Recent observations of protoplanetary disk have reported spiral structures that are potential signatures of embedded planets , and modeling efforts have shown that a single planet can excite multiple spiral arms , in contrast to conventional disk-planet interaction theory .
Using two and three-dimensional hydrodynamics simulations to perform a systematic parameter survey , we confirm the existence of multiple spiral arms in disks with a single planet , and discover a scaling relation between the azimuthal separation of the primary and secondary arm , \phi _ { sep } , and the planet-to-star mass ratio q : \phi _ { sep } = 102 \degree ( q / 0.001 ) ^ { 0.2 } for companions between Neptune mass and 16 Jupiter masses around a 1 solar mass star , and \phi _ { sep } = 180 \degree for brown dwarf mass companions .
This relation is independent of the disk ’ s temperature , and can be used to infer a planet ’ s mass to within an accuracy of about 30 % given only the morphology of a face-on disk .
Combining hydrodynamics and Monte-Carlo radiative transfer calculations , we verify that our numerical measurements of \phi _ { sep } are accurate representations of what would be measured in near-infrared scattered light images , such as those expected to be taken by Gemini/GPI , VLT/SPHERE , or Subaru/SCExAO in the future .
Finally , we are able to infer , using our scaling relation , that the planet responsible for the spiral structure in SAO 206462 has a mass of about 6 Jupiter masses .