Most massive galaxies host a supermassive black hole at their centre. Matter accretion creates an active galactic nucleus (AGN), forming a relativistic particle wind. The wind heats and pushes the interstellar medium, producing galactic-wide outflows. Fast outflows remove the gas from galaxies and quench star formation, and while slower ($v<500$ km s$^ $) outflows are ubiquitous, their effect is less clear but can be both positive and negative. We wish to understand the conditions required for positive feedback. We investigated the effect that slow and warm-hot outflows have on the dense gas clouds in the host galaxy. We aim to constrain the region of outflow and cloud parameter space, if any, where the passage of the outflow enhances star formation. We used numerical simulations of virtual `wind tunnels' to investigate the interaction of isolated turbulent spherical clouds ($10^ $ M$_ sun $) with slow outflows ($10$ km s$^ out 400$ km $) spanning a wide range of temperatures ($10^ $ K). We modelled 57 systems in total. We find that warm outflows compress the clouds and enhance gas fragmentation at velocities $ leq 200$ km s$^ $, while hot ($T_ out = 10^6$ K) outflows increase fragmentation rates even at moderate velocities of $400$ km s$^ $. Cloud acceleration, on the other hand, is typically inefficient, with dense gas only attaining velocities of $ 0.1 v_ out We suggest three primary scenarios where positive feedback on star formation is viable: stationary cloud compression by slow outflows in low-powered AGN, sporadic enhancement in shear flow layers formed by luminous AGN, and self-compression in fragmenting AGN-driven outflows. We also consider other potential scenarios where suitable conditions arise, such as compression of galaxy discs and supernova explosions. Our results are consistent with current observational constraints and with previous works investigating triggered star formation in these disparate domains.
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