Rotational equilibrium of C$_2$ in diffuse interstellar clouds

Context. Recent spectroscopic measurements have revealed absorption from higher rotational levels in C$_2$ than previous observations. These improvements are accompanied by the availability of updated radiative and collisional data. Aims. We revisit the density and radiation field intensity diagnostics provided by the observations of many rotational levels of inter- stellar C$_2$ and extensive molecular information. Methods. We built an excitation model of C2 without spatial structure, including levels up to J= 34 where updated radiative and collisional excitation data are introduced as well as excitation by chemical formation. Results. We confirm the importance of the recent collisional excitation rate coefficients of C$_2$ by molecular H$_2$. We show that the new higher level observations cannot be explained by the standard balance between collisional excitation and radiative transitions. We propose that chemical excitation at formation provides a plausible mechanism to explain the observed high excitation of C$_2$. In addition, it allows us to lift the degeneracy of the density over radiation field strength parameter in the excitation model. Conclusions. A 0D model remains limited and it is highly desirable to use a full Photon Dominated Region (PDR) model, which includes all excitation processes introduced here and full chemical and thermal balance.