FR II radio galaxies at low frequencies - II. Spectral ageing and source dynamics

In this paper, the second in a series investigating Fanaroff-Riley type II (FR II) radio galaxies at low frequencies, we use LOw Frequency ARray (LOFAR) and Very Large Array (VLA) observations between 117 and 456 MHz, in addition to archival data, to determine the dynamics and energetics of two radio galaxies, 3C 452 and 3C 223, by fitting spectral ageing models on small spatial scales. We provide improved measurements for the physical extent of the two sources, including a previously unknown low surface brightness extension to the northern lobe of 3C 223, and revised energetics based on these values. We find spectral ages of 77.05^{+9.22}_{-8.74} and 84.96^{+15.02}_{-13.83} Myr for 3C 452 and 3C 223, respectively, suggesting a characteristic advance speed for the lobes of around 1 per cent of the speed of light. For 3C 452, we show that, even for a magnetic field strength not assumed to be in equipartition, a disparity of a factor of approximately 2 exists between the spectral age and that determined from a dynamical standpoint. We confirm that the injection index of both sources (as derived from the lobe emission) remains steeper than classically assumed values, even when considered on well-resolved scales at low frequencies. However, we find an unexpected sharp discontinuity between the spectrum of the hotspots and the surrounding lobe emission. We suggest that this discrepancy is a result of the absorption of hotspot emission and/or non-homogeneous and additional acceleration mechanisms; as such, hotspots should not be used in the determination of the underlying initial electron energy distribution