Example colour map of the maximum induced eccentricity 2e_f imposed by a planetary perturber on a particle with semi-major axis 100 AU and eccentricity e = 0 as a function of its periastron and eccentricity, as estimated from Eq. (2). The black line corresponds to a 2e_f = 0.3 condition, which was set to mimic the condition for the disk of ζ²  Reticuli. Note that it does not depend on the mass of the planet. The white lines show the parameters for which the typical timescale to reach a steady state at 100 AU is t_prec = 1 Gyr, using Eq. (4). This timescale depends on the mass: m_p = 0.1  M_Jup (solid line), 1  M_Jup (dashed line) and 2  M_Jup (dotted line). For example, a perturber of mass 0.1  M_Jup, periastron q_p = 150 AU and eccentricity e_p = 0.4 is expected to produce a significantly eccentric ring in shorter than 1 Gyr, although spiral patterns may remain since it can take several precession timescales for them to vanish, as was shown by Wyatt (2005).