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 u
nderstand 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.
The very high energy (VHE) gamma ray spectral index of high energy peaked blazars correlates strongly with its corresponding redshift whereas no such correlation is observed in the X-ray or the GeV bands. We attribute this correlation to a result of
photon-photon absorption of TeV photons with the extragalactic background light (EBL) and utilizing this, we compute the allowed flux range for the EBL, which is independent of previous estimates. The observed VHE spectrum of the sources in our sample can be well approximated by a power-law, and if the de-absorbed spectrum is also assumed to be a power law, then we show that the spectral shape of EBL will be $epsilon n(epsilon) sim k log(frac{epsilon}{epsilon_p}) $. We estimate the range of values for the parameters defining the EBL spectrum, $k$ and $epsilon_p$, such that the correlation of the intrinsic VHE spectrum with redshift is nullified. The estimated EBL depends only on the observed correlation and the assumption of a power law source spectrum. Specifically, it does not depend on the spectral modeling or radiative mechanism of the sources, nor does it depend on any theoretical shape of the EBL spectrum obtained through cosmological calculations. The estimated EBL spectrum is consistent with the upper and lower limits imposed by different observations. Moreover, it also agrees closely with the theoretical estimates obtained through cosmological evolution models.
