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Ilona Bednarek Ustroń, 2009 Hyperon Star Model

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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

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Structure of a neutron star Atmosphere Crust: –outer crust – from the atmosphere bottom to the density ND 4 x 10 11 g 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

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Minimal Model Composition: - baryons - p, n, , +, -, 0, -, 0 - mesons - , , , *, - leptons – e, Minimal Model

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Vector Meson Potential softens the equation of state at higher density modifies the density dependence of the symmetry energy

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P (MeV/fm 3 ) EoS and the particle population (MeV/fm 3 )

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Model with nonlinear vector meson interactions

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Equations of State

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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 K sym govern the density dependence of sym around 0

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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) 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 – 1.05 Isoscaling data ~ 0.69

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

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

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

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The mass-radius relations

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Parameters of maximum mass configurations Stellar profiles for different values of the parameter V

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Particle populations of neutron star matter

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Composition of the maximum mass star

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Composition of the maximum mass star for V =0.01

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Location of the crust-core interface - crust thickness = R – R t Astrophysical implications Moment of inertia connected with the crust Using the upper limit of P t 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 < P t < 0.65 MeV fm -3

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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

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