Photochemistry of atomic oxygen green and red-doublet emissions in comets at larger heliocentric distances

In comets the atomic oxygen green to red-doublet emission intensity ratio (G/R ratio) of 0.1 has been used to confirm H$_2$O as the parent species producing oxygen emission lines. The larger ($>$0.1) value of G/R ratio observed in a few comets is ascribed to the presence of higher CO$_2$ and CO relative abundances in the cometary coma. We aim to study the effect of CO$_2$ and CO relative abundances on the observed G/R ratio in comets observed at large ($>$2 au) heliocentric distances by accounting for important production and loss processes of O($^1$S) and O($^1$D) in the cometary coma. Recently we have developed a coupled chemistry-emission model to study photochemistry of O($^1$S) and O($^1$D) atoms and the production of green and red-doublet emissions in comets Hyakutake and Hale-Bopp. In the present work we applied the model to six comets where green and red-doublet emissions are observed when they are beyond 2 au from the Sun. In a water-dominated cometary coma and with significant ($>$10%) CO$_2$ relative abundance, photodissociation of H$_2$O mainly governs the red-doublet emission, whereas CO$_2$ controls the green line emission. If a comet has equal composition of CO$_2$ and H$_2$O, then ~50% of red-doublet emission intensity is controlled by the photodissociation of CO$_2$. The G/R ratio values and green and red-doublet line widths calculated by the model are consistent with the observation. Our model calculations suggest that in low gas production rate comets the G/R ratio greater than 0.1 can be used to constrain the upper limit of CO$_2$ relative abundance provided the slit-projected area on the coma is larger than the collisional zone. If a comet has equal abundances of CO$_2$ and H$_2$O, then the red-doublet emission is significantly ($\sim$50%) controlled by CO$_2$ photodissociation and thus the G/R ratio is not suitable for estimating CO$_2$ relative abundance.