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We present a long-term spectral monitoring of the unique Double Pulsar binaryPSR J0737-3039 corresponding to two "Large Programs" performed by XMM-Newton in2006 and 2011. Spectral variability of pulsar emission in soft X-rays is notevident over 5 years, despite the significant relativistic spin precession inthe considered time span (about 25deg). We provide, for the first time,evidence of hard X-ray emission from the system in the 5-8 keV energy band. Thestandard spectral analysis was coupled to the energy dependent spatial analysisto confirm this excess, most likely ascribed to iron line emission. The FeK-alpha emission line at 6.4-6.97 keV was previously unheard-of innon-accreting binary systems and could testify to the presence of a relic diskthat survived the supernova explosions that terminated the lives of the DoublePulsar's stellar progenitors. The existence of a relic disk in this systemreinforces speculation about the presence of similar structures around otherpeculiar classes of isolated neutron stars.

Long-term study of the Double Pulsar J0737-3039 with XMM-Newton: spectral analysis