Modelling planet-induced gaps and rings in ALMA discs: the role of in-plane radiative diffusion

ALMA observations of protoplanetary discs in dust continuum emission reveal a variety of annular structures. Attributing the existence of such features to embedded planets is a popular scenario, supported by studies using hydrodynamical models. Recent work has shown that radiative cooling greatly influences the capability of planet-driven spiral density waves to transport angular momentum, ultimately deciding the number, position, and depth of rings and gaps that a planet can carve in a disc. However, radiation transport has only been treated via local thermal relaxation, not taking into account radiative diffusion along the disc plane. We compare the previous state-of-the-art models of planet-disc interaction with local cooling prescriptions to our new models that include cooling in the vertical direction and radiative diffusion in the plane of the disc, and show that the response of the disc to the induced spiral waves can differ significantly when comparing these two treatments of the disc thermodynamics. We follow up with synthetic emission maps of ALMA systems, and show that our new models reproduce the observations found in the literature better than models with local cooling. We conclude that appropriate treatment of radiation transport is key to constraining the parameter space when interpreting ALMA observations using the planet-disc interaction scenario.