  Plasma diagnostics are the bases of investigation into the physical and
chemical properties of line-emitting gaseous systems. To perform plasma
diagnostics properly, it is essential to correct the input spectrum for
extinction properly. This is simply because determining the degree of
extinction is dependent on the physical properties of the line-emitting gas.
Hence, both extinction correction and plasma diagnostics have to be performed
simultaneously and self-consistently. By comparing the results of analyses
performed for a sample of nine bright planetary nebulae in M 31 with and
without the proper extinction correction and plasma diagnostics, we demonstrate
how initial assumptions for the physical conditions of the line-emitting gas in
extinction correction would compromise the results of the entire analyses.
While the electron density/temperature are relatively immune to the imposed
inconsistent assumptions, the compromised extinction would cause systematic
offsets in the extinction-corrected line strengths, which consequently would
impose adverse effects on the resulting ionic and elemental abundances, and
other inferences made from the incorrect results. We find that this M 31 PN
sample simply represents those around the high-mass end of the mass range for
low-mass planetary nebula progenitor stars as expected from the existing
theoretical models. It appears that the suspicion raised in the previous study
- these PNe being anomalously nitrogen overabundant - is simply caused by the
apparent underestimate in extinction that originates from the imposed
inconsistent assumptions in extinction correction. In a larger context, the
results of plasma diagnostics in the literature without seeking simultaneous
self-consistency with extinction correction have to be handled cautiously.
Ideally, such previous results should be re-evaluated by seeking simultaneous
self-consistency.
