Inferring Planet Mass from Spiral Structures in Protoplanetary Disks

Abstract: 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, $\phi_{\rm sep}$, and the planet-to-star mass ratio $q$: $\phi_{\rm sep} = 102^{\circ} (q/0.001)^{0.2}$ for companions between Neptune mass and 16 Jupiter masses around a 1 solar mass star, and $\phi_{\rm sep} = 180^{\circ}$ 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 $\phi_{\rm sep}$ 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.