A self-consistent model for dust settling and the vertical shear instability in protoplanetary disks

Fukuhara, Yuya; Okuzumi, Satoshi

doi:10.1093/pasj/psae042

Cited by 2 publications

(1 citation statement)

References 85 publications

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“…If the grains are large and the cooling times are long, it would be possible that the VSI is not able to develop in the first place or is not able to counteract the settling of the grains. Work by Fukuhara et al (2023) and Fukuhara & Okuzumi (2024) has demonstrated that an equilibrium state might be possible in which the turbulent mixing of the VSI exactly counteracts sedimentation. Their studies are based on a semi-analytic model of the VSI turbulence and assume constant settling-mixing equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Vertical shear instability with dust evolution and consistent cooling times

Pfeil,

Birnstiel,

Klahr

2024

A&A

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Context. Gas in protoplanetary disks mostly cools via thermal accommodation with dust particles. Thermal relaxation is thus highly sensitive to the local dust size distributions and the spatial distribution of the grains. So far, the interplay between thermal relaxation and gas turbulence has not been dynamically modeled in hydrodynamic simulations of protoplanetary disks with dust. Aims. We aim to study the effects of the vertical shear instability (VSI) on the thermal relaxation times, and vice versa. We are particularly interested in the influence of the initial dust grain size on the VSI and whether the emerging turbulence is sustained over long timescales. Methods. We ran three axisymmetric hydrodynamic simulations of a protoplanetary disk including four dust fluids that initially resemble MRN size distributions of different initial grain sizes. From the local dust densities, we calculated the thermal accommodation timescale of dust and gas and used the result as the thermal relaxation time of the gas in our simulation. We included the effect of dust growth by applying the monodisperse dust growth rate and the typical growth limits. Results. We find that the emergence of the VSI is strongly dependent on the initial dust grain size. Coagulation also counteracts the emergence of hydrodynamic turbulence in our simulations, as shown by others before. Starting a simulation with larger grains (100 μm) generally leads to a less turbulent outcome. While the inner disk regions (within ∼70 au) develop turbulence in all three simulations, we find that the simulations with larger particles do not develop VSI in the outer disk. Conclusions. Our simulations with dynamically calculated thermal accommodation times based on the drifting and settling dust distribution show that the VSI, once developed in a disk, can be sustained over long timescales, even if grain growth is occurring. The VSI corrugates the dust layer and even diffuses the smaller grains into the upper atmosphere, where they can cool the gas. Whether the instability can emerge for a specific stratification depends on the initial dust grain sizes and the initial dust scale height. If the grains are initially ≳100 μm and if the level of turbulence is initially assumed to be low, we find no VSI turbulence in the outer disk regions.

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Section: Introductionmentioning

confidence: 99%

Vertical shear instability with dust evolution and consistent cooling times

Pfeil,

Birnstiel,

Klahr

2024

A&A

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Modeling protoplanetary disk heating by planet-induced spiral shocks

Ono,

Okamura,

Okuzumi

et al. 2024

Publications of the Astronomical Society of Japan

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We investigate the heating of protoplanetary disks caused by shocks associated with spiral density waves induced by an embedded planet. Using two-dimensional hydrodynamical simulations, we explore the dependence of shock heating rates on various disk and planetary parameters. Our results show that the shock heating rates are primarily influenced by the planet’s mass and the disk’s viscosity, while being insensitive to the thermal relaxation rate and the radial profiles of the disk’s surface density and sound speed. We provide universal empirical formulas for the shock heating rates produced by the primary and secondary spiral arms as a function of orbital radius, viscosity parameter $\alpha$, and planet-to-star mass ratio $q$. The obtained formulas are accurate within a factor of a few for a moderately viscous and adiabatic disk with a planet massive enough that its spiral arms are strongly nonlinear. Using these universal relations, we show that shock heating can overwhelm viscous heating when the disk viscosity is low ($\alpha \lesssim 10^{-3}$) and the planet is massive ($q \gtrsim 10^{-3}$). Our empirical relations for the shock heating rates are simple and can be easily implemented into radially one-dimensional models of gas and dust evolution in protoplanetary disks.

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A self-consistent model for dust settling and the vertical shear instability in protoplanetary disks

Cited by 2 publications

References 85 publications

Vertical shear instability with dust evolution and consistent cooling times

Vertical shear instability with dust evolution and consistent cooling times

Modeling protoplanetary disk heating by planet-induced spiral shocks

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