Physical assumptions versus nature: the shape of the heliosphere

Context. The Interstellar Probe study describes a mission concept with a launch window beginning in 2036, aiming to reach several hundred astronomical units beyond the heliopause within a time frame of at least 50 years. One of the fundamental questions related to this mission is where the boundaries of the heliosphere are and how thick they are. To answer it we need to know the shape of the heliosphere. Over the past 60 years numerous models of the heliosphere have been developed. For a long time these models depicted a heliosphere resembling a comet. Since around 2015 models have been presented that differ significantly from the shape of a comet. Aims. The aim of this paper is to emphasize that the obtained image of the heliosphere depends on the model assumptions contained in these articles. Methods. We review numerous publications examining the shape of the heliosphere. All of these articles use a magnetohydrodynamic (MHD) model of the heliosphere together with various assumptions that simplify the physics of the interaction of the solar wind flowing from the Sun with the surrounding interstellar medium. Results. The result of all these studies is a shape of the heliosphere described as either croissant-like or cometary-like, depending on the assumptions made. Conclusions. We are still uncertain which model represents the real heliosphere. Nature requires a theoretical model that is more accurate. In our opinion the interaction of the solar wind with the interstellar medium must be described by the Boltzmann system of equations using artificial intelligence. In the context of the planned space mission this conclusion is crucial.