The age-velocity dispersion relation of the Galactic discs from LAMOST-Gaia data

We present the age-velocity dispersion relation (AVR) in three dimensions in the solar neighbourhood using 3564 commonly observed sub-giant/red giant branch stars selected from The Large Sky Area Multi-Object Fiber Spectroscopic Telescope, which gives the age and radial velocity, and Gaia, which measures the distance and proper motion. The stars are separated into metal-poor ([Fe/H] < -0.2 dex and metal-rich ([Fe/H] > -0.2 dex) groups, so that the metal-rich stars are mostly alpha-poor, while the metal-poor group are mostly contributed by a-enhanced stars. Thus, the old and metal-poor stars likely belong to the chemically defined thick disc population, while the metal-rich sample is dominated by the thin disc. The AVR for the metal-poor sample shows an abrupt increase at greater than or similar to 7 Gyr, which is contributed by the thick disc component. On the other hand, most of the thin disc stars with [Fe/H] > -0.2 dex display a power-law-like AVR with indices of about 0.3-0.4 and 0.5 for the in-plane and vertical dispersions, respectively. This is consistent with the scenario that the disc is gradually heated by the spiral arms and/or the giant molecular clouds. Moreover, the older thin disc stars (> 7 Gyr) have a rounder velocity ellipsoid, i.e. sigma(phi)/sigma(z), is close to 1.0, probably due to the more efficient heating in vertical direction. Particularly for the old metal-poor sample located with vertical bar z vertical bar > 270 pc, the vertical dispersion is even larger than its azimuthal counterpart. Finally, the vertex deviations and the tilt angles are plausibly around zero with large uncertainties.