Abstract
Short precession periods like 164d of SS433 can be well determined by observations of time scales longer or much longer than the precession period. However, it doesn't work for sources with precession periods of millions of years. This paper utilizes the particular morphologies of X-shaped sources, so that the 3 dimension kinematics of lobes can be obtained. Thus, for the first time, the million-year precession period of X-shaped sources by observer on the Earth can be determined elegantly: $(6.1\pm 1.5)$Myr, $(1.8\pm 0.5)$Myr, and $(3.2\pm 1.2)$Myr for 3C52, 3C223.1 and 4C12.03 respectively. The result naturally explains the asymmetry displayed in the morphology of these sources, and the effect of propagation time on the diversity of morphologies is well demonstrated. The precession period may originate from long-term effects of a binary super-massive black hole system, which is a potential source of gravitational wave radiation.
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