Factories of CO-dark gas: molecular clouds with limited star formation efficiencies by far-ultraviolet feedback

The star formation in molecular clouds is inefficient. The ionizing extreme-ultraviolet radiation (hν ≥ 13.6 eV) from young clusters has been considered as a primary feedback effect to limit the star formation efficiency (SFE). Here, we focus on the effects of stellar far-ultraviolet (FUV) radiation (6 eV ≤ hν ≤ 13.6 eV) during the cloud disruption stage. The FUV radiation may further reduce the SFE via photoelectric heating, and it also affects the chemical states of the gas that is not converted to stars (‘cloud remnants’) via photodissociation of molecules. We have developed a one-dimensional semi-analytical model that follows the evolution of both the thermal and chemical structure of a photodissociation region (PDR) during the dynamical expansion of an H ii region. We investigate how the FUV feedback limits the SFE, supposing that the star formation is quenched in the PDR where the temperature is above a threshold value (e.g. 100 K). Our model predicts that the FUV feedback contributes to reduce the SFEs for massive (Mcl ≳ 105 M⊙) clouds with low surface densities ($\Sigma _{\rm cl}\lesssim 100~{\rm M}_\odot \, {\rm pc}^{-2}$). Moreover, we show that a large part of the H2 molecular gas contained in the cloud remnants should be ‘CO-dark’ under the FUV feedback for a wide range of cloud properties. Therefore, the dispersed molecular clouds are potential factories of CO-dark gas, which returns into the cycle of the interstellar medium.