Nature of eclipses in binary pulsar J0737-3039

We consider magnetohydrodynamical interaction between relativistic pulsar wind and static magnetosphere in binary pulsar system PSR J0737-3039. We construct semi-analytical model describing the form of the interface separating the two pulsars. An assumption of vacuum dipole spin down for Pulsar B leads to eclipse duration ten times longer than observed. Electromagnetic torque on Pulsar B is, in fact, modified due to the interaction with Pulsar A wind, leading to $\sim 50$ decrease in the estimate of Pulsar B magnetic field, $B_B\sim 4.24 \times 10^{10}$ G. The resulting size of magnetosphere is in excellent agreement with the duration of eclipses. We propose that eclipses occur due to synchrotron absorption by mildly relativistic particles in the shocked Pulsar A wind, and estimate the corresponding optical depth. We derive jump conditions at oblique, relativistic, magnetohydrodynamical shocks and discuss the structure of the shocked Pulsar A wind. Finally, we speculate on a possible mechanism of orbital modulation of Pulsar B radio emission.