Anti-correlation between Flux and Photon Index of Hard X-ray Emission from The Crab

Using $\mathit{\text{Swift}}$ Burst Alert Telescope (BAT) event-mode data during Gamma Ray Burst (GRB) occurrences, we conducted spectral analysis for the Crab system. From 38 good observations, which spans over a period of 18 years from 2006 to 2023, we found that the Crab’s X-ray flux does not only flicker, but also significantly anti-correlates to its spectral power-law photon index. Since emission contribution of the Crab pulsar in this energy range is small, this anti-correlation is mainly about the emission of the Crab nebula. We suggest that this anti-correlation is an observational supporting evidence for the long-standing notion that the nebula emission is due to synchrotron radiation of shocked pulsar winds in the nebula.