Influence of energy-dependent particle diffusion on the X-ray spectral curvature of MKN 421

The X-ray spectral curvature of blazars is traditionally explained by an empirical log-parabola function characterized by three parameters, namely the flux, curvature, and spectral index at a given energy. Since their exact relationship with the underlying physical quantities is unclear, interpreting the physical scenario of the source through these parameters is difficult. To attain an insight on the X-ray spectral shape, we perform a detailed study of the X-ray spectra of the blazar MKN 421, using an analytical model where the electron diffusion from the particle acceleration site is energy dependent. The resultant synchrotron spectrum is again determined by three parameters, namely, the energy index of the escape time-scale, the quantity connecting the electron energy to the observed photon energy, and the normalization. The X-ray observations of MKN 421, during 2012 July-2013 April by Nuclear Spectroscopic Telescope Array and Swift-XRT are investigated using this model and we find a significant correlation between model parameters and the observational quantities. Additionally, a strong anticorrelation is found between the fit parameters defining the spectral shape, which was not evident from earlier studies using empirical models. This indicates the flux variations in MKN 421 and possibly other blazars, may arise from a definite physical process that needs to be further investigated.