WASP-12, shrouded in mystery or just cold gas?

Observations of the planet-hosting star WASP-12 show a distinctive depression in the Mg ɪɪ and Ca ɪɪ resonance lines. This has been interpreted as a marker of atmospheric loss from the close-in hot Jupiter WASP-12b and the resulting formation of a gas torus around the star. In this paper we quantify the Mg ii absorption from this torus, compared to that provided by the stellar wind, the stellar astrosphere and the interstellar medium (ISM). To do this we piece together the full density profile of Mg ii from WASP-12 to an observer on Earth using a combination of hydrodynamical simulations and observations. We find that the bulk of the gas along the line of sight is contained within a dense torus close to WASP-12. However, the temperatures in this torus are sufficient to promote Mg into a doubly (Mg ɪɪɪ) or higher ionized state. As a result, the singly ionized fraction (Mg ɪɪ) is low. We find that most of the Mg ɪɪ is not in the torus but in the ISM. Despite this, the total column density of Mg ɪɪ is two orders of magnitude lower than required to explain observations of the system. To resolve this discrepancy, we note that the torus gas is at a temperature where it will cool efficiently. We speculate that the onset of the cooling instability will cause the torus to fragment, forming cold clumps with a higher fraction of Mg ɪɪ, capable of explaining the observed absorption.