hyperon star model
DESCRIPTION
Hyperon Star Model. Ilona Bednarek Ustroń, 2009. Typical neutron star parameters:. Neutron stars are the most compact objects M ~ 1.4 M S 1.44 M S the largest precisely known neutron star mass R ~ 10 km g ~ 2 x 10 14 cm s -2 ~ 7 x 10 14 g cm -3 (2 – 3) 0. - PowerPoint PPT PresentationTRANSCRIPT
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