  We present far-IR (57-196 mu) spectra of 21 protostars in the Orion molecular
clouds, obtained with the Photodetector Array Camera and Spectrometer (PACS)
onboard the Herschel Space observatory, as part of the Herschel Orion Protostar
Survey (HOPS) program. We analyzed the CO emission lines (J_up = 14-46) in the
PACS spectra, extracted within a projected distance of <= 2000 AU centered on
the protostar. The total luminosity of the CO lines observed with PACS (L(CO))
is found to increase with increasing L_bol. The CO rotational temperature
implied by the line ratios increases with J, and at least 3-4 rotational
temperature components are required to fit the observed rotational diagram. The
rotational temperature components are remarkably invariant between protostars
and show no dependence on L_bol, T_bol or envelope density, implying that if
the emitting gas is in LTE, the CO emission must arise in multiple temperature
components that remain independent of L_bol over two orders of magnitudes. The
observed CO emission can also be modeled as arising from a single temperature
gas component or from a medium with a power-law temperature distribution; both
of these require sub-thermally excited molecular gas at low densities (n(H_2)
<= 10^6 cm^-3) and high temperatures (T >= 2000 K). Our results suggest that
the contribution from PDRs along the envelope cavity walls is unlikely to be
the dominant component of the CO emission observed with PACS. Instead, the
"universality" of the rotational temperatures and the observed correlation
between L(CO) and L_bol can most easily be explained if the observed CO
emission originates in shock-heated, hot (T >= 2000 K), sub-thermally excited
(n(H_2) <= 10^6 cm^-3) molecular gas. Post-shock gas at these densities is more
likely to be found within the outflow cavities along the molecular outflow or
along the cavity walls at radii >= several 100-1000 AU.
