The Energy-dependent $\gamma$-ray Morphology of the Crab Nebula Observed with the Fermi Large Area Telescope

Abstract

The Crab Nebula is a bright emitter of non-thermal radiation across the entire accessible range of wavelengths. The spatial and spectral structures of the synchrotron nebula are well-resolved from radio to hard X-ray emission. The un-pulsed emission at GeV to TeV energies is mostly produced via inverse-Compton scattering of energetic electrons with the synchrotron-emitted photons. The spatial structure observed at these energies provides insights into the distribution of electrons and indirectly constrains the so-far unknown structure of the magnetic field in the nebula. Analyzing the LAT data accumulated over $\sim$9.1 years with a properly refined model for the Crab pulsar's spectrum, we determined the 68\% containment radius ($R_{68}$) of the Crab Nebula to be $(0.0330\pm 0.0025_{stat}{{}_{-0.0075}^{+0.0012}}_{sys}{)}^{\circ }$ ($1.98^{\prime }\pm 0.15_{stat}^{\prime }{{}_{-0.45^{\prime }}^{+0.07^{\prime }}}_{sys}$) in the 5--500 GeV band. The estimated systematic uncertainty is based on two factors: (1) different analysis methods, morphological models and event types, and (2) the point-spread-function evaluated with observations of Mkn 421. When comparing the \emph{Fermi} LAT and H.E.S.S. results on the spatial extension, we find evidence for an energy-dependent shrinking of the Crab Nebula's $\gamma$-ray extension ($R_{68}\propto E_{\mathrm{IC}}^{-\alpha }$ where $\alpha =0.155\pm 0.035_{stat}{-0.037}_{sys}$).

Original article published in ApJ on 2019 April 23; Erratum (at the back) submitted to ApJ on 2021 February 1