Measuring turbulence in TW Hydrae with ALMA: methods and limitations^⋆

¹ Max-Planck-Institut für Astronomie, Königstuhl 17 69117 Heidelberg Germany
e-mail: teague@mpia.de
² Univ. Bordeaux, LAB, UMR 5804, 33270 Floirac, France
³ CNRS, LAB, UMR 5804, 33270 Floirac, France
⁴ IRAM, 300 rue de la Piscine, Domaine Universitaire, 38406 Saint-Martin-d’ Hères, France
⁵ SETI Institute, 189 Bernardo Avenue, Mountain View, CA 94043, USA
⁶ NASA Ames Research Center, Moffett Field, CA 94035, USA

Received: 18 March 2016
Accepted: 30 May 2016

Abstract

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 T_ex 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 ≈130 m s^-1 at 40 au, and to drop to ≈50 m s^-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 ≈ 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 ≲ 100 au, within which v_turb was found to drop from 100 m s^-1 (≈0.4 c_s) to zero at 100 au. The parametric model yielded a nearly constant 50 m s^-1 for CS (0.2−0.4 c_s). 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.