  The efficiency of tidal dissipation provides a zeroth-order link to a
planet's physical properties. For super-Earth and sub-Neptune planets in the
range $R_{\oplus}\lesssim R_p \lesssim 4 R_{\oplus}$, particularly efficient
dissipation (i.e., low tidal quality factors) may signify terrestrial-like
planets capable of maintaining rigid crustal features. Here we explore global
constraints on planetary tidal quality factors using a population of planets in
multiple-planet systems whose orbital and physical properties indicate
susceptibility to capture into secular spin-orbit resonances. Planets
participating in secular spin-orbit resonance can maintain large axial tilts
and significantly enhanced heating from obliquity tides. When obliquity tides
are sufficiently strong, planets in low-order mean-motion resonances can
experience resonant repulsion (period ratio increase). The observed
distribution of period ratios among transiting planet pairs may thus depend
non-trivially on the underlying planetary structures. We model the action of
resonant repulsion and demonstrate that the observed distribution of period
ratios near the 2:1 and 3:2 commensurabilties implies $Q$ values spanning from
$Q\approx 10^1-10^7$ and peaking at $Q \approx 10^6$. This range includes the
expected range in which super-Earth and sub-Neptune planets dissipate ($Q
\approx 10^3 - 10^4$). This work serves as a proof of concept for a method of
assessing the presence of two dissipation regimes, and we estimate the number
of additional multi-transiting planetary systems needed to place any bimodality
in the distribution on a strong statistical footing.
