  A dark scalar mediator can easily realize the self-interacting dark matter
scenario and satisfy the constraint of the relic density of the dark matter.
When the hidden sector is highly decoupled from the visible sector, the
gravitational waves produced by the first order phase transition resulted from
this dark scalar mediator will be an important signature to probe the dark
sector physics. The simplest dark sector with one scalar and one Dirac fermion
is studied in this work. A generic quartic finite-temperature potential is used
to induce the strong first order phase transition. A joint analysis of the
self-interacting dark matter, the relic density of the dark matter and the
first order phase transition shows that the mass range of the dark scalar is
about $(4\times 10^{-4} \sim 3)~\rm GeV$. For the dark matter, when the
temperature ratio $\xi$ between the hidden sector and the visible sector is
larger than 0.1, its mass range is about $(10~ \rm MeV\sim 10~ \rm GeV)$. The
produced gravitational waves have a peak frequency of $(10^{-6}\sim 10^{-3})
~\rm Hz$ for a temperature ratio $0.1<\xi<1$, which may be detectable in future
measurements.
