Probing properties of neutron stars with heavy-ion reactions

Outline:

• Symmetry energy at sub-saturation densities constrained by heavy-ion collisions at intermediate energies

Imprints of symmetry energy on gravitational waves(1) Gravitational waves from elliptically deformed pulsars

(2) The axial w-mode of gravitational waves from non-rotating neutron stars

• Symmetry energy at supra-saturation densities constrained by the FOPI/GSI data on the π-/π+ ratio in relativistic heavy-ion collisions

Disturbing/Puzzling(Interesting?) implications for neutron stars

& collaborators:Plamen G. Krastev, Will Newton, De-Hua Wen and Aaron Worley,Texas A&M University-CommerceLie-Wen Chen and Hongru Ma, Shanghai Jiao-Tung UniversityChe-Ming Ko and Jun Xu, Texas A&M University, College StationAndrew Steiner, Michigan State UniversityZhigang Xiao and Ming Zhang, Tsinghua University, ChinaGao-Chan Yong and Xunchao Zhang, Institute of Modern Physics, ChinaChampak B. Das, Subal Das Gupta and Charles Gale, McGill University

Bao-An Li

The multifaceted influence of the isospin dependence of strong interaction

and symmetry energy in nuclear physics and astrophysics

J.M. Lattimer and M. Prakash, Science Vol. 304 (2004) 536-542. A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. 411, 325 (2005).

The latest results: talks by Bill Lynch, Hermann Wolter and Pawel Danielewicz

Recent progress and new challenges in isospin physics with heavy-ion reactions:Bao-An Li, Lie-Wen Chen and Che Ming Ko Physics Reports, 464, 113-281 (2008)arXiv:0804.3580

The Esym (ρ) from model predictions using popular interactions

2

pure neutron matter symmetric nuclear matter2

1( ) ( ) ( )

2sym

EE E E

Examples:

Density

23 RMFmodels

ρ

-

Symmetry energy and single nucleon potential used in the IBUU04 transport model

12'

'0 0 0 0

, 3 , ' 3 '2 2 2 2

0

0

0

1 2 2,

( , , , , ) ( ) ( ) ( ) (1 ) 81

2 2( , ') ( , ')' '1 ( '

' , ( ) 121 , ( ) 96 ,

) / 1 ( ') /

2112 1 1

u l

l u

BU p A A B

C Cf r p f r pd p d p

p p

B BA A

x x x x x

xK MeVx

p

xx

p

��������������

ρ

C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, 034611 (2003).

B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614; NPA 735, 563 (2004).

softsoft

stiff

stiff

MDI single nucleon potential within the HF approach using a modified MDI single nucleon potential within the HF approach using a modified Gogny force:Gogny force:

Density ρ/ρ0

The momentum dependence of the nucleon potential is a result of the non-localityof nuclear effective interactions and the Pauli exclusion principle

The x parameter is introduced to mimic various predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions

Default: Gogny force

Momentum and density dependence of the symmetry (isovector) potential

Lane potential extracted from n/p-nucleus scatterings and (p,n) charge exchange reactions provides only a constraint at ρ0:

Lane 1

1

kin

( ) / 2 ,

28 6 MeV, 0.1 0.2

for E 100 MeV

n p R kin

R

U U U V E

V

P.E. Hodgson, The Nucleon Optical Model, World P.E. Hodgson, The Nucleon Optical Model, World Scientific, 1994 Scientific, 1994

G.W. Hoffmann and W.R. Coker, PRL, 29, 227 (1972).G.W. Hoffmann and W.R. Coker, PRL, 29, 227 (1972).

G.R. Satchler, Isospin Dependence of Optical Model G.R. Satchler, Isospin Dependence of Optical Model Potentials, Potentials, in Isospin in Nuclear Physics, in Isospin in Nuclear Physics, D.H. Wilkinson (ed.), (North-Holland, Amsterdam,1969)D.H. Wilkinson (ed.), (North-Holland, Amsterdam,1969)

/n p isoscalar LaneU U U

Constraints from both isospin diffusion and n-skin in 208Pb

ρ ρ

Neutron-skin from nuclear scattering: V.E. Starodubsky and N.M. Hintz, PRC 49, 2118 (1994);

B.C. Clark, L.J. Kerr and S. Hama, PRC 67, 054605 (2003)

Isospin diffusion data:M.B. Tsang et al., PRL. 92, 062701 (2004); T.X. Liu et al., PRC 76, 034603 (2007)

Hartree-Fock calculationsA. Steiner and B.A. Li, PRC72, 041601 (05)

PREX?

implication

Transport model calculationsB.A. Li and L.W. Chen, PRC72, 064611 (05)

124Sn+112Sn

X=1

X=0

x=-1

MDI potential energy density

1.05

00

0.69 31.631.6( / ( ) ) ) ( /

between the and lines, agrees extremely well with the APx=-x=0 1 R

Symmetry energy constrained at -saturation densiti sub es

symE

L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005)L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005)

(IBUU04)

For more detailsTalk by Bill Lynch

(ImQMD)

Courtesy of M.B. Tsang

X=-1

Partially constrained EOS for astrophysical studies

Danielewicz, Lacey and Lynch, Science 298, 1592 (2002))

Constraining the radii of NON-ROTATING neutron stars

APR: K0=269 MeV.

The same incompressibility for symmetric nuclear matter of K0=211 MeV for x=0, -1, and -2

Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006)

Nuclear lim

its

● .

Astronomers discover a neutron-star spining at 716

Science 311, 1901 (2006).

Plamen Krastev, Bao-An Li and Aaron Worley, APJ, 676, 1170 (2008)

RNS code by Stergioulas & Friedman

Gravitational waves from elliptically deformed

pulsars

Mass quadrupole moment

Breaking stain of crust

EOS

B. Abbott et al., PRL 94, 181103 (2005)B.J. Owen, PRL 95, 211101 (2005)

Solving linearized Einstein’s field equation of General Relativity, the leading contribution to the GW is the mass quadrupole moment

Frequency of the pulsar

Distance to the observer

Constraining the strength of gravitational wavesPlamen Krastev, Bao-An Li and Aaron Worley, Phys. Lett. B668, 1 (2008).

Compare with the upper limits of 76 pulsars from LIGO+GEO observations

It is probably the most uncertain factor

B.J. Owen, PRL 95, 211101 (05)

Phys. Rev. D 76, 042001 (2007)

Spin-down estimate for fast-spinning NSAaron Worley, Plamen Krastev and Bao-An Li (2009)

The moment of inertia is calculated from RNS instead of using the

ellipticity

Testing the standard fudicial value of the moment of inertia

Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008).

(completely due to general relativity)

MNRAS, 299 (1998) 1059-1068

The first w-mode The frequency is inversely proportional to the compactness of the star

The EOS of neutron-rich matter enters here:

MNRAS, 310, 797 (1999)

axial

pola

r

7.2

7.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

1.0 1.2 1.4 1.6 1.8 2.00

1

2

3

4

5

(kH

z)

MDIx0 MDIx-1 APR

wI

(kH

z)

wII

M(Msun

)

Imprints of symmetry energy on the axial w-modeDe-Hua Wen, Bao-An Li and Plamen G. Krastev (2009)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.12 0.14 0.16 0.18 0.20 0.22 0.24

0.40

0.45

0.50

0.55

0.60

MDIx0 MDIx-1 APR

wII

Re

(M)

M/R

Im(M)

0.25

0.30

0.35

0.40

0.45

0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24

0.18

0.20

0.22

0.24

MDIx0 MDIx-1 APR FIT

wI

Re

(M)

M/R

Im(M)

Scaling of the frequency and decay rate of the w-mode

MNRAS, 299 (1998) 1059-1068

MNRAS, 310, 797 (1999)

L. K. Tsui and P. T. Leung, MNRAS, 357, 1029(2005) ; APJ 631, 495(05); PRL 95, 151101 (2005)De-Hua Wen, Bao-An Li and Plamen G. Krastev (2009)

The Esym (ρ) from model predictions using popular interactions

2

pure neutron matter symmetric nuclear matter2

1( ) ( ) ( )

2sym

EE E E

Examples:

Density

23 RMFmodels

ρ

-

EOS of pure neutron matterAlex Brown, PRL85, 5296 (2000).

APR

??????

Can the symmetry energy becomes negative at high densities?Yes, due to the isospin-dependence of the nuclear tensor forceThe short-range repulsion in n-p pair is stronger than that in pp and nn pairs At high densities, the energy of pure neutron matter can be lower than symmetric matter leading to negative symmetry energy

Example: proton fraction with 10 interactions leading to negative symmetry energy

3 30 0(0.048[ / ( )] ( / )() 1 2 )symsymE Ex x

2sym

symmetry energy

because of the term,

for symmetric matter,

it is energetically more favoriable to write =0=1

Negative Isospin separati

-1,

i.e., pure neutron m

on insta

atter +

bil

pu

ity

E

re proton

matter

Why? Can the modern effective field theory verify this?

Pion ratio probe of symmetry energy

at supra-normal densities

0

nn 0 1 5 a) Δ(1232) resonance model pp 5 1 0 in first chance NN scatterings: np(pn) 1 4 1 (negelect rescattering and reabsorption)

2

2

2

)(5

5ZN

NZZ

NZN

R. Stock, Phys. Rep. 135 (1986) 259. b) Thermal model: (G.F. Bertsch, Nature 283 (1980) 281; A. Bonasera and G.F. Bertsch, PLB195 (1987) 521)

exp[2( ) / ]n p kT

H.R. Jaqaman, A.Z. Mekjian and L. Zamick, PRC (1983) 2782.

c) Transport models (more realistic approach): Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701, and several papers by others

31 1( ) {ln ( ) ( )}

2

m mn p mnn p asy asy Coul m T n p

mp

mV V V kT b

m

GCCoefficients2

Is Is ππ--//ππ++ ratio really a good probe of the symmetry energy at supra-normal densities? ratio really a good probe of the symmetry energy at supra-normal densities?

( )like

0 *0

*

1 23 31 23 3

N

N

t

Sub-saturation density: 5% Supra-saturation densities: 25%

X=1

X=-

2X=0

X=-1

0

0X X for

X X for

H

L

XL=XH=1

XL=-2, XH=1

XL=1, XH=-2

XL=XH=-2π

π

E/A=800 MeV, b=0, t=10 fm/c

48 48

124 124 197 197

Isospin asymmetry reached in heavy-ion reactions

2( , ) ( ,0) ( )symE E E

Symmetry energy

density

t=10 fm/c

Correlation between the N/Z and the π-/ π+

(distance from the center of the reaction system)

t=10 fm/c

Another advantage: the π-/ π+ is INsensitive to the incompressibility of symmetric matter and reduces systematic errors, but the high density behavior of the symmetry energy (K

0=211 MeV

is used in the results shown here)

W. Reisdorf et al. for the FOPI/GSI collaboration , NPA781 (2007) 459

IQMD: Isospin-Dependent Quantum Molecular DynamicsC. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka, S.A. Bass, H. Stoecker, W. Greiner Eur. Phys. J. A1 (1998) 151-169

π-/π+ ratio as a probe of symmetry energy at supra-normal densities

lowlow (high)(high) density region is more neutron-rich density region is more neutron-rich withwith stiff stiff (soft)(soft) symmetry energysymmetry energy

2( , ) ( ,0) ( )symE E E

Need a symmetry energy softer than the above to make the pion production region more neutron-rich!

2/3 0

00

2/3100 3(2corresponding t 1) ( )

5o ( )

8 FsymE E

W. Reisdorf et al. for the FOPI collaboration , NPA781 (2007) 459

IQMD: Isospin-Dependent Quantum Molecular Dynamics C. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka, S.A. Bass, H. Stoecker, W. Greiner Eur.Phys.J. A1 (1998) 151-169

Near-threshold π-/π+ ratio as a probe of symmetry energy at supra-normal densities

lowlow (high)(high) density region is more neutron-rich density region is more neutron-rich withwith stiff stiff (soft)(soft) symmetry energysymmetry energy

2( , ) ( ,0) ( )symE E E

Need a symmetry energy softer than the above to make the pion production region more neutron-rich!

2/3 0

00

2/3100 3(2corresponding t 1) ( )

5o ( )

8 FsymE E

IQMD

FRIB/M

SU

RIKEN

Radioactive

Beam

Facilitie

s

N/Z dependence of pion production and effects of the symmetry energyZhi-Gang Xiao, Bao-An Li, L.W. Chen, G.C. Yong and. M. ZhangPRL (2009) in press.

FAIR/G

SI

400 MeV/A

Excitation function

Central density

The softest symmetry energythat the TOV is still stable is x=0.93 giving M_max=0.11 solar mass and R=>28 km

For pure nucleonic matterIF the conclusion is right,Disturbing implications?

K0=211 MeV is used, higher incompressibility

for symmetric matter will lead to higher masses systematically

?

Asymmetric nuclear matter

In hyperonic matter

n e

1.05

0 0

0.6931.6( / ) ( ) 31.6( / )

L=86 25 MeV

symE

Summary

• The symmetry energy at sub-saturation densities is constrained to

• The FOPI/GSI pion data indicates a symmetry energy at supra-saturation densities much softer than the APR prediction

It agrees extremely well with the APR prediction