Phenomenological modelling of the Crab Nebula’s broadband energy spectrum and its apparent extension

Abstract

Context. The Crab Nebula emits exceptionally bright non-thermal radiation across the entire wavelength range from the radio to the most energetic photons. So far, the underlying physical model of a relativistic wind from the pulsar terminating in a hydrodynamic standing shock has remained fairly unchanged since the early 1970s when it was first introduced. One of the predictions of this model is an increase in the toroidal magnetic field downstream from the shock where the flow velocity drops quickly with increasing distance until it reaches its asymptotic value, matching the expansion velocity of the nebula. Aims. The magnetic field strength in the nebula is poorly known. Using the recent measurements of the spatial extension and improved spectroscopy of the gamma-ray nebula, it has become –for the first time – feasible to determine in a robust way both the strength as well as the radial dependence of the magnetic field in the downstream flow. Methods. In this work, we introduce a detailed radiative model which was used to calculate the emission from non-thermal electrons (synchrotron and inverse Compton) as well as from thermal dust present in the Crab Nebula in a self-consistent way to compare it quantitatively with observational data. Special care was given to the radial dependence of the electron and seed field density. Results. The radiative model was used to estimate the parameters related to the electron populations responsible for radio and optical/X-ray synchrotron emission. In this context, the mass of cold and warm dust was determined. A combined fit based upon a χ2 minimisation successfully reproduced 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 ≈1.3 rs (rs: distance of the termination shock from the pulsar). The very high energy (VHE: E > 100 GeV) and ultra-high energy (UHE: E > 100 TeV) gamma-ray spectra set the strongest constraints on the radial dependence of the magnetic field, favouring a model where B(r) = (264 ± 9) μG(r/rs)−0.51 ± 0.03. For a collection of VHE measurements during epochs of higher hard X-ray emission, a significantly different solution B(r) = (167 ± 5) μG(r/rs)−0.29(+0.03, −0.06) is found. Conclusions. The high energy (HE: E > 100 MeV) and VHE gamma-ray observations of the Crab Nebula lift the degeneracy of the synchrotron emission between particle and magnetic field energy density. The reconstructed magnetic field and its radial dependence indicates a ratio of Poynting to kinetic energy flux σ ≈ 0.1 at the termination shock, which is ≈30 times larger than estimated up to now. Consequently, the confinement of the nebula would require additional mechanisms to slow the flow down through, for example, excitation of small-scale turbulence with possible dissipation of the magnetic field.

Hadronic re-acceleration at the Crab pulsar wind termination shock as a source of PeV gamma-rays

“…The flux of escaped shocked protons at the end of the simulation, the resulting gamma-ray spectra from the target region, and the particle distribution inside the simulation at the final timestep are shown in Figures 1 and 2. A variety of different hadronic interaction models are explored when using the distribution shown in Figure 1 as an input to GAMERA; SYBIL 2.1 is chosen for the gamma-ray emission fit shown in Figure 2, which is combined with a multi-band IC model taken from Dirson and Horns [1]. This is as it produces the most optimistic behaviour in terms of having a relatively lower hadronic flux at low energies which then rises at higher energy.…”

“…The Crab Nebula is the most widely studied object in Very-High-Energy (VHE) gamma-ray astrophysics [1][2][3]. It is generally accepted that the primary emission mechanism for gamma-rays above a TeV is Inverse Compton (IC) scattering of photons from a variety of background fields (primarily the Cosmic Microwave background at photon energies above 100 TeV) by electrons accelerated at the termination shock of the relativistic wind of the pulsar [4].…”

“…It is generally accepted that the primary emission mechanism for gamma-rays above a TeV is Inverse Compton (IC) scattering of photons from a variety of background fields (primarily the Cosmic Microwave background at photon energies above 100 TeV) by electrons accelerated at the termination shock of the relativistic wind of the pulsar [4]. The recent detection of PeV gamma-ray emission from the Crab Nebula by LHAASO and limits above 100 TeV from Tibet AS𝛾 [4,5] have re-opened a debate about whether there could be a secondary hadronic component producing the highest energy photons [4,6], which could potentially be observable due to the Klein-Nishina effect suppressing IC emission at the highest energies [1]. This scenario has not been excluded to date, and despite previous studies (e.g.…”

EASpy: fast simulation of fluorescence and Cherenkov light from extended air showers at large zenith angles

“…As a consequence of the limited collection area of the current generation of IACTS, the gamma-ray sky at energies above 100 TeV remains largely unexplored. The photon rate from the Crab Nebula, one of the brightest steady Galactic gamma-ray sources, for a collection area of 𝐴 eff = 1 km 2 is less than one photon per 100 h [1]. One way to increase 𝐴 eff is to use multiple IACTs (∼ 100) commonly placed with a distance of the order of ∼ 100 m apart from each other [2].…”