Upper boundaries of AGN regions in optical diagnostic diagrams
  The distribution of galaxies in optical diagnostic diagrams can provide
information about their physical parameters when compared with ionization
models under proper assumptions. By using a sample of central emitting regions
from the MaNGA survey, we find evidence of the existence of upper boundaries
for narrow-line regions (NLRs) of active galactic nuclei (AGN) in optical BPT
diagrams, especially in the diagrams involving [S II]$\lambda \lambda$6716,
6731/H$\alpha$. Photoionization models can well reproduce the boundaries as a
consequence of the decrease of [S II]$\lambda \lambda$6716, 6731/H$\alpha$ and
[O III]$\lambda$5007/H$\beta$ ratios at very high metallicity. Whilst the exact
location of the upper boundary in the [S II] BPT diagram only weakly depends on
the electron density of the ionized cloud and the secondary nitrogen
prescription, its dependence on the shapes of the input SEDs is much stronger.
This allows us to constrain the power-law index of the AGN SED between 1 Ryd
and $\sim100$ Ryd to be less than or equal to $-1.40\pm 0.05$. The coverage of
the photoionization models in the [N II] BPT diagram has a stronger dependence
on the electron density and the secondary nitrogen prescription. With the
density constrained by the [S II] doublet ratio and the input SED constrained
by the [S II] BPT diagram, we find that the extent of the data in the [N II]
BPT diagram favors those prescriptions with high N/O ratios. Although
shock-ionized cloud can produce similar line ratios as those by
photoionization, the resulting shapes of the upper boundaries, if exist, would
likely be different from those of a photoionizing origin.
