Discovery of a high confidence soft lag from an X-ray flare of Markarian 421

We present the X-ray variability properties of the X-ray and TeV bright blazar Mrk 421 with a ~60 ks long XMM-Newton observation performed on November 9-10, 2005. The source experienced a pronounced flare, of which the inter-band time lags were determined with a very high confidence level. The soft (0.6-0.8 keV) X-ray variations lagged the hard (4-10 keV) ones by 1.09 ks, and the soft lag increases with increasing difference in the photon energy. The energy-dependent soft lags can be well fitted with the difference of the energy-dependent cooling timescales of the relativistic electron distribution responsible for the observed X-ray emission, which constrains the magnetic field strength and Doppler factor of the emitting region to be B\delta^(1/3)~1.78 Gauss.