Multi-wavelength emission in resistive pulsar magnetospheres

TL;DR

This work develops resistive pulsar magnetospheres by solving time-dependent Maxwell equations with a resistive Ohm's law, bridging vacuum and force-free limits through a conductivity parameter $\sigma$ and varied obliquities $\chi$. It then connects the magnetic-field geometry to multi-wavelength emission by computing radio polar-cap, X-ray slot-gap, and gamma-ray striped-wind signatures, producing a comprehensive suite of light curves and sky maps. Key findings show that near-surface polar caps are largely insensitive to resistivity, while Poynting flux and field-line sweep-back near the light-cylinder—and hence $\gamma$-ray and X-ray profiles—are strongly affected by $\sigma$, with the X-ray light curves demonstrating the strongest sensitivity. The framework enables testing how magnetic energy dissipation channels into particle acceleration and radiation, providing a path to constrain the plasma content and energetics of pulsar magnetospheres using current and future multi-wavelength observations.

Abstract

In this paper, we compute a full set of neutron star magnetosphere structures from the basic vacuum regime to the dissipation-less force-free regime by implementing a resistive prescription for the plasma. A comparison to the radiation reaction limit is also discussed. We investigated the impact of these resistive magnetospheres onto the multi-wavelength emission properties based on the polar cap model for radio wavelengths, on the slot gap model for X-rays and on the striped wind model for $γ$-rays.} % methods heading (mandatory) {We performed time-dependent pseudo-spectral simulations of the full Maxwell equations including a resistive Ohm's law. We deduced the polar cap shape and size, the Poynting flux, the magnetic field structure and the current sheet surface, depending on the magnetic obliquity~$χ$ and on the conductivity~$σ$. We found that the geometry of the magnetosphere close to the stellar surface is not impacted by the amount of resistivity. Polar cap rims remain very similar in shape and size. However the Poynting flux varies significantly as well as the magnetic field sweep-back in the vicinity of the light-cylinder. This bending of field lines reflects into the $γ$-ray pulse profiles, changing the $γ$-ray peak separation~$Δ$ as well as the time lag~$δ$ between the radio pulse and $γ$-ray peaks. X-ray pulse profiles are also drastically affected by the resistivity. A full set of multi-wavelength light-curves can be compiled for future comparison with the third $γ$-ray pulsar catalogue. This systematic study will help to constrain the amount of magnetic energy flowing into particle kinetic energy and shared by radiation.

Figures (25)

• Figure 1: Schematic view of the pulsar magnetosphere, showing the separatrix and the emission sites.
• Figure 2: Spin down luminosity depending on the obliquity ${\raisebox{\depth}{$\chi$}}$ of the magnetosphere. The vacuum (VAC) and force-free (FFE) cases are shown as references.
• Figure 3: Spin down luminosity for fixed obliquity ${\raisebox{\depth}{$\chi$}}$ of the magnetosphere. The vacuum (VAC) and force-free (FFE) cases are shown as the limiting cases.
• Figure 4: The ratio ${L_{\rm p}}/{L^{\rm vac}_\perp}$ for $\Gamma=10$ and $\kappa=0$ for millisecond pulsars (MSP) and young pulsars (YP) according to data from 3PC.
• Figure 5: Magnetic field lines in the equatorial plane of an orthogonal rotator for different plasma regimes going from VAC to FFE through RES. The dashed circle depicts the light-cylinder radius and the gray disk the neutron star.