Far infrared CO and H$_2$O emission in intermediate-mass protostars

Intermediate-mass young stellar objects (YSOs) provide a link to understand how feedback from shocks and UV radiation scales from low to high-mass star forming regions. Aims: Our aim is to analyze excitation of CO and H$_2$O in deeply-embedded intermediate-mass YSOs and compare with low-mass and high-mass YSOs. Methods: Herschel/PACS spectral maps are analyzed for 6 YSOs with bolometric luminosities of $L_\mathrm{bol}\sim10^2 - 10^3$ $L_\odot$. The maps cover spatial scales of $\sim 10^4$ AU in several CO and H$_2$O lines located in the $\sim55-210$ $\mu$m range. Results: Rotational diagrams of CO show two temperature components at $T_\mathrm{rot}\sim320$ K and $T_\mathrm{rot}\sim700-800$ K, comparable to low- and high-mass protostars probed at similar spatial scales. The diagrams for H$_2$O show a single component at $T_\mathrm{rot}\sim130$ K, as seen in low-mass protostars, and about $100$ K lower than in high-mass protostars. Since the uncertainties in $T_\mathrm{rot}$ are of the same order as the difference between the intermediate and high-mass protostars, we cannot conclude whether the change in rotational temperature occurs at a specific luminosity, or whether the change is more gradual from low- to high-mass YSOs. Conclusions: Molecular excitation in intermediate-mass protostars is comparable to the central $10^{3}$ AU of low-mass protostars and consistent within the uncertainties with the high-mass protostars probed at $3\cdot10^{3}$ AU scales, suggesting similar shock conditions in all those sources.