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B1957+20 is a millisecond pulsar located in a black widow type compact binarysystem with a low mass stellar companion. The interaction of the pulsar windwith the companion star wind and/or the interstellar plasma is expected tocreate plausible conditions for acceleration of electrons to TeV energies andsubsequent production of very high energy {\gamma} rays in the inverse Comptonprocess. We performed extensive observations with the MAGIC telescopes ofB1957+20. We interpret results in the framework of a few different models,namely emission from the vicinity of the millisecond pulsar, the interaction ofthe pulsar and stellar companion wind region, or bow shock nebula. Nosignificant steady very high energy {\gamma}-ray emission was found. We deriveda 95% confidence level upper limit of 3.0 x 10 -12 cm -2 s -1 on the average{\gamma}-ray emission from the binary system above 200 GeV. The upper limitsobtained with MAGIC constrain, for the first time, different models of thehigh-energy emission in B1957+20. In particular, in the inner mixed wind nebulamodel with mono-energetic injection of electrons, the acceleration efficiencyof electrons is constrained to be below ~(2-10)% of the pulsar spin down power.For the pulsar emission, the obtained upper limits for each emission peak arewell above the exponential cut-off fits to the Fermi-LAT data, extrapolated toenergies above 50 GeV. The MAGIC upper limits can rule out a simple power-lawtail extension through the sub-TeV energy range for the main peak seen at radiofrequencies.

Observation of the Black Widow B1957+20 millisecond pulsar binary system with the MAGIC telescopes