  These last years several Systems with Tightly packed Inner Planets in the
super-Earth mass regime have been discovered harboring chains of resonances. It
is generally believed that planet pairs get trapped in MMR during the migration
phase in the protoplanetary disk, while the tides raised by the host star
provide a source of dissipation on very long timescales. In this work, we aim
to study the departure from exact commensurabilities observed among the STIPs
which harbor 3-planet resonances and analyze how tides play an important role
in shaping the resonance offsets for the STIPs. We analyzed the resonance
offsets between adjacent pairs for five multi-planetary systems, namely
Kepler-80, Kepler-223, K2-138, TOI-178, and TRAPPIST-1, highlighting the
existence of different trends in the offsets. On the one hand, we derived
analytical estimates for the offsets, which confirm that the departure of the
planetary pairs from the nominal MMRs are due to the 3-planet resonant
dynamics. On the other hand, we performed N-body simulations including both
orbital migration and tidal dissipation from the host star with simple
prescriptions in order to test the effectiveness of this mechanism at shaping
the observed trend in the offsets, focusing our study on the preservation of
the resonant patterns in the different systems with the same general setup. We
found that the trends in the offsets of the five detected systems can be
produced by tidal damping effects, regardless of the considered value for the
tidal factor. It is a robust mechanism that relaxes the system towards
equilibrium while efficiently moving it along 3-planet resonances, which
induces the observed resonance offset for each planet pair. In addition, we
showed that for Kepler-80, K2-138, and TOI-178, the amplitudes of the resonant
offsets can also be reproduced with appropriate tidal factor, for the estimated
age of the systems.
