Understanding the X-ray spectral curvature of Mkn 421 using broad-band AstroSat observations

Abstract

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.

Correlations between X-ray spectral parameters of Mkn 421 using long-term Swift–XRT data

“…In §3, we present the spectral study using log-parabola model ( §3.1), Power-law with maximum electron energy model ( §3.2), and Energy dependent model ( §3.3); EDD ( §3.3.1) and EDA ( §3.3.2). In §3.4, we compare the correlation study results with the ones obtained with short-term flare in (Hota et al 2021). Finally, we discuss and conclude the results in §4.…”

“…Furthermore, Goswami et al 2020 showed that the power-law with γmax model can explain the curved spectrum in the X-ray band in case of EHBL source RGB J0710+591, where the synchrotron spectrum corresponding to the decline of the particle number density near the maximum available electron energy, can explain the sharp spectral curvature. Nevertheless, Hota et al 2021 had shown with the approach of spectral parameter correlations that the obtained correlations are not consistent with the predictions from the power-law with γmax model. Instead, they showed that curved spectrum can be interpreted as an outcome of energy dependent acceleration and diffusion of the particles.…”

“…This SYNchrotron CONVolution equation including single-particle emissivity and particle number density is solved numerically and is used as a local convolution model (synconv ⊗ n(ξ)) in XSPEC (Version 12.11.0) software package (Arnaud 1996). In the model, the XSPEC "energy" variable is represented as ξ = √ Cγ such that the corresponding observed photon energy is ǫ = ξ 2 (Hota et al 2021). The (synconv ⊗ n(ξ)) model outputs the synchrotron spectrum for a system with particle density, n(ξ) as an input to the model.…”

“…Here, tesc can not be larger than the free streaming value, tesc,R, and this set limits on γ to γ < γR . Consequently for γ0 < γ and if we neglect the synchrotron energy loss, the electron energy distribution with the energy dependence of tesc will take the form (Hota et al 2021),…”

“…We perform a correlation study between the best fit model parameters and compare them with the ones obtained from the log-parabola spectral fit. Hota et al 2021, used these models and showed that the correlations between the spectral parameters for a single short-term flare with a duration ∼ 400 ksec can be used to constraint different models and provide an assessment of the underlying physical quantities. The motivation of this work is to test whether the correlation results from the long-term observations are consistent with the one obtained from short-term flare (Hota et al 2021).…”