Statistical analysis on XMM-Newton X-ray flares of Mrk 421: distributions of peak flux and flaring time duration

The energy dissipation mechanism in blazar jet is unknown. Blazar's flares could provide insights on this problem. Here we report statistical results of XMM-Newton X-ray flares of Mrk 421. We analyze all public XMM-Newton X-ray observations for Mrk 421, and construct the light curves. Through fitting light curves, we obtain the parameters of flare-profiles, such as peak flux ($F_{\rm p}$) and flaring time duration ($T_{\rm fl}$). It is found that both the distributions of $F_{\rm p}$ and $T_{\rm fl}$ obey a power-law form, with the same index of $\alpha_{\rm F}=\alpha_{\rm T}\approx1$. The statistical properties are consistent with the predictions by a self-organized criticality (SOC) system with energy dissipation in one-dimensional space. This is similar to solar flare, but with different space dimensions of the energy dissipation domain. This suggests that X-ray flaers of Mrk 421 are possibly driven by a magnetic reconnection mechanism. Moreover, in the analysis, we find that variability on timescale of $\sim1000\ $s frequently appears. Such rapid variability indicates a magnetic field of $\geq 2.1\delta_{\rm D}^{-1/3}$ G ($\delta_{\rm D}$ is the Doppler factor) in emission region.