Extreme Hard X-ray Variability in the TeV Blazar Mrk 421: Insights from <em>NuSTAR</em> Observations

In this work, we investigate the hard X-ray variability of the TeV blazar Mrk 421 over both long-term and intra-day timescales to gain insights into the particle acceleration and cooling mechanisms driving its emission. Using 28 NuSTAR observations spanning 2012 to 2024, we conduct detailed spectral and timing analyses. Our findings reveal pronounced flux variability, with changes by up to a factor of 200 over the decade and a 10-fold increase within a period of 15 days during a flaring episode. The flux distribution exhibits a lognormal profile, and a linear root-mean-square (RMS)–flux relation suggests a multiplicative variability process. Spectral analysis indicates that a log-parabolic model best describes most observations, with a strong linear anti-correlation between the photon index and curvature parameter. We also identify a positive correlation between the synchrotron peak energy and flux, accompanied by a subtle “harder-when-brighter” trend. These results align with standard blazar emission models, supporting particle acceleration via shock fronts or magnetic reconnection in the relativistic jet.