Galactic seismology: the evolving ‘phase spiral’ after the Sagittarius dwarf impact

ABSTRACT In 2018, the ESA Gaia satellite discovered a remarkable spiral pattern (‘phase spiral’) in the z − Vz phase plane throughout the solar neighbourhood, where z and Vz are the displacement and velocity of a star perpendicular to the Galactic disc. In response to Binney & Schönrich’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 × 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 ϕD(R, T) = (ΩD(R) + Ωo) T, where ϕD describes the spiral pattern and ΩD = Ω(R) − κ(R)/2, where κ is the epicyclic frequency. While the pattern speed Ωo is small, it is non-zero. The slower bending wave wraps up according to ΩB ≈ ΩD/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 (Mtot ∼ 3 × 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.