Abstract

Understanding planet formation requires one to discern how dust grows in protoplanetary disks. An important parameter to measure in disks is the maximum dust grain size present. This is usually estimated through measurements of the dust opacity at different millimeter wavelengths assuming optically thin emission and dust opacity dominated by absorption. However, Atacama Large Millimeter/submillimeter Array (ALMA) observations have shown that these assumptions might not be correct in the case of protoplanetary disks, leading to overestimation of particle sizes and to underestimation of the disk's mass. Here, we present an analysis of high-quality ALMA and Very Large Array images of the HL Tau protoplanetary disk, covering a wide range of wavelengths, from 0.8 mm to 1 cm, and with a physical resolution of similar to 7.35 au. We describe a procedure to analyze a set of millimeter images without any assumption about the optical depth of the emission, and including the effects of absorption and scattering in the dust opacity. This procedure allows us to obtain the dust temperature, the dust surface density, and the maximum particle size at each radius. In the HL Tau disk, we found that particles have already grown to a few millimeters in size. We detect differences in the dust properties between dark and bright rings, with dark rings containing low dust density and small dust particles. Different features in the HL Tau disk seem to have different origins. Planet-disk interactions can explain substructure in the external half of the disk, but the internal rings seem to be associated with the presence of snow lines of several molecules.