  Spiral arms have been observed in nearly a dozen protoplanetary discs in
near-infrared scattered light and recently also in the sub-millimetre
continuum. While one of the most compelling explanations is that they are
driven by planetary or stellar companions, in all but one cases such companions
have not yet been detected and there is even ambiguity on whether the planet
should be located inside or outside the spirals. Here we use 3D hydrodynamic
simulations to study the morphology of spiral density waves launched by
embedded planets taking into account the vertical temperature gradient, a
natural consequence of stellar irradiation. Our simulations show that the pitch
angle of the spirals in thermally stratified discs is the lowest in the disc
mid-plane and increases towards the disc surface. We combine the hydrodynamic
simulations with 3D radiative transfer calculations to predict that the
pitch-angle of planetary spirals observed in the near-infrared is higher than
in the sub-millimetre. We also find that in both cases the spirals converge
towards the planet. This provides a new powerful observational method to
determine if the perturbing planet is inside our outside the spirals, as well
as map the thermal stratification of the disc.
