Photometry of outer Solar System objects from the Dark Energy Survey II: a joint analysis of trans-Neptunian absolute magnitudes, colors, lightcurves and dynamics

For the 696 trans-Neptunian objects (TNOs) with absolute magnitudes $5.5 < H_r < 8.2$ detected in the Dark Energy Survey (DES), we characterize the relationships between their dynamical state and physical properties -- namely $H_r$, indicating size; colors, indicating surface composition; and flux variation semi-amplitude $A$, indicating asphericity and surface inhomogeneity. We seek ``birth'' physical distributions that can recreate these parameters in every dynamical class. We show that the observed colors of these TNOs are consistent with 2 Gaussian distributions in $griz$ space, ``near-IR bright'' (NIRB) and ``near-IR faint'' (NIRF), presumably an inner and outer birth population, respectively. We find a model in which both the NIRB and NIRF $H_r$ and $A$ distributions are independent of current dynamical states, supporting their assignment as birth populations. All objects are consistent with a common rolling $p(H_r)$, but NIRF objects are significantly more variable. Cold classicals (CCs) are purely NIRF, while hot classical (HC), scattered, and detached TNOs are consistent with $\approx70\%$ NIRB, and resonances' NIRB fractions show significant variation. The NIRB component of the HCs and of some resonances have broader inclination distributions than the NIRFs, i.e. their current dynamics retains information about birth location. We find evidence for radial stratification within the birth NIRB population, in that HC NIRBs are on average redder than detached or scattered NIRBs; a similar effect distinguishes CCs from other NIRFs. We estimate total object counts and masses of each class within our $H_r$ range. These results will strongly constrain models of the outer solar system.