  Direct imaging observations have revealed spiral structures in protoplanetary
disks. Previous studies have suggested that planet-induced spiral arms cannot
explain some of these spiral patterns, due to the large pitch angle and high
contrast of the spiral arms in observations. We have carried out three
dimensional (3-D) hydrodynamical simulations to study spiral wakes/shocks
excited by young planets. We find that, in contrast with linear theory, the
pitch angle of spiral arms does depend on the planet mass, which can be
explained by the non-linear density wave theory. A secondary (or even a
tertiary) spiral arm, especially for inner arms, is also excited by a massive
planet. With a more massive planet in the disk, the excited spiral arms have
larger pitch angle and the separation between the primary and secondary arms in
the azimuthal direction is also larger. We also find that although the arms in
the outer disk do not exhibit much vertical motion, the inner arms have
significant vertical motion, which boosts the density perturbation at the disk
atmosphere. Combining hydrodynamical models with Monte-Carlo radiative transfer
calculations, we find that the inner spiral arms are considerably more
prominent in synthetic near-IR images using full 3-D hydrodynamical models than
images based on 2-D models assuming vertical hydrostatic equilibrium,
indicating the need to model observations with full 3-D hydrodynamics. Overall,
companion-induced spiral arms not only pinpoint the companion's position but
also provide three independent ways (pitch angle, separation between two arms,
and contrast of arms) to constrain the companion's mass.
