Simple Analytical Models of Grain Fragmentation in a Cometary Coma

Abstract Measurements by the dual Langmuir Probe (LAP) on board Rosetta in the inner coma of comet 67​​​​P/Churyumov–Gerasimenko revealed an unexpected ∼50% level of attenuation of the impinging solar extreme-ultraviolet (EUV) radiation while the comet was near perihelion. It was argued that this possibly could be a sign of upstream grain fragmentation. Here the effect of grain fragmentation on the EUV transmission fraction in a cometary coma is looked at through two simple analytical models: a continuous fragmentation model and an abrupt fragmentation model. We assume in both models radially expanding grains that readily reach their respective size-dependent terminal velocity. Without specifying driving mechanisms, we assume in the continuous fragmentation model that any grain splits into the same number of equal-sized fragments at a fixed size- and position-independent rate, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Γ</mml:mi> </mml:math> , as long as said grain has not yet reached a prescribed minimal size from which point it cannot fragment further. In the abrupt fragmentation model, we instead assume that grains undergo complete fragmentation into minimal-sized subunits at a fixed cometocentric distance. In order for the models to produce transmission fraction profiles compatible with the aforementioned LAP observations, specific conditions appear necessary. A particularly puzzling aspect is the apparent requirement that a significant fraction of the dayside dust population disintegrate gradually or abruptly down to sizes of several tens of nanometers already by a distance of several 1000 km.