Magnetic dissipation is frequently invoked as a way of powering the observed
emission of relativistic flows in Gamma Ray Bursts and Active Galactic Nuclei.
Pulsar Wind Nebulae provide closer to home cosmic laboratories which can be
used to test the hypothesis. To this end, we analyze the observational data on
the spindown power of the Crab pulsar, energetics of the Crab nebula, and its
magnetic field. We show that unless the magnetic inclination angle of the Crab
pulsar is very close to 90 degrees the overall magnetization of the striped
wind after total dissipation of its stripes is significantly higher than that
deduced in the Kennel-Coroniti model and recent axisymmetric simulations of
Pulsar Wind Nebulae. On the other hand, higher wind magnetization is in
conflict with the observed low magnetic field of the Crab nebula, unless it is
subject to efficient dissipation inside the nebula as well. For the likely
inclination angle of 45 degrees the data require magnetic dissipation on the
timescale about 80 years, which is short compared to the life-time of the
nebula but long compared to the time scale of Crab's gamma-ray flares.Comment: Accepted for publication in MNRA
