2021MNRAS.503.5948M

Variability is a general property of accretion discs and their associated jets. We introduce a semi-analytical model for particle acceleration and radio jet/lobe evolution and explore the effect of Myr time-scale jet variability on the particles accelerated by an active galactic nucleus (AGN) jet. Our work is motivated by the need for local powerful ultrahigh energy cosmic ray (UHECR) sources and evidence for variability in AGN and radio galaxies. Our main results are (i) UHECR and non-thermal radiative luminosities track the jet power but with a response set by the escape and cooling times, respectively; (ii) jet variability produces structure in the electron, synchrotron, and UHECR spectra that deviates from that produced for a constant jet power - in particular, spectral hardening features may be signatures of variability; (iii) the cutoff in the integrated cosmic ray (CR) spectrum is stretched out due to the variation in jet power (and, consequently, maximum CR energy). The resulting spectrum is the convolution of the jet power distribution and the source term. We derive an approximate form for a lognormal distribution of powers; and (iv) we introduce the idea of ∼10 GeV 'proxy electrons' that are cooling at the same rate that UHECRs of rigidity 10 EV are escaping from the source, and determine the corresponding photon frequencies that probe escaping UHECRs. Our results demonstrate the link between the history of an astrophysical particle accelerator and its particle contents, non-thermal emission, and UHECR spectrum, with consequences for observations of radio galaxies and UHECR source models.