Very high energy gamma radiation associated with the unshocked wind of the Crab pulsar

We show that the relativistic wind of the Crab pulsar, which is commonly thought to be invisible in the region upstream of the termination shock at r ≤ rS ∼ 0.1 pc, in fact could be directly observed through its inverse Compton (IC) γ-ray emission. This radiation is caused by illumination of the wind by low-frequency photons emitted by the pulsar, and consists of two, pulsed and unpulsed, components associated with the nonthermal (pulsed) and thermal (unpulsed) low energy radiation of the pulsar, respectively. These two components of γ-radiation have distinct spectral characteristics, which depend essentially on the site of formation of the kinetic-energy-dominated wind, as well as on the Lorentz factor and the geometry of propagation of the wind. Thus, the search for such specific radiation components in the spectrum of the Crab Nebula can provide unique information about the unshocked pulsar wind that is not accessible at other wavelengths. In particular, we show that the comparison of the calculated flux of the unpulsed IC emission with the measured γ-ray flux of the Crab Nebula excludes the possibility of formation of a kinetic-energy-dominated wind within 5 light cylinder radii of the pulsar, Rw ≥ 5RL. The analysis of the pulsed IC emission, calculated under reasonable assumptions concerning the production site and angular distribution of the optical pulsed radiation, yields even tighter restrictions, namely Rw ≥ 30RL.