Long-term X-ray timing of the double pulsar PSR J0737-3039

The relativistic double neutron star binary PSR J0737-3039 is a truly unique system offering the diagnostics of two interacting radio pulsars in a short orbital period system. Clear evidences of orbital phase-dependent interactions between the two neutron stars are seen both in radio and X-rays observations. We present the timing analysis results of the PSR J0737-3039 observations performed in the context of the 2006 and 2011 XMM-Newton Large programs providing ∼ 20000 X-ray counts overall from the system. Despite only marginal orbital flux variability is detected, both pulsars of the system are clearly seen in X-ray providing physical insights on the physics of the mutual interactions in their close environment. In particular, we discuss possible processes behind the peculiar X-ray brightening of the ``lazy pulsar'' PSR B via energy transfer from the ``power plant'' PSR A.