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Observations of magnetic activity indicators in solar-type stars exhibit arelationship with rotation with an increase until a "saturation" level and amoderate decrease in activity in the very fastest rotators ("supersaturation").While X-ray data have suggested that this relationship is strongly violated inultracool dwarfs (UCDs; spectral type >M7), the limited number of X-raydetections has prevented firm conclusions. In this paper, we analyze the X-rayactivity-rotation relation in 38 ultracool dwarfs. Our sample represents thelargest catalog of X-ray active ultracool dwarfs to date, including seven newand four previously-unpublished Chandra observations presented in a companionpaper. We identify a substantial number of rapidly-rotating UCDs with X-rayactivity extending two orders of magnitude below the expected saturation leveland measure a "supersaturation"-type anticorrelation between rotation and X-rayactivity. The scatter in UCD X-ray activity at a fixed rotation is ~3 timeslarger than that in earlier-type stars. We discuss several mechanisms that havebeen proposed to explain the data, including centrifugal stripping of thecorona, and find them to be inconsistent with the observed trends. Instead, wesuggest that an additional parameter correlated with both X-ray activity androtation is responsible for the observed effects. Building on the results ofZeeman-Doppler imaging of UCD magnetic fields and our companion study ofradio/X-ray flux ratios, we argue that this parameter is the magnetic fieldtopology, and that the large scatter in UCD X-ray fluxes reflects the presenceof two dynamo modes that produce distinct topologies.

Trends in Ultracool Dwarf Magnetism. II. The Inverse Correlation Between X-ray Activity and Rotation as Evidence for a Bimodal Dynamo