Measuring turbulence in TW Hydrae with ALMA: methods and limitations

Aims. We aim to obtain a spatially resolved measurement of velocity dispersions in the disk of TW Hya. Methods. We obtained images with high spatial and spectral resolution 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 was derived with two direct methods and one modelling approach. The first method requires a single transition and derives Tex directly from the line profile, yielding a v turb. The second method assumes that two different molecules are co-spatial, which allows using their relative line widths for calculating T-kin and v(turb). Finally we fitted a parametric disk model in which the physical properties of the disk are described by power laws, to compare our direct methods with previous values. Results. The two direct methods were limited to the outer r > 40 au disk because of beam smear. The direct method found v turb to range from approximate to 130 ms(-1) at 40 au, and to drop to approximate to 50 ms(-1) in the outer disk, which is qualitatively recovered with the parametric model fitting. This corresponds to roughly 0 : 2 0 : 4 c(s). CN was found to exhibit strong non-local thermal equilibrium effects outside r approximate to 140 au, so that v turb was limited to within this radius. The assumption that CN and CS are co-spatial is consistent with observed line widths only within r less than or similar to 100 au, within which v turb was found to drop from 100 ms 1 (approximate to 0.4 c(s)) to zero at 100 au. The parametric model yielded a nearly constant 50 ms(-1) 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. Conclusions. The magnitude of the dispersion is comparable with or below that predicted by the magneto-rotational instability theory. A more precise comparison would require reaching an absolute calibration precision of about 3%, or finding a suitable combination of light and heavy molecules that are co-located in the disk.