Classical, large scale 3D MHD simulations of interacting pulsar wind nebulae

Abstract

Magnetized 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. If a massive star is static with respect to its ambient medium, then its resulting circumstellar medium is elongated along 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 axis of rotation matches the direction of the local magnetization. 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 with 3D MHD simulations are carried out with the PLUTO. We use those models to perform radiative transfer calculations to derive non-thermal radio emission maps of the pulsar wind nebulae. When the polar elongation 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 magnetized supernova ejecta and pulsar wind, resulting in various observable structures, appearing as rectangles, circles, or irregular oblong shapes, in the radio waveband. The angle between the direction of the pulsar rotation axis and that of the local ambient magnetization 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 to 80 kyr), is not strongly affected by that factor.

Figures (20)

• Figure 1: The number density fields in the 3D supernova remnant models of a static $35\, \rm M_{\odot}$ star rotating with $\Omega_{\star}/\Omega_{\rm K} = 0.1$. The ISM magnetic field is aligned with the $Oz$ Cartesian axis and has a strength of $B_{\rm ISM} = 7\, \rm \mu G$. The figures show the supernova remnant in the $z = 0$ (left), $y = 0$ (middle), and $x = 0$ (right) planes of the Cartesian coordinate system, at $50\, \rm kyr$ after the onset of the explosion. The results are shown for an angle $\theta_\mathrm{mag} = 0^\circ$ between the pulsar's rotation axis and the direction of the local ISM. The different contours indicate regions of the supernova remnant with a $50\%$ contribution from pulsar wind (black) and ejecta (cyan), as well as regions with a $10\%$ contribution from Wolf–Rayet (magenta) and red supergiant wind (red) material, respectively. The black cross marks the position of the supernova explosion.
• Figure 2: Time evolution of the number density fields in the 3D supernova remnant models of a static $35\, \rm M_{\odot}$ star rotating with $\Omega_{\star}/\Omega_{\rm K} = 0.1$. The ISM magnetic field is aligned with the $Oz$ Cartesian axis and has a strength of $B_{\rm ISM} = 7\, \rm \mu G$. The figures show the supernova remnant in the $z = 0$ (left), $y = 0$ (middle), and $x = 0$ (right) planes of the Cartesian coordinate system, spanning times from $40\, \rm kyr$ to $80\, \rm kyr$ after the onset of the explosion. The results are shown for an angle $\theta_\mathrm{mag} = 0^\circ$ between the pulsar's rotation axis and the direction of the local ISM. The different contours indicate regions of the supernova remnant with a $50\%$ contribution from pulsar wind (black), ejecta (cyan), Wolf–Rayet (magenta), and red supergiant wind (red) material, respectively. The black cross marks the position of the supernova explosion.
• Figure 3: Rendering of the 3D MHD pulsar wind nebulae and their complex environments. The orange surfaces trace constant density regions of the stellar wind bubble, the red surfaces trace the red supergiant wind, the magenta surface trace the Wolf-Rayet wind, the cyan surface traces the supernova ejecta and the white tubes trace the magnetic field in the pulsar wind. The 3D figures are clipped with two planes permitting a visualization of the internal structure of the plerionic supernova remnant. The displayed models differ only by the angle between the ISM magnetic field lines that shape the main-sequence stellar wind bubble (orange) and the axis of rotation of the pulsar (fixed in all models as being along the vertical direction). The angle is of $\theta_\mathrm{mag}=0^\circ$ (a), $\theta_\mathrm{mag}=30^\circ$ (b), $\theta_\mathrm{mag}=45^\circ$ (c) and $\theta_\mathrm{mag}=90^\circ$ (d), respectively.
• Figure 4: Distribution of the toroidal to total magnetic field ratio $B_{\phi}/B$ in the 3D supernova remnant models. The white arrows trace the magnetic field in the yOz plane for the region of the supernova remnant. The figures show the supernova remnants in the $x = 0$ plane of the Cartesian coordinate system, at time $70\, \rm kyr$ after the onset of the explosion.
• Figure 5: Same as Fig. \ref{['fig:3D_PWN_rendering']}, displaying the 3D magnetic field distribution of the the pulsar wind nebulae within the supernova ejecta. It highlights how the supernova ejecta distribution (itself governed by the circumstellar medium and the magnetization of the ISM) influences the manner the propagation of the pulsar wind and the arrangement of its magnetic field lines. An animated version of this figure is available as online material.