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