MS 0735.6+7421 is a galaxy cluster which hosts a central radio galaxy with a very steep spectrum, 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, have displaced the intra-cluster medium, leaving two pairs of cavities observable in the X-ray, associated to two different outbursts, and have distributed energy to the surrounding medium. In this work we have performed for the first time a detailed, high-resolution spectral study of the source at radio frequencies and investigated its duty cycle to be compared with previous X-ray estimates. We have used new observations at 144 MHz produced with the LOw Frequency ARray (LOFAR) together with archival data at higher frequencies. At LOFAR frequency, the source presents two large outer radio lobes, wider than at higher frequencies, and a smaller Intermediate lobe located south-west of the core. A new inspection of X-ray data, allowed us to identify an intermediate cavity, associated with that lobe, indicating the presence of a further phase of jet activity. The radio lobes have a steep spectrum even at LOFAR frequencies, reaching $alpha_{144}^{610}=2.9$ in the outer lobes and $alpha_{144}^{610}=2.1$ 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, in agreement with the buoyancy and sound crossing time-scales derived from X-ray data. We then reconstructed the duty cycle of the source. There were three phases of jet activity, with the AGN being active for most of the time with only brief quiescent phases, ensuring the repeated heating of the central gas. Finally, energetic estimates revealed that a source of additional pressure support must be present to sustain the bubbles against the pressure of the external medium.
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