Turbulence is a fundamental parameter in models of grain growth during the early stages of planet formation .
As such , observational constraints on its magnitude are crucial .
Here we self-consistently analyze ALMA CO ( 2-1 ) , SMA CO ( 3-2 ) , and SMA CO ( 6-5 ) observations of the disk around TW Hya and find an upper limit on the turbulent broadening of < 0.08c _ { s } ( \alpha < 0.007 for \alpha defined only within 2-3 pressure scale heights above the midplane ) , lower than the tentative detection previously found from an analysis of the CO ( 2-1 ) data .
We examine in detail the challenges of image plane fitting vs directly fitting the visibilities , while also considering the role of the vertical temperature gradient , systematic uncertainty in the amplitude calibration , and assumptions about the CO abundance , as potential sources of the discrepancy in the turbulence measurements .
These tests result in variations of the turbulence limit between < 0.04c _ { s } and < 0.13c _ { s } , consistently lower than the 0.2-0.4c _ { s } found previously .
Having ruled out numerous factors , we restrict the source of the discrepancy to our assumed coupling between temperature and density through hydrostatic equilibrium in the presence of a vertical temperature gradient and/or the confinement of CO to a thin molecular layer above the midplane , although further work is needed to quantify the influence of these prescriptions .
Assumptions about hydrostatic equilibrium and the CO distribution are physically motivated , and may have a small influence on measuring the kinematics of the gas , but they become important when constraining small effects such as the strength of the turbulence within a protoplanetary disk .