Hydrostatic equilibrium of causally consistent and dynamically stable neutron star models

We show that the mass–radius  ( M – R )  relation corresponding to the stiffest equation of state (EOS) does not provide the necessary and sufficient condition of dynamical stability for equilibrium configurations, because such configurations cannot satisfy the 'compatibility criterion'. In this regard, we construct sequences composed of core–envelope models such that, like the central condition belonging to the stiffest EOS, each member of these sequences satisfies the extreme case of the causality condition,   v = c = 1  , at the centre. We thereafter show that the M – R relation corresponding to the said core–envelope model sequences can provide the necessary and sufficient condition of dynamical stability only when the 'compatibility criterion' for these sequences is 'appropriately' satisfied. However, the 'compatibility criterion' can remain satisfied even when the M – R relation does not provide the necessary and sufficient condition of dynamical stability for the equilibrium configurations. In continuation of the results of a previous study, these results explicitly show that the 'compatibility criterion' independently provides, in general, the necessary and sufficient condition of hydrostatic equilibrium for any regular sequence. In addition to its fundamental result, this study can explain simultaneously the higher and the lower values of the glitch healing parameter observed for the Crab-like and Vela-like pulsars respectively, on the basis of the starquake model of glitch generation.