NUCLEAR MATTER NUCLEAR PHYSICS

QCDHADRON PHYSICS

NUCLEARSTRUCTURE

HEAVY IONREACTIONS

MANY-BODYSYSTEMS

ASTROPHYSICS

Specific and non-trivial relationsamong different fields

M. Baldo

CataniaPisa

Milano

Ferrara

M. BaldoG.F. BurgioL.G. CaoM. Di ToroG. GiansiracusaV. GrecoU. LombardoC. MaieronO. NicotraH.J. SchultzeX.R. Zhou

I. BombaciA. FabrociniG. Lugones

A. DragoF. FronteraG. PagliaraI. Parenti

P. AvogadroP.F. Bortignon R.A. BrogliaG. Colo’P. DonatiG. GoriF. RamponiP.M. PizzocheroE. Vigezzi

A. Lavagno

Torino

CT51LS31MI31OG51PI31PI32

Iniziativespecifiche INFN

Roma

O. BenharV. FerrariL. GualtieriS. Marassi

Trieste

S, FantoniA. IlarionovK.E. Schmidt

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.

interactions

matter’s constituents

EOS

R

M

Mmax R M(R), …

“stiff” EOS

“soft”

“soft”

density

Pre

ssur

e “stiff” EOS

Mmax = (1.4 – 2.5) M Oppenheimer-Volkoff mass

M. Baldo, G. Giansiracusa, U. Lombardo, H.Q. Song, PLB 473(2000)1A. Akmal, V.R. Pandharipande, D.G. Ravenhall, PRC58(1998)1804

BBG

Variational

X.R.Zhou, G.F. Burgio, U. Lombardo, H.-J. Schultze, W. Zuo, PRC69(2004)18801

-stable nuclear matter

Equilibrium with respect to the weak interaction processes e

epn

Charge neutrality nnn ep To be solved for any given value of the total baryon number density nB

e

e

epn

nep

np

e

MeVm

e

e 6.105if

0 neutrino-free matter

Composition of asymmetric and beta-stable matterincluding hyperons

•Composition of stellar matter

i) Chemical equilibrium among the

different baryonic species

ii) Charge neutrality

iii) Baryon number conservation

np

ep

n

pn

e

epn

2

I. Vidaña, Ph.D. thesis (2001)

Baryon chemical potentials in dense hyperonic matter

en

n

n + e- - + e

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

Hyperon Stars

Hadronic 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

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-dependentBag constant

G.F. Burgio, M Baldo, P.K.Saku, H.-J. SchultzePhys. Rev. C66(2002)25802

Hybrid star composition

Mass-radiusrelation

Color dielectric model Effective bag constant

C. Maieron, M. Baldo, G.F. Burgio,H.J. Schulze, PRD70(2004)43010

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)

Paired phase favoured for largegaps, which compensate thelocking of chemical potential

Free quarks,electrons

Pairing Bagconstant

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

Hadronic Hadronic MatterMatter

QM dropQM drop

RR Quantum fluctuations of a virtual drop of quark matter in hadron matter

R- R+

EE

U(R) = (4/3) R3 nQ* (Q* - H ) + 4 R2U(R)

R

I.M. Lifshitz and Y. Kagan, 1972; K. Iida and K. Sato, 1998

A closer look at the quark phase transition:A closer look at the quark phase transition:quantum nucleation theory quantum nucleation theory

Z. Berezhiani, I. Bombaci, A. Drago, F, Frontera, A. Lavagno, Apj 586(2003)1250

Tuniv ~ 41017s

Tuniv

The critical mass of metastable Hadronic Stars

Def.: Mcr = MHS(=1yr)

HS with MHS < Mcr are metastable with = 1 yr

The critical mass Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars

HS with MHS > Mcr are very unlikely to be observed

Hadronic Stars: nucleons + hyperons

I.Bombaci, I. Parenti, I. Vidaña, APJ 614(2004)314

A.Drago, G. Pagliara, I. Parenti astro-ph/0608224

What changes in a protoneutron star?Temperature, neutrinotrapping(Nicotra)

Can the deconfinementprocess be associatedwith gamma-ray bursts?(Pagliara)

Can one make a hydrodynamicaldescription of thehadronic -> quarktransition?(Parenti)

O. Nicotra, M. Baldo, G.F. Burgio, H.-J. Schultze, astro-ph/0608021

A. Drago, A. Lavagno, I. Parenti, astro-ph/0512652

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?

M. Di Toro, A. Drago, T. Gaitanos, V. Greco, A. Lavagno, NPA 775(2006)102

132Sn+132Sn

1GeV A

300 MeV A

A signature of strange stars in gravitational waves

O. Benhar, V. Ferrari, L. Gualtieri, S. Marassi, astro-ph/0603464

If the quark phese is describedwithIn the bag model,the frequency of the fundamental mode depends on the value of the bag constant B

Summary of the analysison 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 observationaldata (cooling, glitches …….)

Schematic cross section of a Neutron Star

outer crust nuclei, e-

inner crust nuclei, n, e-

Nuclear matter layer n, p, e- , -

exotic core (a) hyperonic matter (b) kaon condensate (c) quark matter

drip = 4.3 1011 g/cm3

~1.5 1014 g/cm3

M 1.4 M R 10 km

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

nn

p

nn

nn

n

nnnn

density exc spin exc

isospin exc spin-isospin exc

p

n

p

Pairing interaction in neutron and nuclear matter and exchange of p.h. excitations

antiscreening Vind >> Vdir

screeningVind << Vdir

L.G. Cao, U. Lombardo, P. Schuck, nucl-th/0608005

Z

k

nk

Z=1 free Fermi gasZ<1 correlated Fermi system

' '3 ''2 2

' '

1

2 ( )

p pp pp p

p F p

Z V Zd p

Gap Equation

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. VautherinNucl. Phys. A207 (1974) 298

F=13.5MeV

Uniform Matter

Pairing gap in the Wigner cell

Potential in the Wigner cell Pairing gap in uniform neutron matter

Finite size effects on the pairing field

F=13.5MeV

P.M. Pizzochero, F. Barranco,E. Vigezzi, R.A. Broglia, APJ 569(2002)381

The difference is smallbut affects specific heatand the cooling process

Spatial description of (non-local) pairing gap

The local-density approximation overstimates the decrease of the pairing gap in the interior of the nucleus.

R(fm) R(fm)

R(fm)

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

K = 2.25 fm -1

kF(R)

Going beyond mean field: including the effects of polarization (exchange of vibrations) and of finite nuclei at the same time

G. Gori, F. Ramponi, F. Barranco,R.A. Broglia,G. Colo, D. Sarchi,E. Vigezzi, NPA731(2004)401

Spin modes

Density modes

RPA response In

duce

d pa

iring

inte

ract

ion

However, the presence of the nucleus increases the gap by about 50%

With the adopted interaction,screening suppresses the pairing gap very strongly for kF >0.7 fm-1

Argonne (bare and uniform case)

Gogny (bare and uniform case)

Screening, uniform case

Screening + nucleus

M. Baldo, U. Lombardo, E.E: Saperstein, S.V. Tolokonnikov, Nucl. Phys. A736(2004)241

New calculation of the optimal properties of the WIgner-Seitz cell including pairing

Without pairing

With pairing:smoothing ofshell effects

The ‘global’ functional: matching Fayans functional (for finite nuclei) with BBG calculation for neutron matter

Microscopic, ‘exact’descriptionof neutron matter

Phenomenologicalfunctional with gradient terms:‘knows how to dealWit hthe surface’

Matching condition

Simplified pairing description: constant G which reproduces the BCS gap in neutron matter

Comparison between phenomenological forces andmicroscopic calculations (BBG) at sub-saturationdensities.

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

Micr.Correl.term

Phen.gradient.term

+ Spin Orbit, Coulomb

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

peri

od

time

2.5year

As a rule, rotational period of a neutron star slowly increases because the system loses energy emitting electromagnetic radiation.

Glitches

One of the accredited explanations

Superfuid nature of nucleons in the inner crust

Sudden spin ups are measured, at regular intervals

glitch

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)

HFB

Semiclassical

(Avogadro)

P. Avogadro, F. Barranco, R.A. Broglia. E. Vigezzi, nucl-th/0602028

Importance of finite size effects

BBG : PRC 69 , 018801 (20HHJ : Astrophys. J. 525, L45

(1999AP : PRC 58, 1804 (1998)

The baryonic Equations of State

BBG:

density (fm-3)

E/A(MeV))

Comparison between BBG (solid line) Phys. Lett. B 473,1(2000)and variational calculations (diamonds) Phys. Rev. C58,1804(1998)

Pure neutron matterTwo-body forces only.

Kh. Gad Nucl. Phys. 747 (2005) 655

Phenomenolocical area from Danielewicz et al.,Science 298 (2002) 1592

Nonostante le incertezzedell’ analisi sembra esserci unaben definita discriminazionetra le diverse EOS

Schematic cross section of a Neutron Star

outer crust nuclei, e-

inner crust nuclei, n, e-

Nuclear matter layer n, p, e- , -

exotic core (a) hyperonic matter (b) kaon condensate (c) quark matter

drip = 4.3 1011 g/cm3

~1.5 1014 g/cm3

M 1.4 M R 10 km

Composition of asymmetric and beta-stable matter

•Parabolic approximation

),0,(),1,(),(

),(),0,(),,(

2x-1parameter Asymmetry

2

p

YYYsym

YsymYY

pn

xA

Bx

A

BxE

xExA

Bx

A

B

•Composition of stellar matter

i) Chemical equilibrium among the

different baryonic species

ii) Charge neutrality

iii) Baryon number conservation

np

ep

e

epn

Composition of asymmetric and beta-stable matterincluding hyperons

•Parabolic approximation

),0,(),1,(),(

),(),0,(),,(

2x-1parameter Asymmetry

2

p

YYYsym

YsymYY

pn

xA

Bx

A

BxE

xExA

Bx

A

B

•Composition of stellar matter

i) Chemical equilibrium among the

different baryonic species

ii) Charge neutrality

iii) Baryon number conservation

np

ep

n

pn

e

epn

2

extended to hyperons

Composition of hyperonic beta-stable matter

I. Vidaña, I. Bombaci, A. Polls, A. Ramos, Astron. and Astrophys. 399 (2003) 687

Hyperonic Star

MB = 1.34 M

Baryon number density b [fm-3]

Radial coordinate [km ]

Par

ticl

e fr

acti

ons

Hyperonic core NM shell

cru

st

Hyperon influence on hadronic EOS

Composition of asymmetric and beta-stable matter

•Parabolic approximation

),0,(),1,(),(

),(),0,(),,(

2x-1parameter Asymmetry

2

p

YYYsym

YsymYY

pn

xA

Bx

A

BxE

xExA

Bx

A

B

•Composition of stellar matter

i) Chemical equilibrium among the

different baryonic species

ii) Charge neutrality

iii) Baryon number conservation

np

ep

e

epn

•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.

Including hyperons inside the neutron stars

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

Maximum mass configuration of pure nucleonic Neutron Stars for different EOS

Mass-Radius relationMass-Radius relation

• Inclusion of Y decreases the maximum mass value

•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.

Including hyperons inside the neutron stars

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 StarsHybrid Stars

outer crust

inner crust

Hadronic matter layer . n, p, hyperons, e- , -

Quark matter core

Mixed hadron-quark phase

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

Al decrescere del valore della bag constant la massa massimadelle NS tende a crescere. Tuttavia B non puo’ essere troppopiccolo altrimenti lo stato fondamentale della materia nucleareall densita’ di saturazione e’ nella fase deconfinata !

Materia nucleare simmetrica

1.1Q GeV3fm

Density dependent bag “constant”

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 relationshipMaximum 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 2would be a major breakthrough

3. Further constraints can come from other observational

data (cooling, glitches …….)

Comparison between phenomenological forces andmicroscopic calculations (BBG) at sub-saturationdensities.

M.Baldo et al.. Nucl. Phys. A736, 241 (2004)

Trying connection with phenomenology : the case.Density functional from microscopic calculations

microscopic functional

The value of r_n - r_p from mic. fun. is consistent with data

rel. mean field

Skyrme and Gogny

Pb208

Looking for the energyminimum at a fixedbaryon density

Density = 1/30 saturationdensity

Wigner-Seitzapproximation

In search of theenergy minimum as a function ofthe Z value insidethe WS cell

Gamma Ray Bursts (GRBs)

Spatial distribution: isotropic

Distance: “cosmological” d = (1 – 10) 10 9 ly

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 GRBsin the quark deconfinement model

0. Supernova explosion neutron-proton starand then… (delay, mass accretion)

1. Precursor (formation of strangeness) delay… 2. 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-structurewithin each emission episod

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

Detonation or deflagration?A.D., A.Lavagno, I.Parenti, astro-ph/0512652

Supernova-GRB connection: the Quark-Deconfinement Nova model

A reaction that can generate gamma-ray is:A reaction that can generate gamma-ray is:

The efficency of this reaction in a strong gravitational field is The efficency of this reaction in a strong gravitational field is up toup to::

[J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859][J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859]

A reaction that can generate gamma-ray is:A reaction that can generate gamma-ray is:

The efficency of this reaction in a strong gravitational field is The efficency of this reaction in a strong gravitational field is up toup to::

[J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859][J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859]

How to generate GRBs main emission

2 ee

%10

The energy released (in the The energy released (in the strong deflagrationstrong deflagration) is carried out by ) is carried out by neutrinos and antineutrinos.neutrinos and antineutrinos.The energy released (in the The energy released (in the strong deflagrationstrong deflagration) is carried out by ) is carried out by neutrinos and antineutrinos.neutrinos and antineutrinos.

ergEE conv5251 1010

For bare quark starsdirect photon emissioncan be even more efficent!See previous talk byPawel Haensel

Production of gamma-rays

Total energy released from the QDN: 1052 – 1053 erg

+ e+ + e- 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 HSHyS(QS) convertion A.D., A.Lavagno, G.Pagliara, PRD69(2004)057505

Based on the “simple” scheme of Alford and Reddy PRD67(2003)074024

CFL gaps

Potential energy barrier between the metastable hadronic phase and the quark phase

U(R) = (4/3) R3 nQ* (Q* - H ) + 4 R2 = av(P) R3 + asR2

The nucleation time depends dramaticaly on the value of the Hadronic Star’s central pressure (on the HS mass)

P2 > P1 > P0 log(/

sec)

Pres.

Quark droplet nucleation time“mass filtering”

Critical mass forB1/4 = 170 MeV

Mass accretion

Critical mass for= 30 MeV/fm2

B1/4 = 170 MeV

Age of the Universe!

Berezhiani, Bombaci, Drago, Frontera, LavagnoApJ 586 (2003) 1250

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