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Restarted radio galaxies represent a unique tool to investigate the dutycycle of the jet activity in Active Galactic Nuclei. Due to a sharpdiscontinuity of the GHz spectral index distribution within its lobes, theradio galaxy 3C388 has for long being claimed to be a peculiar example of AGNwith multi-epoch activity. In this work we have performed, for the first time,a spatially resolved study of the radio spectrum of this source down toMHz-frequencies, aimed at investigating its radiative age and duty cycle. Wehave used new low frequency observations at 144 MHz performed with LOFAR and at350 MHz performed with the VLA combined with archival data at higherfrequencies. We find that the spectral indices in the lower frequency range144-614 MHz have flatter values ($\sim$0.55-1.14) than those observed in thehigher frequency range 1400-4850 MHz ($\sim$0.75-1.57) but follow the samedistribution across the lobes, with a systematic steepening towards the edges.However, the spectral shape throughout the source is not uniform and oftendeviates from standard models. This suggests that mixing of different particlepopulations is occurring, although it remains difficult to understand whetherthis is caused by observational limitations (insufficient spatial resolutionand/or projection effects) or by the intrinsic presence of multiple particlepopulations, possibly related to the two different outbursts. By usingsingle-injection radiative models we compute that the total source age is$\lesssim$80 Myr and that the duty cycle is about $\rm t_{on}/t_{tot}\sim$ 60%,which is enough to prevent the intracluster medium from cooling according toX-ray estimates. While to date the radio spectral distribution of 3C388 remainsa rare case among radio galaxies, upcoming multi-frequency surveys will soonallow us to investigate whether more sources with the same characteristics doactually exist.

Radio spectral properties and jet duty cycle in the restarted radio galaxy 3C388