arXiv subjects

Jonathan Squire

Publications and source records attributed to Jonathan Squire.

At least 73 records · Page 4Linked to original sources

arXiv2018

Ubiquitous Instabilities of Dust Moving in Magnetized Gas

Squire & Hopkins (2017) 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 which 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 which appear when Lorentz forces are strong and dust streams super-Alfvenically along field lines. We discuss astrophysical applications in the warm ISM, CGM/IGM, HII regions, SNe ejecta/remnants, Solar corona, cool-star winds, GMCs, and AGN.

astro-ph.GA↗

arXiv2018

The Resonant Drag Instability (RDI): Acoustic Modes

Recently, Squire & Hopkins (2017) 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. 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 ($ω^{2}=c_{s}^{2}\,k^{2}$). 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 {\em all} dust-to-gas ratios $μ$ and their growth rates depend only weakly on $μ$ around resonance, as $\simμ^{1/3}$ or $\sim μ^{1/2}$ (depending on wavenumber). The behavior changes depending on whether the drift velocity is larger or smaller than the sound speed $c_{s}$. 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 behavior 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.

astro-ph.SR↗

arXiv2018

Nonlinear Evolution of the Resonant Drag Instability in Magnetized Gas

We investigate, for the first time, the nonlinear evolution of the magnetized "resonant drag instabilities" (RDIs). We explore magnetohydrodynamic (MHD) simulations of gas mixed with (uniform) dust grains subject to Lorentz and drag forces, using the GIZMO code. The magnetized RDIs exhibit fundamentally different behaviour than the purely acoustic RDIs. The dust organizes into coherent structures and the system exhibits strong dust-gas separation. In the linear and early nonlinear regime, the growth rates agree with linear theory and the dust self-organizes into two-dimensional planes or "sheets." Eventually the gas develops fully nonlinear, saturated Alfvénic and compressible fast-mode turbulence, which fills the under-dense regions with a small amount of dust, and drives a dynamo which saturates at equipartition of kinetic and magnetic energy. The dust density fluctuations exhibit significant non-Gaussianity, and the power spectrum is strongly weighted towards the largest (box-scale) modes. The saturation level can be understood via quasi-linear theory, as the forcing and energy input via the instabilities becomes comparable to saturated tension forces and dissipation in turbulence. The magnetized simulation presented here is just one case; it is likely that the magnetic RDIs can take many forms in different parts of parameter space.

astro-ph.GA↗

arXiv2018

Resonant Drag Instabilities in protoplanetary disks: the streaming instability and new, faster-growing instabilities

We identify and study a number of new, rapidly growing instabilities of dust grains in protoplanetary disks, 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 disk "settling instability," which occurs as dust settles vertically into the midplane of a rotating disk. 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 timescales for realistic dust-to-gas ratios are comparable to the disk 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.

astro-ph.EP↗

arXiv2018

Resonant drag instability of grains streaming in fluids

We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any fluid wave. The wave itself can be quite general--sound waves, magnetosonic waves, epicyclic oscillations, and Brunt-Väisälä oscillations each generate instabilities, for example. We derive a simple expression for the growth rates of these "resonant drag instabilities" (RDI). This expression (i) illustrates why such instabilities are so virulent and generic, and (ii) allows for simple analytic computation of RDI growth rates and properties for different fluids. As examples, we introduce several new instabilities, which could see application across a variety of physical systems from atmospheres to protoplanetary disks, the interstellar medium, and galactic outflows. The matrix-based resonance formalism we introduce can also be applied more generally in other (nonfluid) contexts, providing a simple means for calculating and understanding the stability properties of interacting systems.

astro-ph.EP↗

arXiv2017

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the "parasitic instabilities" that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in MHD). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

astro-ph.HE↗

arXiv2017

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 (2016) directly simulated the dynamics of neutral dust grains in super-sonic MHD 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 behavior 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 micron), Lorentz forces suppress dust-to-gas ratio fluctuations, while for large grains (sizes >1 micron), 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.

astro-ph.GA↗

arXiv2017

The distribution of density in supersonic turbulence

We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the density to be arranged into a collection of strong shocks of width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for $\mathcal{M}>1$ turbulence: the density probability distribution and its intermittency (deviation from log-normality), the density variance-Mach number relation, power spectra, and structure functions. For the proposed model parameters, reasonable agreement is seen between model predictions and numerical simulations, albeit within the large uncertainties associated with current simulation results. More generally, the model could provide a useful framework for more detailed analysis of future simulations and observational data. Due to the simple physical motivations for the model in terms of shocks, it is straightforward to generalize to more complex physical processes, which will be helpful in future more detailed applications to the ISM. We see good qualitative agreement between such extensions and recent simulations of non-isothermal turbulence.

astro-ph.GA↗

arXiv2017

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 disk). 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 only apply to ensemble behaviors (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.

astro-ph.GA↗

arXiv2017

Amplitude limits and nonlinear damping of shear-Alfvén waves in high-beta low-collisionality plasmas

This work, which extends Squire et al. [ApJL, 830 L25 (2016)], explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-beta plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, "interrupting" the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional "Braginskii" regime, for both standing and traveling waves. The focus is on simplified models in one dimension, on scales much larger than the ion gyroradius. The effect has interesting implications for the physics of magnetized turbulence in the high-beta conditions that are prevalent in many astrophysical plasmas.

physics.plasm-ph↗

arXiv2016

The magnetic shear-current effect: generation of large-scale magnetic fields by the small-scale dynamo

A novel large-scale dynamo mechanism, the magnetic shear-current effect, is discussed and explored. The effect relies on the interaction of magnetic fluctuations with a mean shear flow, meaning the saturated state of the small-scale dynamo can drive a large-scale dynamo -- in some sense the inverse of dynamo quenching. The dynamo is nonhelical, with the mean-field $α$ coefficient zero, and is caused by the interaction between an off-diagonal component of the turbulent resistivity and the stretching of the large-scale field by shear flow. Following up on previous numerical and analytic work, this paper presents further details of the numerical evidence for the effect, as well as an heuristic description of how magnetic fluctuations can interact with shear flow to produce the required electromotive force. The pressure response of the fluid is fundamental to this mechanism, which helps explain why the magnetic effect is stronger than its kinematic cousin, and the basic idea is related to the well-known lack of turbulent resistivity quenching by magnetic fluctuations. As well as being interesting for its applications to general high Reynolds number astrophysical turbulence, where strong small-scale magnetic fluctuations are expected to be prevalent, the magnetic shear-current effect is a likely candidate for large-scale dynamo in the unstratified regions of ionized accretion disks. Evidence for this is discussed, as well as future research directions and the challenges involved with understanding details of the effect in astrophysically relevant regimes.

astro-ph.HE↗

arXiv2015

Electromotive force due to magnetohydrodynamic fluctuations in sheared rotating turbulence

This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action -- the magnetic analogue of the "shear-current" effect. In addition, consideration of $α$ effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of $α$, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.

astro-ph.HE↗

arXiv2015

Generation of large-scale magnetic fields by small-scale dynamo in shear flows

We propose a new mechanism for turbulent mean-field dynamo in which the magnetic fluctuations resulting from a small-scale dynamo drive the generation of large-scale magnetic fields. This is in stark contrast to the common idea that small-scale magnetic fields should be harmful to large-scale dynamo action. These dynamos occur in the presence of large-scale velocity shear and do not require net helicity, resulting from off-diagonal components of the turbulent resistivity tensor as the magnetic analogue of the "shear-current" effect. Given the inevitable existence of non-helical small-scale magnetic fields in turbulent plasmas, as well as the generic nature of velocity shear, the suggested mechanism may help to explain generation of large-scale magnetic fields across a wide range of astrophysical objects.

astro-ph.SR↗

arXiv2015

Coherent nonhelical shear dynamos driven by magnetic fluctuations at low Reynolds numbers

Nonhelical shear dynamos are studied with a particular focus on the possibility of coherent dynamo action. The primary results -- serving as a follow up to the results of Squire & Bhattacharjee [arXiv:1506.04109 (2015)] -- pertain to the "magnetic shear-current effect" as a viable mechanism to drive large-scale magnetic field generation. This effect raises the interesting possibility that the saturated state of the small-scale dynamo could drive large-scale dynamo action, and is likely to be important in the unstratified regions of accretion disk turbulence. In this paper, the effect is studied at low Reynolds numbers, removing the complications of small-scale dynamo excitation and aiding analysis by enabling the use of quasi-linear statistical simulation methods. In addition to the magnetically driven dynamo, new results on the kinematic nonhelical shear dynamo are presented. These illustrate the relationship between coherent and incoherent driving in such dynamos, demonstrating the importance of rotation in determining the relative dominance of each mechanism.

astro-ph.HE↗

arXiv2014

Statistical simulation of the magnetorotational dynamo

Turbulence and dynamo induced by the magnetorotational instability (MRI) are analyzed using quasi-linear 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 quasi-linear model is qualitatively similar to that of nonlinear MRI turbulence. This indicates that recent convergence problems may be related to 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.

astro-ph.HE↗

arXiv2014

Magnetorotational instability: nonmodal growth and the relationship of global modes to the shearing box

We study the magnetorotational instability (MRI) using nonmodal stability techniques. Despite the spectral instability of many forms of the MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very different to the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localized in a completely different region of space. These ideas lead -- for both axisymmetric and non-axisymmetric modes -- to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary differential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using nonmodal analysis techniques, we conclude by analyzing local MRI growth over finite time-scales using these methods. The strong growth over a wide range of wave-numbers suggests that nonmodal linear physics could be of fundamental importance in MRI turbulence.

astro-ph.HE↗

arXiv2014

Nonmodal growth of the magnetorotational instability

We analyze the linear growth of the magnetorotational instability (MRI) in the short time limit using nonmodal methods. Our findings are quite different to standard results, illustrating that shearing wave energy can grow at the maximum MRI rate, $-dΩ/d \ln r,$ for any choice of azimuthal and vertical wavelengths. In addition, by comparing the growth of shearing waves with static structures, we show that over short time-scales shearing waves will always be dynamically more important than static structures in the ideal limit. By demonstrating that fast linear growth is possible at all wavelengths, these results suggest that nonmodal linear physics could play a fundamental role in MRI turbulence.

physics.plasm-ph↗

arXiv2014

Gauge properties of the guiding center variational symplectic integrator

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms an instability arises because the discrete symplectic structure does not become the continuous structure in the $t \rightarrow 0$ limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the "antisymmetric discretization gauge," in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as $\boldsymbol{A}$ and $ϕ$ are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law

physics.plasm-ph↗