Annular structures in proto-planetary discs, such as gaps and rings, are now ubiquitously found by high-resolution ALMA observations. Under the hypothesis that they are opened by planets, in this paper we investigate how the minimum planet mass needed to open a gap varies across different stellar host masses and distances from the star. The dependence on the stellar host mass is particularly interesting because, at least in principle, gap opening around low mass stars should be possible for lower mass planets, giving us a look into the young, low mass planet population. Using dusty hydrodynamical simulations, we find however the opposite behaviour, as a result of the fact that discs around low mass stars are geometrically thicker: gap opening around low mass stars can require more massive planets. Depending on the theoretical isochrone employed to predict the relationship between stellar mass and luminosity, the gap opening planet mass could also be independent of stellar mass, but in no case we find that gap opening becomes easier around low mass stars. This would lead to the expectation of a {it lower} incidence of such structures in lower mass stars, since exoplanet surveys show that low mass stars have a lower fraction of giant planets. More generally, our study enables future imaging observations as a function of stellar mass to be interpreted using information on the mass vs. luminosity relations of the observed samples.
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