Planet formation at the inner edge of the dead zone -- I: the interplay between accretion outbursts and dust growth

Abstract

The inner edge of the dead zone in protoplanetary disks has been shown to periodically go unstable, leading to accretion outbursts and annular substructure within the dead zone. While dust opacities play a key role in this process, the thermal and dynamical effects of dust drift and growth have not been fully explored. We investigate the evolution of accretion outbursts in the inner disk and their impact on the formation of dust-rich substructure with a fully dynamic dust model. In doing so, we aim to highlight the importance and limitations of dust growth in forming planets in this region. We carry out radiation hydrodynamics simulations of a protoplanetary disk including prescriptions for the structure of the inner edge of the dead zone, viscous and irradiation heating, radiative cooling, dust-gas dynamics, and dust evolution. We find that accretion outbursts at the inner disk edge can lead to the formation of multiple dust rings that extend deep inside the dead zone (~1 au) and diffuse on viscous timescales (~10 kyr for $α$=1e-4). The rings contain dust masses of up to ~1.6 Earth masses, possibly kickstarting planet formation. Dynamic modeling of dust fragmentation enhances the total opacity during the burst, yielding more intense outbursts that penetrate deeper into the dead zone. Our results highlight the thermal and dynamical importance of treating dust dynamics self-consistently in models of accretion outbursts. Additional modeling is needed to characterize the inevitable non-axisymmetric structures arising from accretion outbursts and their observational prospects.

Figures (16)

• Figure 1: "S-curve" of the gas surface density versus temperature at $R=0.3$ au for our fiducial model, discussed in detail in Sect. \ref{['sub:results-fiducial-model']}---1: runaway heating is triggered at the DZIE; 2: burst front passes through; 3: dust sublimation caps temperature during burst; 4: dust recondensation; 5: dust cooling. Gray bands highlight the stable branches corresponding to viscous evolution in the quiescent (bottom) and burst (top) phases. Different colors denote reflares during the same burst cycle.
• Figure 2: Sample dust size distribution, represented with a truncated powerlaw with $q_\mathrm{dust}=-3.5$ and reconstructed with the TriPoD method of pfeil-etal-2024.
• Figure 3: Pre- (left) and post-burst (right) states of the gas surface density (top) and temperature (bottom) for different disk configurations computed using the method described in Sect. \ref{['sec:pre-post-constraints']}. Here, we assume constant dust opacities of $\kappa_\text{d}=700\,\text{cm}^2/\text{g}_\text{dust}$ (including $f_\text{subl}$ from Eq. \ref{['eq:fsubl']}). The mass accretion rate through the outer boundary is approximately $10^{-9}\,\mathrm{M}_\odot/\text{yr}\times\alpha_\text{DZ}/10^{-3}\times{\Sigma_\mathrm{g}}_0/200\,\text{g}/\text{cm}^2$. Dashed-dotted lines in the top panels have a slope $\propto R^{0.81}$---in good agreement with Eq. \ref{['eq:sigma-min-approx']}---and help guide the eye, while in the bottom panels they represent the irradiation temperature.
• Figure 4: Radius--time heatmaps of the gas surface density (top), temperature (middle), and maximum dust grain size (bottom) as functions of radius for our fiducial model with $\alpha_\text{DZ}=10^{-3}$. The burst phase is highlighted with insets and marked with white boxes in the main panels, showcasing the emergence of reflares and substructures in the form of rings during the outburst. The rings diffuse away due to viscosity during the long quiescent phase between bursts.
• Figure 5: Top: accretion rate onto the star (through the inner radial boundary) and accretion luminosity as functions of time for our fiducial model. The inset zooms in on the narrow burst region highlighted in orange. The black line corresponds to exponential growth with an e-folding time of $\sim\!2.2$ kyr. Bottom: total stellar luminosity as a function of time.