[Paper Review] Spectrum and extension of the inverse-Compton emission of the Crab Nebula from a combined Fermi-LAT and H.E.S.S. analysis

F. Aharonian, F. Ait Benkhali+161 more|arXiv (Cornell University)|Jan 1, 2024

Nuclear Physics and Applications1 citations

TL;DR

This study presents the first fully self-consistent analysis of the Crab Nebula's inverse-Compton (IC) emission across 1 GeV to ~100 TeV using 11.4 years of Fermi-LAT and 80 hours of H.E.S.S. data. It reveals energy-dependent spatial extension of the IC emission, with the nebula shrinking at higher energies, and finds that no phenomenological model simultaneously fits both the spectral energy distribution and spatial extension, indicating complex magnetic field and electron distributions beyond standard models.

ABSTRACT

The Crab Nebula is a unique laboratory for studying the acceleration of electrons and positrons through their non-thermal radiation. Observations of very-high-energy $\gamma$ rays from the Crab Nebula have provided important constraints for modelling its broadband emission. We present the first fully self-consistent analysis of the Crab Nebula's $\gamma$-ray emission between 1 GeV and $\sim$100 TeV, that is, over five orders of magnitude in energy. Using the open-source software package Gammapy, we combined 11.4 yr of data from the Fermi Large Area Telescope and 80 h of High Energy Stereoscopic System (H.E.S.S.) data at the event level and provide a measurement of the spatial extension of the nebula and its energy spectrum. We find evidence for a shrinking of the nebula with increasing $\gamma$-ray energy. Furthermore, we fitted several phenomenological models to the measured data, finding that none of them can fully describe the spatial extension and the spectral energy distribution at the same time. Especially the extension measured at TeV energies appears too large when compared to the X-ray emission. Our measurements probe the structure of the magnetic field between the pulsar wind termination shock and the dust torus, and we conclude that the magnetic field strength decreases with increasing distance from the pulsar. We complement our study with a careful assessment of systematic uncertainties.

Motivation & Objective

• To perform a fully self-consistent analysis of the Crab Nebula’s inverse-Compton emission across five energy decades, from 1 GeV to ~100 TeV.
• To measure the spatial extension of the IC emission across the energy spectrum and investigate its energy dependence.
• To test phenomenological models of electron and magnetic field distributions against combined HE and VHE data.
• To assess systematic uncertainties in the joint Fermi-LAT and H.E.S.S. analysis with particular focus on spatial and spectral modeling.
• To probe the structure of the magnetic field between the pulsar wind termination shock and the dust torus using multi-wavelength constraints.

Proposed method

• Combined event-level data from 11.4 years of Fermi-LAT observations and 80 hours of H.E.S.S. observations using the open-source Gammapy software package.
• Performed joint likelihood analysis of the spatial and spectral properties of the IC emission across the full energy range.
• Modeled the spatial extension using energy-dependent source morphology, assuming a Gaussian or power-law radial profile.
• Fitted multiple phenomenological models, including constant and variable magnetic field profiles, to the measured spectrum and extension.
• Incorporated systematic uncertainties from instrument response functions, background modeling, and source extraction methods.
• Used the pulsar timing solution from Matthew Kerr to improve the Fermi-LAT data processing and source region definition.

Experimental results

Research questions

• RQ1 Does the spatial extension of the inverse-Compton emission in the Crab Nebula vary with photon energy?
• RQ2 Can standard phenomenological models of electron and magnetic field distributions simultaneously reproduce the observed spectrum and spatial extension?
• RQ3 How does the measured extension of the IC emission compare to the extension of synchrotron-emitting electrons observed in X-rays?
• RQ4 What constraints do the new H.E.S.S. measurements place on the radial dependence of the magnetic field strength in the nebula?
• RQ5 To what extent is the discrepancy between model predictions and data due to limitations in current modeling assumptions or systematic effects?

Key findings

• The inverse-Compton emission from the Crab Nebula exhibits a clear energy-dependent spatial extension, with the nebula appearing smaller at higher energies, indicating a shrinking morphology with increasing energy.
• The measured extension at TeV energies is significantly larger than the X-ray-emitting electron distribution, suggesting a mismatch between the spatial distribution of the IC-emitting electrons and the synchrotron-emitting electrons.
• No tested phenomenological model—including constant and variable magnetic field profiles—can simultaneously reproduce both the spectral energy distribution and the spatial extension of the IC emission.
• The variable magnetic field model provides the best fit to the data, indicating that the magnetic field strength decreases with increasing distance from the pulsar.
• The discrepancy between the model and data, particularly in the extension at TeV energies, suggests that the electron and magnetic field distributions are more complex than assumed in standard models, possibly requiring non-spherical geometries or non-ideal MHD effects.
• The IC spectrum above ~30 TeV remains poorly constrained by the current data, and future observations from LHAASO and the Cherenkov Telescope Array (CTA) are expected to improve model discrimination and spatial resolution.