  Investigation of the triggering mechanisms of radio AGN is important for
improving our general understanding of galaxy evolution. In the first paper in
this series, detailed morphological analysis of high-excitation radio galaxies
(HERGs) with intermediate radio powers suggested that the importance of
triggering via galaxy mergers and interactions increases strongly with AGN
radio power and weakly with optical emission-line luminosity. Here, we use an
online classification interface to expand our morphological analysis to a much
larger sample of 155 active galaxies (3CR radio galaxies, radio-intermediate
HERGs and Type 2 quasars) that covers a broad range in both 1.4 GHz radio power
and [OIII]$\lambda$5007 emission-line luminosity. All active galaxy samples are
found to exhibit excesses in their rates of morphological disturbance relative
to 378 stellar-mass- and redshift-matched non-active control galaxies
classified randomly and blindly alongside them. These excesses are highest for
the 3CR HERGs (4.7$\sigma$) and Type 2 quasar hosts (3.7$\sigma$), supporting
the idea that galaxy mergers provide the dominant triggering mechanism for
these subgroups. When the full active galaxy sample is considered, there is
clear evidence to suggest that the enhancement in the rate of disturbance
relative to the controls increases strongly with [OIII]$\lambda$5007
emission-line luminosity but not with 1.4 GHz radio power. Evidence that the
dominant AGN host types change from early-type galaxies at high radio powers to
late-type galaxies at low radio powers is also found, suggesting that
triggering by secular, disk-based processes holds more importance for
lower-power radio AGN.
