Erratum: Inferring the origins of the pulsed γ -ray emission from the Crab pulsar with ten-year Fermi -LAT data (Astronomy and Astrophysics (2020) 640 (A43) DOI: 10.1051/0004-361/202038166)
This is a corrigendum to the original article Yeung (2020) and is mostly adapted from Appendix C.4 of the author’s Ph.D. Thesis (Yeung 2021). In Sect. 3.4 of the original article, we deduced from the power law with a scaling factor (PLSF) fitting result that for P2M is lower than that for P1M. Nevertheless, the previous calculation of the significance of this di erence did not consider the covariance of the values for P1M and P2M (it should be noted that the spectral data for P1M and P2M are fit simultaneously such that their solutions share the same scaling factor). After taking this covariance into account, which is computed to be 0.010, we now determine that for P2M is lower than that for P1M by 0:35 - 0:08, which corresponds to 4:2 (much higher than the 2:1 reported in the original paper). Additionally, Fig. 1 demonstrates that the 4 confidence region of values for P1M and P2M excludes all equal-value combinations. The revised significance strengthens the argument that the flux ratio of P1 to P2 still decreases with photon energy even above 10 GeV. This, in turn, strengthens the interpretation that there are anisotropic pulsar winds that could lead to the observed harder spectrum at P2M relative to P1M (as put forward by Aharonian et al. 2012). Moreover, taking the statistical errors into account, the values obtained for MAGIC and VERITAS (both 1.22) are basically consistent with the estimated systematic errors of around 15% on energy scales of IACT telescopes under excellent atmospheric conditions (e.g., Aharonian et al. 2006; Aleksi´c et al. 2016). This provides further confirmation for the physical reasonableness of those fitting results. (Figure Presented).