North-South asymmetries in the Galactic thin disc associated with the vertical phase spiral as seen using LAMOST-Gaia stars

We select 1052 469 (754 635) thin disc stars from Gaia eDR3 and LAMOST DR7 in the range of Galactocentric radius R (guiding centre radius R-g) from 8 to 11 kpc to investigate the asymmetries between the North and South of the disc mid-plane. More specifically, we analyse the vertical velocity dispersion profiles (sigma(nu z) (z)) in different bins of R (R-g) and [Fe/H]. We find troughs in the profiles of sigma(nu z)(z) located in both the North (z - 0.7 kpc) and South (z similar to -0.5 kpc) of the disc at all radial and chemical bins studied. The difference between the Northern and Southern vertical velocity dispersion profiles (Delta sigma(nu z)(vertical bar z vertical bar)) shows a shift between curves of different R and R-g. A similar shift exists in these North-South (NS) asymmetry profiles further divided into different [Fe/H] ranges. The sample binned with R-g more clearly displays the features in the velocity dispersion profiles. The shift in the peaks of the sigma(nu z) profiles and the variation in the phase spiral shape binned by metallicity indicate the variation of the vertical potential profiles and the radial metallicity gradient. The wave-like signal in NS asymmetry of sigma(nu z)(z) largely originates from phase spiral; while the NS asymmetry profiles of [Fe/H] only display a weak wave-like feature near solar radius. We perform a test particle simulation to qualitatively reproduce the observed results. A quantitative explanation of the NS asymmetry in the metallicity profile needs careful consideration of the spiral shape and the perturbation model, and we leave this for future work.