We present a time-resolved X-ray spectral study of the high energy peaked blazar Mkn 421 using simultaneous broadband observations from the LAXPC and SXT instruments on-board AstroSat. The ∼400 ksec long observation taken during 3–8 January, 2017 was divided into segments of 10 ksecs. Each segment was fitted using synchrotron emission from particles whose energy distribution was represented by a log-parabola model. We also considered particle energy distribution models where (i) the radiative cooling leads to a maximum energy (ξmax model), (ii) the system has energy dependent diffusion (EDD) and (iii) has energy dependent acceleration (EDA). We found that all these models describe the spectra, although the EDD and EDA models were marginally better. Time resolved spectral analysis allowed for studying the correlation between the spectral parameters for different models. In the simplest and direct approach, the observed correlations are not compatible with the predictions of the ξmax model. While the EDD and EDA models do predict the correlations, the values of the inferred physical parameters are not compatible with the model assumptions. Thus, we show that spectrally degenerate models, can be distinguished based on spectral parameter correlations (especially those between the model normalization and spectral shape ones) making time-resolved spectroscopy a powerful tool to probe the nature of these systems.
We have performed a detailed analysis of the X-ray spectra of the blazar Mkn 421 using Swift-XRT observations taken between 2005 and 2020, to quantify the correlations between spectral parameters for different models. In an earlier work, it has been shown that such spectral parameter correlations obtained from a single short flare of duration ∼ 5-days of Mkn 421, can be used to distinguish spectrally degenerate models and provide estimates of physical quantities. In this work, we show that the results from the long-term spectral parameter correlations are consistent with those obtained from the single flare. In particular, that the observed spectral curvature is due to maximum cutoff energy in the particle distribution is ruled out. Instead, models where the curvature is due to the energy dependence of escape or acceleration time-scale of the particles are favored. The estimated values of the physical parameters for these models are similar to the ones obtained from the single flare analysis and are somewhat incompatible with the physical assumption of the models, suggesting that more complex physical models are required. The consistency of the results obtained from the long and short-term evolution of the source, underlines the reliability of the technique to use spectral parameter correlations to distinguish physical models.
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