Phenomenological modelling of the Crab Nebula's broad band energy spectrum and its apparent extension

Abstract

The Crab Nebula emits bright non-thermal radiation from radio to the most energetic photons. The underlying physical model of a relativistic wind from the pulsar terminating in a hydrodynamic standing shock remains unchanged since the early 1970s. In this model, an increase of the toroidal magnetic field downstream from the shock is expected. We introduce a detailed radiative model to calculate non-thermal synchrotron and inverse Compton as well as thermal dust emission self-consistently to compare quantitatively with observational data. Special care is given to the radial dependence of electron and seed field density. The radiative model is used to estimate the parameters of electrons and dust in the nebula. A combined fit based upon a ${\chi }^2$ minimisation reproduces successfully the complete data set used. For the best-fitting model, the energy density of the magnetic field dominates over the particle energy density up to a distance of $\approx 1.3r_s$ ($r_s$: distance of the termination shock from the pulsar). The very high energy (VHE: $E>100$ GeV) gamma-ray spectra set the strongest constraints on the radial dependence of the magnetic field: $B(r)=(264\pm 9)\mu \mathrm{G}(r/r_s{)}^{-0.51\pm 0.03}$. The reconstructed magnetic field and its radial dependence indicates a ratio of Poynting to kinetic energy flux $\sigma \approx 0.1$ at the termination shock, $\approx 30$ times larger than estimated up to now. Consequently, the confinement of the nebula would require additional mechanisms to slow down the flow through e.g. excitation of small-scale turbulence with possible dissipation of magnetic field.

accepted for publication in A&A, abbr. abstract, thanks for the excellent review process. The SED data points are now available (see pdf for the link)

References in corpus (19)

• Measurement of the Cosmic Ray e+ plus e- spectrum from 20 GeV to 1 TeV with the Fermi Large Area Telescope
• Observations of the Crab Nebula with H.E.S.S
• Gamma-ray flares from the Crab Nebula
• Discovery of Powerful Gamma-Ray Flares from the Crab Nebula
• A radiation transfer model for the Milky-Way: I. Radiation fields and application to High Energy Astrophysics
• When A Standard Candle Flickers
• High-Energy Gamma Rays from the Milky Way: Three-Dimensional Spatial Models for the Cosmic-Ray and Radiation Field Densities in the Interstellar Medium
• Spitzer Space Telescope Infrared Imaging and Spectroscopy of the Crab Nebula
• The dust and gas content of the Crab Nebula
• Re-detection and a Possible Time Variation of Soft X-ray Polarisation from the Crab
• Broadband X-ray Imaging and Spectroscopy of the Crab Nebula and Pulsar with NuSTAR
• MAGIC very large zenith angle observations of the Crab Nebula up to 100 TeV
• The dust content of the Crab Nebula
• PeV emission of the Crab Nebula: constraints on the proton content in pulsar wind and implications
• Multi-band Emission up to PeV Energy from the Crab Nebula in a Spatially Dependent Lepto-hadronic Model
• Turbulent model of Crab nebula radiation
• Detection of UHE gamma rays from the Crab Nebula: Physical Implications
• 2003-2019 Monitoring of the Crab emission through INTEGRAL SPI, or vice versa
• Fermi Large Area Telescope Observations of the Fast-dimming Crab Nebula in 60-600 MeV

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• Hadronic Re-Acceleration at the Crab Pulsar Wind Termination Shock as a Source of PeV Gamma-Rays
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