SIMBAD references

We have investigated the distributions of stellar azimuthal and radial velocity components V_Φ and V_R in the vertical position-velocity plane Z-V_Z across the Galactic disk of 6.34 <= R <= 12.34 kpc and | Φ| ≲7○ / . 5 using a Gaia and Gaia-LAMOST sample of stars. As found in previous works, the distributions exhibit significant spiral patterns. The V_R 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 V_Φ become more and more relaxed as R increases. The spiral patterns of V_Φ and V_R and the quadrupole patterns of V_R 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 V_Φ and V_R.