  A rather minimal possibility is that dark matter consists of the gauge bosons
of a spontaneously broken symmetry. Here we explore the possibility of
detecting the gravitational waves produced by the phase transition associated
with such breaking. Concretely, we focus on the scenario based on an $SU(2)_D$
group and argue that it is a case study for the sensitivity of future
gravitational wave observatories to phase transitions associated with dark
matter. This is because there are few parameters and those fixing the relic
density also determine the effective potential establishing the strength of the
phase transition. Particularly promising for LISA and even the Einstein
Telescope is the super-cool dark matter regime, with DM masses above
$\mathcal{O}$(100) TeV, for which we find that the gravitational wave signal is
notably strong. In our analysis, we include the effect of astrophysical
foregrounds, which are often ignored in the context of phase transitions.
