Transcript Diapositiva 1 - Beijing Normal University

Int. Workshop on Nuclear Dynamics in HIR
and Neutron Stars
Beijing Normal University, 9-14 July 2007
EoS of Nuclear Matter and Structure of
Neutron Stars
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•
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outline:
observational data of neutron stars
microscopic hadron EoS from pure baryon to
composite matter (leptons,Y,K¯)
onset of transition to quark phase
confinement models of quarks
M-R diagram of NS from general relativity (TOV)
preliminary remarks:
nuclear matter is an homogeneous system made of rigid nucleons interacting via the
nuclear force (surface and coulomb effects are neglected).
neutron stars are compact astrophysical objects, mostly born after the explosion of
supernovae. They are supposed to be made of nuclear matter in their interior.
But, the way they were born, the neutron stars in the inner core are not simply made
of nucleons, but of neutrons and protons in equilibrium with leptons (electrons and muons),
and we should assume that, at increasing density, the threshold for the production of new particles
is reached hyperons, kaons, and quarks.
Therefore we will deal with asymmetric nuclear matter
 beta-equilibrium with electrons and muons : p + e¯ n + 
 hyperonized matter:
n + n  n +  ( p + ¯)
at
 > 2o
 kaon condensation
n  p + K¯
at
 > 2-3o
 transition to quark matter
HP  QP (u,d,s)
at
 ~ 6o
view of a neutron star
Crust : pinning,thermal
emission,…
( Cao talk)
Interior
Facts about Neutron Stars :
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•
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•
M ~ 1 to 2M0 ( M0=1.998·1033g)
R ~ 10 Km
N obs. Pulsars - 1500
P > 1.58 ms (630 Hz)
B = 108 ÷ 1013 Gauss
N.K. Glendenning, Compact Stars, Nuclear Physics , Particle Physics, Springer, 2000
Observed Masses: three main families
J. Lattimer
PSR 1913+16
M = 1.44 M©
PSR J0751+1807
M > 2.1±0.3 M©
Thermal evolution
Non superfluid
p + e-  n +  e
n  p + e- +  e
Superfluid
Yakovlev et al
direct URCA : Yp
(n,p) + p + e-  (n,p) + n + e
(n,p) + n  (n,p) + p + e- + e
>
1
9
modified URCA
due to the poor information from NS we need to make theoretical predictions
as much accurate as possible.
for the EoS of nuclear matter the state of art is quite reasonable since the
theory of nuclear matter has undergone a long term development reaching a high
Degree of sophistication.
The description yperon matter is also satisfactory since we know the N-Y force,
even we still don’t know the Y-Y force.
(see Dang and Takatsuka talks)
the interaction N-K is less known, and all predictions for the k condensation
are still model-dependent.
(see Sun talk)
for the quark phase we have many theories still waiting constraints
(Gao, Liu,Maruyama, Huang, Di Toro,...talks)
Hadron EoS
--empirical constrains --
from the NN experimental phase shifts
 two-body realistic interactions
from B-W nuclear mass formula
saturation properties
EA = -16 MeV

= .17 fm-3
KA = 220 MeV (monopole)
Esym =30 MeV
Saturation curve within the BBG
“gap choice” (U(k)=0 if k≥kF),
and Av14
SP
BBG
“continuous choice”
Coester et al., Phys. Rev. C1, 769 (1970)
 Similar results within the Variational Method
 Possible corrections : many-body forces and/or relativistic effects
Dependence on the many-body scheme
Nucleon-Nucleon Interaction:
Argonne v18
APR : Variational
(Akmal, Pandharipande
& Ravenhall, PRC 58, 1804 (1998))
(Wiringa, Stoks & Schiavilla, Phys. Rev. C51, 38 (1995))
Catania group : BHF
(Akmal, Pandharipande
& Ravenhall, PRC 58, 1804 (1998))
Neutron Matter
?
Symmetric Matter
Three Body Force
TBF provides the repulsion necessary for
1) saturation properties
2) stiff EoS  massive NS
3bf is poorly known
:
 A phenomenological model is built up from the saturation energy of
nuclear matter (or density) and the binding energy of the triton
Urbana IX model :
V ijk  V ijk
2
 V ijk
R
 A microscopic model is based on a meson exchange model
coupled with nucleonic excitations: ((1232),N*(1440),…) consistent
with two body interaction
 Chiral perturbation theory
Effects of TBF
Carlson et al.,
NP A401,(1983) 59
(a) : excitation of a Δ resonance (attractive)
(b) : Roper R resonance (repulsive)
Microscopic model :
P. Grange’ et al,
PR C40, (1989)
1040
(a) : excitation of (Δ,R) resonances
(b) : excitation of a nucleon-antinucleon pair
(relativistic effect on the EOS, repulsive)
Zuo, Lombardo,Lejeune,Mathiot,
N P A706, 418 (2002)
Meson-exchange Model of the
two and three body Interaction


+
,N*
N 
+


+ (-)


+

,N*
baryon exc
N
+


ph exc from
Dirac sea


N*
+
N
+


+
+




N
N*
+

+



N*
N
+



+

N*
+
(-)
impressive
overlap!
N
BHF + (

BHF vs Dirac-BHF
relativistic effects

) = DBHF
but DB misses other TBF effects
EoS
Symmetry energy
 Improved saturation point
 ≈ 0.18 fm-3
 Symmetry energy at saturation Sv≈ 32 MeV
 Incompressibility at saturation K ≈ 210 MeV
EoS of dense matter from HIC
Science 298,
1592 (2002)
• Transverse Flow Measurements
in Au + Au collisions at
E/A=0.5 to 10 GeV
• Pressure determined from
simulations based on the
Boltzmann-Uehling-Uhlenbeck
transport theory
from pure baryon to composite
matter
Composition of Neutron Stars
-equilibrium neutral matter
p  e  n  e
p     n  
e  e     
1  4 Esym 
Yp  

2  ck F 
3
Neutron Stars : Asymmetric and charge neutral beta-stable matter
Compact Stars in GTR : Tolman-Oppenheimer-Volkoff Equations
Only stiff EoS is compatible
with massive NS (2.1 M© )
Mtheor Mobs
Zhou, Burgio,Lombardo,Zuo.
PR. C69, 018801 (2004)
Yperons
INCLUDING HYPERONS
 Possible extension of the BBG theory.
 Few experimental data on NH interaction.
Nijmegen interaction (NSC89)
(Maessen et al., Phys. Rev. C40, 2226 (1989))
 Unknown HH interaction.
 Strong consequences for NS structure.
See F. Burgio et al., Phys. Rev. C58,3688 (1998), ibid. 61, 055801 (2000)
nnn
n  n  p  
.......................
Hyperon onset at density
close to 2-3 times the
saturation value.
Weak dependence on the
adopted 3BF.
Strong softening of the EoS,
no matter the nucleonic
TBF’s.
Hyperon-hyperon interaction ?
Same results by the Barcelona group:
I. Vidana et al., Phys. Rev. C73, 058801 (2006)
with NSC97 Nijmegen potential
(NH + HH inter. (Stoks & Riken,1999))
Appearance of baryonic strange matter not
compatible with any NS mass data
It demands for a stiffening
of the Equation of State!!
K condensation
Bethe-Brown, ApJ 1995
K¯ - condensation
Chemical equilibrium:
nuclear matter: n.p,e,,K,…
n ↔ p + l + l
n ↔ p + K¯
l ↔ l + K¯
EA  K A  V (u)  0u(1  2x)2 S (u)  El  EK
K= e
Proton strangeness
content: a3 ms [MeV]
(a)
(b)
(c)
=-310
=-230
=-134
TBF
Thorsson,Lattimer, Prakash NPA 1994
Zuo,A.Li,ZH Li, Lombardo, PRC 2004
Chemical composition of NS
with K-condensation
‘nuclear matter’ star
Bethe & Brown,ApJ 1995
p
KK-
p
ee-
Zuo,A.Li,ZH Li, Lombardo, PRC 2004
Av18 ( thin )
Av18+TBF ( thick )
model parameter dependence
Critical density c/0
2bf
a3ms=-310
=-222
=-134
2.6
3.4
5.0
2bf+3bf
2.4
in competitiowith Yperons
2.9
3.8
K-condensation vs hyperonization
V18 (or Paris)+ TBF
the two critical density could be comparable!
Critical density (u=/0):
2bf
a3ms=-310 uc=2.6
2bf+3bf
2.4
=-222
=3.4
2.9
=-134
= 5.0
3.8
no kaons
Kaon condensantion
- neutrino trapping -
with kaons
free 
-trapping
with kaons
K threshold model
dependent
EoS with phase transition
to K-condensation
Thorsson,Lattimer, Prakash NPA 1994
Zuo,A.Li,ZH Li, F. Burgio, Lombardo, PRC 2006
K-condensation in NS: Mass-Radius plot
neutrino trapping
Zuo,A.Li,ZH Li, F. Burgio, Lombardo, PRC 2006
Quark phase
Structure of Hybrid Stars
outlook::
 at large  ( 1 fm-3) hadron phase can coexist with deconfined quark
phase, and, eventually, completely dissolve into a pure quark core
(hybrid star) .
 after the recent discovery of massive stars, with M>2M© (2005)
study of hybrid stars it has been addreesed to the evolutionary
scenarios of NS birth
 the low mass and high mass NS could belong to two different evolutionary
scenarios
transition from Hadron to Quark Phase
~1/fm3

dNN~ 1 fm
Since we have no unified theory which describes
both confined and deconfined phases, we use two
separate EOS:
one with hadronic degrees of freedom (HP)
one with quark degrees of freedom (QP)
Which model for Quark Matter ?
c60
Constraints from phenomenology on the
general quark EOS :
i) In symmetric nuclear matter one can expect a transition
to quark matter at some density, but it must be larger than
at least 2-3 times normal nuclear matter density
(no evidence from heavy ion reactions at intermediate energy)
ii) Strongly asymmetric nuclear matter would favour the
appearance of quark phase at lower density
(no experiments so far at (N-Z)/A >> 0.3)
iii) Strange matter stable against two-flavor matter
iv) The maximum mass of neutron stars must be larger than
1.44 solar mass
(not true after 2005 new data with M/M© > 2: PSR J0751+1807 !)
Baym & Chin, PLB62 (1976)241
Chapline and Nauenberg, Nature 264 (1976)
Keister & Kisslinger, PLB64(1976)117
Quark matter models : MIT Bag Model,
Nambu-Jona—Lasinio (NJL)
Color Dielectric (CDM)
DDM Model
DDM: model from deconfined phase to asymptotic freedom
0
Mq  Mq
D
1
 3
QM vs HM EoS in -equilibrium
- crosspoints Yperonized NM
p+e →n+ 
n+n→n+
n+n↔p+¯
Baryonic NM
Maieron,Baldo,Burgio,Schulze,Phys.Rev. D70 (2004)
Three flavor QM
d→u+e+
s→u+e+
u+s↔d+u
quark matter nb=(Nu+Nd+Ns)/3V
nuclear matter  = (N+Z)/ V
●
Peng and Lombardo, PP 2007
hadron-to-quark phase transition
under the total charge neutrality condition
Gibbs equilibrium condition
pHP ( n,e) = pQP (n,e)
HP = QP
THP = TQP
 line pHP under H-charge neutrality is the EoS of pure hadron phase
 line pQP under Q-charge neutrality is the EoS of pure quark phase
 line intersecting the two pressure surfaces is the EoS of
Hadron-Quark mixed phase
n = u + 2 d in he quark phase
Peng and Lombardo, 2007
NP and QP charge neutrality gives a curve
“Hybrid” stars
The value of the maximum
mass lies in the range
between 1.5 and 1.9
solar masses (>1.44 M0).
MDD
1,6
1,4
Hadronic
Phase
1,2
Y Axis Title
 The value of the maximum
mass is mainly determined
by the quark component
of the neutron star and
by the corresponding EOS.
1,0
Quark Phase
0,8
0,6
0,4
0,2
0,0
0
2
4
6
8
10
12
14
16
18
20
X Axis Title
The structure of neutron star is
strongly dependent on the EoS
used for describing the quark phase.
C. Maieron et al., Phys. Rev. D70, 070416 (2004)
F. Burgio et al., Phys. Rev. C66, 025802 (2002)
M. Buballa et al., PLB 562, 153 (2003)
GX Peng and U. Lombardo PP 2007
MIT, DDM :
CDM
:
NJL
:
stable stars are in a quark +
mixed + hadronic phase.
stable stars are only in pure
quark phase.
instability at the quark onset
(hadron + mixed phase)
Two evolutionary scenarios for NS
Haensel, exoct 2007 (Catania, June 11-15)

NS born in core-collapse of massive stars (20-30 M© ) are sufficiently dense
and hot to produce eos-softening quark core resulting in Mmax = 1.5 M ©

NS coupled to a white dwarf companion could increase their mass by accretion
in a long-lived binary sistem up to Mmax  2. M © (no quark core)
Two evolutionary branches of NS
PSR J0751+1807
M 2.10.2 M
pure hadron matter
PSR 1913+16
M 1440.2 M
hybrid neutron star
Final comments
NS mass is a robust constraint of the nuclear matter EoS:
the range 1.5-2.0 solar masses predicted by solving theTOV
eqs is not trivial.
But there are other constraints of the EoS to be investigated:
Superfluidity of the crust (pinning) and of the interior (cooling)
Cooling mechanisms: URCA, opacity, pairing
Magnetic field
Conclusions:
 The EoS of nuclear matter is stiff according to a microscopic theory
constrained by the experimental NN cross section.
 A stiff EoS is also supported by the NS observed masses (and other
observables not discussed here).
 EoS of hadron phase, including yperons, is reasonably described
 EoS of quark phase requires additional study (improving NJL model)
 the low mass (M<1.5M©) stars can be interpreted as hybrid stars
if the critical density of deconfined phase is so low to hinder both
yperons and kaons
 the high mass (M>2.0M©) is interpreted as pure hadron phase
 anyhow the existence of two classes of neutron stars demands
for the study of the evolution of neutron stars
Thank you!
hadron-to-quark phase transition
under charge neutrality condition for the two phases
- Maxwell construction -
Gibbs equilibrium condition
pHP ( n,e) = pQP (n,e)
HP=QP
THP = TQP
no Coulomb, no surface
hadron phase
p+e→n+
n →p+e+
n↔p+K
P + e = n
N + P = K
no  trapping
quark phase
d→u+e+
s→u+e+
u+s↔d+u
u + e = d
d = s
one (two) independent variables in each phase, if charge neutrality is (not) required.
Isospin dependence of critical density
no charge neutrality
Skyrme-like EoS
Kaon condensation in pure hadron phase
with Skirme-like EoS
( the scenario will not significantly change
with the BHF+TBF EoS)
supernovae explosions (high
temperature and isospin and density)
205 MeV is the threshold for hadron stability against two flavor quark matter
M-R plot for Hybrid Stars
1,6
1,4
Y Axis Title
1,2
1,0
0,8
0,6
0,4
0,2
0,0
0
2
4
6
8
10
12
X Axis Title
14
16
18
20
Sensitivity of M/MΘ to constant B
Alford & Reddy,2003
M/M
0
1.33
1.35
1.44
1.52
3.0
3.0
2.0
1.5
quark phase in beta-equilibrium
u,d,s,e-
u + e = d
d = s
DDM vs MIT-B models
charge conservation
 hadron phase
 mixed phase
 quark phase
c  c  c  c  0
HP
p
e
K
c  (1   )  c  0
QP
HP
c  c  c  c  c  c  0
QP
u
s
e
K
d
Phase transition from nuclear matter to SQM
(skyrme-like EoS)
Q matter in beta-equilibrium
(charge neutrality)
DDM vs MIT:
P minimum in DDM
E=0 in the vacumm
Quark matter
hadronization(no quarks)
If D1/2 decreases the crosspoint
Moves to lower density.
Yperon-rich NS
Baldo,Burgio,Schulze, PRC 61 (2000)
MIT bag vs Color Dielectric Model
Yperonized Nuclear Matter
Maieron,Baldo,Burgio,Schulze,
Phys.Rev. D70 (2004)
Neutron Star Structure
extraordinary laboratory for studying states
of nuclear matter
Clusters and light particle condensates
Superfluid states
Coexisting liquid-gas phase
Collective excitations
Nuclei far from stability line
Hypernuclear matter
K condensation
Hadron-to quark mixed phase
Quark matter
Color superconductivity
………
………
from exotic nuclei
Table of Isotopes
Neutron skin
GR in neutron-rich nuclei
Spin-isospin modes (GT)
Super-heavy elements
Exotic HIC at intermediate energy
Light fragment production at Fermi energy
Unstable nucleus-nucleus systems
Isospin distillation
Di Toro et al.
nuclear compressibility, symmetry energy, spin-isospin
Mass-Radius Plot for a NS
from Tolman-Oppenheimer-Volkov Eq. +
EoS: =P()
mass-radius plot
all EoS are consistent with the observed
max mass of NS and the central densities
are also quite large,but we need a very
large max mass, when including hyperons
NS cooling via neutrino emission
(n,p) + p + e-  (n,p) + n + e
(n,p) + n  (n,p) + p + e- + e
p + e-  n + e
n  p + e- + e
modified URCA
1
direct URCA : Yp > 9
The EoS predicts:
1
Yp> 9
 > 0.28 fm-3
central = 6.24 fm-3
Direct URCA processes are allowed to occur!