Multi-wavelength observations of protoplanetary discs as a proxy for the gas disc mass

TL;DR

This study combines hydrodynamical and radiative transfer models to link observed disc substructures with gas surface density, enabling estimation of gas mass in protoplanetary discs based on multi-wavelength observations.

Contribution

It introduces a method to constrain local gas surface density in protoplanetary discs by modeling dust and scattered light observations, connecting substructure morphology to gas mass.

Findings

Small dust grains form spirals due to gas coupling.

Large grains show ring-like structures as they decouple from gas.

Observing ring-like structures in mm grains implies low gas surface density.

Abstract

Recent observations of protoplanetary discs reveal disc substructures potentially caused by embedded planets. We investigate how the gas surface density in discs changes the observed morphology in scattered light and dust continuum emission. Assuming that disc substructures are due to embedded protoplanets, we combine hydrodynamical modelling with radiative transfer simulations of dusty protoplanetary discs hosting planets. The response of different dust species to the gravitational perturbation induced by a planet depends on the drag stopping time - a function of the generally unknown local gas density. Small dust grains, being stuck to the gas, show spirals. Larger grains decouple, showing progressively more axisymmetric (ring-like) substructure as decoupling increases with grain size or with the inverse of the gas disc mass. We show that simultaneous modelling of scattered light and dust continuum emission is able to constrain the Stokes number, ${\rm St}$. Hence, if the dust properties are known, this constrains the local gas surface density, $\Sigma_{\rm gas}$, at the location of the structure, and hence the total gas mass. In particular, we found that observing ring-like structures in mm-emitting grains requires ${\rm St} \gtrsim 0.4$ and therefore $\Sigma_{\rm gas} \lesssim 0.4\,\textrm{g/cm}^{2}$. We apply this idea to observed protoplanetary discs showing substructures both in scattered light and in the dust continuum.