SIMBAD references

We have been observing, thanks to ALMA, the dust distribution in the region of active planet formation around young stars. This is a powerful tool that can be used to connect observations with theoretical models and improve our understanding of the processes at play. We want to test how a multiplanetary system shapes its birth disk and to study the influence of the planetary masses and particle sizes on the final dust distribution. Moreover, we apply our model to the HL Tau system in order to obtain some insights on the physical parameters of the planets that are able to create the observed features. We follow the evolution of a population of dust particles, treated as Lagrangian particles, in two-dimensional locally isothermal disks where two equal-mass planets are present. The planets are kept in fixed orbits and they do not accrete mass. The outer planet plays a major role in removing the dust particles in the co-orbital region of the inner planet and in forming a particle ring which have a steeper density gradient close to the gap edge respect to the single-planet scenario, promoting the development of vortices. The ring and gap width depend strongly on the planetary mass and particle stopping times, and for the more massive cases on the ring clumps in few stable points that are able to collect a high mass fraction. The features observed in the HL Tau system can be explained through the presence of several massive cores that shape the dust disk where the inner planet(s) have a mass of the order of 0.07M_Jup and the outer one(s) of the order of 0.35M_Jup. These values can be significantly lower if the disk mass turns out to be less than previously estimated. By decreasing the disk mass by a factor of 10, we obtain similar gap widths for planets with a mass of 10M_⊕ and 20M_⊕ for the inner and outer planets, respectively. Although the particle gaps are prominent, the expected gaseous gaps are barely visible.