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 \sim 2.7 GeV .
The emission above 3 GeV in this region is detected with a \sim 7 \sigma confidence level .
The \gamma -ray data above \sim 2.7 ~ { } { GeV } are observed to be modulated at the orbital period at the \sim 2.3 \sigma level .
We anticipate that the PLE component dominating below \sim 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 \sim 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 .