We present a deep , low-frequency radio continuum study of the nearby Fanaroff–Riley class I ( FR I ) radio galaxy 3C 31 using a combination of LOw Frequency ARray ( LOFAR ; 30–85 and 115–178 MHz ) , Very Large Array ( VLA ; 290–420 MHz ) , Westerbork Synthesis Radio Telescope ( WSRT ; 609 MHz ) and Giant Metre Radio Telescope ( GMRT ; 615 MHz ) observations .
Our new LOFAR 145-MHz map shows that 3C 31 has a largest physical size of 1.1 Mpc in projection , which means 3C 31 now falls in the class of giant radio galaxies .
We model the radio continuum intensities with advective cosmic-ray transport , evolving the cosmic-ray electron population and magnetic field strength in the tails as functions of distance to the nucleus .
We find that if there is no in-situ particle acceleration in the tails , then decelerating flows are required that depend on radius r as \varv \propto r ^ { \beta } ( \beta \approx - 1 ) .
This then compensates for the strong adiabatic losses due to the lateral expansion of the tails .
We are able to find self-consistent solutions in agreement with the entrainment model of Croston & Hardcastle , where the magnetic field provides \approx 1 / 3 of the pressure needed for equilibrium with the surrounding intra-cluster medium ( ICM ) .
We obtain an advective time-scale of \approx 190 Myr , which , if equated to the source age , would require an average expansion Mach number { \cal M } \approx 5 over the source lifetime .
Dynamical arguments suggest that instead , either the outer tail material does not represent the oldest jet plasma or else the particle ages are underestimated due to the effects of particle acceleration on large scales .