  We calculate the effect of dark matter on the ringdown waveform and shadow of
supermassive black holes at the core of galaxies. Our main focus is on the
supermassive black hole at the core of M87, which is large enough to allow for
viable observational data. We compare the effects of a dark matter spike to
those expected from a galactic halo of the same mass. The radial pressure is
shown to be negligible for both the spike and the halo, implying that there is
no difference between the isotropic case and the anisotropic case. Our
calculation for the halo starts from the Hernquist density function for which
the corresponding metric can be obtained analytically in closed form. The
effect of the spike is orders of magnitude more significant than the halo as
long as the distribution scale of the latter is within a few orders of
magnitude of the value expected from observations. Our results indicate that
the impact of the spike surrounding M87* on the ringdown waveform may in
principle be detectable. Finally, we point out the somewhat surprising fact
that existing Event Horizon Telescope observations of black hole shadows are
within an order of magnitude from being able to detect, or rule out, the
presence of a spike.
