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We know little about the outermost exoplanets in planetary systems, becauseour detection methods are insensitive to moderate-mass planets on wide orbits.However, debris discs can probe the outer-planet population, because dynamicalmodelling of observed discs can reveal properties of perturbing planets. We usefour sculpting and stirring arguments to infer planet properties in 178debris-disc systems from the ISPY, LEECH and LIStEN planet-hunting surveys.Similar analyses are often conducted for individual discs, but we consider alarge sample in a consistent manner. We aim to predict the population ofwide-separation planets, gain insight into the formation and evolutionhistories of planetary systems, and determine the feasibility of detectingthese planets in the near future. We show that a `typical' cold debris disclikely requires a Neptune- to Saturn-mass planet at 10-100 au, with someneeding Jupiter-mass perturbers. Our predicted planets are currentlyundetectable, but modest detection-limit improvements (e.g. from JWST) shouldreveal many such perturbers. We find that planets thought to be perturbingdebris discs at late times are similar to those inferred to be forming inprotoplanetary discs, so these could be the same population if newly formedplanets do not migrate as far as currently thought. Alternatively, youngplanets could rapidly sculpt debris before migrating inwards, meaning that theresponsible planets are more massive (and located further inwards) thandebris-disc studies assume. We combine self-stirring and size-distributionmodelling to show that many debris discs cannot be self-stirred without havingunreasonably high masses; planet- or companion-stirring may therefore be thedominant mechanism in many (perhaps all) debris discs. Finally, we providecatalogues of planet predictions, and identify promising targets for futureplanet searches.

Planet populations inferred from debris discs: insights from 178 debris systems in the ISPY, LEECH and LIStEN planet-hunting surveys