Revealing dust segregation in protoplanetary discs with the help of multi-frequency spectral index maps

Dust is known to drift and grow in protoplanetary discs, which results in dust segregation over the disc extent. Maps of the spectral index $\alpha$ are a common tool for studying the dust content in protoplanetary discs. The analysis of observationally derived maps reveals significant gradients of the spectral index, confirming that dust evolves in the disc, but a more detailed information about the dust redistribution is required to make inferences about the early stages of dust growth. We calculated the spectral index maps based on the results of numerical hydrodynamical simulations using the FEOSAD code, which allows studying a long-term dynamics of a self-gravitating viscous disc populated with coagulating, drifting, and fragmenting dust. Here we demonstrate that values of the spectral index estimated for different wavelength intervals within the far-infrared and radio bands reveal the presence of dust grains of various sizes. Specifically, we show that the disc regions with the maximal spectral index in a specific wavelength interval are the regions with the prevalence of dust grains of a specific size. Thus, a set of spectral index maps derived using different wavelength intervals can be used to recover the dust size-distribution over the disc extent.