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 γ -ray pulsar exhibiting repeated transitions between high γ -ray flux (HGF) and low γ -ray flux (LGF) states. With 17 yr Fermi Large Area Telescope monitoring, we reveal persistent secular evolution and enhanced spin-down rate variability within individual emission states—beneath the quasiperiodic state transitions. After removing discrete jumps, the jump-corrected flux δF γ shows a three-phase evolution: rise ( + 2.0 2 − 0.15 + 0.17 % yr − 1 ), decline ( − 3.7 2 − 0.47 + 0.34 % yr − 1 ), and rapid rise ( + 14 . 9 − 4.4 + 6.4 % yr − 1 ), with all rates quoted relative to the long-term mean flux 〈 F γ 〉 = 7.8 × 10 −10 erg cm −2 s −1 . Moreover, the flux of the LGF state is gradually approaching the stable HGF level at a rate of +0.72% ± 0.11% 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.