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Effects of the nuclear equation of state on the r-mode instability and evolution of neutron stars

I study the effect of nuclear equation of state on the r-mode instability of a rotating neutron star. I consider the case where the crust of the neutron star is perfectly rigid and I employ the related theory introduced by Lindblom {\it et al.} \cite{Lidblom-2000}. The gravitational and the viscous time scales, the critical angular velocity and the critical temperature are evaluated by employing a phenomenological nuclear model for the neutron star matter. The predicted equations of state for the $β$-stable nuclear matter are parameterized by varying the slope $L$ of the symmetry energy at saturation density on the interval $72.5 \ {\rm MeV} \leq L \leq 110 \ {\rm MeV}$. The effects of the density dependence of the nuclear symmetry energy on r-mode instability properties and the time evolution of the angular velocity are presented and analyzed. A comparison of theoretical predictions with observed neutron stars in low-mass x-ray binaries (LMXBs) and millisecond radio pulsars (MSRPs) is also performed and analyzed. I estimate that it may be possible to impose constraints on the nuclear equation of state, by a suitable treatment of observations and theoretical predictions of the rotational frequency and spindown rate evolution of known neutron stars.