Thermal Wave Instability as an Origin of Gap and Ring Structures in Protoplanetary Disks

Abstract

Recent millimeter and infrared observations have shown that gap- and ring-like structures are common in both dust thermal emission and scattered light of protoplanetary disks. We investigate the impact of the so-called thermal wave instability (TWI) on the millimeter and infrared scattered light images of disks. We perform 1+1D simulations of the TWI and confirm that the TWI operates when the disk is optically thick enough for stellar light, i.e., small-grain-to-gas mass ratio of ≳0.0001. The midplane temperature varies as the waves propagate, and hence gap and ring structures can be seen in both millimeter and infrared emission. The millimeter substructures can be observed even if the disk is fully optically thick since it is induced by the temperature variation, while density-induced substructures would disappear in the optically thick regime. The fractional separation between TWI-induced ring and gap is Δr/r ∼ 0.2–0.4 at ∼10–50 au, which is comparable to those found by the Atacama Large Millimeter/submillimeter Array. Due to the temperature variation, snow lines of volatile species move radially and multiple snow lines are observed even for a single species. The wave propagation velocity is as fast as ∼0.6 au yr−1, which can be potentially detected with a multiepoch observation with a time separation of a few years.

A global two-layer radiative transfer model for axisymmetric, shadowed protoplanetary disks

“…Compared to the thermal waves observed in the simulations by Ueda et al (2021, see their figures 2 and 3), our thermal waves are less coherent and propagate inward on different timescales at different radial positions. This can be more clearly seen in figure 11, which shows a spacetime plot of the temperature distribution.…”

“…At r 30 au and r 0.3 au, the thermal wave instability is suppressed for different reasons. In the outer region of r 30 au, the external radiation flux σ SB T 4 ex is comparable to or even dominates over the reprocessed starlight flux F rep,↓ , directly suppressing the thermal wave instability (Ueda et al 2021). In the inner region of r 0.1 au, the finite size of the central star determines the starlight grazing angle (i.e., α * ≈ 4R * /(3πr); see equation ( 9)), which stabilizes the thermal wave instability as it is triggered by the variation of the stellar grazing angle with temperature fluctuations.…”

“…The second complication concerns the instabilities of disks' thermal structure. Dullemond (2000) and Watanabe & Lin (2008) showed that optically thick disks irradiated by the central star are unstable to self-shadowing in the limits of short and long thermal relaxation timescales, respectively (for a more recent study, see Siebenmorgen & Heymann 2012;Ueda et al 2021;Wu & Lithwick 2021). This instability, which we call the thermal wave instability after Watanabe & Lin (2008) 2 , is intrinsically related to the starlight's small grazing angle mentioned above: even a small hill on the irradiation surface can cast a shadow.…”

“…The radial computational domain ranges between 0.03 to 300 au and is divided into 480 logarithmically spaced cells, resulting in a radial resolution of dr/r = 0.019. The adopted radial resolution is two times better than in the simulation by Ueda et al (2021). In section 5.2.2, we also present simulation runs with lower resolution to study the convergence of our simulation results.…”

“…This instability, which we call the thermal wave instability after Watanabe & Lin (2008) 2 , is intrinsically related to the starlight's small grazing angle mentioned above: even a small hill on the irradiation surface can cast a shadow. The hill's starlit inner side warms and expands, while its shadowed outer side cools and contracts, so that the hill propagates towards the star (see figure 1 of Ueda et al 2021 andWu &Lithwick 2021 for a cartoon describing the mechanism of the instability). The surface waves generated by the instability produce the interior temperature's fluctuations that propagate inward on a timescale comparable to the local thermal relaxation timescale at the midplane.…”