Gamma-ray observations of the Crab Nebula: A study of the synchro-compton spectrum

Phase I and II EGRET observations of the Crab Nebula establish the synchro-Compton unpulsed spectrum between approximately 70 MeV and 30 GeV. The soft 70-150 MeV spectrum appears to be a steepened extension of the 1-30 MeV COMPTEL spectrum recently reported by Much et al., indicating that the nebular synchrotron spectrum cuts off with an e-folding energy E₀ ∼ 26 MeV. This energy is consistent with the characteristic synchrotron energy hv_max ∼ (3/4π)²hc/r₀ = 25 MeV (with r₀ being the classical electron radius) expected for the synchrotron burnoff if electrons are accelerated on a timescale equal to the electron gyroperiod in the inner nebula. The 70-150 MeV emission in the exponential tail of this cutoff decreased by a factor of about 2 between 1991 and 1993, which is consistent with an approximately 25% reduction in E₀ over that time. A steady hard, approximately E^-1.85 photon spectrum, added to the synchrotron component, is required for energies up to 10 GeV. This spectrum steepens toward the observed TeV γ-ray spectrum and may represent the expected nebular inverse-Compton (IC) component, which allows a measurement of the mean nebular field strength: from EGRET we obtain B̄ ~∼ 0.13 mG for the radio nebula, whereas the various reported TeV observations correspond to a larger B̄ ∼ 0.26 mG for the smaller optical nebula. The observation of the IC component also allows us to obtain a lower limit to the time-averaged injection rate Ṅ > 4 × 10⁴⁰ s^-1 for all electrons/positrons into the nebula. The combined EGRET/TeV IC spectrum appears to be inconsistent with the assumption of a spherically symmetric particle-dominated pulsar wind with parameter σ ∼ 0.003 (see the work of Kennel & Coroniti).