The Astrophysical Journal, Volume 677, p. 906

arXiv:0710.4138

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We present a detailed analysis of week-long simultaneous observations of the blazar Mrk 421 at 2-60 keV X-rays (RossiXTE) and TeV gamma-rays (Whipple andHEGRA) in 2001. Accompanying optical monitoring was performed with the Mt. Hopkins 48" telescope. The unprecedented quality of this dataset enables us not only to establish the existence of the correlation between the TeV and X-ray luminosities, but also to start unveiling some of its more detailed characteristics, in particular its energy dependence, and time variability. The source shows strong variations in both X-ray and gamma-ray bands, which are highly correlated. No evidence of a non-zero X-ray/gamma-ray interband lag is found on the full week dataset. The upper limit on a delay is approximately 3 ks. A more detailed analysis focused on the March 19 flare, however, reveals that data are not consistent with the peak of the outburst in the 2-4 keV X-ray and TeV band being simultaneous. For this event we estimate a 2.1 +-  0.7 ks lag of the TeV flare with respect to the 2-4 keV X-ray band. The correlation with a higher X-ray energy band, namely 9-15 keV is consistent with coordinated variations, i.e. the gamma-ray rate is better correlated with the harder X-ray rate. The amplitudes of the X-ray and gamma-ray variations are also highly correlated, and the TeV luminosity increases more than linearly with respect to the X-ray one. The high degree of correlation lends further support to the standard model in which a unique electrons population produces the Xrays by synchrotron radiation and the gamma-ray component by inverse Compton scattering. However, the  finding that for the individual best observed flares (March 18/19 and 22/23) the gamma-ray flux scales approximately quadratically with respect to the X-ray flux, poses a serious challenge to emission models for TeV blazars. Rather special conditions and/or  ne tuning of the temporal evolution of the physical parameters of the emission region are required in order to reproduce the quadratic correlation. We briefly discuss the astrophysical consequences of these new findings in the context of the competing models for the jet emission in blazars.