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.

Cet article explore les excursions dans le temps et leurs implications.

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