The warm CO gas along the UV-heated outflow cavity walls: a possible interpretation for the Herschel/PACS CO spectra of embedded YSOs

A fraction of the mid-$J$ ($J$= 14--13 to $J$= 24--23) CO emission detected by the \textit{Herschel}/PACS observations of embedded young stellar objects (YSOs) has been attributed to the UV-heated outflow cavity walls. We have applied our newly developed self-consistent models of Photon-Dominated Region (PDR) and non-local thermal equilibrium line Radiative transfer In general Grid (RIG) to the \textit{Herschel} FIR observations of 27 low mass YSOs and one intermediate mass YSO, NGC7129-FIRS2. When the contribution of the hot component (traced by transitions of $J> 24$) is removed, the rotational temperature of the warm component is nearly constant with $\sim250$ K. This can be reproduced by the outflow cavity wall ($n \geq 10^6\, \mathrm{cm}^{-3}$, $\log G_{0}/n \geq-4.5$, $\mathrm{log} G_0\ge 3$, $T_{\rm gas} \ge 300 $K, and X(CO)$ \ge 10^{-5}$) heated by a UV radiation field with a black body temperature of 15,000 K or 10,000 K. However, a shock model combined with an internal PDR will be required to determine the quantitative contribution of a PDR relative to a shock to the mid-$J$ CO emission.