tokens: the following, we summarize the procedures used in this paper to simulate the auroral radio emission arising from a stellar magnetosphere shaped like a non-central dipole. To calculate the magnetic-field vector generated by an offset dipole, the magnetic-dipole moment is located in a generic grid point ( O ) within the star, identified by its spatial coordinates ( x , y , z ) in the native reference frame Oxyz , where the origin O coincides with the centre of the star, the z -axis is parallel or coincident with the dipole axis, and the x -axis lies into the plane parallel to the z -axis and containing the rotation axis. In the reference frame anchored with the offset dipole, the new coordinates ( X , Y , Z ) of the grid points are defined by the simple coordinates translation ( x x , y y , z z ). In the translated O XYZ reference frame, the Z -axis coincides with the dipole axis and the X -axis is located in the plane passing through the Z -axis and parallel to (or containing) the rotation axis. The corresponding magnitude of the magnetic-dipole moment is defined as follows: where r Z is the distance of the offset dipole from the stellar surface along the direction parallel to Z -axis, and B p is the polar magnetic-field strength, that was fixed equal to 3000G. The three components ( B X , B Y , B Z ) of the magnetic-field vector are calculated in each grid point taking into account the non-central position of the magnetic-dipole moment. In the new reference frame O XYZ , the magnetic vector components are easily calculated using the equations of the simple dipole (see appendix A.2 of Trigilio etal. 2004 ). The magnetic vectorial field is then rotated in the observer reference frame Ox y z , where the origin O coincides with the centre of the star, the x -axis is parallel to the line of sight, and the plane y z coincides with the plane of the sky. The method was described in appendix A.3 of Trigilio etal. ( 2004 ). In the reference frame ( O XYZ ) anchored with the offset dipole, it is also possible to locate the grid points falling inside the auroral cavity using the equation of the dipolar magnetic-field lines, defined by using the equation r L cos 2 , where r is the distance of the grid points to the origin O (where is located). Following the method described in Paper I , it is then possible to find those grid points that radiate auroral radio emission within a beam pattern that intercepts the line of sight and that are tuned at the assigned simulation radio frequency . To take into account the non-central position of the magnetic-dipole moment ( O O ), the distance to the centre of the star from the grid points that are able to radiate detectable auroral radio emission has to be larger than the stellar radius. The star shadowing effect has also been taken into account. APPENDIX B: OFFSET DIPOLE: SIMULATIONS The simulations of the auroral radio-emission visibility from a non-central dipolar field were performed assuming the model parameters
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