The Galactic Disk Phase Spirals at Different Galactic Positions Revealed by Gaia and LAMOST Data

We have investigated the distributions of stellar azimuthal and radial velocity components VΦ and VR in the vertical position–velocity plane Z–VZ across the Galactic disk of 6.34 ≲ R ≲ 12.34 kpc and $| {\rm{\Phi }}| \lesssim 7\buildrel{\circ}\over{.} 5$ using a Gaia and Gaia-LAMOST sample of stars. As found in previous works, the distributions exhibit significant spiral patterns. The VR distributions also show clear quadrupole patterns, which are the consequence of the well-known tilt of the velocity ellipsoid. The observed spiral and quadrupole patterns in the phase space plane vary strongly with radial and azimuthal positions. The phase spirals of VΦ become more and more relaxed as R increases. The spiral patterns of VΦ and VR and the quadrupole patterns of VR are strongest at −2° < Φ < 2° but negligible at 4° < Φ < 6° and −6° < Φ < −4°. Our results suggest an external origin of the phase spirals. In this scenario, the intruder, most likely the previously well-known Sagittarius dwarf galaxy, passed through the Galactic plane in the direction toward either Galactic center or anti-center. The azimuthal variations of the phase spirals also help us constrain the passage duration of the intruder. A detailed model is required to reproduce the observed radial and azimuthal variations of the phase spirals of VΦ and VR.