  Many protoplanetary disks exhibit annular gaps in dust emission, which may be
produced by planets. Simulations of planet-disk interaction aimed at
interpreting these observations often treat the disk thermodynamics in an
overly simplified manner, which does not properly capture the dynamics of
planet-driven density waves driving gap formation. Here we explore substructure
formation in disks using analytical calculations and hydrodynamical simulations
that include a physically-motivated prescription for radiative effects
associated with the planet-induced density waves. For the first time, our
treatment accounts not only for cooling from the disk surface, but also for
radiation transport along the disk midplane. We show that this in-plane
cooling, with a characteristic timescale typically an order of magnitude
shorter than the one due to surface cooling, plays a critical role in density
wave propagation and dissipation (we provide a simple estimate of this
timescale). We also show that viscosity, at the levels expected in
protoplanetary disks ($\alpha \lesssim 10^{-3}$), has a negligible effect on
density wave dynamics. Using synthetic maps of dust continuum emission, we find
that the multiplicity and shape of the gaps produced by planets are sensitive
to the physical parameters---disk temperature, mass, and opacity---that
determine the damping of density waves. Planets orbiting at $\lesssim 20$ au
produce the most diverse variety of gap/ring structures, although significant
variation is also found for planets at $\gtrsim 50$ au. By improving the
treatment of physics governing planet-disk coupling, our results present new
ways of probing the planetary interpretation of annular substructures in disks.
