Herschel far-infrared photometry of the Swift Burst Alert Telescope active galactic nuclei sample of the local universe - III. Global star-forming properties and the lack of a connection to nuclear activity

We combine the Herschel Space Observatory PACS and SPIRE photometry with archival WISE photometry to construct the spectral energy distributions (SED) for over 300 local ($z < 0.05$), ultra-hard X-ray (14 - 195 keV) selected active galactic nuclei (AGN) from the Swift Burst Alert Telescope (BAT) 58 month catalogue. Using a simple analytical model that combines an exponentially cut-off powerlaw with a single temperature modified blackbody, we decompose the SEDs into a host-galaxy and AGN component. We calculate dust masses, dust temperatures, and star-formation rates (SFR) for our entire sample and compare them to a stellar mass-matched sample of local non-AGN galaxies. We find AGN host galaxies have systematically higher dust masses, dust temperatures, and SFRs due to the higher prevalence of late-type galaxies to host an AGN, in agreement with previous studies of the Swift/BAT AGN. We provide a scaling to convert X-ray luminosities into 8 - 1000 $mu$m AGN luminosities, as well as determine the best mid-to-far IR colors for identifying AGN dominated galaxies in the IR regime. We find that for nearly 30 per cent of our sample, the 70 $mu$m emission contains a significant contribution from the AGN ($> 0.5$), especially at higher luminosities ($L_{14-195,rm{keV}} > 10^{42.5}$ ergs s$^{-1}$). Finally, we measure the local SFR-AGN luminosity relationship, finding a slope of 0.18, large scatter (0.37 dex), and no evidence for an upturn at high AGN luminosity. We conclude with a discussion on the implications of our results within the context of galaxy evolution with and without AGN feedback.