Geometry and Kinematics of a Dancing Milky Way: Unveiling the Precession and Inclination Variation across the Galactic Plane via Open Clusters
Zhihong He
Abstract
Abstract This Letter presents a study of the geometry and motion of the Galactic disk using open clusters in the Gaia era. The findings suggest that the inclination θ i of the Galactic disk increases gradually from the inner to the outer disk, with a shift in orientation at the Galactocentric radius of approximately 6 ± 1 kpc. Furthermore, this study brings forth the revelation that the mid-plane of the Milky Way may not possess a stationary or fixed position. A plausible explanation is that the inclined orbits of celestial bodies within our Galaxy exhibit a consistent pattern of elliptical shapes, deviating from perfect circularity; however, more observations are needed to confirm this. An analysis of the vertical motion along the Galactocentric radius reveals that the disk has warped with precession and that the line of node shifts at different radii, aligning with the results from the classical Cepheids. Although there is uncertainty for precession/peculiar motion in solar orbit, after considering the uncertainty, the study derives a median value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>LON</mml:mi> </mml:mrow> </mml:msub> </mml:math> = 6.8 km s −1 kpc −1 in the Galaxy. This value for the derived precession in the outer disk is lower than those in the literature due to the systematic motion in solar orbit ( θ i = 0.°6). The study also finds that the inclinational variation of the disk is significant and can cause systematic motion, with the variation rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> </mml:math> decreasing along the Galactic radius with a slope of −8.9 μ as yr −1 kpc −1 . Moreover, the derived <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> </mml:math> in solar orbit is 59.1 ± 11.2 sample ± 7.7 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> μ as yr −1 , which makes it observable for high-precision astrometry.