Looking for planets with SPHERE in planetary systems with double debris belt

In this work we were interested in systems that own a debris disk with a particular configuration, i.e. two debris belts placed in the inner and outer part of the system. All the objects in the sample were observed with the SPHERE instrument which performs high-contrast direct imaging. Moreover, for each system in the ensemble spectral energy distribution (SED) were available. Positions of the inner and outer belt were obtained by SED fitting on the excesses in the infrared or, when available, from resolved images of the disk. Our main assumption was to take the area between the two belts as empty and we investigated the presence of one or more planets as responsible for the gap. We noted that very few objects have been observed up to date so that we expected the planets to be undetectable for our actual instruments. A planet determines around its orbit a chaotic zone that depends on a certain power law of the ratio between the mass of the planet and the star and on the semi-major axis of the planet. We confronted each couple of values (Mp,ap), derived from the analysis of single and multiple planetary models, with detection limits curves obtained by SPHERE. We tested firstly the case of one single planet on circular orbit with no satisfactory results since we would have need to massive objects. Then we moved to consider one planet on eccentric orbit, verifying previously the equations used by means of numerical integrations. Also with this further assumption the results obtained were quite unlikely (too high masses and/or eccentricities). Thus we moved to consider two and three equal-mass planets on circular orbits and, finally, we got the first good results with respect to detectability because for the latter case we obtained quite low masses for the planets. The last assumption we verified was a system with two equal-mass planets on eccentric orbits. Also this case was of interest since it showed the possible presence of planets with low masses and moderate eccentricities, under detection limits curves. Thus, we concluded our work noticing that the apparent lack of undetected planets in the gap between the two belts could be explained by adding more than one planet in the system and/or taking into account eccentric orbits.