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Compact objects are unique probes of beyond-Standard Model physics. I
will discuss two representative examples in which compact-object
observations can be used to constrain dark matter. During the motion
of a binary pulsar around the Galactic center, the pulsar and its
companion experience a wind of dark-matter particles that can affect
the orbital motion through dynamical friction. This effect produces a
characteristic seasonal modulation of the orbit and causes a secular
change of the orbital period whose magnitude can be well within the
astonishing precision of various binary-pulsar observations.
Furthermore, if ultralight bosonic fields exist in nature, black holes
may undergo superradiant instabilities. This effect, together with
precision measurements of the mass and spin of astrophysical black
holes, has been used to constrain axion-like particles, to derive
bounds on light vector fields and on the mass of the graviton, as well
as to constrain the fraction of primordial black holes in dark matter.
The theoretical potential of these phenomena as
almost-model-independent smoking guns for physics beyond the Standard
Model are presented.