Dust-Dust Collisional Charging and Lightning in Protoplanetary Discs

Abstract

We study the role of dust-dust collisional charging in protoplanetary discs. We show that dust-dust collisional charging becomes an important process in determining the charge state of dust and gas, if there is dust enhancement and/or dust is fluffy, so that dust surface area per disc volume is locally increased. We solve the charge equilibrium equations for various disc environments and dust number density $\eta$, using general purpose graphic processors (GPGPU) and {\sc cuda} programming language. We found that as dust number density $\eta$ increases, the charge distribution experience four phases. In one of these phases the electrostatic field $E$ caused by dust motion increases as $E\propto {\eta }^4$. As a result, macroscopic electric discharge takes place, for example at $\eta =70$ (in units of minimum-mass solar nebula (MMSN) values, considering two groups of fluffy dust with radii $10^{-2}\unit{cm}$, $10^{2}\unit{cm}$). We present a model that describes the charge exchange processes in the discs as an electric circuit. We derive analytical formulae of critical dust number density for lightning, as functions of dust parameters. We estimate the total energy, intensity and event ratio of such discharges (`lightning'). We discuss the possibility of observing lightning and sprite discharges in protoplanetary discs by Astronomically Low Frequency ({\em ALF}) waves, {\em IR} images, {\em UV} lines, and high energy gamma rays. We also discuss the effects of lightning on chondrule heating, planetesimal growth and magnetorotational instability of the disc.

27 pages, 38 figures, Accepted to MNRAS on 2009 October 8. Received 2009 October 5; in original form 2009 August 11

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• Harvesting the decay energy of ${}^{26}$Al to drive lightning discharge in protoplanetary discs
• Atmospheric electrification in dusty, reactive gases in the solar system and beyond
• Compound chondrule formation via collision of supercooled droplets
• Observation of bottom-up formation for charged grain aggregates related to pre-planetary evolution beyond the bouncing barrier
• Compound chondrule formation in optically thin shock waves
• Ejection of Chondrules from Fluffy Matrices
• Development of a Method for the Observation of Lightning in Protoplanetary Disks Using Ion Lines
• Chondrule Accretion with a Growing Protoplanet
• Ionizing Protoplanetary Disks in Pebble Collisions
• Charged Clouds of Ionized Gas Emerge from Tribocharging Grains
• The Dissolution of Planetesimals in Electrostatic Fields
• Runaway electrification of friable self-replicating granular matter
• Fast-moving electrostatic solitons in a plasma with turbulence heating