Interpreting Crab Nebula’s synchrotron spectrum: two acceleration mechanisms

We outline a model of the Crab pulsar wind nebula with two different populations of synchrotron emitting particles, arising from two different acceleration mechanisms: (i) Component-I due to Fermi-I acceleration at the equatorial portion of the termination shock, with particle spectral index pI ≈ 2.2 above the injection break corresponding to γwindσwind ∼ 105, peaking in the ultraviolet (UV, γwind ∼ 102 is the bulk Lorentz factor of the wind, σwind ∼ 103 is wind magnetization); and (ii) Component-II due to acceleration at reconnection layers in the bulk of the turbulent Nebula, with particle index pII ≈ 1.6. The model requires relatively slow but highly magnetized wind. For both components, the overall cooling break is in the infrared at ∼0.01 eV, so that the Component-I is in the fast cooling regime (cooling frequency below the peak frequency). In the optical band, Component-I produces emission with the cooling spectral index of αo ≈ 0.5, softening towards the edges due to radiative losses. Above the cooling break, in the optical, UV, and X-rays, Component-I mostly overwhelms Component-II. We hypothesize that acceleration at large-scale current sheets in the turbulent nebula (Component-II) extends to the synchrotron burn-off limit of ϵs ∼ 100 MeV. Thus in our model acceleration in turbulent reconnection (Component-II) can produce both hard radio spectra and occasional gamma-ray flares. This model may be applicable to a broader class of high-energy astrophysical objects, like active galactic nuclei and gamma-ray burst jets, where often radio electrons form a different population from the high-energy electrons.