Ilona Bednarek Ustroń, 2009

Hyperon Star Model

Typical neutron star parameters:

Neutron stars are the most compact objects

• M ~ 1.4 MS

1.44 MS the largest precisely known neutron star mass

• R ~ 10 km• g ~ 2 x 1014cm s-2

~ 7 x 1014 g cm-3 (2 – 3) 0

Structure of a neutron star

• Atmosphere • Crust:

– outer crust – from the atmosphere bottom to the density

ND 4 x 1011g cm-3

– inner crust – from ND to t (~ (0.3- 0.5) x 0) – the inner edge separates the nonhomogenous crust from the homogenous liquid core, the transition density depends on the nuclear compression modulus and the density dependence of the nuclear symmetry energy

• Core:

– outer core - 0.5 0 2 0 – neutrons, protons, electrons and muons

– inner core - 2 0 does not occur in low mass stars whose outer core extends to the very center – hyperons

Neutron Star Structure

Minimal Model

• Composition:

- baryons - p, n, , +, -, 0, -, 0

- mesons - , , , *, - leptons – e,

LMBM LLLL

Minimal Model

Vector Meson Potential

softens the equation of state at higher density

modifies the density dependence of the symmetry energy

P(MeV/fm3)

EoS and the particle population

(MeV/fm3)

Model with nonlinear vector meson interactions

Equations of State

Additional nonlinear vector meson interactions modify:

- density dependence of the EoS- density dependence of the symmetry energy

The energy per particle of nuclear matter

The EoS around saturation density

The values of L and Ksym govern the density dependence of sym around 0

pn

pnaf

)()()0,(),( 42aasyma fOff

)( 0 symJ

2

2

1)0,( xKa vv

0

0

3

x

2

2

1)( xKLxJ symsym

Recent research in intermediate-energy heavy ion collisions is consistent with the following density dependence for < 0

The approximate formula for the core-crust transition density. (Prakash et al. 2007)

0

)( Jsym

Constraints from neutron skins - t ~ 0.095 0.01 fm-3 does not support the direct URCA process Results from microscopic EoS of Friedman and

Pandharipande t ~ 0.096 fm-3

Isospin diffusion ~ 0.69 – 1.05Isoscaling data ~ 0.69

v

symtt K

Ku

23

2

3

2

0

Properties of nuclear matter for nononlinear modelsNonlinear models -- properties of nuclear matter

The EoS for the entire density span

Outer crust – Baym-Pethick-Sutherland EoS of a cold nonaccreating neutron star (Baym et al. 1971)

Inner crust – polytropic form of the EoS (Carriere et al., 2003 )

3/43/4

3/43/4

3/43/4

3/4

outt

outt

outt

outttout

PPb

PPa

baP

out = 2.46 x 10-4 fm-3 the density separating the inner from the outer crust

The mass-radius relations for different values of the transition density

The mass-radius relations

Parameters of maximum mass configurations

Stellar profiles for different values of the parameter V

Particle populations of neutron star matter

Composition of the maximum mass star

Composition of the maximum mass star for V=0.01

Location of the crust-core interface

- crust thickness = R – Rt

2

2

21

Rc

GMM

R

Astrophysical implications

Rf

M

PR

cI

I t

12

6exp2)(

3

8 112

4

2

Moment of inertia connected with the crust

Using the upper limit of Pt the constraints for the minimum radius R for a given mass M for Vela can be obtained

The pressure at the boundary is very sensitive to the density dependence of the symmetry energy. 0.20 MeV fm-3 < Pt < 0.65 MeV fm-3

kmM

MR

S

9.36.3

• Extended vector meson sector

• EoS - considerably stiffer in the high density limit – higher value of the maximum mass

• Modification of the density dependence of the

symmetry energy

• Transition density sensitive to the value of the parameter V

• Modified structure of a neutron star

Summary and Conclusion