  We conduct the first systematic survey of a comprehensive set of the twenty
optical coronal lines in the spectra of nearly 1 million galaxies observed by
the Sloan Digital Sky Survey (SDSS) Data Release 8 catalog. This includes often
overlooked high ionization-potential (IP) lines such as [Ar X] $\lambda$5533,
[S XII] $\lambda$7609, [Fe XI] $\lambda$7892, and [Fe XIV] $\lambda$5303. We
find that, given the limited sensitivity of SDSS, strong coronal line emission
is extremely rare, with only $\sim 0.03$% of the sample showing at least one
coronal line, significantly lower than the fraction of galaxies showing optical
narrow line ratios ($\sim 17$%) or mid-infrared colors ($\sim 2$%) indicative
of nuclear activity. The coronal line luminosities exhibit a large dynamic
range, with values ranging from $\sim10^{34}$ to $10^{42}$ erg s$^{-1}$. We
find that a vast majority ($\sim 80$%) of coronal line emitters in dwarf
galaxies ($M_* < {9.6} \times 10^9$ M$_\odot$) do not display optical narrow
line ratios indicative of nuclear activity, in contrast to higher mass galaxies
($\sim 17$%). Moreover, we find that the highest ionization potential lines are
preferentially found in lower mass galaxies. These findings are consistent with
the theory that lower mass black holes found in lower mass galaxies produce a
hotter accretion disk, which in turn enhances the higher ionization coronal
line spectrum. Future coronal line searches with 30 m class telescopes or JWST
may provide a pathway into uncovering the intermediate mass black hole
population.
