Interpreting Crab Nebula’s 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 ≈ 2.2 above the injection break corresponding to γ wind σ wind ∼ 10 5 , peaking in the UV (γ wind ∼ 10 2 is the bulk Lorentz factor of the wind, σ wind ∼ 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 ≈ 1.6. The model requires relatively slow but highly magnetized wind. For both components the overall cooling break is in the infra-red 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 α o ≈ 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 s ∼ 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. arXiv:1811.01767v3 [astro-ph.HE] 19 Jul 2019 1. In the radio the spectral index is α r = 0.3 (so that νF ν ∝ ν 0.7 ). It is homogeneous over the Nebula (Bietenholz et al. 1997).2. In the infra-red the situation is complicated -a large thermal component from filaments complicates the analysis, see §3.33. In the optical the spectrum softens to α o ∼ 0.6 (so that νF ν ∝ ν 0.4 ).4. The overall spectral distribution of νF ν in the Crab Nebula has a peak in the UV, at ∼ 1 eV. Above the peak the spectrum has α ≈ 1.15. An additional feature present in the hard X-ray spectrum is softening at ∼ 130 keV, with a corresponding break with ∆α = 0.43 (Meyer et al. 2010) (see §2.2 for further discussions)

Spectral energy distribution modeling of broadband emission in the pulsar wind nebula 3C 58

“…The low‐energy distribution may correspond to unshocked polar wind with < γ e > ≈ γ w and the high‐energy one to the shock‐accelerated equatorial wind with < γ e > ≈ γ w σ w , where σ w is the magnetization parameter (magnetic‐to‐particle energy ratio), and γ w is the pre‐shock Lorentz factor of the pulsar wind. These distributions are similar to those predicted in a theoretical model (Lyutikov et al ) and/or particle‐in‐cell (PIC) simulations (Sironi & Spitkovsky ). The low‐energy population is expected to have a sharp cutoff at γ e ≈ γ w σ w (e.g., Lyutikov et al ; Werner et al ), but Lyutikov et al () hypothesized that the distribution may extend to higher energies via turbulence acceleration.…”

“…These distributions are similar to those predicted in a theoretical model (Lyutikov et al ) and/or particle‐in‐cell (PIC) simulations (Sironi & Spitkovsky ). The low‐energy population is expected to have a sharp cutoff at γ e ≈ γ w σ w (e.g., Lyutikov et al ; Werner et al ), but Lyutikov et al () hypothesized that the distribution may extend to higher energies via turbulence acceleration. So we search for a high‐energy tail in the low‐energy population with our SED model, but find that the high‐energy cutoff of the low‐energy distribution needs to be sharp (e.g., a power law with a slope p 2 ≤ − 5) for 3C 58.…”

“…The inferred distributions of the two populations are power laws in γ e = 1–4 × 10 4 with p = − 0.8 and in γ e ≈ 10 5 − 6 × 10 8 with p ≈ − 2.7 (Figure top left). Note that the lower bound for γ e of the low‐energy population is not well constrained, and using a larger value (e.g., 100; Lyutikov et al ) is also possible. A small gap (i.e., γ e = 4 × 10 4 − 10 5 ) between the energy distributions is necessary like in the case of the Crab nebula (e.g., Bandiera et al ; Meyer et al ).…”

“…In particular, the low‐energy distribution we inferred (Figure ) does not appear to be Maxwellian‐like. We also checked to see if the low‐energy population has a hard high‐energy tail as hypothesized previously (Lyutikov et al ). Our model prefers a sharp cutoff at γ e = 4 × 10 4 , implying no significant high‐energy tail.…”

“…For (1), we use two populations of electrons as suggested observationally (Bandiera et al ; Meyer et al ) and theoretically (e.g., Lyutikov et al ). In the latter, the authors hypothesized possible existence of two populations of electrons (Lyutikov et al ; Sironi & Spitkovsky ): a low‐energy distribution ( γ e < 10 5 ; perhaps the unshocked pulsar wind) and a shock‐accelerated one with γ e ≥ 10 5 . The former may be further accelerated via turbulent reconnection and develop a high‐energy tail.…”