  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)
non-equilibrium weak processes, which increase the bulk viscosity, and thus
suppress the r-mode instability. Existing calculations of the instability
windows for hyperon NSs generally use reaction rates calculated for the
$\Sigma^-\Lambda$ hyperonic composition via the contact $W$ boson exchange
interaction. In contrast, here we employ hyperonic equations of state where the
$\Lambda$ and $\Xi^-$ are the first hyperons to appear (the $\Sigma^-$'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 non-paired $npe\mu\Lambda\Xi^-$ matter
using the meson exchange weak interaction. A number of viscosity-generating
non-equilibrium 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.
