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Flash ionisation signature in coherent cyclotron emission from Brown Dwarfs

Brown dwarfs form mineral clouds in their atmospheres, where charged particles can produce large-scale discharges in form of lightning resulting in a substantial sudden increase of local ionisation. Brown dwarfs are observed to emit cyclotron radio emission. We show that signatures of strong transient atmospheric ionisation events (flash ionisation) can be imprinted on a pre-existing radiation. Detection of such flash ionisation events will open investigations into the ionisation state and atmospheric dynamics. Such ionisation events can also result from explosion shock waves, bursts or eruptions. We present an analytical model that describes the modulation of a pre-existing electromagnetic radiation by a time-dependent (flash) conductivity that is characteristic for flash ionisation events like lightning. Our conductivity model reproduces the conductivity function derived from observations of Terrestrial Gamma Ray Flashes, and is applicable to astrophysical objects with strong temporal variations in the local ionization, as in planetary atmospheres and protoplanetary disks. We show that the field responds with a characteristic flash-shaped pulse to a conductivity flash of intermediate intensity. More powerful ionisation events result in smaller variations of the initial radiation, or in its damping. We show that the characteristic damping of the response field for high-power initial radiation carries information about the ionisation flash magnitude and duration. The duration of the pulse amplification or the damping is consistently shorter for larger conductivity variations and can be used to evaluate the intensity of the flash ionisation. Our work suggests that cyclotron emission could be probe signals for electrification processes inside BD atmosphere.