  We propose synchrotron absorption in a magnetosheath forming a cocoon around
the magnetosphere of pulsar B to be the origin of the eclipse phenomena seen in
the recently discovered double pulsar system PSRJ07370-3039 A & B. The model
predicts the eclipses will clear at frequencies higher than those of the
observations reported to date (nominally, above $\nu \sim 5$ GHz.) The model
also predicts synchrotron emission at the level of a few to 10 $\mu$Jy, peaking
at $\nu \sim 2-5$ GHz with possible orbital modulation. We use simplified
semi-analytic models and particle-in-cell simulations to elucidate the
structure of the B magnetosphere, showing that B's magnetic field is confined
to within a radius less than 50,000 km from B,on the side facing A. We estimate
a ``propellor'' spindown torque on B, which is the dominant torque on this
star, which yields a polar dipole field $\sim 7 \times 10^{11}$ Gauss (magnetic
moment $\mu_B \sim 3.5 \times 10^{29}$ cgs). The model can explain the known
eclipses only if the A wind's density is at least 4 orders of magnitude greater
than is expected from popular pair creation models, and discuss the
implications of this result for our general understanding of pulsar physics.
Our proposal was outlined in Kaspi et al. (2004) and Demorest et al. (2004); a
similar proposal has been made by Lyutikov (2004).
