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 relativisic 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 1.4 M _ { \odot } ( 2 M _ { \odot } ) .
Outside this range it is not possible to draw any conclusion on L from this pulsar .