The unusual 3D distribution of NaCl around the asymptotic giant branch star IK Tau

NaCl is a diatomic molecule with a large dipole moment, which allows for its detection even at relatively small abundances. It has been detected towards several evolved stars, among which is the AGB star IK Tau, around which it is distributed in several clumps that lie off-center from the star. We aim to study the three-dimensional distribution of NaCl around the AGB star IK Tau, and to obtain the abundance of NaCl relative to H$_2$ for each of the clumps. First, a new value for the maximum expansion velocity is determined. The observed ALMA channel maps are then deprojected to create a three-dimensional model of the distribution of NaCl. This model is then used as input for the radiative transfer modelling code magritte, which is used to obtain the NaCl abundances of each of the clumps by comparing the observations with the results of the magritte simulations. Additionally, the rotational temperature of the clumps is determined using population diagrams. We derive an updated value for the maximum expansion velocity of IK Tau $\upsilon_\mathrm{exp}$ = 28.4 km/s. A spiral-like shape can be discerned in our three-dimensional distribution model of the NaCl. This spiral lies more or less in the plane of the sky. The distribution is also flatter in the line-of-sight direction than in the plane of the sky. We find clump abundances between $9 \times 10^{-9}$ and $5 \times 10^{-8}$ relative to H$_2$, where the relative abundance is typically lower for clumps closer to the star. For the first time, we used deprojection to understand the three-dimensional environment of an AGB star and calculated the fractional abundance of NaCl in clumps surrounding the star.