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We investigate how a protoplanetary disc's susceptibility to gravitationalinstabilities and fragmentation depends on the mass of its host star. We use 1Ddisc models in conjunction with 3D SPH simulations to determine the criticaldisc-to-star mass ratios at which discs become unstable against fragmentation,finding that discs become increasingly prone to the effects of self-gravity aswe increase the host star mass. The actual limit for stability is sensitive tothe disc temperature, so if the disc is optically thin stellar irradiation candramatically stabilise discs against gravitational instability. However, evenwhen this is the case we find that discs around $2$M$_{\odot}$ stars are proneto fragmentation, which will act to produce wide-orbit giant planets and browndwarfs. The consequences of this work are two-fold: that low mass stars couldin principle support high disc-to-star mass ratios, and that higher mass starshave discs that are more prone to fragmentation, which is qualitativelyconsistent with observations that favour high-mass wide-orbit planets aroundhigher mass stars. We also find that the initial masses of these planetsdepends on the temperature in the disc at large radii, which itself depends onthe level of stellar irradiation.

Fragmentation favoured in discs around higher mass stars