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##### Nuclear symmetry energy and the r-mode instability of neutron stars

**Authors**: I. Vidaña

**Ref.**: Physical Review C **85**, 045808 (2012)

**Abstract**: We analyze the role of the symmetry energy slope parameter L on the r-mode instability of neutron stars. Our study is performed using both microscopic and phenomenological approaches of the nuclear equation of state. The microscopic ones include the Brueckner-Hartree-Fock approximation, the well known variational equation of state of Akmal, Pandharipande, and Ravenhall, and a parametrization of recent auxiliary field diffusion Monte Carlo calculations. For the phenomenological approaches, we use several Skyrme forces and relativistic mean-field models. Our results show that the r-mode instability region is smaller for those models which give larger values of L. The reason is that both bulk (ξ) and shear (η) viscosities increase with L and, therefore, the damping of the mode is more efficient for the models with larger L. We show also that the dependence of both viscosities on L can be described at each density by simple power-laws of the type ξ=AξLBξ and η=AηLBη. Using the measured spin frequency and the estimated core temperature of the pulsar in the low-mass x-ray binary 4U 1608-52, we conclude that observational data seem to favor values of L larger than ∼50 MeV if this object is assumed to be outside the instability region, its radius is in the range 11.5–12 (11.5–13) km, and its mass 1.4M⊙ (2M⊙). Outside this range it is not possible to draw any conclusion on L from this pulsar.