Sub-Alfvènic Spreading of 3D Collisionless Magnetic Reconnection and Application to Two-Ribbon Solar Flares

Ribbons in two-ribbon solar flares are observed to elongate in time along the polarity inversion line in addition to their well-known apparent motion away from it. This has been attributed to the spreading of initially localized magnetic reconnection in time. Similar spreading of reconnection has been observed in other settings, including laboratory experiments, Earth's magnetotail, and Earth's dayside magnetopause. Understanding how reconnection spreads is an important aspect of understanding flare evolution including plasma energization and particle acceleration, since these phenomena are associated with the properties of the magnetic reconnection including its physical size. An interesting observational result, both in solar flares and Earth's magnetosphere, is that the reconnection tends to spread slower than the Alfven speed. We investigate the effect of the thickness of the current sheet being non-uniform on the speed of 3D spreading of magnetic reconnection. We perform a parametric study using 3D two-fluid numerical simulations of initially localized anti-parallel magnetic reconnection and present a theory for the out-of-plane spreading velocity as a function of the initial current sheet thicknesses of the fluted current sheet. We find the spreading in fluted current sheets is slower than spreading in uniform sheets with the same thickness in as its broader region. This result provides a potential explanation of why 3D reconnection can spread at sub-Alfvenic speeds.