CO in Protostars (COPS): $Herschel$-SPIRE Spectroscopy of Embedded
  Protostars
  We present full spectral scans from 200-670$\mu$m of 26 Class 0+I
protostellar sources, obtained with $Herschel$-SPIRE, as part of the
"COPS-SPIRE" Open Time program, complementary to the DIGIT and WISH Key
programs. Based on our nearly continuous, line-free spectra from 200-670
$\mu$m, the calculated bolometric luminosities ($L_{\rm bol}$) increase by 50%
on average, and the bolometric temperatures ($T_{\rm bol}$) decrease by 10% on
average, in comparison with the measurements without Herschel. Fifteen
protostars have the same Class using $T_{\rm bol}$ and $L_{\rm bol}$/$L_{\rm
submm}$. We identify rotational transitions of CO lines from J=4-3 to J=13-12,
along with emission lines of $^{13}$CO, HCO$^+$, H$_{2}$O, and [CI]. The ratios
of $^{12}$CO to $^{13}$CO indicate that $^{12}$CO emission remains optically
thick for $J_{\rm up}$ < 13. We fit up to four components of temperature from
the rotational diagram with flexible break points to separate the components.
The distribution of rotational temperatures shows a primary population around
100 K with a secondary population at $\sim$350 K. We quantify the correlations
of each line pair found in our dataset, and find the strength of correlation of
CO lines decreases as the difference between $J$-level between two CO lines
increases. The multiple origins of CO emission previously revealed by
velocity-resolved profiles are consistent with this smooth distribution if each
physical component contributes to a wide range of CO lines with significant
overlap in the CO ladder. We investigate the spatial extent of CO emission and
find that the morphology is more centrally peaked and less bipolar at high-$J$
lines. We find the CO emission observed with SPIRE related to outflows, which
consists two components, the entrained gas and shocked gas, as revealed by our
rotational diagram analysis as well as the studies with velocity-resolved CO
emission.
