  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.
