Gas versus dust sizes of protoplanetary discs: effects of dust evolution

¹ Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
e-mail: trapman@strw.leidenuniv.nl
² Max-Planck-Institute für Extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany
³ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei München, Germany
⁴ Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1090 GE Amsterdam, The Netherlands

Received: 27 November 2018
Accepted: 13 March 2019

Abstract

Context. The extent of the gas in protoplanetary discs is observed to be universally larger than the extent of the dust. This is often attributed to radial drift and grain growth of the millimetre grains, but line optical depth produces a similar observational signature.

Aims. We investigate in which parts of the disc structure parameter space dust evolution and line optical depth are the dominant drivers of the observed gas and dust size difference.

Methods. Using the thermochemical model DALI with dust evolution included we ran a grid of models aimed at reproducing the observed gas and dust size dichotomy.

Results. The relation between R_dust and dust evolution is non-monotonic and depends on the disc structure. The quantity R_gas is directly related to the radius where the CO column density drops below 10¹⁵ cm⁻² and CO becomes photodissociated; R_gas is not affected by dust evolution but scales with the total CO content of the disc. While these cases are rare in current observations, R_gas/R_dust > 4 is a clear sign of dust evolution and radial drift in discs. For discs with a smaller R_gas/R_dust, identifying dust evolution from R_gas/R_dust requires modelling the disc structure including the total CO content. To minimize the uncertainties due to observational factors requires FWHM_beam < 1× the characteristic radius and a peak S/N > 10 on the ¹²CO emission moment zero map. For the dust outer radius to enclose most of the disc mass, it should be defined using a high fraction (90–95%) of the total flux. For the gas, any radius enclosing >60% of the ¹²CO flux contains most of the disc mass.

Conclusions. To distinguish radial drift and grain growth from line optical depth effects based on size ratios requires discs to be observed at high enough angular resolution and the disc structure should to be modelled to account for the total CO content of the disc.