A broadband radio study of PSR J0250+5854: the slowest-spinning radio pulsar known

We present radio observations of the most slowly rotating known radio pulsar PSR J0250+5854. With a 23.5 s period, it is close, or even beyond, the $P$-$dot{P}$ diagram region thought to be occupied by active pulsars. The simultaneous observations with FAST, the Chilbolton and Effelsberg LOFAR international stations, and NenuFAR represent a five-fold increase in the spectral coverage of this object, with the detections at 1250 MHz (FAST) and 57 MHz (NenuFAR) being the highest- and lowest-frequency published respectively to date. We measure a flux density of $4pm2$ $mu$Jy at 1250 MHz and an exceptionally steep spectral index of $-3.5^{+0.2}_{-1.5}$, with a turnover below $sim$95 MHz. In conjunction with observations of this pulsar with the GBT and the LOFAR Core, we show that the intrinsic profile width increases drastically towards higher frequencies, contrary to the predictions of conventional radius-to-frequency mapping. We examine polarimetric data from FAST and the LOFAR Core and conclude that its polar cap radio emission is produced at an absolute height of several hundreds of kilometres around 1.5 GHz, similar to other rotation-powered pulsars across the population. Its beam is significantly underfilled at lower frequencies, or it narrows because of the disappearance of conal outriders. Finally, the results for PSR J0250+5854 and other slowly spinning rotation-powered pulsars are contrasted with the radio-detected magnetars. We conclude that magnetars have intrinsically wider radio beams than the slow rotation-powered pulsars, and that consequently the latters lower beaming fraction is what makes objects such as PSR J0250+5854 so scarce.