Study of underlying particle spectrum during huge X-ray flare of Mkn 421
  in April 2013
  Context: In April 2013, the nearby (z=0.031) TeV blazar, Mkn 421, showed one
of the largest flares in X-rays since the past decade. Aim: To study all
multiwavelength data available during MJD 56392 to 56403, with special emphasis
on X-ray data, and understand the underlying particle energy distribution.
Methods: We study the correlations between the UV and gamma bands with the
X-ray band using the z-transformed discrete correlation function. We model the
underlying particle spectrum with a single population of electrons emitting
synchrotron radiation, and do a statistical fitting of the simultaneous,
time-resolved data from the Swift-XRT and the NuSTAR. Results: There was rapid
flux variability in the X-ray band, with a minimum doubling timescale of $1.69
\pm 0.13$ hrs. There were no corresponding flares in UV and gamma bands. The
variability in UV and gamma rays are relatively modest with $ \sim 8 \% $ and
$\sim 16 \% $ respectively, and no significant correlation was found with the
X-ray light curve. The observed X-ray spectrum shows clear curvature which can
be fit by a log parabolic spectral form. This is best explained to originate
from a log parabolic electron spectrum. However, a broken power law or a power
law with an exponentially falling electron distribution cannot be ruled out
either. Moreover, the excellent broadband spectrum from $0.3-79$ keV allows us
to make predictions of the UV flux. We find that this prediction is compatible
with the observed flux during the low state in X-rays. However, during the
X-ray flares, the predicted flux is a factor of $2-50$ smaller than the
observed one. This suggests that the X-ray flares are plausibly caused by a
separate population which does not contribute significantly to the radiation at
lower energies. Alternatively, the underlying particle spectrum can be much
more complex than the ones explored in this work.
