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 EUV radiation ($h \nu \geq 13.6$ eV) from young clusters has been considered as a primary feedback effect to limit the star formation efficiency (SFE). We here focus on effects of the stellar FUV radiation (6 eV $\leq h \nu \leq$ 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-analytic model which follows the evolution of both the thermal and chemical structure of a photodissociation region (PDR) during the dynamical expansion of an HII 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., 100K). Our model predicts that the FUV feedback contributes to reduce the SFEs for the massive ($M_{\rm cl} \gtrsim 10^5 M_{\odot}$) clouds with the low surface densities ($\Sigma_{\rm cl} \lesssim 100$ M$_{\odot}$pc$^{-2}$). Moreover, we show that a large part of the H$_2$ 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 the CO-dark gas, which returns into the cycle of the interstellar medium.