Probing disk cooling with time-dependent features

Measuring cooling times and fundamental disk properties, such as gas density and grain size, from how dust and gas respond to shadows

Shadows have now been seen in dozens of protoplanetary disks in near-infrared scattered light, cast by misaligned or warped inner disks. In some systems, such as HD 143006, matching dips also appear in the millimeter dust continuum and in molecular-line emission, likely tracing how the dust and gas temperatures respond to the missing starlight. This turns every shadowed disk into a natural thermodynamics experiment.

The science case

How quickly a disk heats and cools is one of its most important and least constrained properties. The cooling time controls which instabilities operate, such as the vertical shear instability, how planets open gaps and launch spirals, and how disks respond to shadows. Yet it is almost never measured directly.

As gas and dust orbit into and out of a shadow, they cool and then reheat. Dust is heated by starlight and cools radiatively; gas exchanges heat with the dust through collisions. The amplitude of the temperature dip, and the azimuthal phase lag between the shadow and the temperature response, therefore encode two timescales: the radiative cooling time and the dust–gas collisional coupling time, each compared with the time it takes to orbit through the shadow.

How dust and gas respond to a shadow. Stellar light scattered by dust sets the equilibrium temperature, which is reduced in the shadow (yellow). Dust heats and cools radiatively (green), and gas exchanges heat with the dust through collisions (blue), while orbital motion advects energy downstream. At the disk surface (top), the dust follows the shadow with no lag, while the gas lags by an amount set by the shorter of its collisional coupling and line-cooling times. In the midplane (bottom), the dust lags by its radiative cooling time βcont, and the gas lags further by the dust–gas collisional coupling time βcoll. Zhang, Ma et al. (submitted).

Because these timescales depend on the gas density and on the size of the dust grains, measuring them gives a new, thermodynamical way to weigh disks and to constrain grain sizes, independent of the usual dust-continuum arguments. With PhD student Xiaoyi Ma (KIAA, Peking University), Jane Huang, Zhaohuan Zhu, and Simon Casassus, I developed a fast framework that predicts the thermal response of dust and gas to a shadow and identifies distinct response regimes set by the hierarchy of these timescales (Zhang et al., 2026).

Testing the framework against radiation hydrodynamics

Left: gas temperature response in Athena++ radiation-hydrodynamical simulations of a disk with a shadow, for rotation rates from Ω = 0 to 10 ΩK; the white line marks where the temperature dip lies, which shifts further downstream as the gas orbits faster through the shadow. Right: the measured phase lag of the gas temperature against the radiative cooling time βcont,g (in units of the orbital time), for different rotation rates, surface densities, and opacities, compared with the framework's analytic predictions (lines). Zhang, Ma et al. (submitted).

What comes next

Measurements of shadow depth and phase lag in scattered light, millimeter continuum, and molecular-line temperature maps can now be turned into constraints on cooling times, gas densities, and grain sizes. Moving shadows add a new dimension: as Gaia DR4 and multi-epoch imaging reveal how shadows rotate, the same framework links shadow motion to the inner disks that cast them. See machine learning and AI-assisted inference for how I plan to measure shadow motions across many disks.

References

2026

  1. Submitted
    Thermal Response of Dust and Gas to Shadows in Protoplanetary Disks I: A Beta-Cooling Framework
    Shangjia Zhang, Xiaoyi Ma, Jane Huang, Zhaohuan Zhu, and Simon Casassus
    Submitted to ApJ, Aug 2026