Francesca Gulminelli - LPC Caen, France

Collaboration:Adriana Raduta IFIN BucharestMicaela Oertel LUTH Meudon FrancePanagiota Papakonstantinou IPNO FranceJerôme Margueron IPNO France

Phase diagram of stellar matter and its impact on

astrophysics

2/27

A

yp 1/2@~10T 12K~r r0

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

yp 1/5@~6T K~r r0

corecrust

yp 1/3@~10T 11K~r r0

Dense matter is abundantly produced in a core-collapse supernova event leading to a neutron star (or black hole)

Time

A.Fantina, PhD thesis, 2011

3/27

Phases  of dense matter in neutron stars

Baryon density

G.Watanabe et al, PRL 2009

pasta

QGP?

4/27

20

20

0 M

eV

1 5?Density /r r0

Tem

pera

ture

QGP

Gas Liquid

Hadronic matter

Phases of dense matter in heavy-ion collisions

LHC

RHIC

FAIR

GANIL

5/27

20

20

0 M

eV

1 5?Density /r r0

Tem

pera

ture

QGP

Gas Liquid

Hadronic matter

Phases of dense matter in heavy-ion collisions

This talk: Stellar matter versus nuclear matter phase diagram

The sub-saturation regime : Coulomb effects and dishomogeneous phases

The super-saturation regime: Hyperonic matter & strangeness phase transition

T

rBp

asta

QGP???

This talk: Stellar matter versus nuclear matter phase diagram

The sub-saturation regime : Coulomb effects and dishomogeneous phases

The super-saturation regime: Hyperonic matter & strangeness phase transition

T

rBp

asta

QGP???

G Lcoex

Coulomb effects

Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background

T. Maruyama et al. PRC 72, 015802 (2005)

Den

sité

/ fm

-3

0.08

0.06

0.04

0.02

0

r = 0.04 fm-3 r = 0.08 fm-3 r = 0.05 fm-3 r = 0.02 fm-3

pne

0 5 10Rayon / fm

0 50 5 100 5 10

Density /r r0

Tem

pera

ture

Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background

The low density phase is a Wigner cristal

Density /r r0

Tem

pera

ture

Coulomb effects

Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background

The low density phase is a Wigner cristal Phase coexistence i.e. macroscopic density dishomogeneities,

would imply a macroscopic charge => a diverging energy density

Coulomb effectsDensity /r r0

Tem

pera

ture

Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background

The low density phase is a Wigner cristal Phase coexistence i.e. macroscopic density dishomogeneities,

would imply a macroscopic charge =>a diverging energy density

Dishomogeneities occur on a microscopic scale only: a continuous transition through a cluster phase (inner crust)

Coulomb effectsDensity /r r0

Tem

pera

ture

Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background

The low density phase is a Wigner cristal Phase coexistence i.e. macroscopic density dishomogeneities,

would imply a macroscopic charge =>a diverging energy density

Dishomogeneities occur on a microscopic scale only: a continuous transition through a cluster phase (inner crust)

Illustration via a phenomenological model

Coulomb effectsDensity /r r0

Tem

pera

ture

The extended NSE model Mixture of nucleons, clusters

of all sizes, photons, electrons, positrons, neutrinos

Nucleons treated in the Skyrme-HF approximation with realistic effective interactions

Nuclei form a statistical ensemble of excited clusters interacting via Coulomb and excluded volume

Thermodynamic consistency between the different components

, , ,p lep e n NT y T T

22

* *ˆ ˆ, , exp

3 3pN n

n n p sp mfn p

V VT h h

T m m

{ } 4

3/ 2 ,

, ,!

( )2

A

A

Ay p

nA

Nn A A

e yAAy T

A N n AyY A

Tn

m TV V g T e

,

;

nucleons clusi i

nucleons clus nucleons clusi i i

i n p

P P P

A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012)

The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012) No plateau in the EoS

B

mI=1.6MeV =T 1.6 MeV

The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012) No plateau in the EoS

Thermodynamics very different from a first order phase transition

Inaccessible in the standard grand-canonical NSE

Large distribution of cluster size

B

S. R. Souza, et al,, Astrophys. J. 707, 1495 (2009),M. Hempel and J. Schaffner-Bielich, Nucl. Phys. A 837, 210 (2010) S. I. Blinnikov, et al, Astronomy & Astrophysics 535, A37 (2011). …………(among others)………

mI=1.6MeV =T 1.6 MeV

The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012) No plateau in the EoS

Thermodynamics very different from a first order phase transition

Inaccessible in the standard grand-canonical NSE

Large distribution of cluster size

The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012) No plateau in the EoS

Thermodynamics very different from a first order phase transition

Inaccessible in the standard grand-canonical NSE

Large distribution of cluster size

Important for e-capture and n-dynamics

Towards a quantitative EoS

The nuclear cluster energy functional is modified by the external nucleon gas

Does excluded volume account for this effect ?

M.Hempel et al PRC 84, 055804 (2011)

In medium effects calculated from a HF calculation in the WS cell

Application to the NSE model in progress

P.Papakonstantinou, et al., in preparation

𝑒𝑛𝑢𝑐𝑙 (𝐴 ,δ )= (𝑎𝑉𝑚(𝜌)+𝑎𝑠𝑦𝑚

𝑚 (𝜌)𝛿2 ) 𝐴+(𝑎𝑠𝑦𝑚

𝑚 (𝜌)+𝑎𝑠𝑑𝑚 (𝜌)𝛿2 ) 𝐴2/3

This talk: Stellar matter versus nuclear matter phase diagram

The sub-saturation regime : Coulomb effects and dishomogeneous phases

The super-saturation regime: Hyperonic matter & strangeness phase transition

T

rBp

asta

QGP???

Hyperons in dense stellar matter Hypernuclei: L

potential attractive at low density

Hyperon d.o.f tend to soften the EoS

Still compatible with 2Mo NS if the hyperon-hyperon coupling is strongly repulsive at high density

M.Oertel et al, http://arxiv.org/abs/1202.2679

I.Vidana et al, Europhys.Lett.94:11002,2011

Strangeness phase transition Attractive - N L and - L L

interaction at low rB

, repulsive at high rB

e(r) has a minimum =>dilute/dense PT ? e(rL) has a minimum

=> non-strange/strange PT ? Illustration with a simple

model: n- L equilibrium in the HF approximation; energy functional from Balberg & Gal

S.Balberg A.Gal NPA 625(1997)435

YL=

rn=0.45 fm-3

rn=0.3 fm-3

rn=0.15 fm-3

rr rS(fm-3)

n- L phase diagram different first and second

order phase transitions I: L’s in neutron matter II: n-L liquid-gas III: neutrons in L matter

F.G.,A.Raduta and M.Oertel, in preparation

n- L phase diagram different first and second

order phase transitions I: L’s in neutron matter II: n-L liquid-gas III: neutrons in L matter

F.G.,A.Raduta and M.Oertel, in preparation

m S

=0

n- L phase diagram different first and second

order phase transitions I: L’s in neutron matter II: n-L liquid-gas III: neutrons in L matter

=> Coexisting hyperon-rich & hyperon-poor regions along the physical trajectory mS=0

F.G.,A.Raduta and M.Oertel, in preparation

m S

=0

mS

=0

n- L phase diagram different first and second

order phase transitions I: L’s in neutron matter II: n-L liquid-gas III: neutrons in L matter

=> Coexisting hyperon-rich & hyperon-poor regions along the physical trajectory mS=0

=> Explores a critical point at T>0: n opacity?

F.G.,A.Raduta and M.Oertel, in preparation

m S

=0

crit

ical p

oin

t

J.Margueron et al, PRC70 (2004) 028801

mS

=0

Conclusion: Stellar matter phase diagram

The sub-saturation regime : Coulomb effects and phase transition quenching A specific thermodynamics Wide distribution of clusters Important for e-capture and n -interaction

The super-saturation regime: A possible strangeness phase transition Consequences on EoS, NS mass, n - transport ? Constraints on Y-N and Y-Y interaction needed

28/27

Frustration and dishomogeneous phases

Frustration is a generic phenomenon in physics

It occurs whenever matter is subject to opposite interactions (here: nuclear & coulomb) on comparable length scales

Global variations of the order parameter (here: density) are replaced by local variations

=>Phase coexistence is quenched

=>dishomogeneous phases arise

=>Ensemble equivalence is violated q

T

Tcr

dishomogeneousphase

P.Viot G.Tarjus PRE2001

Example: frustrated Ising ferromagnets

P.Viot G.Tarjus PRE2001

Fe,

2 2

avec 0

N

N

s sq'H s sr

M s

i ji j

i j i j ij

ii

• Frustration in soft-matter: diblock copolymer melts, cross linked

copolymer mixtures, interpenetrating networks, oil-water surfactant mixtures• Frustration in magnetism: ultrathin magnetic films• Frustration in glasses: doped Mott insulator, supercooled liquids

q

T

Tcr

dishomogeneousphase