  In a supernova core, magnetic fields cause a directional variation of the
neutrino refractive index so that resonant flavor oscillations would lead to a
deformation of the "neutrinosphere" for, say, tau neutrinos. The associated
anisotropic neutrino emission was proposed as a possible origin of the observed
pulsar proper motions. We argue that this effect was vastly overestimated
because the variation of the temperature over the deformed neutrinosphere is
not an adequate measure for the anisotropy of neutrino emission. The neutrino
flux is generated inside the neutron star core and is transported through the
atmosphere at a constant luminosity, forcing the temperature gradient in the
atmosphere to adjust to the inflow of energy from below. Therefore, no emission
anisotropy is caused by a deformation of the neutrinosphere to lowest order. An
estimate of the higher-order corrections must take into account the modified
atmospheric temperature profile in response to the deformation of the
neutrinosphere and the corresponding feedback on the core. We go through this
exercise in the framework of a simplified model which can be solved
analytically.
