Unfolding the X-ray spectral curvature of Mkn 421 for further clues

The X-ray observations of Mkn 421 show significant spectral curvature that can be reproduced by a log-parabola function. The spectra can also be fitted by an analytical model considering synchrotron emission from an electron distribution that is accelerated at a shock front with an energy-dependent diffusion (EDD model). The spectral fit of NuSTAR and Swift-XRT observations using EDD model during different flux states reveals that the model parameters are strongly correlated. We perform a detailed investigation of this correlation to decipher the information hidden underneath. The model predicts the synchrotron peak energy to be correlated with the peak spectral curvature, which is consistent with the case of Mkn 421. Expressing the energy dependence of the diffusion in terms of the magnetohydrodynamic turbulence energy index, it appears that the turbulence shifts from Kolmogorov/Kraichnan type to Bohm limit during high flux states. Further, the correlation between the best-fitting parameters of EDD model lets us derive an expression for the product of source magnetic field(B) and jet Doppler factor(δ) in terms of synchrotron and Compton peak energies. The synchrotron peak energy is obtained using the simultaneous Swift-XRT-NuSTAR observations, whereas the Compton peak energy is estimated by performing a linear regression analysis of the archival spectral peaks. The deduced δB varies over a wide range; however, it satisfies reasonably well with the values estimated solely from the spectral peak energies independent of the EDD model. This highlights the plausible connection between the microscopic description of the electron diffusion with the macroscopic quantities deciding the broad-band spectrum of Mkn 421.