  It has been recently suggested that the multiple concentric rings and gaps
discovered by ALMA in many protoplanetary disks may be produced by a single
planet, as a result of the complex propagation and dissipation of the multiple
spiral density waves it excites in the disk. Numerical efforts to verify this
idea have largely utilized the so-called locally isothermal approximation with
a prescribed disk temperature profile. However, in protoplanetary disks this
approximation does not provide an accurate description of the density wave
dynamics on scales of tens of au. Moreover, we show that locally isothermal
simulations tend to overestimate the contrast of ring and gap features, as well
as misrepresent their positions, when compared to simulations in which the
energy equation is evolved explicitly. This outcome is caused by the
non-conservation of the angular momentum flux of linear perturbations in
locally isothermal disks. We demonstrate this effect using simulations of
locally isothermal and adiabatic disks (with essentially identical temperature
profiles) and show how the dust distributions, probed by mm wavelength
observations, differ between the two cases. Locally isothermal simulations may
thus underestimate the masses of planets responsible for the formation of
multiple gaps and rings on scales of tens of au observed by ALMA. We suggest
that caution should be exercised in using the locally isothermal simulations to
explore planet-disk interaction, as well as in other studies of wave-like
phenomena in astrophysical disks.
