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Understanding planet formation requires to discern how dust grows inprotoplanetary disks. An important parameter to measure in disks is the maximumdust grain size present. This is usually estimated through measurements of thedust opacity at different millimeter wavelengths assuming optically thinemission and dust opacity dominated by absorption. However, ALMA observationshave shown that these assumptions might not be correct in the case ofprotoplanetary disks, leading to overestimation of particle sizes and tounderestimation of the disk's mass. Here, we present an analysis of highquality ALMA and VLA images of the HL Tau protoplanetary disk, covering a widerange of wavelengths, from 0.8 mm to 1 cm, and with a physical resolution of$\sim$7.35 au. We describe a procedure to analyze a set of millimeter imageswithout any assumption about the optical depth of the emission, and includingthe effects of absorption and scattering in the dust opacity. This procedureallows us to obtain the dust temperature, the dust surface density and themaximum particle size at each radius. In the HL Tau disk, we found thatparticles have already grown up to a few millimeters in size. We detectdifferences in the dust properties between dark and bright rings, with darkrings containing low dust density and small dust particles. Different featuresin the HL Tau disk seem to have different origins. Planet-disk interactions canexplain substructure at the external half of the disk, but the internal ringsseem to be associated to the presence of snow lines of several molecules.

The Radial Distribution of Dust Particles in the HL Tau Disk from ALMA and VLA Observations