Expanding nebulae are produced by mass loss from stars, especially during late stages of evolution. Multi-dimensional simulation of these nebulae requires high resolution near the star and permits resolution that decreases with distance from the star, ideally with adaptive timesteps. We report the implementation and testing of static mesh-refinement in the radiation-magnetohydrodynamics code pion, and document its performance for 2D and 3D calculations. The bow shock produced by a hot, magnetized, slowly rotating star as it moves through the magnetized ISM is simulated in 3D, highlighting differences compared with 2D calculations. Latitude-dependent, time-varying magnetized winds are modelled and compared with simulations of ring nebulae around blue supergiants from the literature. A 3D simulation of the expansion of a fast wind from a Wolf-Rayet star into the slow wind from a previous red supergiant phase of evolution is presented, with results compared with results in the literature and analytic theory. Finally the wind-wind collision from a binary star system is modelled with 3D MHD, and the results compared with previous 2D hydrodynamic calculations. A python library is provided for reading and plotting simulation snapshots, and the generation of synthetic infrared emission maps using torus is also demonstrated. It is shown that state-of-the-art 3D MHD simulations of wind-driven nebulae can be performed using pion with reasonable computational resources. The source code and user documentation is made available for the community under a BSD3 licence.

The nearby, massive, runaway star ζ Ophiuchi has a large bow shock detected in optical and infrared light and, uniquely among runaway O stars, diffuse X-ray emission detected from the shocked stellar wind. Here we make the first detailed computational investigation of the bow shock of ζ Ophiuchi, to test whether a simple model of the bow shock can explain the observed nebula, and to compare the detected X-ray emission with simulated emission maps. We reanalysed archival Chandra observations of the thermal diffuse X-ray emission from the shocked wind region of the bow shock, finding total unabsorbed X-ray flux in the 0.3–2keV band corresponding to a diffuse X-ray luminosity of LX = 2.33−1.54+1.12 × 1029 erg s−1, consistent with previous work. The diffuse X-ray emission arises from the region between the star and the bow shock. Three-dimensional magnetohydrodyanmic simulations were used to model the interaction of the star’s wind with a uniform interstellar medium (ISM) using a range of stellar and ISM parameters motivated by observational constraints. Synthetic infrared, Hα, soft X-ray, emission measure, and radio 6 GHz emission maps were generated from three simulations, for comparison with the relevant observations. Simulations where the space velocity of ζ Ophiuchi has a significant radial velocity produce infrared emission maps with the opening angle of the bow shock in better agreement with observations than for the case where motion is fully in the plane of the sky. All three simulations presented here have X-ray emission fainter than observed, in contrast to results for NGC 7635. The simulation with the highest pressure has the closest match to X-ray observations, with a flux level within a factor of two of the observational lower limit, and emission weighted temperature of log10(TA/K) = 6.4, although the morphology of the diffuse emission appears somewhat different. The observed X-ray emission is from a filled bubble that is brightest near the star, whereas simulations predict brightening towards the contact discontinuity as density increases. This first numerical study of the bow shock and wind bubble around ζ Ophiuchi uses a relatively simple model of a uniform ISM and ideal-magnetohydrodynamics, and can be used as a basis for comparing results from models incorporating more physical processes, or higher resolution simulations that may show more turbulent mixing.

Context. In recent years, winds from massive stars have been considered promising sites for investigating relativistic particle acceleration. In particular, the resulting bow-shaped shocks from the interaction of the supersonic winds of runaway stars with interstellar matter have been intensively observed at many different wavelengths, from radio to γ-rays. Aims. In this study we investigate the O4If star, BD+43° 3654, the bow shock of which is, so far, the only one proven to radiate both thermal and non-thermal emission at radio frequencies. In addition, we consider NGC 7635, the Bubble Nebula, as a bow shock candidate and examine its apex for indications of thermal and non-thermal radio emission. Methods. We observed both bow shocks in radio frequencies with the Very Large Array (VLA) in the C and X bands (4–8 GHz and 8–12 GHz) and with the Effelsberg telescope at 4–8 GHz. We analysed single-dish and interferometric results individually, in addition to their combined emission, obtained spectral index maps for each source, and calculated their spectral energy distributions. Results. We find that both sources emit non-thermal emission in the radio regime, with the clearest evidence for NGC 7635, whose radio emission has a strongly negative spectral index along the northern rim of the bubble. We present the first high-resolution maps of radio emission from NGC 7635, finding that the morphology closely follows the optical nebular emission. Our results are less conclusive for the bow shock of BD+43° 3654, as its emission becomes weaker and faint at higher frequencies in VLA data. Effelsberg data show a much larger emitting region (albeit a region of thermal emission) than is detected with the VLA for this source. Conclusions. Our results extend the previous radio results from the BD+43° 3654 bow shock to higher frequencies, and with our NGC 7635 results we double the number of bow shocks around O stars with detected non-thermal emission, from one to two. Modelling of the multi-wavelength data for both sources shows that accelerated electrons at the wind termination shock are a plausible source for the non-thermal radio emission, but energetics arguments suggest that any non-thermal X-ray and γ-ray emission could be significantly below existing upper limits. Enhanced synchrotron emission from compressed galactic cosmic rays in the radiative bow shock could also explain the radio emission from the BD+43° 3654 bow shock, but not from NGC 7635. The non-detection of point-like radio emission from BD+43° 3654 puts an upper limit on the mass-loss rate of the star that is lower than values quoted in the literature.