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 $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$, $T_{\mathrm{b}\mathrm{o}\mathrm{l}}$ 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 ($L_{\mathrm{C}\mathrm{O}}^{\mathrm{f}\mathrm{i}\mathrm{r}}$) and the bolometric luminosity ($L_{\mathrm{b}\mathrm{o}\mathrm{l}}$) of the protostars with $L^{\rm fir}{\rm CO}$ $\propto$ $L_{\mathrm{b}\mathrm{o}\mathrm{l}}^{0.7}$. We, however, do not find a strong correlation between $L_{\mathrm{C}\mathrm{O}}^{\mathrm{f}\mathrm{i}\mathrm{r}}$ and protostellar evolutionary indicators, $T_{\mathrm{b}\mathrm{o}\mathrm{l}}$ and $L_{\mathrm{b}\mathrm{o}\mathrm{l}}\mathrm{/}{L}_{\mathrm{s}\mathrm{m}\mathrm{m}}$. FIR CO emission from protostars traces the currently shocked gas by jets/outflows, and $L^{\rm fir}{\rm CO}$isproportionaltotheinstantaneousmasslossrate,$\dot{M}{\rm{out}}$\mathrm{.}Thecorrelationbetween$L^{\rm fir}{\rm CO}$and$L_{\rm{bol}}$isindicativeofinstantaneous$\dot{M}{\rm{out}}$ tracking instantaneous ${\dot{M}}_{\mathrm{a}\mathrm{c}\mathrm{c}}$. The lack of correlation between $L^{\rm fir}{\rm CO}$andevolutionaryindicators$T_{\rm{bol}}$and$L_{\rm {bol}}/L_{\rm {smm}}$suggeststhat$\dot{M}{\rm{out}}$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.