Interplanetary Scintillation studies with the Murchison Wide-field Array
  III: Comparison of source counts and densities for radio sources and their
  sub-arcsecond components at 162 MHz
  We use Murchison Widefield Array observations of interplanetary scintillation
(IPS) to determine the source counts of point ($<$0.3 arcsecond extent) sources
and of all sources with some subarcsecond structure, at 162 MHz. We have
developed the methodology to derive these counts directly from the IPS
observables, while taking into account changes in sensitivity across the survey
area. The counts of sources with compact structure follow the behaviour of the
dominant source population above $\sim$3 Jy but below this they show Euclidean
behaviour. We compare our counts to those predicted by simulations and find a
good agreement for our counts of sources with compact structure, but
significant disagreement for point source counts. Using low radio frequency
SEDs from the GLEAM survey, we classify point sources as Compact Steep-Spectrum
(CSS), flat spectrum, or peaked. If we consider the CSS sources to be the more
evolved counterparts of the peaked sources, the two categories combined
comprise approximately 80% of the point source population. We calculate
densities of potential calibrators brighter than 0.4 Jy at low frequencies and
find 0.2 sources per square degrees for point sources, rising to 0.7 sources
per square degree if sources with more complex arcsecond structure are
included. We extrapolate to estimate 4.6 sources per square degrees at 0.04 Jy.
We find that a peaked spectrum is an excellent predictor for compactness at low
frequencies, increasing the number of good calibrators by a factor of three
compared to the usual flat spectrum criterion.
