Predicting the incidence of planet and debris discs as a function of stellar mass

The mass of solids in a young circumstellar disc may be the key factor in its efficiency in building planetesimals and planetary cores, and dust observed around young T Tauri and Herbig Ae stars can be used as a proxy for this initial solid content. The dust-mass distributions are taken from recent millimetre-wavelength data and fitted using survival analysis to take into account upper limits, and threshold disc masses for building planets and belts of comets are estimated. Amongst A stars, 20 per cent gas giant and 55 per cent debris disc systems are predicted, in good agreement with observations. For M stars, the predicted and observed planet frequencies agree at similar to 2-3 per cent, and this low incidence is explained by a lack of massive discs. However, debris is predicted around approximate to 14 per cent of M stars, while only similar to 2 per cent such systems have so far been found. This suggests that deeper searches such as with Herschel and SCUBA-2 may find a cold disc population previously missed around these low-luminosity stars. Also, an estimate of the efficiency of building millimetre-detected dust into planetary cores suggests that about one-third of M stars could host an Earth-mass planet - but as the dust is spread over large disc areas, such planets may orbit far from the star.