Observational Signatures of Tightly Wound Spirals Driven by Buoyancy Resonances in Protoplanetary Disks

Abstract

Besides the spirals induced by the Lindblad resonances, planets can generate a family of tightly wound spirals through buoyancy resonances. The excitation of buoyancy resonances depends on the thermal relaxation timescale of the gas. By computing timescales of various processes associated with thermal relaxation, namely, radiation, diffusion, and gas-dust collision, we show that the thermal relaxation in protoplanetary disks' surface layers ($Z/R\gtrsim0.1$) and outer disks ($R\gtrsim100$ au) is limited by infrequent gas-dust collisions. The use of isothermal equation of state or rapid cooling, common in protoplanetary disk simulations, is therefore not justified. Using three-dimensional hydrodynamic simulations, we show that the collision-limited slow thermal relaxation provides favorable conditions for buoyancy resonances to develop. Buoyancy resonances produce predominantly vertical motions, whose magnitude at the $^{12}$CO emission surface is of order of $100~{\rm m~s}^{-1}$ for Jovian-mass planets, sufficiently large to detect using molecular line observations with ALMA. We generate synthetic observations and describe characteristic features of buoyancy resonances in Keplerian-subtracted moment maps and velocity channel maps. Based on the morphology and magnitude of the perturbation, we propose that the tightly wound spirals observed in TW Hya could be driven by a (sub-)Jovian-mass planet at 90 au. We discuss how non-Keplerian motions driven by buoyancy resonances can be distinguished from those driven by other origins. We argue that observations of multiple lines tracing different heights, with sufficiently high spatial/spectral resolution and sensitivity to separate the emission arising from the near and far sides of the disk, will help constrain the origin of non-Keplerian motions.