Collisional excitation of c-MgC2 by Helium

Abstract

ABSTRACT The cyclic form of magnesium dicarbide molecule (c-MgC$_2$) has been detected in the carbon-rich circumstellar envelope of IRC+10216 and is considered as a valuable tracer for characterizing the physical conditions of the surrounding gas. In order to make the most of c-MgC$_2$ observations and accurately derive the physical conditions of the media where c-MgC$_2$ is detected, radiative transfer modelling, including collisional and radiative (de-)excitations, have to be performed. Here, we study the excitation of c-MgC$_{2}$ induced by collisions with He (as a proxy for H$_2$). A new 3D potential energy surface (PES) is constructed using highly correlated ab initio methods. This PES reveals a minimum with a well depth of 20.66 cm$^{-1}$ below the c-MgC$_2$-He dissociation limit. Using this PES, we compute excitation cross sections for transitions between the low-lying rotational energy levels of c-MgC$_2$ using the time-independent quantum mechanical close-coupling formalism. These cross sections are then thermally averaged over a Boltzmann energy distribution in order to derive excitation rate coefficients at low temperatures ($T \le 30$ K). To evaluate the impact of these new rate coefficients on the interpretation of c-MgC$_2$ observational spectra, we perform radiative transfer calculations. We find that a very high gas density ($n \gt 10^6$ cm$^{-3}$) is needed in order for the collisional excitation to compete with the radiative de-excitation. We also find that the excitation temperatures of the observed lines predicted by our model differ by a factor two from the value derived from the observations in IRC+10216 circumstellar envelope, indicating that the excitation of c-MgC$_{2}$ may also be driven by a strong radiative pumping in such media. Therefore, a more sophisticated non-LTE modelling, that takes into account the collisional and radiative excitations as well as the radiative pumping, is required to accurately interpret the observational spectra of c-MgC$_2$.