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Recent sub-arcsecond resolution surveys of the dust continuum emission from nearby protoplanetary disks showed a strong correlation between the sizes and luminosities of the disks. We aim to explain the origin of the (sub-)millimeter size-luminosity relation (SLR) between the $68\%$ effective radius ($r_{eff}$) of disks with their continuum luminosity ($L_{mm}$), with models of gas and dust evolution in a simple viscous accretion disk and radiative transfer calculations. We use a large grid of models ($10^{5}$ simulations) with and without planetary gaps, varying the initial conditions of the key parameters. We calculate the disk continuum emission and the effective radius for all models as a function of time. By selecting those simulations that continuously follow the SLR, we can derive constraints on the input parameters of the models. We confirm previous results that models of smooth disks in the radial drift regime are compatible with the observed SLR ($L_{mm}\propto r_{eff}^{2}$) but only smooth disks cannot be the reality. We show that the SLR is more widely populated if planets are present. However they tend to follow a different relation than smooth disks, potentially implying that a mixture of smooth and sub-structured disks are present in the observed sample. We derive a SLR ($L_{mm}\propto r_{eff}^{5/4}$) for disks with strong sub-structure. To be compatible with the SLR, models need to have an initially high disk mass ($\geq 2.5 \cdot 10^{-2}M_{\star}$) and low turbulence-parameter $\alpha$ values ($\leq 10^{-3}$). Furthermore, we find that the grain composition and porosity drastically affects the evolution of disks on the size-luminosity diagram where relatively compact grains that include amorphous carbon are favoured. Moreover, a uniformly optically thick disk with high albedo ($0.9$) that follows the SLR cannot be formed from an evolutionary procedure., Comment: Replaced with the published version in A&A. 19+11 pages, 11+10 figures

The mass of protoplanetary disks is arguably one of their most important quantities shaping their evolution toward planetary systems, but it remains a challenge to determine this quantity. Using the high spatial resolution now available on telescopes such as the Atacama Large Millimeter/submillimeter Array (ALMA), recent studies derived a relation between the disk surface density and the location of the "dust lines". This is a new concept in the field, linking the disk size at different continuum wavelengths with the radial distribution of grain populations of different sizes. We aim to use a dust evolution model to test the dependence of the dust line location on disk gas mass. In particular, we are interested in the reliability of the method for disks showing radial substructures, as recent high-resolution observations revealed. Our models show that the determination of the dust line location is a promising approach to the mass estimate of protoplanetay disks, but the exact relation between the dust line location and disk mass depends on the structure of the particular disk. We calibrated the relation for disks without evidence of radial structures, while for more complex structures we ran a simple dust evolution model. However, this method fails when there is evidence of strong dust traps. It is possible to reveal when dust evolution is dominated by traps, providing the necessary information for when the method should be applied with caution., 14 pages, 18 figures, accepted by Astronomy & Astrophysics

The solid accretion rate, necessary to grow gas giant planetary cores within the disk lifetime, has been a major constraint for theories of planet formation. We tested the solid accretion rate efficiency on planetary cores of different masses embedded in their birth disk, by means of 3D radiation-hydrodynamics, where we followed the evolution of a swarm of embedded solids of different sizes. We found that using a realistic equation of state and radiative cooling, the disk at 5 au is able to cool efficiently and reduce its aspect ratio. As a result, the pebble isolation mass is reached before the core grows to 10 Earth masses, stopping efficiently the pebble flux and creating a transition disk. Moreover, the reduced isolation mass halts the solid accretion before the core reaches the critical mass, leading to a barrier to giant planet formation, and it explains the large abundance of super-Earth planets in the observed population., Published in A&A, 8 pages, 9 figures