2021MNRAS.504.3168B

In 2018, the ESA Gaia satellite discovered a remarkable spiral pattern ('phase spiral') in the z - V_z phase plane throughout the solar neighbourhood, where z and V_z are the displacement and velocity of a star perpendicular to the Galactic disc. In response to Binney & Schonrich's analytic model of a disc-crossing satellite to explain the Gaia data, we carry out a high-resolution, N-body simulation (N ≃ 10⁸ particles) of an impulsive mass (2 x 10¹⁰ M_☉) that interacts with a cold stellar disc at a single transit point. The disc response is complex since the impulse triggers a superposition of two distinct bisymmetric (m = 2) modes - a density wave and a corrugated bending wave - that wrap up at different rates. Stars in the faster density wave wrap up with time T according to ph_D(R, T) = (Ω_D(R) + Ω_o) T, where ph_D describes the spiral pattern and Ω_D = Ω(R) - κ(R)/2, where κ is the epicyclic frequency. While the pattern speed Ω_o is small, it is non-zero. The slower bending wave wraps up according to Ω_B ≃ Ω_D/2 producing a corrugated wave. The bunching effect of the density wave triggers the phase spiral as it rolls up and down on the corrugated wave ('roller coaster' model). The phase spiral emerges slowly about ΔT ≃ 400 Myr after impact. It appears to be a long-lived, disc-wide phenomenon that continues to evolve over most of the 2 Gyr simulation. Thus, given Sagittarius' (Sgr) low total mass today (M_tot ∼ 3 x 10⁸ M_☉ within 10 kpc diameter), we believe that the phase spiral was excited by the disc-crossing dwarf some 1-2 Gyr before the recent transit. For this to be true, Sgr must be losing mass at 0.5-1 dex per orbit loop.