The role of detailed gas and dust opacities in shaping the evolution of the inner disc edge subject to episodic accretion

TL;DR

This work analyzes how detailed gas and dust opacities, including frequency-dependent irradiation, shape the inner regions of protoplanetary discs and their episodic MRI-driven outbursts. By implementing DIANA dust opacities and Malygin gas opacities in a 2D axisymmetric radiation hydrodynamics framework with accretion luminosity feedback, the authors show that gas opacities move the DZIE and dust sublimation fronts inward, while dust opacities dominate the thermodynamics of the burst cycle. The frequency-bin irradiation introduces an equilibrium temperature degeneracy, alters the two-regime thermal structure, and shifts the location of key surfaces, leading to notable changes in the inner disc’s density structure and S-curves. Despite these changes, the periodic MRI-driven instability persists, though its detailed evolution and stability in non-axisymmetric settings require 3D modelling and more comprehensive thermo-chemical treatments; observational implications, such as enhanced near-IR emission and potential line features, warrant further study.

Abstract

We investigate the effects of different dust and gas opacity descriptions on the structure and evolution of the inner regions of protoplanetary discs. The influence on the episodic instability of the inner rim is hereby of central interest. 2D axisymmetric radiation hydrodynamic models are employed to simulate the evolution of the inner disc over several thousand years. Our simulations greatly expand on previous models by implementing detailed opacity descriptions in terms of their mean and frequency-dependent values, allowing us to also consider binned frequency-dependent irradiation. The adaptive opacity description significantly affects the structure of the inner disc rim, with gas opacities exerting the greatest influence. The resulting effects include shifts in the position of both the dust sublimation front and the dead zone inner edge, a significantly altered temperature in the dust-free region and the manifestation of an equilibrium temperature degeneracy as a sharp temperature transition. The episodic instability due to MRI activation in the dead zone still occurs, but at lower inner disc densities. While the gas opacities set the initial conditions for the instability, the evolution of the outburst itself is mainly governed by the dust opacities. The analysis of criteria for non-axisymmetric instabilities reveals possible breaking of the density peaks produced by the burst. However, due to the periodicity of the instability, the inner edge itself may remain stable throughout quiescent phases according to linear criteria. Although the thermal structure of the inner disc is crucially affected by different opacity descriptions, the mechanism of the periodic instability of the DZIE remains active and is only marginally influenced by gas opacities. The observational consequences of the severely altered temperatures may be significant and require further investigation.

Figures (15)

• Figure 1: Planck (panels a and b) and Rosseland (panels c and d) mean opacities used in our models. Panels (a) and (c) show maps of the temperature- and pressure-dependent gas mean opacities. The pink lines represent the dust mean opacities as functions of temperature. Panels (b) and (d) show the final effective mean opacities with the lime-coloured contour indicating the dust sublimation temperature, $T_\mathrm{S}$, for each pressure value. The white and black dots mark the temperature--pressure pairs that occur in our simulations, representing a snapshot of the quiescent and the outburst stage, respectively.
• Figure 2: Frequency-dependent gas and dust opacities in relation to the irradiating black body spectrum of the central star. The black lines indicate the Planck function of the irradiation, where the dash-dotted line represents the star during the quiescent phase (with negligible contribution from the accretion luminosity), whereas the dashed line shows the irradiating spectrum that includes the effect of the maximum accretion luminosity occurring in our models. The separation of the frequency space into the 50 bins is indicated by the thin vertical lines, where each bin is coloured according to its relative spectral weight. The orange crosses mark the dust opacities in their respective bins, multiplied by the maximum dust-to-gas mass ratio $f_0$. The gas opacities in each bin have been evaluated for a density of $10^{-10}\,\mathrm{g\,cm^{-3}}$ and are shown for two representative temperatures: 1000 K (blue crosses) and 3000 K (magenta crosses).
• Figure 3: Comparison between the models $\texttt{MREF}^*$ and DUST. Panel (a) shows a map of the temperature difference between the two models at a stage when the MRI active region has reached its largest extent during a burst. The black, green and magenta contour lines represent the MRI transition, the dust sublimation front and the $\tau_\mathrm{rad}=1$ surface, respectively, where the dashed lines correspond to DUST and the solid lines to $\texttt{MREF}^*$. Panels (b) and (c) show the surface density and the total vertical optical depth, respectively, of both models at two different stages: the initial hydrostatic structure (blue) and the state after the initial burst, when most of the density bumps have diffused (red).
• Figure 4: Differences between the models DUST and FULL during quiescence (panel a) and outburst (panel b). The coloured contour lines represent the same transitions as in Fig. \ref{['fig:MREF_DUST_diff']}, with the solid lines corresponding to DUST and the dashed lines to FULL. The upper halves of the panels show the differences in temperature between the two models, while the lower halves depict the absolute temperature of DUST.
• Figure 5: Evolution of the outburst in the FULL model compared to $\texttt{MREF}^*$. The different columns correspond to different evolutionary stages, starting from the ignition of the burst at $t=t_\mathrm{TI}$, chronologically proceeding through the burst stage and ending with the beginning of the next quiescent state at $t=t_\mathrm{quies}$. The top row shows the temperature maps of FULL with the black and green contour lines marking the MRI-transition and the dust sublimation front. The middle row depicts the surface densities for both $\texttt{MREF}^*$ and FULL at the same stages during their respective evolution. The vertical dotted lines in the first panel indicate the locations of the DZIE in the corresponding model of the same colour. The panels in the second, third and fourth column also show the respective profiles of $\Sigma_\mathrm{min}^\mathrm{crit}$ together with a reference power law profile of $r^{0.7}$. The bottom row represents the aspect ratios $H/r$ of both models. The $r^{1/4}$ profile indicates the slope of $H/r$ in the outer disc (>2 AU). In the high-state regions, an additional reference profile of $r^{0.48}$ is shown.