  Supermassive black hole binaries source gravitational waves measured by
Pulsar Timing Arrays. The frequency spectrum of this stochastic background is
predicted more precisely than its amplitude. We argue that Dark Matter friction
can suppress the spectrum around nHz frequencies, where it is measured,
allowing to derive robust and significant bounds on the Dark Matter density,
which, in turn, controls indirect detection signals from galactic centers. A
precise spectrum of gravitational waves would translate in a tomography of the
DM density profile, potentially probing DM particle-physics effects that induce
a characteristic DM density profile, such as DM annihilations or de Broglie
wavelength.
