Fascinating paper. They suggest that the most consistent explanation for the observations is that the Earth was hit by a carbon rich comet. I'm skeptical of the former though because a comet containing that much carbon would have to be very large and so would expect larger general effects from that. If it was pure dry ice then it would have a radius of 12km to generate a 3000GT increase in carbon in the atmosphere. Because methane is less dense, about the same radius is needed for that compound too despite its lower molecular mass per atom of carbon. That is the same scale as the object that ended the Cretaceous period though, of course, less massive if the Chicxulub impactor was rocky. And it seems unlikely that it would be pure carbon dioxide or methane and then would need to be even bigger. Perhaps the object was smaller but the impact occurred in a limestone area?