Nuclear Isovector Equation-of-State (EOS)

and Astrophysics

Hermann WolterDep. f. Physik, LMU

Topics:

1. Phase diagram of strongly interacting matter and exploration via heavy ion collisions

2. Symmetric and asymmetric EoS, density dependence of symmetry energy

3. Description of Heavy Ion collisions with transport equations

4. Some results from HI studies

5. Comparison to neutron star observables

6. Summary and Outlook

Connection to Universe Cluster

EoS, esp. Symmetry energy at high density

Interpretation of heavy ion collision exp.

(Astrophysical reaction rates by indirect methods)

Schematic Phase Diagram of Strongly Interacting Matter

Quark-hadron coexistence

Liquid-gas coexistenceSIS

Schematic Phase Diagram of Strongly Interacting Matter

Liquid-gas coexistence

Quark-hadron coexistence

Z/N

1

0

SIS

neutron starsExotic nuclei

Theoretical Treatment of Nuclear Matter

Vij

Non-relativistic:

Hamiltonian H = Ti + Vij,; V nucleon-nucleon interaction

Comparisons of calculations:

Empirical saturation point

Relativistic:

Hadronic Lagrangian

nucleon, resonances

mesons 0

,...),,,,;(

,

ii

L

dx

dL

L

The nuclear EoS-UncertaintiesThe nuclear EoS-Uncertainties

stiff

soft

C. Fuchs, H.H. Wolter, WCI book, EPJA 30 (2006 )5

the nuclear EoS

iso-stiff

iso-soft

Symmetry energy

Esym

m

[MeV

]

Transport Descriptions of Heavy Ion Collisions

Heavy ion collisions -> Non-Equilibrium Phenomena -> Transport Theory

Transport description of heavy ion collisions:

For Wigner transform of the one-body density: f(r,p;t)

,fIfUfm

p

t

fcollp

Vlasov eq.; mean field 2-body hard collisions

)1)(1()1)(1(

)()()2(

1

432432

432143213412

124322

3

ffffffff

EEEEppppd

dvdpdpdp

loss term gain term

11 1

12

3 4

AN

iii tppgtrrg

Ntprf

1

))((~))((1

);,(

Simulation with Test Particles:

Hamiltonian EoM test particles

High Density

Symmetric Nuclear Matter

Observables

V2: Elliptic flowV1: Sideward flow

...2cos),(cos),(1(),,;(: 210 ttt pyvpyvNbpyNFlow

T.Gaitanos, Chr. Fuchs, Nucl. Phys. 744 (2004)

Isospin Transport through Neck:

AMeVSnSn 50,124,112124,112

Rami imbalance ratio:

,...,,,;,;2

3112112124124

112112124124

Het

ZNITPi

II

IIIR

ii

iiMi

i

asysoft eos superasystiff eos

experimental data(B. Tsang et al. PRL 92 (2004) )

ASYSOFT EOS – FASTER EQUILIBRATION

Baran, Colonna, Di Toro, Zielinska-Pfabe, Wolter, PRC 72 (2005) 064620

Kaon Production:

A good way to determine the symmetric EOS (C. Fuchs, A.Faessler, et al., PRL 86(01)1974)

Also useful for Isovector EoS?

-charge dependent thresholds

- in-medium effective masses

-Mean field effects

Main production mechanism: NNBYK, pNYK

Astrophysical Implications of Iso-Vector EOS

Neutron Star Structure

Constraints on the Equation-of-state

- from neutron stars: maximum mass

gravitational mass vs.

baryonic mass

direct URCA process

mass-radius relation

- from heavy ion collisions: flow constraint

kaon producton

Equations of State tested:

Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802

Neutron star masses and cooling and iso-vector EOS

Tolman-Oppenheimer-Volkov equation to determine mass of neutron star

Proton fraction and direct URCA

cooling neutrinofast %,11 :ld thresho

:processURCA direct

)( :neutrality charge and mequilibriu

y

enp

yZ

N y

e

sym

Onset of direct URCA

Forbidden by Direct URCA constraint

Typical neutron stars

Heaviest observed neutron star

Further Neutron Star Constraints:

Mass-Radius Relation:

Gravitational vs. Baryon Mass

Max

imu

m m

ass

Dir

ect

Urc

a C

oo

lin

g l

imit

Mas

s-R

adiu

s R

elat

ion

s

Gra

vita

tio

nal

vs.

Bar

yon

M

ass

Hea

vy I

on

Co

llis

ion

o

bse

vab

les

Summary and Outlook:

1. Equation of State at high densities can be tested in the laboratory in heavy ion collisions

2. Symmetry Energy (neutron matter) is particularly uncertain

3. Is important for the structure of exotic nuclei (nucleosynthesis) and for astrophysics

4. Comparison to neutron star observables (not completely satisfactory, yet); also supernovae

Collaborators:

C. Fuchs (Tübingen), T. Gaitanos (Giessen)

D. Blaschke, et al., (Rostock-Breslau)

M. Di Toro, M. Colonna, et al., (LNS Catania)