Transcript Diapositiva 1

Specific and non-trivial relations
among different fields
NUCLEAR
STRUCTURE
MANY-BODY
SYSTEMS
QCD
HADRON PHYSICS
NUCLEAR PHYSICS
ASTROPHYSICS
M. Baldo
NUCLEAR MATTER
HEAVY ION
REACTIONS
Catania
Ferrara
Milano
M. Baldo
G.F. Burgio
L.G. Cao
M. Di Toro
G. Giansiracusa
V. Greco
U. Lombardo
C. Maieron
O. Nicotra
H.J. Schultze
X.R. Zhou
A. Drago
F. Frontera
G. Pagliara
I. Parenti
P. Avogadro
P.F. Bortignon
R.A. Broglia
G. Colo’
P. Donati
G. Gori
F. Ramponi
P.M. Pizzochero
E. Vigezzi
Pisa
Roma
I. Bombaci
A. Fabrocini
G. Lugones
Trieste
O. Benhar
V. Ferrari
L. Gualtieri
S. Marassi
Iniziative
specifiche
INFN
Torino
S, Fantoni
A. Ilarionov
K.E. Schmidt
A. Lavagno
CT51
LS31
MI31
OG51
PI31
PI32
I. Bombaci NPA 754(2005)335c
J.M. Lattimer , M. Prakash, Science 304(2004)
The structure and the properties of a compact star (“NS”) are
determined by the equation of state (EOS) of dense hadronic matter.
matter’s constituents
EOS
interactions
Pressure
Mmax = (1.4 – 2.5) M
“stiff” EOS
Mmax
R
M(R), …
Oppenheimer-Volkoff mass
M
“stiff” EOS
“soft”
“soft”
density
R
BBG
Variational
M. Baldo, G. Giansiracusa, U. Lombardo, H.Q. Song, PLB 473(2000)1
A. Akmal, V.R. Pandharipande, D.G. Ravenhall, PRC58(1998)1804
X.R.Zhou, G.F. Burgio, U. Lombardo, H.-J. Schultze, W. Zuo, PRC69(2004)18801
-stable nuclear matter
p  e  n   e
if
 e m  105.6MeV
e      e   
n  p  e  e

p    n  

    0
neutrino-free matter
 Equilibrium with
n   p  e
respect to the weak
interaction processes
   e

np  ne  n
Charge neutrality
To be solved for any given value of the total baryon number density nB
Composition of asymmetric and beta-stable matter
including hyperons
•Composition of stellar matter
n   p  e
i) Chemical equilibrium among the
e  
different baryonic species
2 n   p    
n  
 p  e    
ii) Charge neutrality
iii) Baryon number conservation

   p  n    
Baryon chemical potentials in dense hyperonic matter
n + e-  - + e
n  
 n  e  

I. Vidaña, Ph.D. thesis (2001)
BHF
GM3
GM3 EOS: Glendenning, Moszkowski, PRL 67(1991)
Relativistic Mean Field Theory of hadrons interacting via meson exchange
H.J. Schulze, A. Polls,
A. Ramos, I. Vidana
PRC 73, 058801
(2006)
Quark Matter in Neutron Stars
QCD
Ultra-Relativistic
Heavy Ion Collisions
Quark-deconfinement phase
transition
The core of the most
massive Neutron Stars
is one of the best candidates
in the Universe where such
a deconfined phase of
quark matter can be found
2SC
“Neutron Stars”
“traditional”
Neutron Stars
Hadronic
Stars
Hyperon Stars
Hybrid Stars
Strange Stars
Quark
Stars
Including Quark matter
Since we have no theory which describes both confined and
deconfined phases, one uses two separate EOS for baryon
and quark matter assuming a first order phase transition.
a) Baryon EOS.
b) Quark matter EOS.
MIT bag model
Nambu-Jona Lasinio
Color dielectric model
G.F. Burgio, M Baldo, P.K.Saku, H.-J. Schultze
Phys. Rev. C66(2002)25802
The value of B is constrained in
symmetric matter from reaction
experiments, suggesting that
transition to quark matter does
not occur before 1 GeV/fm3
Symmetric matter
β-stable matter
Density-dependent
Bag constant
Hybrid star composition
Mass-radius
relation
Color dielectric model
C. Maieron, M. Baldo, G.F. Burgio,
H.J. Schulze, PRD70(2004)43010
Effective bag constant
Color and flavour-conserving transition from
a hadronic to a superconducting quark star
No transition
Transition to a hybrid star
Transition to a strange star
G. Lugones, I. Bombaci, Phys. Rev. D72(2005)65021
Densities of u,d,s quark are the same in the two phases
Pairing between u and d, u and d quarks (same chemical potential)
Free quarks,
electrons
Pairing
Bag
constant
Paired phase favoured for large
gaps, which compensate the
locking of chemical potential
A. Lavagno, G. Pagliara, EPJ A27(2006)289
M. Baldo, M. Buballa, G.F. Burgio, F.Neumann,
M. Oertel, H.J. Schultze, PLB 562(2003)153
A closer look at the quark phase transition:
quantum nucleation theory
I.M. Lifshitz and Y. Kagan, 1972; K. Iida and K. Sato, 1998
QM drop
Quantum fluctuations of a virtual drop of
quark matter in hadron matter
R
Hadronic
Matter
U(R)
U(R) = (4/3) R3 nQ* (Q* - H ) + 4 R2
E
R-
R+
R
Z. Berezhiani, I. Bombaci, A.
Drago, F, Frontera, A. Lavagno,
Apj 586(2003)1250
Tuniv
Tuniv ~ 41017s
The critical mass of metastable Hadronic Stars
Def.:
Mcr = MHS(=1yr)
HS with MHS < Mcr are metastable with  = 1 yr  
HS with MHS > Mcr are very unlikely to be observed
The critical mass Mcr plays the role of an effective
maximum mass for the hadronic branch of compact stars
Hadronic Stars: nucleons + hyperons
I.Bombaci, I. Parenti, I. Vidaña, APJ 614(2004)314
What changes in a
protoneutron star?
Temperature, neutrino
trapping
(Nicotra)
O. Nicotra, M. Baldo, G.F. Burgio, H.-J. Schultze, astro-ph/0608021
Can one make a
hydrodynamical
description of the
hadronic -> quark
transition?
(Parenti)
A. Drago, A. Lavagno, I. Parenti, astro-ph/0512652
Can the deconfinement
process be associated
with gamma-ray bursts?
(Pagliara)
A.Drago, G. Pagliara, I. Parenti astro-ph/0608224
A. Drago, A. Lavagno. G. Pagliara, Nucl. Phys. B138(2005)522
M. Alford, M. Braby, M. Paris, S. Reddy,
APJ 629(2005)969
Can we approach the quark phase transition
with neutron-rich heavy-ion beams?
132Sn+132Sn
1GeV A
300 MeV A
M. Di Toro, A. Drago, T. Gaitanos, V. Greco, A. Lavagno, NPA 775(2006)102
A signature of strange stars in gravitational waves
If the quark phese is described
withIn the bag model,
the frequency of the
fundamental mode depends
on the value of the bag constant B
O. Benhar, V. Ferrari, L. Gualtieri, S. Marassi, astro-ph/0603464
Summary of the analysis
on quark NS content
1. The transition to quark matter in NS looks likely,
but the amount of quark matter and the transition density
depend on the quark matter model.
2. If the “observed” high NS masses (about 2 solar mass)
have to be reproduced, additional repulsion is needed
with respect to “naive” quark models .
3. Further constraints can come from other observational
data (cooling, glitches …….)
Schematic cross section of a Neutron Star
outer crust
nuclei, edrip = 4.3 1011 g/cm3
inner crust
nuclei, n, e~1.5 1014 g/cm3
Nuclear matter layer
n, p, e- , -
M  1.4 M
R  10 km
exotic core
(a) hyperonic matter
(b) kaon condensate
(c) quark matter
Superfluidity (homogeneous matter)
In most calculations, 1S0 pairing is neutron
matter Is strongly suppressed by medium
effects
A recent calculation based on Quantum
Montecarlo yields a nuch smaller reduction of
the gaps
A. Fabrocini, S. Fantoni, A. Yu Ilarionov,
K.E: Schmidt, PRL 95(2005)192501
Pairing interaction in neutron and nuclear matter and exchange of p.h. excitations
n
n
n
n n n
density exc
n
spin exc
p
p
n
n
n
isospin exc
n
n
spin-isospin exc
antiscreening
Vind > Vdir
L.G. Cao, U. Lombardo, P.
Schuck, nucl-th/0608005
screening
Vind < Vdir
Z=1 free Fermi gas
Z<1 correlated Fermi system
Gap Equation
nk
Z pV pp ' Z p '
1 3 '
p    d p
 p'
2
2
2
( p '   F )   p '
Z
k
Comparison with finite nuclei: attractive contributions from surface vibrations prevail
120Sn
Pairing gap due to exchange of
density+spin fluctuations
Pairing gap due to exchange of
of density density fluctuations only
G. Gori, F. Ramponi, F. Barranco,R.A. Broglia,
P.F. Bortignon ,G. Colo, E. Vigezzi, PRC72(2005)11302
The inner crust: coexistence of finite nuclei with a sea of free neutrons
J. Negele, D. Vautherin
Nucl. Phys. A207 (1974) 298
Finite size effects on the pairing field
Potential in the Wigner cell
Pairing gap in uniform neutron matter
F=13.5MeV
Pairing gap in the Wigner cell
Uniform Matter
The difference is small
but affects specific heat
and the cooling process
F=13.5MeV
P.M. Pizzochero, F. Barranco,
E. Vigezzi, R.A. Broglia, APJ 569(2002)381
Spatial description of (non-local) pairing gap
The range of the force is small compared to the coherence length, but not compared to the
diffusivity of the nuclear potential
K = 0.25 fm -1
kF(R)
K = 2.25 fm -1
R
(
f
m
approximation overstimates the decrease
)
in the interior of the nucleus.
R(fm)
The local-density
R(fm)
of the pairing gap
Going beyond mean field: including the effects of polarization
(exchange of vibrations) and of finite nuclei at the same time
Induced pairing interaction
Spin modes
Density modes
RPA response
G. Gori, F. Ramponi, F. Barranco,R.A. Broglia,
G. Colo, D. Sarchi,E. Vigezzi, NPA731(2004)401
Argonne (bare and uniform case)
Gogny (bare and uniform case)
With the adopted interaction,
screening suppresses the pairing
gap very strongly for kF >0.7 fm-1
Screening + nucleus
Screening, uniform case
However, the presence of the
nucleus increases the gap by
about 50%
New calculation of the optimal properties of the WIgner-Seitz cell including pairing
Without pairing
With pairing:
smoothing of
shell effects
M. Baldo, U. Lombardo, E.E: Saperstein, S.V. Tolokonnikov, Nucl. Phys. A736(2004)241
The ‘global’ functional: matching Fayans functional (for finite nuclei) with
BBG calculation for neutron matter
Phenomenological
functional with
gradient terms:
‘knows how to deal
Wit hthe surface’
Microscopic, ‘exact’
description
of neutron matter
Matching condition
Simplified pairing description: constant G which reproduces the BCS gap in neutron matter
Comparison between phenomenological forces and
microscopic calculations (BBG) at sub-saturation
densities.
M. Baldo, C. Maieron, P.Schuck, X. Vinas, Nucl. Phys. A736(2004)241
Making the connection with finite nuclei:
Microscopic functionals in neutron matter with gradient terms
+ Spin Orbit, Coulomb
Micr.
Correl.
term
Phen.
gradient.
term
A related but different approach: constraining the parameters of Skyrme interaction
with the results of Brueckner calculations in homogeneous matter
L.G. Cao, U. Lombardo, C.W. Shen, N.Van Giai, PRC73(2006)14313
Glitches
period
As a rule, rotational period of a neutron star slowly
increases because the system loses energy emitting
electromagnetic radiation.
glitch
Sudden spin ups are measured, at regular intervals
2.5year
time
One of the accredited
explanations
Superfuid nature of
nucleons in the inner crust
P.W. Anderson and N.Itoh, Nature 256(1975)25
A superfluid in a rotating container develops an array of microscopic linear vortices
Vortices may pin to container impurities, what may modify their dynamics.
Sudden unpinning at critical period difference, due to Magnus force, would
cause the glitch.
P.W. Anderson and N.Itoh, Nature 256(1975)25
Calculations of pinned vortices:
-R. Epstein and G. Baym, Astrophys. J. 328(1988)680
Analytic treatment based on the Ginzburg-Landau equation
-F. De Blasio and O. Elgaroy, Astr. Astroph. 370,939(2001)
Numerical solution of De Gennes equations with a fixed nuclear mean field and
imposing cylindrical symmetry (spaghetti phase)
-P.M. Pizzochero and P. Donati, Nucl. Phys. A742,363(2004)
Semiclassical model with spherical nuclei and fixed nuclear mean field.
HFB calculation of vortex in uniform neutron matter
Y. Yu and A. Bulgac, PRL 90, 161101 (2003)
Importance of finite size effects
Semiclassical
HFB
(Avogadro)
P. Avogadro, F. Barranco, R.A.
Broglia. E. Vigezzi, nuclth/0602028
The baryonic Equations of State
BBG:
BBG : PRC 69 , 018801 (20
HHJ : Astrophys. J. 525, L45
(1999
AP : PRC 58, 1804 (1998)
Pure neutron matter
Two-body forces only.
E/A
(MeV)
)
density (fm-3)
Comparison between BBG (solid line)
Phys. Lett. B 473,1(2000)
and variational calculations (diamonds)
Phys. Rev. C58,1804(1998)
Phenomenolocical area
from Danielewicz et al.,
Science 298 (2002) 1592
Nonostante le incertezze
dell’ analisi sembra esserci una
ben definita discriminazione
tra le diverse EOS
Kh. Gad Nucl. Phys. 747 (2005) 655
Schematic cross section of a Neutron Star
outer crust
nuclei, edrip = 4.3 1011 g/cm3
inner crust
nuclei, n, e~1.5 1014 g/cm3
Nuclear matter layer
n, p, e- , -
M  1.4 M
R  10 km
exotic core
(a) hyperonic matter
(b) kaon condensate
(c) quark matter
Composition of asymmetric and beta-stable matter
•Parabolic approximation
Asymmetryparameter 
n   p
 1 - 2x p

B
B
(  ,  , xY )  (  ,   0, xY )   2 E sym (  , xY )
A
A
B
B
E sym (  , xY )  (  ,   1, xY )  (  ,   0, xY )
A
A
•Composition of stellar matter
 n   p  e
i) Chemical equilibrium among the
different baryonic species
e   
ii) Charge neutrality
 p  e   
iii) Baryon number conservation
   p  n
Composition of asymmetric and beta-stable matter
including hyperons
•Parabolic approximation
Asymmetryparameter 
n   p
 1 - 2x p

B
B
(  ,  , xY )  (  ,   0, xY )   2 E sym (  , xY )
A
A
B
B
E sym (  , xY )  (  ,   1, xY )  (  ,   0, xY )
A
A
•Composition of stellar matter
n   p  e
i) Chemical equilibrium among the
e  
different baryonic species
2 n   p    
n  
 p  e    
extended to hyperons
ii) Charge neutrality
iii) Baryon number conservation

   p  n    
Composition of hyperonic beta-stable matter
Baryon number density b [fm-3]
Hyperonic Star
MB = 1.34 M
Hyperonic core
NM
shell
Radial coordinate [km ]
I. Vidaña, I. Bombaci,
A. Polls, A. Ramos,
Astron. and Astrophys.
399 (2003) 687
Hyperon influence on hadronic EOS
Composition of asymmetric and beta-stable matter
•Parabolic approximation
Asymmetryparameter 
n   p
 1 - 2x p

B
B
(  ,  , xY )  (  ,   0, xY )   2 E sym (  , xY )
A
A
B
B
E sym (  , xY )  (  ,   1, xY )  (  ,   0, xY )
A
A
•Composition of stellar matter
 n   p  e
i) Chemical equilibrium among the
different baryonic species
e   
ii) Charge neutrality
 p  e   
iii) Baryon number conservation
   p  n
Including hyperons inside the neutron stars
•Shift of the hyperon onset points
down to 2-3 times saturation density
•At high densities N and Y present almost in
the same percentage.
Maximum mass configuration of pure
nucleonic Neutron Stars for different EOS
EOS
MG/M
R(km)
nc / n0
BBB1
1.79
9.66
8.53
BBB2
1.92
9.49
8.45
WFF
2.13
9.40
7.81
BPAL12
1.46
9.04
10.99
BPAL22
1.74
9.83
9.00
BPAL32
1.95
10.54
7.58
Mass-Radius relation
• Inclusion of Y decreases the maximum mass value
Including hyperons inside the neutron stars
•Shift of the hyperon onset points
down to 2-3 times saturation density
•At high densities N and Y present almost in
the same percentage.
H.J. Schulze et al., PRC 73, 058801 (2006)
Hyperons in Neutron Stars: implications for the stellar structure
The presence of hyperons reduces the maximum mass of
neutron stars: Mmax  (0.5 – 0.8) M
Therefore, to neglect hyperons always leads to an overstimate of
the maximum mass of neutron stars
Microscopic EOS for hyperonic matter:
“very soft” EOS
non compatible with measured NS masses.
Need for extra pressure
at high density
Improved NY, YY
two-body interaction
Three-body forces:
NNY, NYY, YYY
Quark Matter in Neutron Stars
QCD
Ultra-Relativistic
Heavy Ion Collisions
Quark-deconfinement phase
transition expected at
c  (3 – 5) 0
The core of the most
massive Neutron Stars
is one of the best candidates
in the Universe where such
a deconfined phase of
quark matter can be found
2SC
Hybrid Stars
outer crust
inner crust
Hadronic matter layer
.
n, p, hyperons, e- , Mixed
hadron-quark
phase
Quark matter core
Including Quark matter
Since we have no theory which describes both confined and
deconfined phases, we uses two separate EOS for baryon
and quark matter and assumes a first order phase transition.
a) Baryon EOS.
BBG
AP
HHJ
b) Quark matter EOS.
MIT bag model
Nambu-Jona Lasinio
Coloror dielectric model
Materia nucleare simmetrica
Al decrescere del valore della bag constant la massa massima
delle NS tende a crescere. Tuttavia B non puo’ essere troppo
piccolo altrimenti lo stato fondamentale della materia nucleare
all densita’ di saturazione e’ nella fase deconfinata !
Density dependent bag “constant”
 Q  1.1
3
GeV fm
Evidence for “large” mass ?
Nice et al. ApJ 634, 1242 (2005)
PSR J0751+1807
M = 2.1 +/- 0.2
Ozel, astro-ph /0605106
EXO 0748 – 676
M > 1.8
Quaintrell et al. A&A 401, 313 (2003)
NS in VelaX-1
1.8 < M < 2
J.M. Lattimer , M. Prakash, Science 304(2004)
Mass radius relationship
Maximum mass
Some (tentative) conclusions
1. The transition to quark matter in NS looks likely,
but the amount of quark matter depends on the quak
matter model.
2. If the “observed” high NS masses (about 2 solar mass)
have to be reproduced, additional repulsion is needed
with respect to “naive” quark models .
The situation resembles the one at the beginning of NS
physics with the TOV solution for the free neutron gas
The confirmation of a mass definitely larger than 2
would be a major breakthrough
3. Further constraints can come from other observational
data (cooling, glitches …….)
Comparison between phenomenological forces and
microscopic calculations (BBG) at sub-saturation
densities.
M.Baldo et al.. Nucl. Phys. A736, 241 (2004)
208
Trying connection with phenomenology : the
Pb case.
Density functional from microscopic calculations
rel. mean field
Skyrme and Gogny
microscopic functional
The value of r_n
- r_p
from mic. fun. is consistent with data
Looking for the energy
minimum at a fixed
baryon density
Density = 1/30 saturation
density
Wigner-Seitz
approximation
In search of the
energy minimum
as a function of
the Z value inside
the WS cell
Gamma Ray Bursts (GRBs)
 Spatial distribution: isotropic
 Distance: “cosmological” d = (1 – 10) 10 ly
9
 Energy range:
100 keV – a few MeV
 Emitted energy: ~ 10 51 erg (beamed / jets)
J.S. Bloom, D.A. Frail, S.R. Kulkarni, ApJ 594, 2003
 Duration:
1 – 300 s
Two different types: short GRBs and long GRBs
Temporal structure of GRBs
0. Supernova explosion
and then… (delay ? how long?)
1. Precursor
 delay…
2. Main event with quiescent times
3. Early X-ray afterglow, plateau and flares
Temporal structure of GRBs
in the quark deconfinement model
0.
Supernova explosion  neutron-proton star
and then… (delay, mass accretion)
1.
2.
Precursor (formation of strangeness)  delay…
Main event (formation of normal quark matter),
quiescent time, then...
formation of superconducting quarks
No need to inject energy continously
during the precursor and the main event!
3.
Early X-ray afterglow, plateau and flares (differential
rotation, expulsion of the toroidal magnetic field,
Haensel et al. in preparation, see previous talk)
Analysis of time intervals between peaks
within each emission episod
A.D., G.Pagliara, astro-ph/0512602
Same temporal micro-structure
within each emission episod
Detonation or deflagration?
A.D., A.Lavagno, I.Parenti, astro-ph/0512652
Main results:
 Never a detonation (no mechanical shock)
 Always a deflagration with an unstable front
 Convection can develop if hyperons are present
in the hadronic phase or if diquark can
condensate
Supernova-GRB connection:
the Quark-Deconfinement Nova model
How to generate GRBs main emission
The energy released (in the strong deflagration) is carried out by
neutrinos and antineutrinos.
A reaction that can generate gamma-ray is: For bare quark stars
   e  e  2


direct photon emission
can be even more efficent!
See previous talk by
Pawel Haensel
The efficency of this reaction in a strong gravitational field is up to:
  10%
[J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859]
E   Econv  10 10 erg
51
52
Production of gamma-rays
Total energy released from the QDN:
+
e+ + e-
1052 – 1053 erg
2
E =  Econv
(1) Ignoring strong gravit. effects on the cross section
 = Newt  0.01
(2) In a strong gravitational field
(Salmonson and Wilson, ApJ 517,(1999))
GR = (10 – 30) Newt
at
r  R  R  (1.5 – 2.0) 2GM/c2
E = 1051 — 1052 erg
Total energy released in the stellar conversion
Finite size effects on the H-Q phase transition
The formation of a
critical-size drop of QM
is not immediate:
P = P – P0
overpressure with respect
to P0
above P0 hadronic matter is
in a metastable state
Quark matter drops form via
a quantum nucleation process
Energy released in the HSHyS(QS) convertion
A.D., A.Lavagno, G.Pagliara, PRD69(2004)057505
CFL gaps
Based on the “simple” scheme of Alford and Reddy PRD67(2003)074024
Potential energy barrier between
the metastable hadronic phase and the quark phase
P2 > P1 > P 0
log(/sec)
U(R) = (4/3) R3 nQ* (Q* - H ) + 4 R2 = av(P) R3 + asR2
Pres.
The nucleation time depends dramaticaly on the value
of the Hadronic Star’s central pressure (on the HS mass)
Quark droplet nucleation time
“mass filtering”
Berezhiani, Bombaci, Drago, Frontera, Lavagno
ApJ 586 (2003) 1250
Critical mass for
s = 0
B1/4 = 170 MeV
Critical mass for
 = 30 MeV/fm2
B1/4 = 170 MeV
Age of the
Universe!
Mass accretion
Conclusions
• The conversion of an hadronic star into a hybrid or quark star can be
at the origine of (at least part of) the long GRBs.
• While in the collapsar model SN explosion and GRB need to be
almost simultaneous, in the QM formation model a time delay
between SN and GRB can exist, and its duration is regulated by
mass accretion.
• The formation of diquark condensate can significantly increase the
total energy released. “Evidence” of two active periods in long
GRBs. The first transition, from hadronic matter to unpaired (or
2SC) quark matter acts as a “mass filter”. The second transition,
producing (g)CFL quark matter can be described as a decay
having a life-time of order tens of seconds
QM formation after deleptonization and cooling
Pons et al. PRL 86 (2001) 5223