Secular Evolution of PSR J2021+4026: Long-Term γ-Ray Flux and Spin-Down Variability Beyond State Transitions

TL;DR

Using 17 years of Fermi-LAT data, this study isolates secular flux evolution in PSR J2021+4026 from discrete HGF/LGF state transitions by constructing a jump-corrected flux $δF_γ$. A six-parameter piecewise-linear model reveals three phases—rise (~10 yr), decline (~6 yr), and rapid rise (~1 yr)—with phase-averaged rates $R_{phase}$ of +2.02%/yr, −3.72%/yr, and +14.9%/yr, and LGF flux converging toward HGF at +0.72%/yr while HGF remains nearly constant at about −0.08%/yr. Seven state transitions (A–H) over 17 years accompany enhanced spin-down variability $|ν̇|$ during certain states, indicating a link between secular magnetospheric evolution and timing noise. Together, the results point to a dissipative relaxation toward a stable high-flux equilibrium, enriching our understanding of long-term magnetospheric dynamics in gamma-ray pulsars.

Abstract

PSR J2021+4026 is a remarkable $γ$-ray pulsar exhibiting repeated transitions between high $γ$-ray flux (HGF) and low $γ$-ray flux (LGF) states. With 17-yr Fermi-LAT monitoring, we reveal persistent secular evolution and enhanced spin-down rate variability within individual emission states -- beneath the quasi-periodic state transitions. After removing discrete jumps, the jump-corrected flux $δF_γ$ shows a three-phase evolution: rise ($+2.02^{+0.17}_{-0.15}\%~\mathrm{yr}^{-1}$), decline ($-3.72^{+0.34}_{-0.47}\%~\mathrm{yr}^{-1}$), and rapid rise ($+14.9^{+6.4}_{-4.4}\%~\mathrm{yr}^{-1}$), with all rates quoted relative to the long-term mean flux $\langle F_γ\rangle=7.8\times 10^{-10}\,\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$. Moreover, the flux of the LGF state is gradually approaching the stable HGF level at a rate of $+0.72 \pm 0.11\%~\mathrm{yr}^{-1}$. These results demonstrate that secular flux evolution in PSR J2021+4026 operates largely independently of discrete state transitions, yet jointly with them drives the system toward a stable high-flux equilibrium.

Figures (2)

• Figure 1: Energy flux and spin evolution of PSR J2021$+$4026. Panel (a): 30-day binned flux measurements with $1\sigma$ uncertainties (black points) and per-state fluxes with $3\sigma$ confidence intervals (orange bands). The cyan and red dashed lines are the linear fits to the fluxes in the HGF and LGF states respectively. Panel (b): Jump-corrected flux $\delta F_\gamma$, obtained by removing the mean offset and inter-state flux jumps; the orange piecewise linear curve shows the best fit to the secular evolution. Panels (c) and (d): Timing evolution in $\nu$ and $\dot{\nu}$; panel (c) displays the timing residuals $\delta \nu$ after subtracting the linear trend and mean offset. Vertical and horizontal error bars indicate $1\sigma$ uncertainties and ephemeris time spans, respectively. Vertical dotted lines mark the state transitions reported in Fiori:2024nleWang:2023ioh and this work.
• Figure 2: Two-dimensional histogram of the normalized pulse profile versus time, with phases and time each divided into 32 bins and 31 bins, smoothed via Gaussian interpolation. Horizontal dotted lines mark the state transitions. The main pulse, aligned to phase 0, is indicated in red.