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 ($\xi$) and shear ($\eta$) 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 $\xi =A_{\xi }{L}^{B_{\xi }}$ and $\eta =A_{\eta }{L}^{B_{\eta }}$. 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 $\sim$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 $1.4M_{\odot }$ ($2M_{\odot }$). Outside this range it is not possible to draw any conclusion on $L$ from this pulsar.

• Received 21 February 2012

DOI:https://doi.org/10.1103/PhysRevC.85.045808