Inferring the presence of planets by application of the Γ-L* relationship to unresolved debris discs

Circumstellar debris discs are tenuous, remnant rings of icy and rocky material left over from planet(esimal) formation processes. Such structures are analogous to the Asteroid and Edgeworth-Kuiper belts in the Solar system and are therefore indicative of planetary systems around their host star. They also act as tracers of the presence of unseen planetary companions that perturb the disc's dust-producing planetesimals. Resolved imaging of discs can reveal the presence of asymmetries potentially indicative of disc-planet interactions. However, most debris discs remain unresolved, so interpretation of their architectures is subject to great uncertainty.

A relationship between stellar luminosity and the dust grain properties has been determined, based on a sample of resolved debris discs. This can be expressed as a trend between stellar luminosity (L*) and the ratio of the resolved and blackbody extent of the disc (Γ = Robs/Rbb). We have examined a larger sample of debris discs, both resolved and unresolved, observed at far-infrared wavelengths by Herschel and Spitzer, in order to determine the fidelity of that relationship. We further examine whether the inferred extents of these discs are consistent with self-stirring models or may be indicative of dynamical perturbation by a companion. A comparison of the extents for discs resolved at millimetre wavelenghts and our model predictions yields good agreement between the two, suggesting that the Γ-L* relationship is a fair predictor of actual disc extent for most systems. Using simple stirring models for comparison, we identify several systems with larger than expected radii given the stellar ages.

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