Dust Morphology Under Changing Dust Mass Ratios in Protoplanetary Discs

Abstract

Protoplanetary disc mass is one of the most fundamental properties of a planet-forming system, as it sets the total mass budget available for planet formation. However, obtaining disc mass measurements remain challenging, since it is not possible to directly detect H$_2$, and CO abundance ratios are poorly constrained. Dynamical measurements of the disc mass are now possible, but they are not suited to all discs since the measurements typically require well-behaved emission surfaces. A long-standing method is to obtain continuum flux measurements from the dust emission, and convert to a total disc mass by assumption of the dust-to-gas mass ratio, $ε$. This quantity is poorly constrained in protoplanetary discs. % We investigate the impact of $ε$ on the morphology of planet-containing hydrodynamical simulations of dusty protoplanetary accretion discs, and suggest that if a planet mass estimate can be obtained, then disc morphology could be used to constrain $ε$ in observed systems relative to each other, improving the total disc mass estimates of protoplanetary discs.

Figures (8)

• Figure 1: Dust surface density of simulated discs with $a=0.1$mm. The left column is simulated with the back reaction, and the right column is simulated without the back reaction. Each row is a different $\epsilon$, increasing down the page and into Figure \ref{['fig:Sarracen2']}. At every simulated value of $\epsilon$, we see a remarkably different dust distribution. Discs without the back reaction have well defined outer edges at $\sim$100 au, and larger, higher density inner discs. Additionally, discs with and without the back reaction display different symmetries.
• Figure 2: Dust surface density of simulated discs with $a=0.1$mm. The left column is simulated with the back reaction, and the right column is simulated without the back reaction. The top row is $\epsilon = 0.10$ and the bottom row is $\epsilon = 0.50$. The disc that includes the back reaction and with $\epsilon=0.50$ has the least prominent gap of any of the discs simulated and also has smoothest overall distribution. Additionally, in these high $\epsilon$ simulation, the role of $\epsilon$ and the back reaction in gap closing is readily apparent. Simulations with the back reaction have gaps spanning a smaller azimuthal angle over all
• Figure 3: Measured gap depth at the planet location and gap maximum for all simulations. The top row is $\Delta\Sigma_\mathrm{dust}$ with the back reaction on and the bottom row is $\Delta\Sigma_\mathrm{dust}$ with the back reaction off. The left column shows results for constant grain size of a = $0.1$mm, and the right column shows results for constant St number of $0.1$. Data sets for St=0.1 with the back reaction is missing a point at $\epsilon=0.50$.
• Figure 4: Reduced surface densities of simulations with constant grain size of $a=0.1$ mm (left column) and constant St number of $0.1$ (right column). The location of each planet is plotted at its radius in the same color as the associated profile. Vertical displacement is solely to prevent overplotting in the case of planets being at approximately the same radius. In the bottom left plot, some behaviour of the $\epsilon=0.50$ profile is omitted to better visual more shallow gap profiles.
• Figure 5: Measured gap depth in dust density compared to the analytical prescription from tanaka_eccentric_2022 (Equation \ref{['eq:estimatedGap']}). In the simulations with constant grain size, gaps in dust are suppressed by the back reaction as $\epsilon$ increases (top left). Without the back reaction, gaps increase as $\epsilon$ increases (bottom left). Neither has good agreement with the analytical prescription. In the simulations with constant St number, there is an apparent regime transition around $\epsilon=0.10$ without the back reaction (bottom right). Unfortunately, $\epsilon=0.50$ was computationally prohibitive with the back reaction on, so it is unclear if that regime transition would be present there as well (top right). Overplotted in all plots except the bottom right is a fit of $\epsilon^{\xi}$ to the measured data. The value of $\xi$ is presented in the legend of the related scenario and characterizes how measured gap depths change with respect $\epsilon$ for a given scenario.