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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.