tokens: that discs are around half as common in binary systems closer than ∼20 au as they are around single stars or stars with wide stellar companions (Yelverton et al. 2019 ). There are competing theories for the formation of both giant planets and close binaries. The formation of close binaries may result from turbulent fragmentation of a molecular cloud, or may occur somewhat later via gravitational instability in a circumstellar disc (see e.g. Kratter 2011 for a review). Giant planets could either form via core accretion or, like close binaries, via the direct gravitational collapse of a circumstellar disc (see e.g. Mordasini et al. 2010 for a review). Thus, it is possible that giant planets and close binary companions form via essentially the same mechanism. If this were the case, then it may be expected that giant planets and close binaries have similar effects on debris discs, which is not what we observe. This could suggest that the two kinds of companion do not both form in the same way, though it could alternatively be the case that they do both form via gravitational instability but that the more massive stellar companions stir planetesimal discs more effectively and thus drive faster collisional decay. 4.4.2 Comparison with directly imaged planets Meshkat et al. ( 2017 ) found tentative evidence that giant planets at tens to hundreds of au – i.e. those probed by direct imaging – are more common in systems with detected debris discs than in those without, at the 88 per cent confidence level. While this result cannot be considered statistically significant, it is none the less suggestive that planets at separations comparable to typical debris discs have a stronger correlation with these discs than the much closer-in planets studied in this paper (recall from Table 6 that we found a difference at a lower confidence level of ∼70 per cent). The apparently contrasting results for planets on close and wide orbits could be understood in terms of a simple model in which the majority of planets form via core accretion regardless of separation, and in which RV planets like those in our study form within a few au (rather than migrating in from large semimajor axes). Within this model, detection of a planet through RV would suggest that planetesimals were able to form in the inner planetary system, while detection of a Kuiper belt analogue would indicate that planetesimals formed in the outer region of the system. However, it is not necessarily the case that the formation of planetesimals at close separations implies that the same should be possible at much larger separations (and vice versa), since, for example, the dust density in protoplanetary discs tends to decrease with stellocentric distance (e.g. Andrews et al. 2009 ), while ice particles that may aid planetesimal growth cannot exist within a few au of the star (e.g. Johansen et al. 2014 ). Additionally, the dynamical environment in the inner and outer systems may be different if undetected
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