Evolution of grain size distribution in galactic discs

Context. Dust is formed out of stellar material and it is constantly affected by different mechanisms occurring in the interstellar medium. Depending on their size, the behaviour of dust grains vary under these mechanisms and, therefore, the dust grain size distribution evolves as part of the dust evolution itself. Following how the grain size distribution evolves is a difficult computing task that has only recently become the subject of consideration. Smoothed particle hydrodynamic (SPH) simulations of a single galaxy, together with cosmological simulations, are producing the first predictions of the evolution of dust grain size distribution. Aims. We compare, for the first time, the evolution of the dust grain size distribution as predicted by SPH simulations and results from observations. We are able to validate not only the predictions of the evolution of the small-to-large grain mass ratio (DS/DL) within a galaxy, but we also provide observational constraints for recent cosmological simulations that include the grain size distribution in the dust evolution framework. Methods. We selected a sample of three spiral galaxies with different masses: M 101, NGC 628, and M 33. We fitted the dust spectral energy distribution across the disc of each object and derived the abundance of the different grain types included in the dust model. We analysed how the radial distribution of the relative abundance of the different grain size populations changes over the whole disc within each galaxy. The DS/DL ratio as a function of the galactocentric distance and metallicity is directly compared to what has been predicted by the SPH simulations. Results. We find a good agreement between the observed radial distribution of DS/DL and what was obtained from the SPH simulations of a single galaxy. The comparison agrees with the expected evolutionary stage of each galaxy. We show that the central parts of NGC 628 at a high metallicity and with a high molecular gas fraction are mainly affected not only by accretion, but also by the coagulation of dust grains. The centre of M 33, having a lower metallicity and lower molecular gas fraction, presents an increase in the DS/DL ratio, demonstrating that shattering is very effective for creating a large fraction of small grains. Finally, the observational results provided by our galaxies confirm the general relations predicted by the cosmological simulations based on the two-grain size approximation. However, we also present evidence that the simulations could be overestimating the amount of large grains in high massive galaxies.