The study of pulsar glitch phenomena serves as a valuable probe into the dynamic properties of matter under extreme high-density conditions, offering insights into the physics within neutron stars. Providing theoretical explanations for the diverse manifestations observed in different pulsars has proven to be a formidable challenge. By analyzing the distribution of glitch sizes and waiting times, along with the evolution of cumulative glitch sizes over time, we have uncovered a long-term clustering phenomenon for pulsar glitches. This perspective allows us to approach the distinct glitch representations in various pulsars from a unified standpoint, connecting the same periodicity of observational data to the randomness. Without relying on specific physical models, we utilized the coefficient of variation to numerically determine optimal clustering numbers and clustering periods for sample pulsars. Our analysis involving 27 pulsars has revealed a clear linear relationship between the glitch cluster period and characteristic age. Of interest, the cumulative distribution of functions of cluster sizes and interval times have the same patterns, which can be synchronously fitted by Gaussian processes. These results may indicate novel understandings of glitches and the resulting processes.

It was previously believed that the long-term persistent increase in the spin-down rate of the Crab pulsar following a glitch is direct evidence of a starquake-induced glitch or at least related to a starquake. Using radio data covering 1710 days following the 2017 glitch, we obtain an extreme persistent increase of the spin-down rate, which allows us to test the two prevailing models related to a starquake through an interrelation analysis between the glitch size (the amplitude of the frequency step at a glitch) and the persistent increase in the spin-down rate of the star. Our results do not support the hypothesis that glitches induce the external torque variation of the Crab pulsar, which may indicate no occurrence of a starquake during the Crab pulsar glitch. This can explain why no changes in the radio and X-ray flux, pulse profile, and spectrum of the Crab pulsar have been observed. We also suggest an internal mechanism due to superfluidity as an explanation for the long-term persistent shift in the spin-down rate of the Crab pulsar following the relatively large glitches.

In theory, burst activity of the magnetar can lead to the formation of fireballs trapped by the magnetic field and corotating with the star. However, smoking-gun observational evidence of the fireball is elusive. We envisage that the fireball emission should occasionally be eclipsed by the magnetar, especially when the burst duration is comparable to the magnetar’s spin period. In this work, we first discover a peculiar type of burst whose light curve has a plateau-like feature among the long bursts of the magnetar SGR J1935+2154 detected by GECAM and Fermi/Gamma-ray Burst Monitor. Then, based on these bursts, we identified four burst candidates with eclipse-like characteristics. By fitting their light curves with the eclipse fireball model, the viewing angle of the magnetar relative to its spin axis is estimated to be 17° ± 10°, and the distances from the fireballs to the magnetar are found to be more than 5 times the magnetar’s radius, indicating that the fireballs are suspended in the magnetosphere rather than adhering to the magnetar surface. Furthermore, we find that this configuration is well consistent with the implication of the cyclotron resonance scattering feature we found in their spectra. Our results suggest that some intermediate X-ray bursts may originate from magnetic reconnection within the magnetosphere rather than the starquake.

Fast radio bursts (FRBs) are millisecond-duration extragalactic radio transients, some of which are associated with compact persistent radio sources (PRSs), hinting at a physical connection. While several models have been proposed to explain PRSs and their connection to FRBs, direct observational tests remain limited. Here, we report for the first time a correlated trend between the long-term variation of the PRS flux density and the burst energetics of FRB 20190520B and FRB 20240114A, suggesting a physical coupling between the PRS and FRB activity. We further examine additional repeaters with compact PRSs and find no clear correlation between PRS luminosity and burst activity, likely due to the limited observations. These results are consistent with scenarios in which both the PRS and FRB activity may be powered by a common energy reservoir, such as the magnetic or rotational energy of a magnetar.