High-resolution international LOFAR observations of 4C 43.15 Spectral ages and injection indices in a high-z radio galaxy

It has long been known that radio sources with the steepest spectra are preferentially associated with the most distant galaxies, the a - z relation, but the reason for this relation is an open question. The spatial distribution of spectra in high-z radio sources can be used to study this relation, and low-frequency observations are particularly important in understanding the particle acceleration and injection mechanisms. However, the small angular sizes of high-z sources together with the inherently low resolution of low-frequency radio telescopes until now has prevented high angular resolution low-frequency observations of distant objects. Here we present subarcsecond observations of a z = 2.4 radio galaxy at frequencies between 121 and 166 MHz. We measure the spatial distribution of spectra, and discuss the implications for models of the alpha-z relation. We targeted 4C 43.15 with the High Band Antennas of the International LOFAR Telescope with a range of baselines up to 1300 km. At the central frequency of 143 MHz we achieve an angular resolution of similar to 0.3 ''. By complementing our data with archival Very Large Array data we study the spectral index distribution across 4C 43.15 between 55 MHz and 8.4 GHz at resolutions of 0.4 '' and 0.9 ''. With a magnetic field strength of B = 5.2 nT and fitted injection indices of alpha(north)(inj) = -0.8 and alpha(south)(inj) = -0.6, fitting a Tribble spectral ageing model results in a spectral age of tau(spec) = 1.1 +/- 0.1 Myr. We conclude that our data on In] 4C 43.15 indicates that inverse Compton losses could become comparable to or exceed synchrotron losses at higher redshifts and that inverse Compton losses could be a viable explanation for the alpha-z relation. Statistical studies of these objects will become possible in the future when wide-area subarcsecond surveys start.