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We aim to develop a simple prescription for migration and accretion in 1Ddisc models, calibrated with results of 3D hydrodynamic simulations. Our focuslies on non-self-gravitating discs, but we also discuss to what degree ourprescription could be applied when the discs are self-gravitating.  We study migration using torque densities. Our model for the torque densityis based on existing fitting formulas, which we subsequently modify to preventpremature gap-opening. At higher planetary masses, we also apply torquedensities from hydrodynamic simulations directly to our 1D model. These torquedensities allow modelling the orbital evolution of an initially low-mass planetthat undergoes runaway-accretion to become a massive planet. The two-wayexchange of angular momentum between disc and planet is included. This leads toa self-consistent treatment of gap formation that only relies on directlyaccessible disc parameters. We present a formula for Bondi- and Hill- gasaccretion in the disc-limited regime. This formula is self-consistent in thesense that mass is removed from the disc in the location from where it isaccreted.  We find that the resulting evolution in mass and semi-major axis in the 1Dframework is in good agreement with those from 3D hydrodynamical simulationsfor a range of parameters.  Our prescription is valuable for simultaneously modelling migration andaccretion in 1D-models. We conclude that it is appropriate and beneficial toapply torque densities from hydrodynamic simulations in 1D models, at least inthe parameter space we study here. More work is needed to in order to determinewhether our approach is also applicable in an even wider parameter space and insituations with more complex disc thermodynamics, or when the disc isself-gravitating.

Calibrated Gas Accretion and Orbital Migration of Protoplanets in 1D Disc Models