We report on evidence for orbital phase-dependence of the gamma-ray emission from PSR B1957+20 black widow system by using the data of the Fermi Large Area Telescope. We divide an orbital cycle into two regions: a region containing the inferior conjunction, and the other region containing rest of the orbital cycle. We show that the observed spectra for the different orbital regions are fitted by different functional forms. The spectrum of the orbital region containing inferior conjunction can be described by a power-law with an exponential cutoff (PLE) model, which gives the best-fit model for the orbital phase that does not contain the inferior conjunction, plus an extra component above ~2.7 GeV. The emission above 3 GeV in this region is detected with a ~7-sigma confidence level. The gamma-ray data above ~2.7 GeV are observed to be modulated at the orbital period at the ~2.3-sigma level. We anticipate that the PLE component dominating below ~2.7 GeV originates from the pulsar magnetosphere. We also show that the inverse-Compton scattering of the thermal radiation of the companion star off a cold ultra-relativistic pulsar wind can explain the extra component above ~2.7 GeV. The black widow pulsar PSR B1957+20 may be the member of a new class of object, in the sense that the system is showing gamma-ray emission with both magnetospheric and pulsar wind origins.
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