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The relation between nuclear ($\lesssim$ 50 pc) star formation and nucleargalactic activity is still elusive: theoretical models predict a link betweenthe two, but it is unclear whether active galactic nuclei (AGNs) should appearat the same time, before or after nuclear star formation activity is ongoing.We present a study of this relation in a complete, volume-limited sample ofnine of the most luminous ($\log L_{\rm 14-195 keV} > 10^{42.5}$ erg/s) localAGNs (the LLAMA sample), including a sample of 18 inactive control galaxies (6star-forming; 12 passive) that are matched by Hubble type, stellar mass (9.5$\lesssim$ log M_star/M_sun $\lesssim$ 10.5), inclination and distance. Thisallows us to calibrate our methods on the control sample and perform adifferential analysis between the AGN and control samples. We perform stellarpopulation synthesis on VLT/X-SHOOTER spectra in an aperture corresponding to aphysical radius of $\approx$ 150 pc. We find young ($\lesssim$ 30 Myr) stellarpopulations in seven out of nine AGNs and in four out of six star-formingcontrol galaxies. In the non-star-forming control population, in contrast, onlytwo out of twelve galaxies show such a population. We further show that theseyoung populations are not indicative of ongoing star-formation, providingevidence for models that see AGN activity as a consequence of nuclear starformation. Based on the similar nuclear star-formation histories of AGNs andstar-forming control galaxies, we speculate that the latter may turn into theformer for some fraction of their time. Under this assumption, and making useof the volume-completeness of our sample, we infer that the AGN phase lasts forabout 5 % of the nuclear starburst phase.

LLAMA: Stellar populations in the nuclei of ultra hard X-ray selected AGN and matched inactive galaxies