Mid-$J$ CO Line Observations of Protostellar Outflows in the Orion
  Molecular Clouds
  Ten protostellar outflows in the Orion molecular clouds were mapped in the
$^{12}$CO/$^{13}$CO ${J=6\rightarrow5}$ and $^{12}$CO ${J=7\rightarrow6}$
lines. The maps of these mid-$J$ CO lines have an angular resolution of about
10$''$ and a typical field size of about 100$''$. Physical parameters of the
molecular outflows were derived, including mass transfer rates, kinetic
luminosities, and outflow forces. The outflow sample was expanded by
re-analyzing archival data of nearby low-luminosity protostars, to cover a wide
range of bolometric luminosities. Outflow parameters derived from other
transitions of CO were compared. The mid-$J$ ($J_{\rm up} \approx 6$) and
low-$J$ ($J_{\rm up} \leq 3$) CO line wings trace essentially the same outflow
component. By contrast, the high-$J$ (up to $J_{\rm up} \approx 50$)
line-emission luminosity of CO shows little correlation with the kinetic
luminosity from the ${J=6\rightarrow5}$ line, which suggests that they trace
distinct components. The low/mid-$J$ CO line wings trace long-term outflow
behaviors while the high-$J$ CO lines are sensitive to short-term activities.
The correlations between the outflow parameters and protostellar properties are
presented, which shows that the strengths of molecular outflows increase with
bolometric luminosity and envelope mass.
