  Magnetars are a subclass of neutron stars whose intense soft-gamma-ray bursts
and quiescent X-ray emission are believed to be powered by the decay of a
strong internal magnetic field. We reanalyze neutrino emission in such stars in
the plausibly relevant regime in which the Landau band spacing of both protons
and electrons is much larger than kT (where k is the Boltzmann constant and T
is the temperature), but still much smaller than the Fermi energies. Focusing
on the direct Urca process, we find that the emissivity oscillates as a
function of density or magnetic field, peaking when the Fermi level of the
protons or electrons lies about 3kT above the bottom of any of their Landau
bands. The oscillation amplitude is comparable to the average emissivity when
the Landau band spacing mentioned above is roughly the geometric mean of kT and
the Fermi energy (excluding mass), i. e., at fields much weaker than required
to confine all particles to the lowest Landau band. Since the density and
magnetic field strength vary continuously inside the neutron star, there will
be alternating surfaces of high and low emissivity. Globally, these
oscillations tend to average out, making it unclear whether there will be any
observable effects.
