Measuring turbulence in TW Hydrae with ALMA: methods and limitations

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.

Radiation Hydrodynamical Turbulence in Protoplanetary Disks: Numerical Models and Observational Constraints

“…By carefully investigating for CO, CN and CS observations of the disk system TW Hya, Teague et al (2016) found an upper limit of the turbulence causing line broadening, consistent with v turb ≤ 0.2c s . Another ALMA observation of the disk HD 163296 in different CO lines by Flaherty et al (2015) supports the general finding of relatively low turbulent velocities in the disk.…”

A Surface Density Perturbation in the TW Hydrae Disk at 95 au Traced by Molecular Emission

“…Within this radius the continuum emission dominates the weaker CS emission, thus continuum subtrac- tion may affect the assumed inner radii of CS. Outside of this, the emission falls off and is detected to ∼ 3.7 (Teague et al 2016), comparable to that of CO and scattered light (Andrews et al 2012;Debes et al 2013). …”

“…The change in density structure and Elsasser number over this boundary forms axisymmetric zonal flows, carving the gap. A measurement of the radial extent of the dead-zone (or confirmation of its presence) would provide a great test for this instability, however previous analyses of the ionization and turbulent velocity structures have yet to detect the edge (Cleeves et al 2015b;Teague et al 2016). Furthermore, Flock et al (2015) note that no structure is seen in simulated scattered light images, contrary to the case for TW Hya.…”

“…In the modelling we assumed a turbulent broadening component of v turb = 0.3c s where c s is the local soundspeed (Teague et al 2016). The collisional rates for CS were taken from Lique et al (2010), stored in the LAMDA database 3 .…”

The Emerging Paradigm of Pebble Accretion

“…In that case the midplane-relevant here-stays laminar. Given these uncertaintiesindeed˛T is very hard to constrain observationally (Teague et al 2016)-it is best to consider˛T as a free parameter and test how it affects the pebble accretion rates.…”