Long-term timing evolution of four Anomalous X-Ray Pulsars

Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are believed to be manifestations of magnetars. Typically, AXPs exhibit higher X-ray luminosities, whereas SGRs are generally fainter and display significantly high signal-to-noise ratios only during their outburst phases. In this work, we report the long-term timing evolution of four AXPs: 1E 2259+586, 4U 0142+61, 1RXS J170849.0-400910 and 1E 1841-045, which were regularly monitored with NICER from 2017 to 2024. Over this period, we identify a total of 10 timing events. In addition to one glitch and one anti-glitch in 1E 2259+586 reported in literature, we detect another 8 new timing events: 5 glitches, 2 anti-glitches, and 1 unusual state transition event. Notably, both anti-glitches were observed in 4U 0142+61, making it the most frequent source of such events, and there is a hint of regular evolution in its pulse profile. In the case of 1RXS J170849.0-400910, it continues to exhibit pronounced high-frequency timing anomalies and undergoes a state transition event. Finally, we study the evolution of the pulse profiles and find that the profiles of 1E 2259+586 and 4U 0142+61 both evolve. This is consistent with the earlier finding that pulse profile evolution is a generic feature of magnetars.