Transcript Slajd 1
Hyperon Star Model
Ilona Bednarek
Ustroń, 2009
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
NeutronofStar
Structure
Structure
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
Minimal
Model
Minimal Model
• Composition:
- baryons - p, n, , +, -, 0, -, 0
- mesons - , , , *,
- leptons – e,
L LBM LM LL
Vector Meson Potential
softens the equation of state
at higher density
modifies the density
dependence of the symmetry
energy
EoS and the particle population
P
(MeV/fm3)
(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
(, f a ) (,0) sym ( ) f O( f )
2
a
1
2
( ,0) av K v x 2
x
4
a
0
30
n p
fa
n p
The EoS around saturation density
1
2
sym ( ) J Lx K sym x 2
J sym ( 0 )
The values of L and Ksym govern the density dependence of sym around 0
Recent research in intermediate-energy heavy ion collisions is consistent
with the following density dependence for < 0
sym ( ) J
0
Isospin diffusion ~ 0.69 – 1.05
Isoscaling data ~ 0.69
The approximate formula for the core-crust transition density.
(Prakash et al. 2007)
t 2 2 K sym
ut
0 3 3 2Kv
Constraints from neutron skins - t ~ 0.095 0.01 fm-3
Results from microscopic EoS of Friedman and
Pandharipande t ~ 0.096 fm-3
does not
support the
direct URCA
process
Properties models
of nuclear
for nononlinear
Nonlinear
-- matter
properties
of nuclear models
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 )
P a b 4 / 3
4/3
Pout t4 / 3 Pt out
a
4/3
t4 / 3 out
b
Pt Pout
4/3
t4 / 3 out
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
Astrophysical implications
Location of the crust-core interface
- crust thickness = R – Rt
R2
1 2
M
GM
2
Rc
Moment of inertia connected with the crust
6
I 8 R 4 Pt 1 1
2
f ( ) 2 exp
2
I
3c M
2 1 R
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
Using the upper limit of Pt the constraints for the minimum radius R for a
given mass M for Vela can be obtained
R 3.6 3.9
M
km
MS
Summary and Conclusion
• 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