  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.
