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

TL;DR

This study analyzes nearly a decade of Fermi LAT data to measure the energy-dependent gamma-ray size of the Crab Nebula, revealing a shrinking extension at higher energies and providing insights into electron distribution and magnetic field structure.

Contribution

It presents the first detailed measurement of the Crab Nebula's gamma-ray morphology across energies, highlighting an energy-dependent shrinking of the nebula's size.

Findings

Measured the nebula's 68% containment radius in the 5-500 GeV range.

Found evidence for the nebula's gamma-ray extension decreasing with energy.

Quantified the energy dependence with a power-law index of approximately 0.155.

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 $({0.0330\pm0.0025_{stat}}{^{+0.0012}_{-0.0075}}_{sys})^\circ$ (${1.98'\pm0.15'_{stat}}{^{+0.07'}_{-0.45'}}_{sys}$) 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 $\alpha=0.155\pm0.035_{stat}{-0.037}_{sys}$).

Full text

Erratum: “The Energy-dependent $\gamma$-ray Morphology of the Crab Nebula Observed with the Fermi Large Area Telescope” (2019, ApJ, 875, 123)

Paul K. H. Yeung

Institute for Experimental Physics, Department of Physics, University of Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany

Dieter Horns

Institute for Experimental Physics, Department of Physics, University of Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany

(Received February 1, 2021) ††journal: ApJ

In our original article Yeung & Horns (2019), the superimposed spatial model assigned to the whole Crab (i.e. a superposition of a point component [pulsar] and an extended component [nebula]) was following the analysis scheme of Fermi-LAT Collaboration & Biteau (2018). Nevertheless, there is a deficiency of our $\gamma$-ray extension measurements for the Crab Nebula, which is stemming from the Crab pulsar’s model. There is not only deviation in spectral modelling for the pulsar component, but also inaccuracy in convolving the pulsar’s spatial morphology (i.e. the point source morphology) with the PSF. According to Figure 3 of our Yeung (2020), the pulsar’s differential flux accounts for $\sim$(15–72)% of the Crab’s total differential flux from 5 to 40 GeV. Therefore, the aforementioned systematic effect associated with the pulsar component was particularly large for the 5–40 GeV extension measurements reported in our original article.

With regards to this issue, we perform follow-up checks for the 5–40 GeV extension sizes by selecting only off-pulse phase data for analyses and, accordingly, removing the pulsar component from the source model. We adopt the timing solution of the Crab pulsar provided by M. Kerr. We define the off-pulse phase in the same way as in our Yeung & Horns (2020). We perform binned maximum-likelihood analyses, with an angular bin size of $0.01^{\circ}$, on P8R3 data accumulated over the first 10 years of observations. We adopt the 4FGL point source catalogue (The Fermi-LAT collaboration, 2019), the Galactic diffuse model “gll-iem-v07” and the isotropic diffuse model “iso-P8R2-CLEAN-V6-v07”. Other details of data reduction criteria and analysis procedures roughly follow our original article.

It turns out that the disk radius of the Crab Nebula is revised to be $0.041^{+0.016}_{-0.025}$, $0.070^{+0.008}_{-0.009}$ and $0.042^{+0.009}_{-0.011}$ deg in 5–10, 10–20 and 20–40 GeV respectively. Moreover, the revised disk radii in the combined 5–20 GeV segment and the broad 5–500 GeV band are $0.064^{+0.007}_{-0.008}$ and $0.047^{+0.005}_{-0.006}$ deg respectively.

As demonstrated in Figure 1, these revised results do not throw doubt on the conclusions on excess 5–20 GeV extensions (relative to the radio extension) and on energy-dependent shrinking in our original paper.