A Thermodynamic View of Dusty Protoplanetary Disks

Abstract

Small solids embedded in gaseous protoplanetary disks are subject to strong dust-gas friction. Consequently, tightly coupled dust particles almost follow the gas flow. This near conservation of the dust-to-gas ratio along streamlines is analogous to the near conservation of entropy along flows of (dust-free) gas with weak heating and cooling. We develop this thermodynamic analogy into a framework to study dusty gas dynamics in protoplanetary disks. We show that an isothermal dusty gas behaves like an adiabatic pure gas, and that finite dust-gas coupling may be regarded as effective heating/cooling. We exploit this correspondence to deduce that (1) perfectly coupled, thin dust layers cannot cause axisymmetric instabilities; (2) radial dust edges are unstable if the dust is vertically well-mixed; (3) the streaming instability necessarily involves a gas pressure response that lags behind dust density; and (4) dust-loading introduces buoyancy forces that generally stabilize the vertical shear instability associated with global radial temperature gradients. We also discuss dusty analogs of other hydrodynamic processes (e.g., Rossby wave instability, convective overstability, and zombie vortices) and how to simulate dusty protoplanetary disks with minor tweaks to existing codes for pure gas dynamics.

How Efficient Is the Streaming Instability in Viscous Protoplanetary Disks?

“…In addition to the full, two-fluid treatment of dusty gas described above, we also supplement some of our calculations with the 'one-fluid' model of dusty gas first described by Laibe & Price (2014); Price & Laibe (2015) and further developed by Lin & Youdin (2017). In Appendix A we extend the one-fluid model to include dust diffusion and non-linear drag laws and compare it with the full two-fluid treatment.…”

“…Here we describe the 'one-fluid' model of dusty gas developed by Lin & Youdin (2017), based on the earlier studies of Laibe & Price (2014) and Price & Laibe (2015). We extend these models by including dust diffusion, but neglect gas viscosity for simplicity (see Lovascio & Paardekooper 2019, for a viscous, but diffusionless version of the one-fluid model).…”

“…A26 agrees with Eq. 97 of Lin & Youdin (2017) in the diffusionless limit with Epstein drag (D = b = 0) and |n| 1. The latter dispersion relation was also derived by Jacquet et al (2011), Laibe & Price (2014), and is consistent with the original SI analysis of YG05.…”

The coexistence of the streaming instability and the vertical shear instability in protoplanetary disks

“…However, Lin & Youdin (2017) and Lin (2019) show that, if the drag back-reaction of the dust onto the gas is taken into account as well, the dust, which sediments to the mid-plane, introduces an effective vertical buoyancy -it "weighs down" the gas -that can quench the vertical shear instability. If they are tightly coupled, gas and dust can be described as a single fluid, with a density equal to the sum of the gas and the dust density, but a pressure that is solely due to the gas.…”

The resonant drag instability of dust streaming in turbulent protoplanetary disc

“…For example, Lin (2019) showed that the dust backreaction on gas partially suppresses the hydrodynamic turbulence generated by the vertical shear instability. This is caused by the additional stabilising buoyancy produced by solids, see Lin & Youdin (2017). From the other side, it is possible to estimate τ , when the effective viscosity or/and diffusivity suppress RDI caused by the dust settling.…”