Classical, large-scale 3D magneto-hydrodynamic simulations of interacting pulsar wind nebulae

¹ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans s/n, 08193 Barcelona, Spain
² Institut d’Estudis Espacials de Catalunya (IEEC), 08034 Barcelona, Spain
³ Institució Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona, Spain

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Received: 26 June 2025
Accepted: 23 February 2026

Abstract

Context. Magnetised rotating neutron stars, or pulsars, are a possible end product of massive star evolution. Their relativistic wind successively interacts with the supernova ejecta of their defunct progenitor, then with the circumstellar medium of the progenitor, and eventually with the interstellar medium. The distribution of those materials governs the morphology, mixing of chemical elements, and emission properties of the shocks present in plerionic supernova remnants.

Aims. If a massive star is static with respect to its ambient medium, then its resulting circumstellar medium is elongated in the direction of the local magnetic field, and its supernova remnant transiently appears as a rectangle. The pulsar wind nebula forming in it is, in its turn, elongated, as long as the pulsar’s axis of rotation matches the direction of the local magnetisation. In this work, we explore how the angle between the direction of the local magnetic field of the interstellar medium and the pulsar axis of rotation influences the shaping of its pulsar wind nebula.

Methods. Three-dimensional magneto-hydrodynamic simulations were carried out with the PLUTO code to model the pulsar wind nebula formed by a static pulsar inside of a supernova remnant left behind by a massive Wolf-Rayet-evolving progenitor at rest in an organised, magnetised ambient medium. We used those models to perform radiative transfer calculations to derive non-thermal radio emission maps of the pulsar wind nebulae.

Results. When the polar elongations of the pulsar develop, they bend in opposite directions under the effects of the cavity carved by the stellar wind and already filled by supernova ejecta. This induces a complex distribution of magnetised supernova ejecta and pulsar wind, resulting in various observable structures, appearing as rectangles, circles, or irregular oblong shapes, in the radio waveband.

Conclusions. The angle between the direction of the pulsar rotation axis and that of the local ambient magnetisation is a governing parameter for the shaping and non-thermal radio properties of the pulsar wind nebulae of static massive stars; however, the mixing of material, once the pulsar wind nebula is old (50–80 kyr), is not strongly affected by that factor.