Constraining the AGN duty cycle in the cool-core cluster MS 0735.6+7421 with LOFAR data

Context. MS 0735.6+7421 is a galaxy cluster that hosts a central radio galaxy with a very steep spectrum. The spectrum is produced by one of the most powerful known jetted active galactic nuclei (AGN). The radio plasma, ejected at nearly light speed from the central AGN, has displaced the intra-cluster medium, leaving two pairs of cavities observable in the X-ray. The cavities are associated with two different outbursts and have distributed energy to the surrounding medium. While the age of the cavities has previously been estimated from the X-rays, no confirmation from radio data is available. Furthermore, the radio spectrum has only been derived from integrated flux density measurements so far, and the spatial distribution that would help us to understand the nature of this source is still lacking. Aims. We perform for the first time a detailed, high-resolution spectral study of the source at radio frequencies and investigate its duty cycle. We compare this with previous X-ray estimates. Methods. We used new observations at 144 MHz produced with the LOw Frequency ARray (LOFAR) together with archival data at higher frequencies (235, 325, 610, 1400, and 8500 MHz), to investigate the spectral properties of the source. We also used radiative models to constrain the age of the source. Results. At the LOFAR frequency, the source presents two large outer radio lobes that are wider than at higher frequencies, and a smaller intermediate lobe that is located south-west of the core. A new inspection of X-ray data allowed us to identify an intermediate cavity that is associated with this lobe. It indicates a further phase of jet activity. The radio lobes have a steep spectrum even at LOFAR frequencies, reaching α = 2.9 in the outer lobes and α = 2.1 in the intermediate lobe. Fitting the lobe spectra using a single injection model of particle ageing, we derived a total age of the source between 170 and 106 Myr. This age agrees with the buoyancy and sound-crossing timescales derived from X-ray data. The resolution of the spectral age map we performed allows us to reconstruct the duty cycle of the source. In three phases of jet activity, the AGN was active for most of the time with only brief quiescent phases that ensured the repeated heating of the central gas. Finally, we estimated the minimum energy inside the outer lobes. We find that a source of additional pressure support must be present to sustain the bubbles against the pressure of the external medium.