probing properties of neutron stars with heavy-ion reactions outline: symmetry energy at...
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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
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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
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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
-
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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
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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
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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
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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
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Partially constrained EOS for astrophysical studies
Danielewicz, Lacey and Lynch, Science 298, 1592 (2002))
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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
● .
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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
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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
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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)
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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
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Testing the standard fudicial value of the moment of inertia
Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008).
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(completely due to general relativity)
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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
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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)
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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)
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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
??????
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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?
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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
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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
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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
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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)
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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
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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
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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
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Excitation function
Central density
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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
?
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Asymmetric nuclear matter
In hyperonic matter
n e
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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