Bulk viscosity in neutron stars with hyperon cores
It is well known that r-mode oscillations of rotating neutron stars may be unstable with respect to the gravitational wave emission. It is highly unlikely to observe a neutron star with the parameters within the instability window, a domain where this instability is not suppressed. But if one adopts the "minimal" (nucleonic) composition of the stellar interior, a lot of observed stars appear to be within the r-mode instability window. One of the possible solutions to this problem is to account for hyperons in the neutron-star core. The presence of hyperons allows for a set of powerful (lepton-free) nonequilibrium weak processes, which increase the bulk viscosity and thus suppress the r-mode instability. Existing calculations of the instability windows for hyperon neutron stars generally use reaction rates calculated for the Σ-Λ hyperonic composition via the contact W -boson-exchange interaction. In contrast, here we employ hyperonic equations of state where the Λ and Ξ- are the first hyperons to appear (the Σ-'s, if they are present, appear at much larger densities) and consider the meson-exchange channel, which is more effective for the lepton-free weak processes. We calculate the bulk viscosity for the nonpaired n p e μ Λ Ξ- matter using the meson-exchange weak interaction. A number of viscosity-generating nonequilibrium processes is considered (some of them for the first time in the neutron-star context). The calculated reaction rates and bulk viscosity are approximated by simple analytic formulas, easy to use in applications. Applying our results to calculation of the instability window, we argue that accounting for hyperons may be a viable solution to the r-mode problem.