  We use a simple, self-consistent, self-gravitating semi-analytic disc model
to conduct an examination of the parameter space in which self-gravitating
discs may exist. We then use Monte-Carlo radiative transfer to generate
synthetic ALMA images of these self-gravitating discs to determine the subset
of this parameter space in which they generate non-axisymmetric structure that
is potentially detectable by ALMA. Recently, several transition discs have been
observed to have non-axisymmetric structure that extends out to large radii. It
has been suggested that one possible origin of these asymmetries could be
spiral density waves induced by disc self-gravity. We use our simple model to
see if these discs exist in the region of parameter space where self-gravity
could feasibly explain these spiral features. We find that for self-gravity to
play a role in these systems typically requires a disc mass around an order of
magnitude higher than the observed disc masses for the systems. The spiral
amplitudes produced by self-gravity in the local approximation are relatively
weak when compared to amplitudes produced by tidal interactions, or spirals
launched at Lindblad resonances due to embedded planets in the disc. As such,
we ultimately caution against diagnosing spiral features as being due to
self-gravity, unless the disc exists in the very narrow region of parameter
space where the spiral wave amplitudes are large enough to produce detectable
features, but not so large as to cause the disc to fragment.
