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