Constraining the EOS of neutron-rich nuclear matter and properties of neutron stars with central heavy-ion reactions

1
Constraining the EOS of neutron-rich nuclear
matterand properties of neutron stars with
central heavy-ion reactions
Bao-An Li
collaborators Wei-Zhou Jiang, Plamen G.
Krastev, Richard Nobra, Will Newton, De-Hua Wen
and Aaron Worley, Texas AM University-Commerce Li
e-Wen Chen and Hongru Ma, Shanghai Jiao-Tung
University Che-Ming Ko and Jun Xu, Texas AM
University, College Station Andrew Steiner,
Michigan State University Zhigang Xiao and Ming
Zhang, Tsinghua University, China Gao-Chan Yong
and Xunchao Zhang, Institute of Modern Physics,
China Champak B. Das, Subal Das Gupta and Charles
Gale, McGill University

• Outline
• Indication on the symmetry energy at
  sub-saturation densities from the NSCL/MSU
  isospin diffusion data
• Astrophysical implications (1) Core-crust
  transition density of neutron stars
• 
  (2) Gravitational waves
  from elliptically deformed pulsars
• Indication on the symmetry energy at
  supra-saturation densities from the FOPI/GSI
  p-/p data
• Summary

2
What is the Equation of State in the extended
isospin space? (EOS of neutron-rich matter)
symmetry energy
Isospin asymmetry
?n neutron density ?p proton density Nucleon
density ??n?p
d
12
12
12
Energy per nucleon in symmetric matter
18
18
3
Energy per nucleon in asymmetric matter
Symmetric matter
?n?p
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 (2008)arXiv0804.3580
density
???
0
??n?p
d
???
1
Isospin asymmetry
3
The Esym (?) from model predictions using popular
interactions
Examples
EOS of pure neutron matter Alex Brown, PRL85,
5296 (2000).
23 RMF models
?
APR
-
Density
4
The multifaceted influence of the isospin
dependence of strong interactionand 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).
(QCD)
(Effective Field Theory)
isodiffusion
Isospin physics
n/p
p-/p
isotransport
in
isocorrelation
Terrestrial Labs
isofractionation
t/3He
K/K0
isoscaling

5
Symmetry energy and single nucleon potential used
in the IBUU04 transport model
The x parameter is introduced to mimic various
predictions on the symmetry energy by different
microscopic nuclear many-body theories using
different effective interactions
stiff
?
soft
Default Gogny force
Density ?/?0
Single nucleon potential within the HF approach
using a modified Gogny force

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

6
Momentum dependence of the isoscalar potential
Compared with variational many-body theory
7
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 ?0
P.E. Hodgson, The Nucleon Optical Model, World
Scientific, 1994 G.W. Hoffmann and W.R. Coker,
PRL, 29, 227 (1972). G.R. Satchler, Isospin
Dependence of Optical Model Potentials, in
Isospin in Nuclear Physics,
D.H. Wilkinson (ed.), (North-Holland,
Amsterdam,1969)
8
Constraints from both isospin diffusion and
n-skin in 208Pb
Isospin diffusion data M.B. Tsang et al., PRL.
92, 062701 (2004) T.X. Liu et al., PRC 76,
034603 (2007)
Transport model calculations B.A. Li and L.W.
Chen, PRC72, 064611 (05)
?
? ?
J.R. Stone
implication
PREX?
Hartree-Fock calculations A. Steiner and B.A. Li,
PRC72, 041601 (05)
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)
9
L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett
94, 32701 (2005)
10
Neutron Star Crust

• Rotational glitches small changes in period from
  sudden unpinning of superfluid vortices.
• Evidence for solid crust.
• 1.4 of Vela moment of inertia glitches.
• Needs to know the density and pressure at the
  transition to calculate the fractional moment of
  inertia of the curst

core
crust
Kazuhiro Oyamatsu, Kei Iida Phys. Rev. C75
(2007) 015801
Can one extract transition density from heavy-ion
collisions?
Chuck Horowitz at WCI3, Texas, 2005
Yes, the symmetry energy constrained by the
isospin diffusion experiments at the NSCL is in
the same density range of the inner crust
11
Onset of instability in the uniform npe matter
Thermodynamic approach
Dynamical approach
K?0
If one uses the parabolic approximation (PA)
Then the stability condition is
Stability condition
gt0
Similarly one can use the RPA
12
What we found about the core-crust transition
density
Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma,
arXiv0807.4477
It is NOT accurate enough to know the symmetry
energy, one almost has to know the exact EOS of
n-rich matter
Why? Because it is the determinant of the
curvature matrix that determines the stability
condition Example
Thermodynamical method
The quartic term is also important for direct
URCA, Andrew Steiner, arXivnucl-th/0607040
13
Constraint on the core-crust transition density
Transition pressure
pasta
Need to reduce the error bars with more precise
data and calculations!
Kazuhiro Oyamatsu, Kei Iida
Phys. Rev. C75 (2007) 015801
Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma,
arXiv0807.4477
14
Partially constrained EOS for astrophysical
studies
Plamen Krastev, Bao-An Li and Aaron Worley,
Phys. Lett. B668, 1 (2008).
Danielewicz, Lacey and Lynch, Science 298, 1592
(2002))
15
Astrophysical impacts of the partially
constrained symmetry energy

• Nuclear constraints on the moment of inertia of
  neutron starsarXiv0801.1653
• Aaron Worley, Plamen Krastev and Bao-An
  Li, The Astrophysical Journal 685, 390 (2008).
• Constraining properties of rapidly rotating
  neutron stars using data from heavy-ion
  collisions arXiv0709.3621
• Plamen Krastev, Bao-An Li and Aaron
  Worley, The Astrophysical Journal, 676, 1170
  (2008)
• Constraining time variation of the gravitational
  constant G with terrestrial nuclear laboratory
  data arXivnucl-th/0702080
• Plamen Krastev and Bao-An Li, Phys. Rev.
  C76, 055804 (2007).
• Constraining the radii of neutron stars with
  terrestrial nuclear laboratory data
• Bao-An Li and Andrew Steiner, Phys.
  Lett. B642, 436 (2006). arXivnucl-th/0511064
• Nuclear limit on gravitational waves from
  elliptically deformed pulsars
• Plamen Krastev, Bao-An Li and Aaron
  Worley, Phys. Lett. B668, 1 (2008).
  arXiv0805.1973
• Locating the inner edge of neutron star crust
  using nuclear laboratory data,
• Jun Xu, Lie-Wen Chen, Bao-An Li and
  HongRu Ma arXiv0807.4477

16
What are Gravitational Waves?

• Gravitational Waves Ripples in space-time

Traveling GW
Gravity J.B. Hartle
Lx
Lx1 h(t)
Amplitude parameterized by (tiny) dimensionless
strain h h(t) DL/L
proper separation between two masses
The expected signal has the form (P. Jaranowski,
Phys. Rev. D58, 063001 (1998) )
F and Fx plus and cross polarization, bounded
between -1 and 1 h0 amplitude of the
gravitational wave signal, y polarization
angle of signal i inclination angle of source
with respect to line of sight, F(t)- phase of
pulsar
17
Why do we need to study Gravitational
Waves? Michael LandryLIGO Hanford
Observatoryand California Institute of Technology

• Test General Relativity
• Quadrupolar radiation? Travels at speed of light?
• Unique probe of strong-field gravity
• Gain different view of Universe
• Sources cannot be obscured by dust / stellar
  envelopes
• Detectable sources are some of the most
  interesting,
• least understood in the Universe
• Opens up entirely new non-electromagnetic
  spectrum

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Gravitational Wave Interferometer Projects
Michelson-Morley IFO
LIGO, GEO, TAMA VIRGO taking data LISA is a
ESA-NASA project
18
Gravitational Waves
19
Possible sources of Gravitational Waves
Examples
Supernovae / GRBs bursts

• Compact binary inspiral chirps

Orbital decay of the Hulse-Taylor binary neutron
star system (Nobel prize in 1993) is the best
evidence so far.
Elliptically deformed pulsars
periodic
Non-radial oscillations of neutron stars
20
Gravitational waves from elliptically deformed
pulsars
Solving linearized Einsteins field equation of
General Relativity, the leading contribution to
the GW is the mass quadrupole moment
Frequency of the pulsar
Distance to the observer
Breaking stain of crust
Mass quadrupole moment
EOS
B. Abbott et al., PRL 94, 181103 (2005) B.J.
Owen, PRL 95, 211101 (2005)
21
Estimate of gravitational waves from
spinning-down of pulsars Assumption
spinning-down is completely due to the GW
radiation
Standard fiducial value

• Solid black lines LIGO and GEO science
  requirement, for T1 year
• Circles upper limits on gravitational waves from
  known EM pulsars, obtained from measured spindown
• Only known, isolated targets shown here

GEO
LIGO
The LIGO Scientific Collaboration, Phys. Rev. D
76, 042001 (2007)
22
Testing the standard fudicial value of the moment
of inertia
Aaron Worley, Plamen Krastev and Bao-An Li, The
Astrophysical Journal 685, 390 (2008).
23
The ellipticity of pulsars
EOS
Plamen Krastev, Bao-An Li and Aaron Worley,
Phys. Lett. B668, 1 (2008).
24
Constraining the strength of gravitational
wavesPlamen Krastev, Bao-An Li and Aaron
Worley, Phys. Lett. B668, 1 (2008).
Compare with the latest upper limits from
LIGOGEO observations
Phys. Rev. D 76, 042001 (2007)
It is probably the most uncertain factor
B.J. Owen, PRL 95, 211101 (05)
25
Pion ratio probe of symmetry energyat
supra-normal densities
GC Coefficients2
26
Isospin asymmetry reached in heavy-ion reactions
48
48
E/A800 MeV, b0, t10 fm/c
124
124
197
197
27
t10 fm/c
t10 fm/c
Correlation between the N/Z and the p-/ p
Another advantage the p-/ p is NOT sensitive to
the incompressibility of symmetric matter, but
the high density behavior of the symmetry energy
(K0211 MeV is used in the results shown here)
(distance from the center of the reaction system)
28
Formation of dense, asymmetric nuclear matter
Symmetry energy
Stiff
Central density
Soft
density
p-/ p probe of dense matter
Soft Esym
Stiff Esym
n/p ratio at supra-normal densities
29
p-/p ratio as a probe of symmetry energy at
supra-normal densities
W. Reisdorf et al. for the FOPI/GSI 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
Need a symmetry energy softer than the above to
make the pion production region more neutron-rich!
low (high) density region is more neutron-rich
with stiff (soft) symmetry energy
30
N/Z dependence of pion production and effects of
the symmetry energy
Softer symmetry energy
FRIB?
APR
Stiff symmetry energy
31
Zhigang Xiao, Bao-An Li, Lie-Wen Chen, Gao-Chan
Yong, Ming Zhang
arXiv0808.0186
Excitation function
Central density
?
MSU-TPC?
32
Astrophysical implications
For pure nucleonic matter
K0211 MeV is used, higher incompressibility for
symmetric matter will lead to higher masses
systematically
The softest symmetry energy that the TOV is still
stable is x0.93 giving M_max0.1 solar mass
and Rgt40 km
33
Can the symmetry energy becomes negative at high
densities? Yes, due to the isospin-dependence of
the nuclear tensor force The 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
34
In hyperonic matter
Asymmetric nuclear matter
35
Summary

• Based on the NSCL/MSU data, the symmetry energy
  at sub-saturation
• densities is constrained to

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