A Periodicity Analysis of the X-ray Flux Variations of the BL Lac Mrk 421

In this paper, we present the X-ray light curve (15-50keV) for the BL Lac Mrk 421 observed by the Burst Alert Telescope (BAT) on the Swift Gamma-Ray-Burst (GRB) Explorer from February 12, 2005 to November 26, 2012. We use the discrete correlation function (DCF) method, Jurkevich's method, and the power-spectrum method to analyze the data, and find consistent results. We find two flux-variation periods of Mrk 421, (1.7±0.1)yr and (3.7±0.1)yr. The period of 3.7yr in the X-ray band is consistent with the period of 3.95yr for the radio fluxes in the 22GHz and 37GHz bands as found by previous studies (Li et al. 2011). The 1.7yr periodic variation can be well explained by the model of the non-ballistic helical motion driven by the orbital motion in a binary black hole system (BBHS).