With upcoming missions such as the James Webb Space Telescope, the European Extremely Large Telescope, and the Atmospheric Remote-sensing Infrared Exoplanet Large-survey, we soon will be on the verge of detecting and characterizing Earth-like exoplanetary atmospheres for the first time. These planets are most likely to be found around smaller and cooler K- and M-type stars. However, recent observations showed that their radiation environment might be much harsher than that of the Sun. Thus, the exoplanets are most likely exposed to an enhanced stellar radiation environment, which could affect their habitability, for example, in the form of a hazardous flux of energetic particles. Knowing the stellar radiation field, and being able to model the radiation exposure on the surface of a planet, is crucial to assess its habitability. In this study, we present 3D magnetohydrodynamic-based model efforts investigating M-stars, focusing on V374 Peg, Proxima Centauri, and LHS 1140, chosen because of their diverse astrospheric quantities. We show that V374 Peg has a much larger astrosphere (ASP) than our Sun, while Proxima Centauri and LHS 1140 most likely have ASPs comparable to or even much smaller than the heliosphere, respectively. Based on a 1D transport model, for the first time, we provide numerical estimates of the modulation of Galactic cosmic rays (GCRs) within the three ASPs. We show that the impact of GCRs on the Earth-like exoplanets Proxima Centauri b and LHS 1140 b cannot be neglected in the context of exoplanetary habitability.

The interpretation of recent observations of bow shocks around O-stars and the creation of corresponding models require a detailed understanding of the associated (magneto-)hydrodynamic structures. We base our study on three-dimensional numerical (magneto-)hydrodynamical models, which are analyzed using the dynamically relevant parameters, in particular, the (magneto)sonic Mach numbers. The analytic Rankine-Hugoniot relation for HD and MHD are compared with those obtained by the numerical model. In that context we also show that the only distance which can be approximately determined is that of the termination shock, if it is a hydrodynamical shock. For MHD shocks the stagnation point does not, in general, lie on the inflow line, which is the line parallel to the inflow vector and passing through the star. Thus an estimate via the Bernoulli equation as in the HD case is, in general, not possible. We also show that in O-star astrospheres, distinct regions exist in which the fast, slow, Alfvénic, and sonic Mach numbers become lower than one, implying sub-slow magnetosonic as well as sub-fast and sub-sonic flows. Nevertheless, the analytic MHD Rankine Hugoniot relations can be used for further studies of turbulence and cosmic ray modulation.

Context. Three-dimensional models of astrospheres have recently become of interest. However, comparisons between these models and observations are non-trivial because of the two-dimensional nature of observations. Aims. By projecting selected physical values of three-dimensional models of astrospheres onto the surface of a sphere that is centred on a virtual all-sky observer, these models can be compared to observational data in different observables: the column density, bremsstrahlung flux, rotation measure, Hα flux, and synchrotron or cyclotron flux. Methods. Projections were calculated by rotating and moving the astrosphere model to the desired position and orientation and by then computing the value of a given patch on the sphere by a modified line-of-sight integration. Contributions to the selected observable made by all model cells that are connected to the patch by the line of sight in question were taken into account.Results. When the model produces a bow shock, a distinct parabolic structure produced by the outer astrosheath can be seen in every observable of the projection, the exact shape depending on the orientations of the line of sight and the stellar motion. Of all four examined astrosphere models, only that of λ Cephei shows fluxes that are higher than current observational thresholds. This is due to the strong stellar wind and interstellar inflow of the λ Cephei model.

Thanks to dedicated long-term missions like Voyager and GOES over the past 50 years, much insight has been gained on the activity of our Sun, the solar wind, its interaction with the interstellar medium, and, thus, about the formation, the evolution, and the structure of the heliosphere. Additionally, with the help of multi-wavelength observations by the Hubble Space Telescope, Kepler, and TESS, we not only were able to detect a variety of extrasolar planets and exomoons but also to study the characteristics of their host stars, and thus became aware that other stars drive bow shocks and astrospheres. Although features like, e.g., stellar winds, could not be measured directly, over the past years several techniques have been developed allowing us to indirectly derive properties like stellar mass-loss rates and stellar wind speeds, information that can be used as direct input to existing astrospheric modeling codes. In this review, the astrospheric modeling efforts of various stars will be presented. Starting with the heliosphere as a benchmark of astrospheric studies, investigating the paleo-heliospheric changes and the Balmer $\text{H}\upalpha$ H α projections to $1~\text{pc}$ 1 pc , we investigate the surroundings of cool and hot stars, but also of more exotic objects like neutron stars. While pulsar wind nebulae (PWNs) might be a source of high-energy galactic cosmic rays (GCRs), the astrospheric environments of cool and hot stars form a natural shield against GCRs. Their modulation within these astrospheres, and the possible impact of turbulence, are also addressed. This review shows that all of the presented modeling efforts are in excellent agreement with currently available observations.

Context. While the shapes of many observed bow shocks can be reproduced by simple astrosphere models, more elaborate approaches have recently been used to explain differing observable structures. Aims. By placing perturbations of an otherwise homogeneous interstellar medium in front of the astrospheric bow shock of the runaway blue supergiant λ Cephei, the observable structure of the model astrosphere is significantly altered, providing insight into the origin of perturbed bow shock images. Methods. Three-dimensional single-fluid magnetohydrodynamic (MHD) models of stationary astrospheres were subjected to various types of perturbations and simulated until stationarity was reached again. As examples, simple perturbations of the available MHD parameters (number density, bulk velocity, temperature, and magnetic field) as well as a more complex perturbation were chosen. Synthetic observations were generated by line-of-sight integration of the model data, producing Hα, 70 μm dust emission, and bremsstrahlung maps of the perturbed astrosphere’s evolution. Results. The resulting shock structures and observational images differ strongly depending on the type of the injected perturbation and the viewing angles, forming arc-like protrusions or bifurcations of the bow shock structure, as well as rings, arcs, and irregular structures detached from the bow shock.