Between 25-50 % of white dwarfs (WD) present atmospheric pollution by metals, mainly by rocky material, which has been detected as gas/dust discs, or in the form of photometric transits in some WDs. Planets might be responsible for scattering minor bodies that can reach stargazing orbits, where the tidal forces of the WD can disrupt them and enhance the chances of debris to fall onto the WD surface. The planet-planet scattering process can be triggered by the stellar mass-loss during the post main-sequence evolution of planetary systems. In this work, we continue the exploration of the dynamical instabilities that can lead to WD pollution. In a previous work we explored two-planet systems found around main-sequence (MS) stars and here we extend the study to three-planet system architectures. We evolved 135 detected three-planet systems orbiting MS stars to the WD phase by scaling their orbital architectures in a way that their dynamical properties are preserved by using the $N$-body integrator package Mercury. We find that 100 simulations (8.6 %) are dynamically active (having planet losses, orbit crossing and scattering) on the WD phase, where low mass planets (1-100 $mathrm{M}_oplus$) tend to have instabilities in Gyr timescales while high mass planets ($>100~mathrm{M}_oplus$) decrease the dynamical events more rapidly as the WD ages. Besides, 19 simulations (1.6 %) were found to have planets crossing the Roche radius of the WD, where 9 of them had planet-star collisions. Our three-planet simulations have an slight increase percentage of simulations that may contribute to the WD pollution than the previous study involving two-planet systems and have shown that planet-planet scattering is responsible of sending planets close to the WD, where they may collide directly to the WD, become tidally disrupted or circularize their orbits, hence producing pollution on the WD atmosphere.
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