Updating quasar bolometric luminosity corrections. III. [O III]
  bolometric corrections
  We present quasar bolometric corrections using the [O III] $\lambda5007$
narrow emission line luminosity based on the detailed spectral energy
distributions of 53 bright quasars at low to moderate redshift
($0.0345<z<1.0002$). We adopted two functional forms to calculate
$L_{\textrm{iso}}$, the bolometric luminosity determined under the assumption
of isotropy: $L_{\textrm{iso}}=A\,L_{[O\,III]}$ for comparison with the
literature and log$(L_{iso})=B+C\,$log$(L_{[O\,III]})$, which better
characterizes the data. We also explored whether "Eigenvector 1", which
describes the range of quasar spectral properties and quantifies their
diversity, introduces scatter into the $L_{[O\,III]}-L_{iso}$ relationship. We
found that the [O III] bolometric correction can be significantly improved by
adding a term including the equivalent width ratio $R_{Fe\,II}\equiv
EW_{Fe\,II}/EW_{H\beta}$, which is an Eigenvector 1 indicator. Inclusion of
$R_{Fe\,II}$ in predicting $L_{iso}$ is significant at nearly the $3\sigma$
level and reduces the scatter and systematic offset of the luminosity
residuals. Typically, [O III] bolometric corrections are adopted for Type 2
sources where the quasar continuum is not observed and in these cases,
$R_{Fe\,II}$ cannot be measured. We searched for an alternative measure of
Eigenvector 1 that could be measured in the optical spectra of Type 2 sources
but were unable to identify one. Thus, the main contribution of this work is to
present an improved [O III] bolometric correction based on measured bolometric
luminosities and highlight the Eigenvector 1 dependence of the correction in
Type 1 sources.
