Title:Sub-Day Timescale X-ray Spectral Variability of the TeV Blazars Mrk 421 and 1ES 1959+650

Abstract:We present X-ray spectra ($0.7-20$ keV) of two high synchrotron-peaked blazars Mrk 421 and 1ES 1959+650 from simultaneous observations by the SXT and LAXPC instruments onboard \textit{AstroSat} and the \textit{Swift}-XRT during multiple intervals in 2016-19. The spectra of individual epochs are satisfactorily fitted by the log-parabola model. We carry out time-resolved X-ray spectroscopy using the \textit{AstroSat} data with a time resolution of $\sim$10 ks at all epochs, and study the temporal evolution of the best-fit spectral parameters of the log-parabola model. The energy light curves, with duration ranging from $0.5-5$ days, show intra-day variability and change in brightness states from one epoch to another. We find that the variation of the spectral index ($\alpha$) at hours to days timescale has an inverse relation with the energy flux and the peak energy of the spectrum, which indicates a harder-when-brighter trend in the blazars. The variation of curvature ($\beta$) does not follows a clear trend with the flux and has an anti-correlation with $\alpha$. Comparison with spectral variation simulated using a theoretical model of time variable nonthermal emission from blazar jets shows that radiative cooling and gradual acceleration of emitting particles belonging to an initial simple power-law energy distribution can reproduce most of the variability patterns of the spectral parameters at sub-day timescales.