The double pulsar system J0737-3039 appears associated with a continuous
radio emission, nearly three times stronger than that of the two pulsars
together. If such an emission comes from a tranparent cloud its spatial extent
(> 10^13 cm) should be substantially larger than the orbital separation.
Assuming homogeneity and equipartition, the cloud magnetic field is 0.03 G and
the electron characteristic energy ~ 60 MeV. This is consistent with supposing
that relativistic electrons produced in the shock formed by the interaction of
the more luminous pulsar wind with the magnetosphere of the companion flow away
filling a larger volume. Alternatively, the unpulsed emission may directly come
from the bow shock if some kind of coherent mechanism is at work. Possible
observational signatures that can dicriminate between the two pictures are
shortly discussed.Comment: 4 pages, no figures, accepted for publication in A&A (Letters