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.

arXiv commentaccepted 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 (62)

• Maps of Dust IR Emission for Use in Estimation of Reddening and CMBR Foregrounds
• A 3D Dust Map Based on Gaia, Pan-STARRS 1 and 2MASS
• 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
• The Swift/BAT Hard X-ray Transient Monitor
• Gamma-ray flares from the Crab Nebula
• Discovery of Powerful Gamma-Ray Flares from the Crab Nebula
• The Crab Nebula and Pulsar between 500 GeV and 80 TeV: Observations with the HEGRA stereoscopic air Cherenkov telescopes
• The Crab pulsar in the 0.75-30 MeV range as seen by CGRO COMPTEL
• Three-Dimensional Magnetohydrodynamic Simulations of the Crab Nebula
• First Detection of Photons with Energy Beyond 100 TeV from an Astrophysical Source
• Gamma-ray Activity in the Crab Nebula: The Exceptional Flare of April 2011
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Planets and Celestial Calibration Sources
• A Cool Dust Factory in the Crab Nebula: A Herschel Study of the Filaments
• A radiation transfer model for the Milky-Way: I. Radiation fields and application to High Energy Astrophysics
• The Crab Nebula as a standard candle in very high-energy astrophysics
• When A Standard Candle Flickers
• Measurement of the Crab Nebula Spectrum Past 100 TeV with HAWC
• Angular, spectral, and time distributions of highest energy protons and associated secondary gamma-rays and neutrinos propagating through extragalactic magnetic and radiation fields
• The origin of peculiar jet-torus structure in the Crab nebula
• Spatial Variation of the X-ray spectrum of the Crab Nebula
• Measurement of the Crab Nebula spectrum over three decades in energy with the MAGIC telescopes
• 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
• Cross-calibration of the X-ray Instruments onboard the Chandra, INTEGRAL, RXTE, Suzaku, Swift, and XMM-Newton Observatories using G21.5-0.9
• Time-dependent modeling of pulsar wind nebulae: Study on the impact of the diffusion-loss approximations
• The dust and gas content of the Crab Nebula
• Re-detection and a Possible Time Variation of Soft X-ray Polarisation from the Crab
• The High Energy Emission of the Crab Nebula from 20 keV to 6 MeV with INTEGRAL
• The Importance of Physical Models for Deriving Dust Masses and Grain Size Distributions in Supernova Ejecta I: Radiatively Heated Dust in the Crab Nebula
• The Crab Nebula's Wisps in Radio and Optical
• 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
• Measurement of the absolute Crab flux with NuSTAR
• H.E.S.S. Observations of the Crab during its March 2013 GeV Gamma-Ray Flare
• On Calibrations using the Crab Nebula and Models of the Nebular X-ray Emission
• Interpreting Crab Nebula synchrotron spectrum: two acceleration mechanisms
• The dust content of the Crab Nebula
• Chandra, Keck and VLA Observations of the Crab Nebula during the 2011-April Gamma-ray Flare
• A search for enhanced very high energy gamma-ray emission from the March 2013 Crab Nebula flare
• Advances in the RXTE Proportional Counter Array Calibration: Nearing the Statistical Limit
• Rapid Gamma-ray flux variability during the 2013 March Crab Nebula flare
• On the X-ray Image of The Crab Nebula: Comparison with Chandra Observations
• VLBI imaging of a flare in the Crab Nebula: More than just a spot
• Characterization of the Inner Knot of the Crab: The Site of the Gamma-ray Flares?
• In-flight measurement of the absolute energy scale of the Fermi Large Area Telescope
• PeV emission of the Crab Nebula: constraints on the proton content in pulsar wind and implications
• Unraveling the Geometry of the Crab Nebula's "Inner Ring"
• On the Radio Emitting Particles of the Crab Nebula: Stochastic Acceleration Model
• Temporal Variability of the X-ray Emission of the Crab Nebula Torus
• Six years of VERITAS observations of the Crab Nebula
• Modeling the effect of small-scale magnetic turbulence on the X-ray properties of Pulsar Wind Nebulae
• NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution
• Gamma-Ray Spectra & Variability of the Crab Nebula Emission Observed by BATSE
• 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
• Spectroscopy and 3D imaging of the Crab nebula
• 2003-2019 Monitoring of the Crab emission through INTEGRAL SPI, or vice versa
• Confinement of the Crab Nebula with tangled magnetic field by its supernova remnant
• Fermi Large Area Telescope Observations of the Fast-dimming Crab Nebula in 60-600 MeV
• The Energy-dependent $\gamma$-ray Morphology of the Crab Nebula Observed with the Fermi Large Area Telescope

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