The Disc Miner : I. A statistical framework to detect and quantify kinematical perturbations driven by young planets in discs

Context. The study of disc kinematics has recently opened up as a promising method to detect unseen planets. However, a systematic, statistically meaningful analysis of such an approach remains missing in the field. Aims. The aim of this work is to devise an automated, statistically robust technique to identify and quantify kinematical perturbations induced by the presence of planets in a gas disc, and to accurately infer the location of the planets. Methods. We produced hydrodynamical simulations of planet-disc interactions with different planet masses, namely 0.3, 1.0, and 3.0 MJup, at a radius of Rp = 100 au in the disc, and performed radiative transfer calculations of CO to simulate observables for a disc inclination of - 45°, and for 13 planet azimuths. We then fitted the synthetic data cubes with a Keplerian model of the channel-by-channel emission using the DISCMINER package. Lastly, we compared the synthetic cubes with the best-fit model to: extract deviations from Keplerian rotation; and quantify both large-scale and localised intensity, line width, and velocity fluctuations triggered by the embedded planets and provide strong constraints on their location in the disc. We assess the statistical significance of the detections using the peak and variance of the planet-driven velocity fluctuations. Results. Our findings suggest that a careful inspection of line intensity profiles to analyse gas kinematics in discs is a robust method to reveal embedded, otherwise unseen planets, as well as the location of gas gaps. We claim that a simultaneous study of line-of-sight velocities and intensities is crucial to understanding the origin of the observed velocity perturbations. In particular, the combined contribution of the upper and lower emitting surfaces of the disc plays a central role in setting the observed gas velocities. This joint effect is especially prominent and hard to predict at the location of a gap or cavity, which can lead to artificial deviations from Keplerian rotation depending on how the disc velocities are retrieved. Furthermore, regardless of their origin, gas gaps alone are capable of producing kink-like features on intensity channel maps, which are often attributed to the presence of planets. Our technique, based on line centroid differences, takes all this into account to capture only the strongest, localised, planet-driven perturbations. It does not get confused by axisymmetric velocity perturbations that may result from non-planetary mechanisms. The method can detect all three simulated planets, at all azimuths, with an average accuracy of ±3° in azimuth and ±8 au in radius. As expected, velocity fluctuations driven by planets increase in magnitude as a function of the planet mass. Furthermore, owing to disc structure and line-of-sight projection effects, planets at azimuths close to ±45° yield the highest velocity fluctuations, whereas those at limiting cases, 0° and ±90°, drive the lowest. The observed peak velocities typically range within 40-70, 70-170, and 130-450 m s-1 for 0.3, 1.0, and 3.0 MJup planets, respectively. Our analysis indicates that the variance of peak velocities is boosted near planets because of organised gas motions prompted by the localised gravitational well of planets. We propose an approach that exploits this velocity coherence to provide, for the first time, statistically significant detections of localised planet-driven perturbations in the gas disc kinematics.