  The evolution of deeply embedded young stellar objects (YSOs) has
traditionally been traced through dust continuum spectral energy distributions
(SEDs), but the use of CO excitation as an evolutionary probe has not yet been
explored due to lack of high-J CO observations. The aim is to constrain the
physical characteristics (excitation, kinematics, column density) of the warm
gas toward 26 low-mass Class 0 and I YSOs using spectrally-resolved Herschel
Space Observatory data of high-J lines of CO. Data are complemented by
ground-based observations from APEX and the JCMT to compare those with the
colder gas traced by lower-J CO lines. This is the first large spectrally
resolved high-J CO survey conducted for these types of sources. The median
excitation temperatures for 12CO, 13CO and C18O derived from single-temperature
fits to the J_u=2-10 integrated intensities are ~70K, 48K and 37K,
respectively, with no significant difference between Class 0 and I sources and
no trend with M_env or L_bol. Thus, in contrast with the continuum SEDs, the
spectral line energy distributions (SLEDs) do not show an evolution during the
embedded stage. In contrast, the integrated line intensities of all CO
isotopologs show a clear decrease with evolutionary stage as the envelope is
dispersed. The H2O 110-101/CO 10-9 intensity ratio does not change
significantly with velocity, in contrast with the H2O/CO 3-2 ratio, indicating
that CO 10-9 is the lowest transition for which the line wings probe the same
warm shocked gas as H2O. Modeling of the full suite of C18O lines indicates an
abundance profile for Class 0 sources that is consistent with a freeze-out zone
below 25 K and evaporation at higher temperatures, with but some fraction of
the CO transformed into other species in the cold phase. In contrast,
observations for two Class I sources in Ophiuchus are consistent with a
constant high CO abundance profile.
