Abstract
We study the stability against infinitesimal radial oscillations of neutron stars generated by a set of equations of state obtained from first-principle calculations in cold and dense QCD and constrained by observational data. We consider mild and large violations of the conformal bound, $c_{s} = 1/\sqrt{3}$, in stars that can possibly contain a quark matter core. Some neutron star families in the mass-radius diagram become dynamically unstable due to large oscillation amplitudes near the core.
Highlights
The equation of state (EoS) for neutron star matter, including the constraints from electric charge neutrality and beta equilibrium, is needed as the input to determine the structural properties of neutron stars (NS)
We study the stability against infinitesimal radial oscillations of neutron stars generated by a set of equations of state obtained from first-principle calculations in cold and dense QCD and constrpaiffinffi ed by observational data
By solving the oscillation equations for the representative tabulated EoSs discussed in Sec
Summary
The equation of state (EoS) for neutron star matter, including the constraints from electric charge neutrality and beta equilibrium, is needed as the input to determine the structural properties of neutron stars (NS) It has to cover a wide range of densities, from below the nuclear saturation density, n0 1⁄4 0.16 fm−3, up to about 10n0 [1], a real challenge. We use Cases 3 and 4 (without loss of generality) to show that those prominent lumps are dynamically unstable, not in the usual sense of having the (squared) fundamental-mode frequency negative, i.e., f2n1⁄40 < 0 Instead, their respective infinitesimal Lagrangian radial displacement, ξn1⁄40 1⁄4 ðΔr=rÞn1⁄40, produces large values (∼30), in contrast to the condition of being small, i.e., 0 < ξ ≤ 1, thereby allowing us to classify them, strictly speaking, as metastable.
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