Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

Figure 4.9: The left panel shows the mass-radius relation of the neutron stars (dotted line)from the GNDF and the hybrid stars (solid line). The right panel shows the number densityprofile of a hybrid star which have M= 1.44M ⊙ . At r ∼ 5.0 km, the phase transition tonuclear matter takes place, and protons and neutrons exit. When r=8.2 km, the phasetransition to nuclear matter is completed and there is no more quark matter.As in the case of uniform matter, we assume beta-stable matter so that the chemical potentialsof the nuclear matter and quark matter have the relationµ n = µ p +µ eµ d = µ s = µ u +µ e .(4.45)Fig. 4.8 shows the energy density and pressure as a function of number density. The dotted(dashed) line represents nuclear (quark) matter. The solid line denotes the mixed phase.The phase transition begins when the baryon density becomes 1.386ρ 0 and all nucleons turninto quark matter when the baryon density becomes 5.236ρ 0 .If there is a phase transition in the core of a cold neutron star, the mass and radius arequite different from the case of a pure-nuclear-matter neutron star. The left panel of Fig.4.9 shows the mass-radius relation of the neutron stars (dotted line) and hybrid stars (solidline). The right panel shows the number density profiles of a quark matter and nuclearmatter of 1.44M ⊙ hybrid star. The maximum mass of a cold neutron star with mixed phase(hybrid star) is1.441M ⊙ andthe central density of theneutron star is 9.585ρ 0 . The mass andradius curve with the mixed phase indicates where the mixed phase exists. As the distancefrom the center of the hybrid star increases, the phase transition to nuclear matter takesplace so that neutrons and protons appear (r ∼ 5.0km). Far from the center, the phasetransition is completed (r = 8.2km); pure nuclear matter exists only for larger radii. Theexistence of quark matter in the hybrid star can be explained by angular momentum lossof the proto-neutron star. That is, a fast-rotating neutron stars loses angular momentumbecause of magnetic dipole radiation; the central density of the neutron star increases dueto the decrease in centripetal force, then quark matter appears. Since quark matter has alower energy density than pure nuclear matter, we might expect heating of the neutron starfrom latent heat from quark matter.68