On the cavity of a debris disc carved by a giant planet

Abstract

One possible explanation of the cavity in debris discs is the gravitational perturbation of an embedded giant planet. Planetesimals passing close to a massive body are dynamically stirred resulting in a cleared region known as the chaotic zone. Theory of overlapping mean-motion resonances predicts the width of this cavity. To test whether this cavity is identical to the chaotic zone, we investigate the formation of cavities by means of collisionless N-body simulations assuming a 1.25-10 Jupiter mass planet with eccentricities of 0-0.9. Synthetic images at millimetre wavelengths are calculated to determine the cavity properties by fitting an ellipse to 14 percent contour level. Depending on the planetary eccentricity, e_pl, the elliptic cavity wall rotates as the planet orbits with the same (e_pl<0.2) or half (e_pl>0.2) period that of the planet. The cavity centre is offset from the star along the semi-major axis of the planet with a distance of d=0.1q^-0.17e_pl^0.5 in units of cavity size towards the planet's orbital apocentre, where q is the planet-to-star mass ratio. Pericentre (apocentre) glow develops for e_pl<0.05 (e_pl>0.1), while both are present for 0.05<=e_pl<=0.1. Empirical formulae are derived for the sizes of the cavities: da_cav=2.35q^0.36 and da_cav=7.87q^0.37e_pl^0.38 for e_pl<=0.05 and e_pl>0.05, respectively. The cavity eccentricity, e_cav, equals to that of the planet only for 0.3<=e_pl<=0.6. A new method based on ALMA observations for estimating the orbital parameters and mass of the planet carving the cavity is also given.

arXiv comment14 pages, 8 figures, accepted for publication in MNRAS

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