The duty cycle of the radio galaxy B2 0258+35

Radio loud Active Galactic Nuclei are episodic in nature, cyclingthrough periods of activity and quiescence. In this work we investigate the duty cycle of the radio galaxyB2~0258+35, which was previously suggested to be a restarted radio galaxybased on its morphology. The radio source consists of a pair of kpc-scale jets embedded in two large-scale lobes(~240 kpc) with relaxed shape and very low surface brightness, which resemble remnants of a past AGN activity. We have combined new LOFARdata at 145 MHz and new SRT data at 6600 MHz with available WSRT data at 1400 MHz to investigate the spectral properties of the outer lobesand derive their age. Interestingly, the spectrum of both the outer Northern and Southern lobesis not ultra-steep as expected for an old ageing plasma with spectral indexvalues equal to $\rm \alpha_{1400}^{145}=0.48\pm0.11$ and $\rm \alpha_{6600}^{1400}=0.69\pm0.20$ in the outer Northern lobe, and $\rm \alpha_{1400}^{145}=0.73\pm0.07$ in the outer Southern lobe. Moreover, despite the wide frequency coverage available for the outer Northern lobe(145-6600~MHz), we do not identify a significant spectral curvature (SPC$\simeq$0.2$\pm0.2$). While mechanisms such as in-situ particle reacceleration, mixing or compression can temporarily play a role in preventing the spectrum from steepening, in no case seem the outer lobesto be compatible with being very old remnants of past activity as previously suggested (with age $\gtrsim$ 80 Myr). We conclude that either the large-scale lobesare still fuelled by the nuclear engineor the jets have switched off no more than a few tens of Myrago. Our study shows the importance of combining morphological and spectral properties to reliably classify the evolutionary stage of low surface brightness, diffuse emission that low frequency observations are revealing around a growing number of radio sources.