Recent observations show that chromospheric activity in late-M and L dwarfs is much lower than in the earlier M types, in spite of comparatively rapid rotation. We investigate the possibility that this drop-off in activity results from the very high electrical resistivities in the dense, cool and predominantly neutral atmospheres of late-M and L dwarfs. We calculate magnetic field diffusivities in the atmospheres of objects with effective temperatures in the range 3000-1500 (mid-M to L), using the atmospheric structure models of Allard and Hauschildt. We find that the combination of very low ionization fraction and high density in these atmospheres results in very large resistivities due to neutral-charged particle collisions, and efficient field diffusion. The resistivities are found to increase with both decreasing optical depth, and decreasing effective temperature. As a result, any existing magnetic fields are increasingly decoupled from atmospheric motions as one moves from mid-M to L; we quantify this through a simple Reynolds number calculation. This, coupled with the difficulty in transporting magnetic stresses through the highly resistive atmosphere, can account for the observed drop in activity from mid-M to L, assuming activity in these objects is magnetically driven. We also examine the issue of acoustic heating, and find that this appears inadequate to explain the observed H-alpha fluxes in mid-M to L dwarfs. Consequently, magnetic heating does seem to be the most viable mechanism for generating activity in these objects. Finally, we speculate on a possible flare mechanism in these cool dwarfs.
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