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 per cent contour level .
Depending on the planetary eccentricity , e _ { \mathrm { pl } } , the elliptic cavity wall rotates as the planet orbits with the same ( e _ { \mathrm { pl } } < 0.2 ) or half ( e _ { \mathrm { pl } } > 0.2 ) period that of the planet .
The cavity centre is offset from the star along the semimajor axis of the planet with a distance of d = 0.1 q ^ { -0.17 } e _ { \mathrm { 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 _ { \mathrm { pl } } < 0.05 ( e _ { \mathrm { pl } } > 0.1 ) , while both are present for 0.05 \leq e _ { \mathrm { pl } } \leq 0.1 .
Empirical formulae are derived for the sizes of the cavities : \delta a _ { \mathrm { cav } } = 2.35 q ^ { 0.36 } and \delta a _ { \mathrm { cav } } = 7.87 q ^ { 0.37 } e _ { \mathrm { pl } } ^ { 0.38 } for e _ { \mathrm { pl } } \leq 0.05 and e _ { \mathrm { pl } } > 0.05 , respectively .
The cavity eccentricity , e _ { \mathrm { cav } } , equals to that of the planet only for 0.3 \leq e _ { \mathrm { pl } } \leq 0.6 .
A new method based on Atacama Large Millimeter/submillimeter Array observations for estimating the orbital parameters and mass of the planet carving the cavity is also given .