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On the 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. We discuss possible Pulsar B torque modification and magnetic field estimates due to the interaction with Pulsar A wind. Unless the orbital inclination is $\leq 86 ^\circ$, the duration of eclipses is typically shorter than the one implied by the size of the eclipsing region. We propose that eclipses occur due to synchrotron absorption by mildly relativistic particles in the shocked Pulsar A wind. The corresponding optical depth may be high enough if Pulsar A wind density is at the upper allowed limits. 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.