Constraining the gas distribution in the PDS 70 disc as a method to assess the effect of planet-disc interactions

Abstract

Context. Embedded planets are potentially the cause of substructures, such as gaps and cavities, observed in the continuum images of several protoplanetary discs. Likewise, gas distribution is expected to change in the presence of one or several planets, and the effect can be detected with current observational facilities. Thus, the properties of the substructures observed in the continuum as well as in line emission encode information about the presence of planets in a system and how they interact with the natal disc. The pre-transitional disc around the star PDS 70 is the first case of two young planets being imaged within a dust-depleted gap that was likely carved by the planets themselves. Aims. We aim to determine the spatial distribution of the gas and dust components in the PDS 70 disc. The axisymmetric substructures observed in the resulting profiles are interpreted in the context of planet-disc interactions. Methods. We developed a thermo-chemical forward model for an axisymmetric disc to explain a subset of the Atacama Large Millimeter/Submillimeter Array (ALMA) band 6 observations of three CO isotopologues plus the continuum towards PDS 70. The model accounts for the continuum radiative transfer, steady-state chemistry, and gas thermal balance in a self-consistent way and produces synthetic observables via ray tracing. Results. We demonstrate that the combination of a homogeneous dust size distribution across the disc and relatively low values of viscosity (α ≲ 5 × 10-3) can explain the band 6 continuum observations. For the gas phase, analysis of the synthetic observables points to a gas density peak value of ~0.1 g cm-2 located at 75 au and a minimum of ~10-3 g cm-2 at 20 au. The location of the minimum matches the semi-major axis of the innermost planet PDS 70 b. Combining the gas and dust distributions, the model results in a variable gas-to-dust ratio profile throughout the disc that spans two orders of magnitude within the first 130 au and shows a step gradient towards the outer disc, which is consistent with the presence of a pressure maxima driven by planet-disc interactions. Particularly, the mean gas-to-dust ratio within the dust gap between 16 and 41 au is found to be ~630. We find a gas density drop factor of ~19 at the location of the planet PDS 70 c with respect to the peak gas density at 75 au. Combining this value with results from the literature on the hydrodynamics of planet-disc interactions, we find this gas gap depth to be consistent with independent planet mass estimates from infrared observations. Our findings point towards gas stirring processes taking place in the common gap due to the gravitational perturbation of the two planets. Conclusions. The distribution of gas and dust in the PDS 70 disc can be constrained by forward modelling the spatially resolved observations from high-resolution and high-sensitivity instruments like ALMA. This information is a key piece in the qualitative and quantitative interpretation of the observable signatures of planet-disc interactions.