On the propagation of Alfvén waves in the dusty interstellar medium. Can we neglect dust inertia in molecular clouds?

Abstract

Alfvén waves are fundamental magnetized modes which play an important role in the dynamics of magnetized flows such as the interstellar medium (ISM). In weakly ionised medium, their propagation critically depends on the ionisation rate but also on the charge carriers which, depending on gas density can be ions, electrons or dust grains. The latter in particular are well known to have a drastic influence on the magnetic resistivities in the dense ISM such as collapsing dense cores. Yet, in most calculations, for numerical reasons, the grain inertia is usually neglected. We investigate analytically the propagation of Alfvén waves both in a single-size and multi-size grain medium such as the ISM and we obtain exact expressions giving wavenumbers as a function of wave frequencies. These expressions are then solved analytically or numerically taking into account or neglecting grain inertia. Whereas at large wavelengths, neglecting grain inertia is a very good approximation, the situation is rather different for wavelengths shorter than a critical value, which broadly scales as $1/n$, $n$ being the gas density. More precisely, when inertia is neglected the waves do not propagate at short wavelengths or, due to the Hall effect, develop for one circular polarisation only, a whistler mode such that ${\mathcal{R}}_e(\omega )\propto k^2$, whereas the other polarisation presents a zero group velocity, i.e. ${\mathcal{R}}_e(\omega )\propto k^0$. When grain inertia is accounted for, the propagation of the two polarisations tend to be more symmetrical and the whistler mode is only present at density higher than $\simeq 10^8$ cm${}^{-3}$. At lower density it is replaced by a mode having ${\mathcal{R}}_e(\omega )\propto k^{\simeq 1.2}$. Abridged

submitted in A&A, comments welcome

References in corpus (20)

• Closed-form expressions for particle relative velocities induced by turbulence
• Magnetic processes in a collapsing dense core. I Accretion and Ejection
• Magnetically self-regulated formation of early protoplanetary discs
• The role of magnetic fields in the formation of protostellar discs
• Formation and Evolution of Disks around Young Stellar Objects
• Cosmic ray feedback from supernovae in dwarf galaxies
• Cosmic Ray Transport, Energy Loss, and Influence in the Multiphase Interstellar Medium
• Protostellar collapse: the conditions to form dust rich protoplanetary disks
• The Effect of Misalignment between Rotation Axis and Magnetic Field on Circumstellar Disk
• Dust coagulation feedback on magnetohydrodynamic resistivities in protostellar collapse
• Protostellar collapse simulations in spherical geometry with dust coagulation and fragmentation
• Alfvenic Turbulence Beyond the Ambipolar Diffusion Scale
• Small dust grain dynamics on adaptive mesh-refinement grids. I. Methods
• Rapid Elimination of Small Dust Grains in Molecular Clouds
• Fast methods for tracking grain coagulation and ionization. I. Analytic derivation
• Neutral vs Ion Linewidths in Barnard 5: Evidence for Penetration by MHD Waves
• Dust coagulation and fragmentation in a collapsing cloud core and their influence on non-ideal magnetohydrodynamic effects
• Impact of dust size distribution including large dust grains on magnetic resistivity: an analytical approach
• Universal protoplanetary disk size under complete non-ideal magnetohydrodynamics: The interplay between ion-neutral friction, Hall effect, and the Ohmic dissipation
• Driven waves in a two-fluid plasma

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