshi et al.	

Hot topic : Bose-Fermi superfluid mixture !!
Strongly correlated
Fermion Pairs	

Fermi Superfluid	

6Li (Fermi)	

Momentum
distribution ofpaired Fermions	
Possible Thermometer for 6Li gas 	BEC	

7Li (Bose)	

Momentum
distribution of
BosonsStrangeness Matter in Neutron Stars
Explored by Experiments at J-PARC
Baryon-baryon Interaction with Multi-StrangenessT.Takahashi(KEK), K.Nakazawa(Gifu U.), S.Sato (JAEA), H.Takahashi(KEK),
M.Naruki(Kyoto U.), K.Imai(JAEA), H.Sako(JAEA), S.Hasegawa(JAEA),
M.Sumihama (Gifu U.)

Strangeness in the Neutron-rich Nuclear Matter
H. Tamura(Tohoku U.), A. Sakaguchi(Osaka U.), H. Outa(RIKEN),
K. Miwa (Tohoku U.), T. Koike (Tohoku U.), S.Ajimura(RCNP),
T. Fukuda(OECU), T.Suzuki (U.Tokyo), S.Nakamura (Tohoku U.)

Hyperon Matter should appear at Higher Density(ρ > ~2ρ0)	

2/3
!2
2
3π ρ
Fermi energy:	
ε F =
2 mB

(

)

(n )
µY = mY + ε F (Y ) µ n = mn + ε FΛ	mΛ-mn=175 MeV	n	

⇒ ρ th (Λ ) ≈ 2 ρ 0

J.Schaffner-Bielich, NPA804(2008)309	

In reality:
(n)

ρ0	

(n)

µ n = mn + ε F + U n (k F )µY = mY + ε F (Y ) + U Y (k F (Y ) )YY, YN, YNN Interactions
Should be (in high density neutron matter)
determined.	
 Essential! 	

N.B.	
For two(or more) kinds of Fermions ρ à 	 ρ = ρ n + ρ Λ + ...
Hyperons in NSà Softening of EOS	à Lower <E>	àHow to solve 2M puzzle?à3-Body force (YNN, YYY) ? 	

Kinetic energy	

Baryon-baryon interaction with multi-strangeness	ΞN→ΛΛ Conversion	 ΞN interaction	 ΛΛ interaction	
(S= -2)	
p	
Ξ-	
(S= -1)	
Λ	

Ξ0	

T.Takahashi (KEK)
Nakazawa(Gifu U.) et al.

EOS at	high-density	
region 	Λ	

Search for H and Studyof ΛΛ correlation	
Spectroscopy ofΞ hypernuclei	

Emulsion experiments& Automatic scanning	

S-2S	

TPC +SC Helmholtz Magnet	
12 C (estimated)	
Ξ

Invariant mass of ΛΛ	
πp
6
ΛΛ He
4

Nagara Event
6 He	
ΛΛ

He

10

5
Λ He

5
0

0

5

10μm

t

Ξ-

KURAMA spectrometer as a tagger of the (K-,K+)
reaction for emulsion and H search exp.
Most of the detectors are ready to install.
(waiting for beam time allocation)

KURAMA magnet

TOF wallDC1

KL chamber

AIDA chamber

Discovery of Ξ-nucleus for the first time
– KISO Event – K.Nakazawa et al.(PTEP in Press)	
In the test application of Overall Scanning Method, to the emulsion
sample irradiated before, we found the event in which Ξ- is deeply boundin 14N. àThis is the first evidence of Ξ-nucleus 	ΞN interaction is attractive	
Ξ-	Ξ- + 14N → 10ΛBe(#1) + 5ΛHe(#2) 	
10 Be	
Λ

5 He	
ΛNewpaper（2015/1/19）	

Binding energy of Ξ> 1.11±0.25 MeV c.f. 0.17 MeV（atomic orbit）
4.38±0.25MeV if 10ΛBe is in ground state.	

E07 will be carried out in 2016 to find ~100
double-strangeness events by both Hybrid
method and overall scanning method.

Strangeness in n-rich matter
Determine hyperon mixing in ρ=2~3ρ0region where hyperons begin to appear	E40n(2b) n-rich hypernuclei

E10

n

Λ

p

p/n

+

PiID coun?

Σ-n attractive	n(Unique method) Sakaguchi, Ajimura, Fukuda-> Λnn int. in n-rich environment=> Fraction of Λ in n-starSearch for 6ΛH: Not observed in (π-,K+)
Sugimura et al. PLB729 (2014) 39. 	

LH2 target

Forward calorimeter(Unique method ) Koike, Tamura-> Details of ΛN, ΛNN int.

Κ

n

Λ

fraction	

n

π

Σ

Calo

Σ

E13

Fiber tracπΛ-Σ coherent coupling=> Σ- exists in n-star or not(2a) γ spectroscopy ofΛ hypernucleipUltra-fast (x100)
Tracking detector
Using MPPC

(1) Σ+p scattering（unique） Miwa, Tamura-> Σ-n (= Σ+p) int.

H.Tamura,Miwa,Koike(Tohoku U.)	Sakaguchi(Osaka U.), Outa (RIKEN)
et al.	

Λ	

Σ-n repulsive	γ	(3) K- nuclear bound states Outa, Suzuki-> KbarN int. in matter E15, E27 p	
 p	
=> K condensation in n star?
	

K-	

ρ 	

New development of Research on
Neutron Stars
by X- and Gamma-Rays Observatory	

X-ray
Burst	

T. Takahashi(JAXA), T. Tamagawa (RIKEN),
T. Dotani(JAXA), M.Tsujimoto(JAXA), S. Miyazaki (NAO)	
Direct observation of Radius of N-Star by ASTRO-H (2015)

NS	

Companionstar	àGravitational Redshift of narrow absorption linesof heavy elements in the X-ray burst --- Sensitive to R/M of Neutron Star (NS)	

Soft X-ray Spectrometer (SXS)-- Micro Calorimeter Spectrometer	
T. Takahashi et al., Proc. SPIE Int. Soc. Opt. Eng. 8443 (2012) 1Z

Expected Redshift Spectrum

Model X-ray Spectrumof Continuous Parts	

Redshift	

Amplitudeof X-ray	

X-ray Radiation
including absorption lines	
Gravitational
Redshift	E	Neutron Star	

Hot atmosphere	

E/E0à R/M	

E0:Original Energy	

Energy (keV)	

Corona	Blackbody(NS Surface)	
Disk	
Energy (keV)	

Data –Fit(Ｄ+Ｃ+Ｂ)

Model Spectrum	

Fe	
Fe	
S	

S	

Energy (keV)	

Micro-calorimeter and Dewar

Slide by
T.Takahashi(JAXA)	

NASA/GSFC

5	
  mm	
  
(Takahashi et al., 2012, SPIE, 8443, 1)

Theoretical studies of neutron star andnuclear matter (A.Ohnishi, K. Morita et al.)	

• Construction  of  NS  matter  EOSUnderstanding  NS  phenomena

Hint  for  BBB  force  ?
Nagar
a	

RHIC	

T. Miyatsu, S. Yamamuro, K. Nakazato,
ApJ 777 (2013), 4.	

Crust Oscillation and EOS

Pygmy  res.
and  Sym.  E

N N N N N
N Λ N Λ N
Λ Λ N	 Λ Λ	K. Morita, T. Furumoto, A. Ohnishi,
T. Inakura, T.
PRC91 (2015), 024916.
H. Sotani, K.Nakazato, K. Iida, K. Oyamatsu,
Nakatsukasa, K. Yabana, à Talk by K.Morita (Mar.4)	
Mon. Not. Roy. Astron. Soc. 434 (2013), 2060	
 PRC84 (2011) 021302 	

Summary
Neutron-rich Nuclei

Hypernuclei/Hyperons• Neutron Skin Thickness• Pygmy Dipole Resonance• Giant Monopole Resonance• Many-Body correlation(superfluidity, 3N)

•
•
•
•

Nuclear Force
Nuclear Masses
Heavy Ion Collisions
Mean Field TheoryΛ (S= -1)
Σ+, Σ-, Σ0 (S= -1)
Ξ+, Ξ-,Ξ0 (S= -2)	Cold Fermi
Gas
EOS at very
low dense limit	

• Structure of Hypernuclei• Scattering of Hyperons• Interactions of Hyperons

EOS of Asymmetric Nuclear Matter/ Hyperons

Neutron Star

Bulk Property (Radius, Mass)
Superfluidity, Glitch
Composition, Quark/Strangeness Phase
Gravitational Wave

Theories	Special Thanks to Colleagues in

Grant-in-aid for innovative area:“ Nuclear Matter in neutron Stars investigated by experiments
and astronomical observations”
	
H. Tamura (Tohoku U.)
T.Takahashi (KEK), T.Murakami(Kyoto U.),T. Nakamura(Tokyo Tech), S.Horikoshi(Tokyo.U),
T. Takahashi(JAXA),A.Ohnishi(YITP)	Some Remarks	
2/3

ε F = (3π 2 ρ )Λ	mΛ-mn=175 MeV	

p	

n	

ρ0	

High-momentum n Interaction?	
 Low-momentum p, Λ …	d ∝ 1 / ρ 1/ 3
separation	

~8ρ0	

3ρ0à0.7d08ρ0à0.5d0	
~3ρ0	

How such interactions withlarge asymmetry inmomenta are understood?
3-Body Forces?
NNN,YNN,YYY in dense N
matter? 	
QCD has an answer?