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

Abstract

PSR J2021+4026 is a remarkable $\gamma$-ray pulsar exhibiting repeated transitions between high $\gamma$-ray flux (HGF) and low $\gamma$-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 $\delta F_{\gamma }$ shows a three-phase evolution: rise ($+2.02_{-0.15}^{+0.17}\%{\mathrm{yr}}^{-1}$), decline ($-3.72_{-0.47}^{+0.34}\%{\mathrm{yr}}^{-1}$), and rapid rise ($+14.9_{-4.4}^{+6.4}\%{\mathrm{yr}}^{-1}$), with all rates quoted relative to the long-term mean flux $⟨F_{\gamma }⟩=7.8\times 10^{-10}\mathrm{erg}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. 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.

6 pages, 3 figures