Interpreting Crab Nebula synchrotron spectrum: two acceleration mechanisms

Abstract

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 $p_I \approx 2.2$ above the injection break corresponding to $\gamma_{wind} \sigma_{wind} \sim 10^5$, peaking in the UV ($\gamma_{wind} \sim 10^2$ is the bulk Lorentz factor of the wind, $\sigma _{wind} \sim 10^3$ is wind magnetization); (ii) Component-II due to acceleration at reconnection layers in the bulk of the turbulent Nebula, with particle index $p_{II} \approx 1.6$. The model requires relatively slow but highly magnetized wind. For both components the overall cooling break is in the infra-red at $\sim 0.01$ 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 $\alpha_o \approx 0.5$, 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 $\epsilon_s \approx 100$ 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 AGNe and GRB jets, where often radio electrons form a different population from the high energy electrons.