Strong softening with density jump The third family of compact stars

Such a phase transition corresponds to A = pB/pA > Acrit. In this case the appearance of a small core of phase B destabilizes the neutron star. Using Eqs. (7.65) one can see that in the presence of such a core dM/ dpc < 0. These configurations are therefore unstable and collapse into stable configurations with large cores of phase B. The instability condition A > | (1 + P0/pAc2) had been first derived by Seidov (1971) using the static energy method. Ten

13This property stems from the the linear response theory formulated in 1986-1987 (Haensel et al., 1986a; Zdunik etal., 1987). Later it was rederived by Lindblom (1998) who used detailed and strict mathematical analysis of equilibrium configurations for an EOS exhibiting first-order phase transition.

Figure 7.11. Vicinity of the "reference configuration" C0 with Pc = P0 in the M — R plane for phase transitions with A < Acrit (left) and A > Acrit (right). The dotted segment corresponds to unstable two-phase configurations. Arrows connect configurations with the same baryon numbers.

Figure 7.11. Vicinity of the "reference configuration" C0 with Pc = P0 in the M — R plane for phase transitions with A < Acrit (left) and A > Acrit (right). The dotted segment corresponds to unstable two-phase configurations. Arrows connect configurations with the same baryon numbers.

years later this condition was rediscovered by Kaempfer (1981) who studied the necessary condition for the onset of neutron star collapse initiated by a phase transition in its center. It is worth to mention that the Newtonian version of this criterion (A > f) had been first obtained by Lighthill (1950) (see also Ramsey, 1950) in the context of stability of planets. Relativistic effects stabilize neutron stars with small cores of phase B by increasing Acrit. The increase can be as high as ~ 0.2. The dynamics of the collapse of configurations with a small core of phase B will be studied in § 7.9.8.

Stable equilibrium configurations of neutron stars split into two families visualized in Fig. 7.10b. The superdense branch CminCmax forms the third family of compact stars, apart from white dwarfs and lower-density neutron stars. Contrary to the instability triggered by second-order phase transition (associated with the hyperonization or the appearance of a mixed phase of quarks and baryons, § 7.9.3), for the instability at A > Acrit one typically has Mmax < Mjax and Amax < Ajax (see, e.g., Brown & Weise, 1976; Haensel &Proszynski, 1982;Migdal etal., 1990). Possible observational consequences of this behavior are described in § 7.9.8.

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