Measuring Turbulence in TW Hya with ALMA

Measuring Turbulence in TW Hya with ALMA: Methods and Limitations

Authors:

Teague et al

Abstract:

We obtain high spatial and spectral resolution images of the CO J=2-1, CN N=2-1 and CS J=5-4 emission with ALMA in Cycle~2. The radial distribution of the turbulent broadening is derived with three approaches: two `direct' and one modelling. The first requires a single transition and derives \Tex{} directly from the line profile, yielding a \vturb{}. The second assumes two different molecules are co-spatial thus their relative linewidths allow for a calculation of \Tkin{} and \vturb{}. Finally we fit a parametric disk model where physical properties of the disk are described by power laws, to compare our `direct' methods with previous values. The two direct methods were limited to the outer r>40~au disk due to beam smear. The direct method found \vturb{} ranging from ≈~\vel{130} at 40~au, dropping to ≈~\vel{50} in the outer disk, qualitatively recovered with the parametric model fitting. This corresponds to roughly 0.2−0.4 cs. CN was found to exhibit strong non-LTE effects outside r≈140~au, so \vturb{} was limited to within this radius. The assumption that CN and CS are co-spatial is consistent with observed linewidths only within r≲100~au, within which \vturb{} was found to drop from \vel{100} (≈ 0.4 cs) to nothing at 100~au. The parametric model yielded a near constant \vel{50} for CS (0.2−0.4 cs). We demonstrate that absolute flux calibration is and will be the limiting factor in all studies of turbulence using a single molecule. The magnitude of the dispersion is comparable with or below that predicted by the magneto-rotational instability theory. A more precise comparison would require to reach an absolute calibration precision of order 3\%, or to find a suitable combination of light and heavy molecules which are co-located in the disk.