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We perform a systematic study of the dependence of the r-mode phenomenologyin normal fluid pulsar neutron stars on the symmetry energy slope parameter$L$. An essential ingredient in this study is the bulk viscosity, which isevaluated consistently for several equations of state corresponding todifferent values of the slope parameter $L$. Direct Urca processes, which areallowed from a critical $L$-value onwards, enhance the bulk viscosity and havelarge influence on the $r$-mode features, such as the instability boundary andspin-down properties of newborn neutron stars. The magnitude of the changes inthe $r$-mode properties induced by the direct Urca processes are driven by the$L$-value of the equation of state and the mass of the pulsar. The study hasbeen done by using a family of equations of state of $\beta$-equilibratedneutron star matter obtained with the finite range simple effectiveinteraction, which provides realistic results for nuclear matter and finitenuclei properties. These equations of state predict the same properties insymmetric nuclear matter and have the same value of the symmetry energyparameter, $E_s(\rho_0)$, but differ in the slope parameter $L$. The rangechosen for the variation of $L$ is decided from the tidal deformability dataextracted from the GW170817 event and the maximum mass constraint.

Constraints from GW170817 on the bulk viscosity of neutron star matter and the r-mode instability