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The combined X-ray and $γ$-ray modeling of millisecond pulsars PSR J0030+0451 in the dissipative magnetospheres

Gang Cao, Xiongbang Yang

TL;DR

The paper addresses how millisecond pulsar PSR J0030+0451 can exhibit observed NICER X-ray hotspots and Fermi $\gamma$-ray emission through a self-consistent magnetospheric model. It constructs dissipative FF+AE dipole plus off-centred quadrupole fields via a 3D pseudo-spectral solver, then computes X-ray emission with ray-tracing in Schwarzschild spacetime and $\gamma$-ray emission from particle trajectories following the local accelerating field, finally comparing to NICER and Fermi data. The results reproduce the X-ray double-peak profile and the GeV-cutoff $\gamma$-ray spectrum, implying a multipolar surface field and current-sheet–driven high-energy emission; the fit favors a large dipole inclination $\chi_{D}$ in the range $70^{\circ}$–$90^{\circ}$ and supports a self-consistent multiwavelength modeling approach. This framework advances MSP interpretation by linking surface magnetic topology to outer magnetospheric radiative processes and can be extended to other MSPs and polarization predictions.

Abstract

Modeling of the NICER X-ray light curves of millisecond pulsars PSR J0030+0451 provides a strong evidence for the existence of non-dipole magnetic fields. We study the X-ray and $γ$-ray emission of PSR J0030+0451 in the dissipative dipole plus off-centred quadrupole magnetospheres. The dissipative FF+AE dipole magnetospheres by combining force-free (FF) and Aristotelian electrodynamics (AE) are solved by a 3D pseudo-spectral method in the rotating coordinate system. We use the FF+AE dipole plus off-centred quadrupole fields with minimum free parameters to reproduce two hotspot configurations found by the NICER observations. The X-ray and $γ$-ray emission from PSR J0030+0451 are simultaneously computed by using a ray-tracing method and a particle trajectory method. The modelled X-ray and $γ$-ray emission is then directly compared with those of PSR J0030+0451 from the NICER and Fermi observations. Our results can well reproduce the observed trends of the NICER X-ray and Fermi $γ$-ray emission for PSR J0030+0451.

The combined X-ray and $γ$-ray modeling of millisecond pulsars PSR J0030+0451 in the dissipative magnetospheres

TL;DR

The paper addresses how millisecond pulsar PSR J0030+0451 can exhibit observed NICER X-ray hotspots and Fermi -ray emission through a self-consistent magnetospheric model. It constructs dissipative FF+AE dipole plus off-centred quadrupole fields via a 3D pseudo-spectral solver, then computes X-ray emission with ray-tracing in Schwarzschild spacetime and -ray emission from particle trajectories following the local accelerating field, finally comparing to NICER and Fermi data. The results reproduce the X-ray double-peak profile and the GeV-cutoff -ray spectrum, implying a multipolar surface field and current-sheet–driven high-energy emission; the fit favors a large dipole inclination in the range – and supports a self-consistent multiwavelength modeling approach. This framework advances MSP interpretation by linking surface magnetic topology to outer magnetospheric radiative processes and can be extended to other MSPs and polarization predictions.

Abstract

Modeling of the NICER X-ray light curves of millisecond pulsars PSR J0030+0451 provides a strong evidence for the existence of non-dipole magnetic fields. We study the X-ray and -ray emission of PSR J0030+0451 in the dissipative dipole plus off-centred quadrupole magnetospheres. The dissipative FF+AE dipole magnetospheres by combining force-free (FF) and Aristotelian electrodynamics (AE) are solved by a 3D pseudo-spectral method in the rotating coordinate system. We use the FF+AE dipole plus off-centred quadrupole fields with minimum free parameters to reproduce two hotspot configurations found by the NICER observations. The X-ray and -ray emission from PSR J0030+0451 are simultaneously computed by using a ray-tracing method and a particle trajectory method. The modelled X-ray and -ray emission is then directly compared with those of PSR J0030+0451 from the NICER and Fermi observations. Our results can well reproduce the observed trends of the NICER X-ray and Fermi -ray emission for PSR J0030+0451.
Paper Structure (9 sections, 24 equations, 5 figures)

This paper contains 9 sections, 24 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Magnetospheric models
  3. Vacuum Dipole and Off-centred Quadrupole Magnetospheres
  4. FF+AE Dipole Magnetospheres
  5. Magnetospheric Configuration
  6. Ray-tracing Method for X-rays
  7. Particle trajectory method for $\gamma$-rays
  8. results
  9. Discussion and Conclusions

Figures (5)

  • Figure 1: The polar caps from the FF+AE dipole plus off-centred quadrupole fields (the red curves) and the vacuum dipole plus off-centred quadrupole fields (the blue curves).
  • Figure 2: The Distribution of the magnetic field lines and the accelerating electric fields from the FF+AE dipole plus off-centred quadrupole field.
  • Figure 3: A comparison of the predicted X-ray light curves and the NICER observed ones for PSR J0030+0451. The NICER observed data is taken from bog19.
  • Figure 4: The sky maps and a comparison of the predicted $\gamma$-ray light curves and the Fermi observed ones for PSR J0030+0451. The Fermi observed data is taken from data taken from abd13.
  • Figure 5: A comparison of the predicted $\gamma$-ray phase-averaged spectra and the Fermi observed ones for PSR J0030+0451. The Fermi observed data is taken from abd13.