Investigating the Anti-Correlation between Photon Index and Flux of the Crab using RXTE and NuSTAR

We present a systematic study of the recently reported anti-correlation between X-ray flux and photon index ($\mathrm{\Gamma }$) in the Crab Nebula, using archival RXTE/PCA (3 - 50 keV), RXTE/HEXTE (20 - 100 keV), and NuSTAR (3 - 78 keV) observations. Spectra were extracted in soft (3 - 10 keV) and hard bands (10 - 50 keV, 10 - 78 keV, 20 - 100 keV) and fitted with an absorbed power-law model. Across all instruments and energy ranges, we confirm the existence of a persistent negative correlation – harder spectra at higher flux levels. The correlation is stronger in the hard bands compared to the soft bands. This is consistent with synchrotron emission modulated by magnetic field variations in the pulsar wind nebula.