Flows around galaxies I -- The dependency of galaxy connectivity on cosmic environments and effects on the star-formation rate

With the aim of bringing substantial insight to the fundamental question of how galaxies acquire their material for star-formation, we present the first comprehensive characterisation of the galaxy connectivity (i.e. the number of small-scale filamentary streams connected to a galaxy) in relation with the cosmic environment, and a statistical exploration of the impact of connectivity on the star-formation rate at z=2. We detect kpc-scale filaments directly connected to galaxies by applying the DisPerSE filament finder to the DM density around 2942 central galaxies ($M_* > 10^{8}$ $\mathrm{M}_\odot / h$) of the TNG50-1 simulation. Our results demonstrate that galaxy connectivity spans a broad range (from 0 to 9), with more than half of the galaxies connected to two or three streams. We examine a variety of factors that could influence the connectivity finding out that it increases with mass, decreases with local density for low mass galaxies, and does not depend on local environment, estimated by the Delaunay tessellation, for high mass galaxies. We further classify galaxies according to their location in different cosmic web environments, and we highlight the influence of the large-scale structure on the number of connected streams. Our results reflect the different strengths of the cosmic tides, which can prevent the formation of coherent streams feeding the galaxies, or even disconnect the galaxy from its local web. Finally, we show that, at fixed local density, the star-formation rate (SFR) of low mass galaxies is up to $5.9\sigma$ enhanced due to connectivity. This SFR boost is even more significant ($6.3\sigma$) for galaxies embedded in cosmic filaments, where the available matter reservoirs are large. A milder impact is found for high mass galaxies, hinting at different relative efficiencies of matter inflow via small-scale streams in galaxies of different masses.