Neutron star stability with equations of state breaking the conformal QCD limit

We explore the structural stability of neutron stars against radial pulsations obtained by a set of equations of state calculated from successive interpolations between perturbative QCD at high densities and chiral effective field theory at low densities being constrained also by observational data at intermediate densities. In order to do this, we solve a pair of first-order coupled differential equations equivalent to the original Sturm-Liouville problem to obtain the zero-mode frequencies characterizing stable stars. Besides, we study the effects of mild and large breakings of the conformal limit put for the speed of sound, ${c}_{s}^{2}=1/3$, in stars that can possibly contain cold quark matter at their cores. We find that some neutron-star families display an unusual humps in the mass-radius diagram which are associated to large non-linear oscillation amplitudes near the core.