The uninterrupted 7 day ASCA observations of the TeV blazar Mrk 421 in 1998 have clearly revealed that X-ray flares occur repeatedly. In this paper, we present the results of the time-resolved spectral analysis of the combined data taken by ASCA, RXTE, BeppoSAX, and the Extreme Ultraviolet Explorer (EUVE). In this object - and in many other TeV blazars - the precise measurement of the shape of the X-ray spectrum, which reflects the high-energy portion of the synchrotron component, is crucial in determining the high-energy cutoff of the accelerated electrons in the jet. Thanks to the simultaneous broadband coverage, we measured the 0.1-25 keV spectrum resolved on timescales as short as several hours, providing a great opportunity to investigate the detailed spectral evolution at the flares. By analyzing the time-subdivided observations, we parameterize the evolution of the synchrotron peak, where the radiation power dominates, by fitting the combined spectra with a quadratic form [where the νFν flux at the energy E obeys logνFnu;(E) = log (νFν,peak) - const (log E-log Epeak)2]. In this case, we show that there is an overall trend that the peak energy E peak and peak flux νFν,peak increase or decrease together. The relation of the two parameters is best described as E peak ∝ νFν,peak0.7 for the 1998 campaign. Similar results were derived for the 1997 observations, while the relation gave a smaller index when both 1997 and 1998 data were included. On the other hand, we show that this relation, and also the detailed spectral variations, differs from flare to flare within the 1998 campaign. We suggest that the observed features are consistent with the idea that flares are due to the appearance of a new spectral component. With the availability of the simultaneous TeV data, we also show that there exists a clear correlation between the synchrotron peak flux and the TeV flux.
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