Dust and power: Unravelling the merger-active galactic nucleus connection in the second half of cosmic history

Galaxy mergers represent a fundamental physical process under hierarchical structure formation, but their role in triggering active galactic nuclei (AGNs) is still unclear. We aim to investigate the merger-AGN connection using state-of-the-art observations and novel methods for detecting mergers and AGNs. We selected stellar mass-limited samples at redshift $z<1$ from the Kilo-Degree Survey (KiDS), focussing on the KiDS-N-W2 field with a wide range of multi-wavelength data. We analysed three AGN types, selected in the mid-infrared (MIR), X-ray, and via spectral energy distribution (SED) modelling. To identify mergers, we used convolutional neural networks (CNNs) trained on two cosmological simulations. We created mass- and redshift-matched control samples of non-mergers and non-AGNs. We first investigated the merger-AGN connection using a binary AGN/non-AGN classification. We observed a clear AGN excess (of a factor of $2-3$) in mergers with respect to non-mergers for the MIR AGNs, along with a mild excess for the X-ray and SED AGNs. This result indicates that mergers could trigger all three types, but are more connected to the MIR AGNs. About half of the MIR AGNs are in mergers but it is unclear whether mergers are the main trigger. For the X-ray and SED AGNs, mergers are unlikely to be the dominant triggering mechanism. We also explored the connection using the continuous AGN fraction $f_ AGN $ parameter. Mergers exhibit a clear excess of high $f_ AGN $ values relative to non-mergers, for all AGN types. We unveil the first merger fraction $f_ merger - f_ AGN $ relation with two distinct regimes. When the AGN is not very dominant, the relation is only mildly increasing or even flat, with the MIR AGNs showing the highest $f_ merger $. In the regime of very dominant AGNs ($f_ AGN merger $ shows the same steeply rising trend with increasing $f_ AGN $ for all AGN types. These trends are also seen when plotted against AGN bolometric luminosity. We conclude that mergers are most closely connected to dust-obscured AGNs, generally linked to a fast-growing phase of the supermassive black hole. Such mergers therefore stand as the main (or even the sole) fuelling mechanism of the most powerful AGNs.