  Context: A mysterious X-ray nebula, showing a remarkably linear geometry, was
recently discovered close to the Guitar Nebula, the bow-shock nebula associated
with B2224+65, which is the fastest pulsar known. The nature of this X-ray
feature is unknown, and even its association with pulsar B2224+65 is unclear.
Aims: We attempt to develop a self-consistent scenario to explain the complex
phenomenology of this object. Methods: We assume that the highest energy
electrons accelerated at the termination shock escape from the bow shock and
diffuse into the ambient medium, where they emit synchrotron X-rays. The linear
geometry should reflect the plane-parallel geometry of its ambient field.
Results: We estimate the Lorentz factor of the X-ray emitting electrons and the
strength of the magnetic field. The former (~10^8) is close to its maximum
possible value, while the latter, at ~45 uG, is higher than typical
interstellar values and must have been amplified in some way. The magnetic
field must also be turbulent to some degree to trap the electrons sufficiently
for synchrotron X-ray emission to occur effectively. We propose a
self-consistent scenario in which, by some streaming instability, the electrons
themselves generate a turbulent field in which they then diffuse. Some
numerical coincidences are explained, and tests are proposed to verify our
scenario. Conclusions: Electron leaking may be common in the majority of pulsar
bow-shock nebulae, even though the X-ray nebulosity in general is too diffuse
to be detectable.
