  We investigate the effects ultralight bosonic field dark matter may have on
the dynamics of unstable differentially-rotating neutron stars prone to the
bar-mode instability. To this aim we perform numerical simulations in general
relativity of rotating neutron stars accreting an initial spherically symmetric
bosonic field cloud, solving the Einstein-(complex, massive) Klein-Gordon-Euler
and the Einstein-(complex) Proca-Euler systems. We find that the presence of
the bosonic field can critically modify the development of the bar-mode
instability of neutron stars, depending on the total mass of the bosonic field
and on the boson particle mass. In some cases, the accreting bosonic field can
even quench the dominant $\ell=m=2$ mode of the bar-deformation by dynamically
forming a mixed (fermion-boson) star that retains part of the angular momentum
of the original neutron star. However, the mixed star undergoes the development
of a mixed bar that leads to significant gravitational-wave emission,
substantially different to that of the isolated neutron star. Our results
indicate that dark-matter accretion in neutron stars could change the frequency
of the expected emission of the bar-mode instability, which would have an
important impact on ongoing searches for continuous gravitational waves.
