A multi-band study of pulsar glitches with Fermi-LAT and Parkes

Pulsar glitch is a phenomenon characterized by abrupt changes in the spin period over less than a minute. We present a comprehensive analysis of glitches in four gamma-ray pulsars by combining the timing observation data from \textit{Fermi} Large Area Telescope (\textit{Fermi}-LAT) and Parkes 64 m radio telescope. The timing data of five pulsars, namely PSRs J1028$-$5819, J1420$-$6048, J1509$-$5850, J1709$-$4429 (B1706$-$44) and J1718$-$3825, are examined over 14 yr of observations for each. A total of 12 glitches are identified in four pulsars, including a previously unreported glitch. That is, a new small glitch is identified for PSR J1718$-$3825 in MJD $\sim$ 59121(8), with a fractional glitch size of $\Delta \nu/\nu \sim 1.9(2) \times 10^{-9}$. For PSR J1420$-$6048, our investigation confirms the presence of two linear recovery terms during the evolution of $\dot{\nu}$ following glitches 4, 6 and 8. Moreover, an exponential recovery process was identified after glitch 8, with a recovery fraction ($Q$) of $Q = 0.0131(5)$ and a corresponding timescale of $\tau_{\rm d} = 100(6)$ d. Regarding the fourth glitch of PSR J1709$-$4429, our analysis reveals the presence of two exponential recovery terms with degree of recovery and decay time-scales $Q$1 = 0.0104(5), $\tau_{\rm d1}=72(4)$ d and $Q$2 = 0.006(1), $\tau_{\rm d2}=4.2(6)$ d, respectively. For the remaining previously reported glitches, we also refine the glitch epochs and recovery process through precise fitting of the timing data. We discuss how multi-band data of glitches can help better characterize the glitch recoveries and constrain the underlying physics of glitch events. Our findings demonstrate that the accumulation of observational data reveals the rich complexity of the glitch phenomenon, aiding in the search for a well-established interpretation.