A phase-resolved Fermi-LAT analysis of the mode-changing pulsar PSR J2021+4026 shows hints of a multipolar magnetosphere

Abstract

Context. The radio-quiet γ-ray pulsar PSR J2021+4026 is a peculiar Fermi-LAT pulsar showing repeated and quasi-periodic mode changes. Its γ-ray flux shows repeated variations between two states at intervals of ∼3.5 years. These events occur over timescales < 100 days and are correlated with sudden changes in the spin-down rate. Multiwavelength observations also revealed an X-ray phase shift relative to the γ-ray profile for one of the events. PSR J2021+4026 is currently the only known isolated γ-ray pulsar showing significant variability, and thus it has been the object of thorough investigations. Aims. The goal of our work is to study the mode changes of PSR J2021+4026 with improved detail. By accurately characterizing variations in the γ-ray spectrum and pulse profile, we aim to relate the Fermi-LAT observations to theoretical models. We also aim to interpret the mode changes in terms of variations in the structure of a multipolar dissipative magnetosphere. Methods. We continually monitored the rotational evolution and the γ-ray flux of PSR J2021+4026 using more than 13 years of Fermi-LAT data with a binned likelihood approach. We investigated the features of the phase-resolved spectrum and pulse profile, and from these we inferred the macroscopic conductivity, the electric field parallel to the magnetic field, and the curvature radiation cutoff energy. These physical quantities are related to the spin-down rate and the γ-ray flux and therefore are relevant to the theoretical interpretation of the mode changes. We introduced a simple magnetosphere model that combines a dipole field with a strong quadrupole component. We simulated magnetic field configurations to determine the positions of the polar caps for different sets of parameters. Results. We clearly detect the previous mode changes and confirm a more recent mode change that occurred around June 2020. We provide a full set of best-fit parameters for the phase-resolved γ-ray spectrum and the pulse profile obtained in five distinct time intervals. We computed the relative variations in the best-fit parameters, finding typical flux changes between 13% and 20%. Correlations appear between the γ-ray flux and the spectral parameters, as the peak of the spectrum shifts by ∼10% toward lower energies when the flux decreases. The analysis of the pulse profile reveals that the pulsed fraction of the light curve is larger when the flux is low. Finally, the magnetosphere simulations show that some configurations could explain the observed multiwavelength variability. However, self-consistent models are required to reproduce the observed magnitudes of the mode changes.