The evolution of far-infrared CO emission from protostars
  We investigate the evolution of far-IR CO emission from protostars observed
with Herschel/PACS for 50 sources from the combined sample of HOPS and DIGIT
Herschel key programs. From the uniformly sampled spectral energy
distributions, we computed $L_{\rm{bol}}$, $T_{\rm{bol}}$ and $L_{\rm
{bol}}/L_{\rm {smm}}$ for these sources to search for correlations between
far-IR CO emission and protostellar properties. We find a strong and tight
correlation between far-IR CO luminosity ($L^{\rm fir}_{\rm CO}$) and the
bolometric luminosity ($L_{\rm{bol}}$) of the protostars with $L^{\rm fir}_{\rm
CO}$ $\propto$ $L_{\rm{bol}}^{0.7}$. We, however, do not find a strong
correlation between $L^{\rm fir}_{\rm CO}$ and protostellar evolutionary
indicators, $T_{\rm{bol}}$ and $L_{\rm {bol}}/L_{\rm {smm}}$. FIR CO emission
from protostars traces the currently shocked gas by jets/outflows, and $L^{\rm
fir}_{\rm CO}$ is proportional to the instantaneous mass loss rate,
$\dot{M}_{\rm{out}}$. The correlation between $L^{\rm fir}_{\rm CO}$ and
$L_{\rm{bol}}$ is indicative of instantaneous $\dot{M}_{\rm{out}}$ tracking
instantaneous $\dot{M}_{\rm{acc}}$. The lack of correlation between $L^{\rm
fir}_{\rm CO}$ and evolutionary indicators $T_{\rm{bol}}$ and $L_{\rm
{bol}}/L_{\rm {smm}}$ suggests that $\dot{M}_{\rm{out}}$ and, therefore,
$\dot{M}_{\rm{acc}}$ do not show any clear evolutionary trend. These results
are consistent with mass accretion/ejection in protostars being episodic. Taken
together with the previous finding that the time-averaged mass
ejection/accretion rate declines during the protostellar phase (e.g., Bontemps
et al. 1996), our results suggest that the instantaneous accretion/ejection
rate of protostars is highly time variable and episodic, but the amplitude
and/or frequency of this variability decreases with time such that the time
averaged accretion/ejection rate declines with system age.
