Oslo 2007

Oslo 2007

core crust

crustcore

Supernova remnant and neutron star in Puppis A (ROSAT x-ray)

e-

P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. Hasnaoui

GANIL, Caen, France

Two general results: Thermodynamics => limiting T > Tcritical Scalings => No-Criticality

Nuclear and compact-star matter:

Oslo 2007

core crust

crustcore

Supernova remnant and neutron star in Puppis A (ROSAT x-ray)

e-

P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. Hasnaoui

GANIL, Caen, France

Two general results: Thermodynamics => limiting T > Tcritical Scalings => No-Criticality

Nuclear and compact-star matter:

Oslo 2007

core crust

crustcore

Supernova remnant and neutron star in Puppis A (ROSAT x-ray)

Nuclear and compact-star matter:

e-

P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. Hasnaoui

GANIL, Caen, France

Three main differences: Order

N => First order up Tcritical

n*=> Continuous Temperature

N => reduces limiting Tn*=> increases limiting

T Scalings

N => Critical linen*=> No criticality

Oslo 2007

GasLiquid

Density 0

Dense matter EOS

Neutron Stars

Tem

pera

ture

20

200

MeV

1 5?

Plasma of Quarks and

Gluons

Nucleus

Critical points (second order)

Tem

pera

ture

Collisions

HeavyIons

Thermodynamics Mechanical, thermal,

chemical properties Role of Coulomb

(Frustration) Structure of matter

Neutrino transport

Oslo 2007

Order of Phase transition (infinite systems)

1

Oslo 2007

Order of Phase transition (infinite systems)

Order of transition:discontinuity in

Ehrenfest’s definition

€

∂βn logZ

First order:discontinuous EOS:

€

<E>=−∂β logZ

R. Balian, Springer (1982)

Thermodynamical potentialsnon analytical at

L.E. Reichl, Texas Press (1980)

€

N→ ∞

€

Z = e−βE ( n)

(n )∑ ⎛

⎝ ⎜ ⎞ ⎠ ⎟

Thermodynamical potentials

€

F =−T logZ

€

F =−T logZ

Ener

gy

Temperatureß

E1

E2

Caloric curve

Temperatureß

Log

Z

Thermodynamical potential

Oslo 2007

Order of Phase transition (infinite systems)

Nuclear Matter Case

Oslo 2007

p

n

p

Grand potential 2 fluids (protons and neutrons)

Coexistence

Any 2-fluids EOS: (e.g. Mean-Field SLy4)

€

G = PV = −T logZ(β ,μn,μ p )

np

Fold

Discontinuity in

First order transi. Liquid-gas

€

p =∂μ p lnZ /βV

Gas

Liquidjum

p

Gas

Liquid

Oslo 2007

Isospin in coexistence

Neutron density

Proton density

n

p

p

pn

n

Oslo 2007

Isospin in coexistence: distillation

Z/A order parameter (Except symmetric matter)

Neutron density

Proton density<=

n

p

p

pn

n

Oslo 2007

Isospin in coexistence: distillation

Z/A order parameter (Except symmetric matter)

Oslo 2007

Isospin in coexistence: distillation

Z/A order parameter

Isospin distillation

(Except symmetric matter)

Gas: + asymmetric

Liquid: + symmetric

Oslo 2007

Z/A=cst transformation

Z/A order parameter

=> Z/A=cst transfo.follows the coexistence

(Except symmetric matter)

Oslo 2007

Z/A=cst transformation

Z/A order parameter

Continuous P() & q()Z/A=cst transformation

but Discontinuous EOS

first order transition

=> Z/A=cst transfo.follows the coexistence

This is not a plateau

Oslo 2007

Z/A=cst transformation

Z/A order parameter

Continuous P() & q()Z/A=cst transformation

but Discontinuous EOS

first order transition

=> Z/A=cst transfo.follows the coexistence

This is not a plateau

Oslo 2007

Order of Phase transition (infinite systems)

Star Matter Case

Oslo 2007

Star Matter Case

∞

Ex: Mean field free E=> Diverge if c≠0

=> Is the sum if c= 0

= (e + p)/2

= e + p

Single free density=> Single chem. pot. No thermo defined for

c≠0 => c not defined

c = 0 Coulomb Divergence=> strict neutrality

Electrons & Coulomb

Oslo 2007

Star Matter Case

∞

Ex: Mean field free E=> Diverge if c≠0

=> Is the sum if c= 0

Electron densityProton density

p

p n

Oslo 2007

function of = e + p

Continuous transformation as function of = e + p

Star Matter Case

∞

Ex: Mean field free E=> Diverge if c≠0

=> Is the sum if c= 0

strict neutrality

Oslo 2007

function of = e + p

Continuous transformation as function of = e + p

Star Matter Case

∞

Ex: Mean field free E=> Diverge if c≠0

=> Is the sum if c= 0

strict neutrality

Electron density

Oslo 2007

function of = e + p

Continuous transformation as function of

= e + p

Star Matter Case

∞

Ex: Mean field free E=> Diverge if c≠0

=> Is the sum if c= 0

strict neutrality

density

Oslo 2007

function of = e + p

Continuous transformation as function of = e + p

Star Matter Case

∞

Ex: Mean field free E=> Diverge if c≠0

=> Is the sum if c= 0

strict neutrality

density

= e + p (MeV)

Oslo 2007

Coulomb interaction on L-G transition

2

Oslo 2007

Coulomb expected to reduce L-G transition

Oslo 2007

Coulomb expected to reduce L-G transition

Nuclei Reduces instability &

bimodality Reduces limiting temperature

Bonche-Levit-Vautherin Nucl. Phys. A427 (1984) 278

Oslo 2007

Coulomb expected to reduce L-G transition

Nuclei Reduces instability &

bimodality Reduces limiting temperature

Bonche-Levit-Vautherin Nucl. Phys. A427 (1984) 278

Supernovae core & neutron* Reduces pasta phases Reduces instabilities

C. Ducoin, Ph. Ch., F. Gulminelli to be published

q

r = 2/k

Oslo 2007

Coulomb expected to reduce L-G transition

Nuclei Reduces instability &

bimodality Reduces limiting temperature

Bonche-Levit-Vautherin Nucl. Phys. A427 (1984) 278

Supernovae core & neutron* Reduces pasta phases Reduces instabilities

Providência, Brito, Avancini, Menezes, Ph. Ch, Phys. Rev. C 73, 025805 (2006) and to appear in PRC

q

r = 2/k

Oslo 2007

Coulomb expected to reduce L-G transition

Problems: Phase transition

With critical phenomena With long range forces With finite size fluctuations

Approximations not valid Mean-field not correct

Supernovae core & neutron* Reduces pasta phases Reduces instabilities

Providência, Brito, Avancini, Menezes, Ph. Ch, Phys. Rev. C 73, 025805 (2006) and to appear in PRC

q

r = 2/k

Oslo 2007

Coulomb expected to reduce L-G transition

Problems: Phase transition

With critical phenomena With long range forces With finite size fluctuations

Approximations not valid Mean-field not correct

Solution: Phase transition

= universal phenomena

Study exactly solvable models eg Ising

Ising (Lattice-Gas) extensively used to study liquid-gas phase transition in nuclei

Oslo 2007

Beyond mean-field: Ising*

Oslo 2007

Beyond mean-field: Ising*

Oslo 2007

Event distribution: bimodality => phases

Oslo 2007

Event distribution: bimodality => phases

Oslo 2007

Oslo 2007

Phase diagram:

Oslo 2007

Phase diagram: Ising

L=10Phase diagram

Gas Liquid

Oslo 2007

Phase diagram: Ising

Comparison of Ising model and the Ising* (star matter)

Ising star

L=10

Finite size scaling

Phase diagram

Gas Liquid

Critical point

Oslo 2007

Phase diagram: Ising

Comparison of Ising model with Ising* (star matter)

Ising star

IsingL=10

Oslo 2007

Phase diagram: Ising / Ising*

Comparison of Ising model with Ising* (star matter) Strong increase of the Limiting temperature

not decrease like in MF & nuclei -

Ising star

Ising

Oslo 2007

Phase diagram: Ising / Ising*

Comparison of Ising model with Ising* (star matter) Strong increase of the Limiting temperature

not decrease like in MF & nuclei -

Ising star

Ising

Oslo 2007

Event distribution:

Oslo 2007

Fluctuating partitions at critical point

qiqj/rij= ij/rij=>∞ diverging observable

Bimodality below critical point => phase transition

Event distribution: Ising

Tc IsingTe

mpe

ratu

re Coulomb qiqj/rij

Nuclear ’ninj

critical point

coexistence

Oslo 2007

Fluctuating partitions at critical point

qiqj/rij= ij/rij=>∞ diverging observable

Bimodality below critical point => phase transition

Event distribution: Ising

Tc IsingTe

mpe

ratu

re Coulomb qiqj/rij

Nuclear ’ninj

Ising

Oslo 2007

Fluctuating partitions at critical point

qiqj/rij= ij/rij=>∞ diverging observable

Event distribution: Ising

Tc IsingTe

mpe

ratu

re Coulomb qiqj/rij

Nuclear ’ninj

Ising

Oslo 2007

Fluctuating partitions at critical point

quenched by Coulomb interaction with electrons

Event distribution: Ising / Ising*

Ising Star Ising

Tlimit

Tc IsingTe

mpe

ratu

re

Nuclear ninj

Coulomb qiqj/rij

P~eqiqj/rij

Oslo 2007

Fluctuating partitions at critical point

quenched by Coulomb interaction with electrons

The system is driven back to coexistence ie bimodality

Event distribution: Ising / Ising*

Ising Star Ising

Tlimit

Tc IsingTe

mpe

ratu

re

Nuclear ninj

Coulomb qiqj/rij

P~ecqiqj/rij

Oslo 2007

Fluctuating partitions at critical point

quenched by Coulomb interaction with electrons

Event distribution: Ising / Ising*

Ising Star Ising

Tlimit

Tc IsingTe

mpe

ratu

re

Nuclear ninj

Coulomb qiqj/rij

Oslo 2007

Fluctuating partitions at critical point

quenched by Coulomb interaction with electrons

Need higher T to suppress bimodality ie higher limiting temperature

Event distribution: Ising / Ising*

Ising Star Ising

Tlimit

Tc IsingTe

mpe

ratu

re

Nuclear ninj

Coulomb qiqj/rij

Oslo 2007

Event distribution and finite-size scaling

Oslo 2007

Event distribution and finite-size scaling

3

Oslo 2007

Fluctuating partitions at critical point

qiqj/rij= ij/rij=>∞ diverging observable

Event distribution and finite-size scaling

Tc IsingTe

mpe

ratu

re Coulomb qiqj/rij

Nuclear ’ninj

critical point

coexistence

Ising

Oslo 2007

Tc IsingTe

mpe

ratu

re

Tc Ising

T<Tc Ising

Coulomb qiqj/rij

Nuclear ninj

Fluctuating partitions at critical point

Diverging correlation length =>

qiqj/rij>= ij/rij=>∞ is a diverging observable

Event distribution and finite-size scaling

Ising

Oslo 2007

Fluctuating partitions at critical point

Diverging correlation length =>

qiqj/rij>= ij/rij=>∞ is a diverging observable

Impossible for charged system => not critical

Event distribution and finite-size scaling

Ising Star Ising

Tc IsingTe

mpe

ratu

re Tlimit star>Tlimit

Tc Ising

T<Tc Ising

Coulomb qiqj/rij

Nuclear ninj

Oslo 2007

Fluctuating partitions at critical point

Diverging correlation length =>

qiqj/rij>= ij/rij=>∞ is a diverging observable

Impossible for charged system => not critical

Event distribution and finite-size scaling

Ising Star Ising

Tc IsingTe

mpe

ratu

re Tlimit star>Tlimit

Tc Ising

T<Tc Ising

Coulomb qiqj/rij

Nuclear ninjcharged system => not critical

Oslo 2007

Finite size scaling an hyperscaling:

Oslo 2007

Finite size scaling an hyperscaling:

Ising Star Ising

Bulk Tlim

Divergence of the correlation length

Scaling of the limiting T at finite L

Scaling No-scaling

Oslo 2007

Finite size scaling an hyperscaling:

Ising Star Ising

Oslo 2007

Finite size scaling an hyperscaling:

T>Tlim susceptibility

except too close from critical point

T>Tlim correlation link to Liquid-Gas fluctuation

Hyperscaling

Oslo 2007

Finite size scaling an hyperscaling:

Ising T>Tlim susceptibility

except too close from critical point

T>Tlim correlation link to Liquid-Gas fluctuation

Hyperscaling

Scaling

Oslo 2007

Finite size scaling an hyperscaling:

Ising Star Ising T>Tlim susceptibility

except too close from critical point

T>Tlim correlation link to Liquid-Gas fluctuation

Hyperscaling

Scaling No-scaling

Oslo 2007

Finite size scaling an hyperscaling:

Ising Star Ising T>Tlim susceptibility

except too close from critical point

T>Tlim correlation link to Liquid-Gas fluctuation

Hyperscaling

Scaling No-scaling

Oslo 2007

core crust

crustcore

Supernova remnant and neutron star in Puppis A (ROSAT x-ray)

Nuclear and compact-star matter:

e-

P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. Hasnaoui

GANIL, Caen, France

Three main differences: Order

N => First order up Tcritical

n*=> Continuous Temperature

N => reduces limiting Tn*=> increases limiting

T Scalings

N => Critical linen*=> No criticality

Oslo 2007

core crust

crustcore

Supernova remnant and neutron star in Puppis A (ROSAT x-ray)

e-

P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. Hasnaoui

GANIL, Caen, France

Two Consequences: Matter properties => dynamics of SN Clustering => neutrino propagation

Nuclear and compact-star matter: Three main differences:

Order N => First order up Tcritical

n*=> Continuous Temperature

N => reduces limiting Tn*=> increases limiting

T Scalings

N => Critical linen*=> No criticality

Oslo 2007

*****Chapitre 2

Oslo 2007

Star Matter Case

Electrons & Coulomb

Coulomb Divergence

Ex: Mean field Free energy

=> Diverge if c≠0

=> Is the sum if c= 0

c = e - p = 0

Single free density=> Single chem. pot. No thermo defined for

c≠0 => c not defined

= (e + p)/2

= e + p

Oslo 2007

Star Matter Case

Electrons & Coulomb

Coulomb Divergence=> strict neutrality

Ex: Mean field free E=> Diverge if c≠0

=> Is the sum if c= 0

c = 0

Single free density=> Single chem. pot. No thermo defined for

c≠0 => c not defined

= (e + p)/2

= e + p

∞

Oslo 2007

Star Matter Case

c = 0 strict neutrality

∞

Ex: Mean field free E=> Diverge if c≠0

=> Is the sum if c= 0

Oslo 2007

core crust

crustcore

Supernova remnant and neutron star in Puppis A (ROSAT x-ray)

Ising analogue to compact-star matter:

e-

P. Napolitani, Ph. Chomaz, C. Ducoin, F. Gulminelli, K. Hasnaoui

GANIL, Caen, France

Two general results: Thermodynamics => limiting T > Tcritical Scalings => No-Criticality