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We investigate a mechanism to form and keep a planar spatial distribution ofsatellite galaxies in the Milky Way (MW), which is called the satellite plane.It has been pointed out that the {\Lambda}CDM cosmological model hardlyexplains the existence of such a satellite plane, so it is regarded as one ofthe serious problems in the current cosmology. We here focus on a rotation ofthe gravitational potential of a host galaxy, i.e., so-called a figurerotation, following the previous suggestion that this effect can induce thetilt of a so-called tube orbit. Our calculation shows that a figure rotation ofa triaxial potential forms a stable orbital plane perpendicular to therotational axis of the potential. Thus, it is suggested that the MW's dark halois rotating with its axis being around the normal line of the satellite plane.Additionally, we find that a small velocity dispersion of satellites isrequired to keep the flatness of the planar structure, namely the standardderivation of their velocities perpendicular to the satellite plane needssmaller than their mean rotational velocity on the plane. Although not all theMW's satellites satisfy this condition, some fraction of them called membersatellites, which are prominently on the plane, satisfy it. We suggest thatthis picture explaining the observed satellite plane can be achieved by thefilamentary accretion of dark matter associated with the formation of the MWand a group infall of member satellites along this cosmic filament.

New insights on the dynamics of satellite galaxies: effects of the figure rotation of a host galaxy