  Observations have suggested that some low-mass stars have larger radii than
predicted by 1-D structure models. Some theoretical models have invoked very
strong interior magnetic fields (of order 1 MG or more) as a possible cause of
such large radii. Whether fields of that strength could in principle by
generated by dynamo action in these objects is unclear, and we do not address
the matter directly. Instead, we examine whether such fields could remain in
the interior of a low mass object for a significant time, and whether they
would have any other obvious signatures. First, we estimate timescales for the
loss of strong fields by magnetic buoyancy instabilities. We consider a range
of field strengths and simple morphologies, including both idealized flux tubes
and smooth layers of field. We confirm some of our analytical estimates using
thin flux tube magnetohydrodynamic (MHD) simulations of the rise of buoyant
fields in a fully-convective M-dwarf. Separately, we consider the Ohmic
dissipation of such fields. We find that dissipation provides a complementary
constraint to buoyancy: while small-scale, fibril fields might be regenerated
faster than they rise, the dissipative heating associated with such fields
would in some cases greatly exceed the luminosity of the star. We show how
these constraints combine to yield limits on the internal field strength and
morphology in low-mass stars. In particular, we find that for stars of 0.3
solar masses, no fields in flux tubes stronger than about 800 kG are
simultaneously consistent with both constraints.
