# Different dust and gas radial extents in protoplanetary disks: consistent models of grain growth and CO emission

## TL;DR

This study models the dust and gas distributions in protoplanetary disks, showing that differences in their radial extents are mainly due to optical depth effects, with implications for interpreting ALMA observations.

## Contribution

It introduces a comprehensive model combining dust evolution and radiative transfer to explain dust and gas size discrepancies without solely relying on radial drift.

## Key findings

- Gas and dust sizes differ mainly due to optical depth effects.
- Grain growth and settling thermally decouple gas and dust components.
- Model successfully reproduces CO snowline in HD 163296 using ice mixture binding energy.

## Abstract

ALMA observations of protoplanetary disks confirm earlier indications that there is a clear difference between the dust and gas radial extents. The origin of this difference is still debated, with both radial drift of the dust and optical depth effects suggested in the literature. In this work, the feedback of realistic dust particle distributions onto the gas chemistry and molecular emissivity is investigated, with a particular focus on CO isotopologues. The radial dust grain size distribution is determined using dust evolution models that include growth, fragmentation and radial drift. A new version of the code DALI is used to take into account how dust surface area and density influence the disk thermal structure, molecular abundances and excitation. The difference of dust and gas radial sizes is largely due to differences in the optical depth of CO lines and millimeter continuum, without the need to invoke radial drift. The effect of radial drift is primarily visible in the sharp outer edge of the continuum intensity profile. The gas outer radius probed by $^{12}$CO emission can easily differ by a factor of $\sim 2$ between the models for a turbulent $\alpha$ ranging between typical values. Grain growth and settling concur in thermally decoupling the gas and dust components, due to the low collision rate with large grains. As a result, the gas can be much colder than the dust at intermediate heights, reducing the CO excitation and emission, especially for low turbulence values. Also, due to disk mid-plane shadowing, a second CO thermal desorption (rather than photodesorption) front can occur in the warmer outer mid-plane disk. The models are compared to ALMA observations of HD 163296 as a test case. In order to reproduce the observed CO snowline of the system, a binding energy for CO typical of ice mixtures needs to be used rather than the lower pure CO value.