Jonathan Squire

Statistical simulation of the magnetorotational dynamo

Turbulence and dynamo induced by the magnetorotational instability (MRI) are analyzed using quasilinear statistical simulation methods. It is found that homogenous turbulence is unstable to a large-scale dynamo instability, which saturates to an inhomogenous equilibrium with a strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the dependence of the angular momentum transport on Pm in the quasilinear model is qualitatively similar to that of nonlinear MRI turbulence. This demonstrates the importance of the large-scale dynamo and suggests how dramatically simplified models may be used to gain insight into the astrophysically relevant regimes of very low or high Pm.

The dynamics of charged dust in magnetized molecular clouds

We study the dynamics of large, charged dust grains in turbulent giant molecular clouds (GMCs). Massive dust grains behave as aerodynamic particles in primarily neutral dense gas, and thus are able to produce dramatic small-scale fluctuations in the dust-to-gas ratio. Hopkins & Lee directly simulated the dynamics of neutral dust grains in supersonic magnetohydrodynamic turbulence, typical of GMCs, and showed that the dust-to-gas fluctuations can exceed factor ∼1000 on small scales, with important implications for star formation, stellar abundances and dust behaviour and growth. However, even in primarily neutral gas in GMCs, dust grains are negatively charged and Lorentz forces are non-negligible. Therefore, we extend our previous study by including the effects of Lorentz forces on charged grains (in addition to drag). For small-charged grains (sizes ≪ 0.1 μm), Lorentz forces suppress dust-to-gas ratio fluctuations, while for large grains (sizes ≳ 1 μm), Lorentz forces have essentially no effect, trends that are well explained with a simple theory of dust magnetization. In some special intermediate cases, Lorentz forces can enhance dust–gas segregation. Regardless, for the physically expected scaling of dust charge with grain size, we find the most important effects depend on grain size (via the drag equation) with Lorentz forces/charge as a second-order correction. We show that the dynamics we consider are determined by three dimensionless numbers in the limit of weak background magnetic fields: the turbulent Mach number, a dust drag parameter (proportional to grain size) and a dust Lorentz parameter (proportional to grain charge); these allow us to generalize our simulations to a wide range of conditions.

Scaling laws of passive-scalar diffusion in the interstellar medium

Passive-scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the fundamental scaling laws remain poorly understood in the highly supersonic, magnetized, shearing regime relevant for the ISM. We therefore study the full scaling laws governing passive-scalar transport in idealized simulations of supersonic turbulence. Using simple phenomenological arguments for the variation of diffusivity with scale based on Richardson diffusion, we propose a simple fractional diffusion equation to describe the turbulent advection of an initial passive scalar distribution. These predictions agree well with the measurements from simulations, and vary with turbulent Mach number in the expected manner, remaining valid even in the presence of a large-scale shear flow (e.g. rotation in a galactic disc). The evolution of the scalar distribution is not the same as obtained using simple, constant ‘effective diffusivity’ as in Smagorinsky models, because the scale dependence of turbulent transport means an initially Gaussian distribution quickly develops highly non-Gaussian tails. We also emphasize that these are mean scalings that apply only to ensemble behaviours (assuming many different, random scalar injection sites): individual Lagrangian ‘patches’ remain coherent (poorly mixed) and simply advect for a large number of turbulent flow-crossing times.

Resonant drag instabilities in protoplanetary discs: the streaming instability and new, faster growing instabilities

We identify and study a number of new, rapidly growing instabilities of dust grains in protoplanetary discs, which may be important for planetesimal formation. The study is based on the recognition that dust–gas mixtures are generically unstable to a resonant drag instability (RDI), whenever the gas, absent dust, supports undamped linear modes. We show that the ‘streaming instability’ is an RDI associated with epicyclic oscillations; this provides simple interpretations for its mechanisms and accurate analytic expressions for its growth rates and fastest growing wavelengths. We extend this analysis to more general dust streaming motions and other waves, including buoyancy and magnetohydrodynamic oscillations, finding various new instabilities. Most importantly, we identify the disc ‘settling instability,’ which occurs as dust settles vertically into the mid-plane of a rotating disc. For small grains, this instability grows many orders of magnitude faster than the standard streaming instability, with a growth rate that is independent of grain size. Growth time scales for realistic dust-to-gas ratios are comparable to the disc orbital period, and the characteristic wavelengths are more than an order of magnitude larger than the streaming instability (allowing the instability to concentrate larger masses). This suggests that in the process of settling, dust will band into rings then filaments or clumps, potentially seeding dust traps, high-metallicity regions that in turn seed the streaming instability, or even overdensities that coagulate or directly collapse to planetesimals.

Ubiquitous instabilities of dust moving in magnetized gas

Squire & Hopkins showed that coupled dust–gas mixtures are generically subject to ‘resonant drag instabilities’ (RDIs), which drive violently growing fluctuations in both. But the role of magnetic fields and charged dust has not yet been studied. We therefore explore the RDI in gas that obeys ideal MHD and is coupled to dust via both Lorentz forces and drag, with an external acceleration (e.g. gravity, radiation) driving dust drift through gas. We show this is always unstable, at all wavelengths and non-zero values of dust-to-gas ratio, drift velocity, dust charge, ‘stopping time’ or drag coefficient (for any drag law), or field strength; moreover, growth rates depend only weakly (sub-linearly) on these parameters. Dust charge and magnetic fields do not suppress instabilities, but give rise to a large number of new instability ‘families,’ each with distinct behavior. The ‘MHD-wave’ (magnetosonic or Alfven) RDIs exhibit maximal growth along ‘resonant’ angles where the modes have a phase velocity matching the corresponding MHD wave, and growth rates increase without limit with wavenumber. The ‘gyro’ RDIs are driven by resonances between drift and Larmor frequencies, giving growth rates sharply peaked at specific wavelengths. Other instabilities include ‘acoustic’ and ‘pressure-free’ modes (previously studied), and a family akin to cosmic ray instabilities that appear when Lorentz forces are strong and dust streams super-Alfvenically along field lines. We discuss astrophysical applications in the warm ISM, circum-galactic medium/inter-galactic medium (CGM/IGM), H II regions, SNe ejecta/remnants, Solar corona, cool-star winds, GMCs, and AGN.

The Resonant Drag Instability (RDI): Acoustic Modes

Recently, Squire & Hopkins showed any coupled dust–gas mixture is subject to a class of linear ‘resonant drag instabilities’ (RDI). These can drive large dust-to-gas ratio fluctuations even at arbitrarily small dust-to-gas mass ratios μ. Here, we identify and study both resonant and new non-resonant instabilities, in the simple case where the gas satisfies neutral hydrodynamics and supports acoustic waves (ω^2=c^2_sk^2). The gas and dust are coupled via an arbitrary drag law and subject to external accelerations (e.g. gravity, radiation pressure). If there is any dust drift velocity, the system is unstable. The instabilities exist for all dust-to-gas ratios μ and their growth rates depend only weakly on μ around resonance, as ∼μ^(1/3) or ∼μ^(1/2) (depending on wavenumber). The behaviour changes depending on whether the drift velocity is larger or smaller than the sound speed cs. In the supersonic regime, a ‘resonant’ instability appears with growth rate increasing without limit with wavenumber, even for vanishingly small μ and values of the coupling strength (stopping time). In the subsonic regime, non-resonant instabilities always exist, but their growth rates no longer increase indefinitely towards small wavelengths. The dimensional scalings and qualitative behaviour of the instability do not depend sensitively on the drag law or equation of state of the gas. The instabilities directly drive exponentially growing dust-to-gas-ratio fluctuations, which can be large even when the modes are otherwise weak. We discuss physical implications for cool-star winds, AGN-driven winds and torii, and starburst winds: the instabilities alter the character of these outflows and could drive clumping and/or turbulence in the dust and gas.