The LAMOST Spectroscopic Survey of Supergiants in M31 and M33

We present systematic identifications of supergiants of M31/M33 based on massive LAMOST spectroscopic survey. Radial velocities of nearly 5000 photometrically selected M31/M33 supergiant candidates have been properly derived from the qualified spectra released in LAMOST DR10. By comparing their radial velocities with those predicted from the rotation curves of M31, as well as utilizing {\it Gaia} astrometric measurements to exclude foreground contaminations, 199 supergiant members in M31, including 168 Rank1' and 31 Rank2’, have been successfully identified. This sample contains 62 blue supergiants (BSGs, all Rank1'), 134 yellow supergiants (YSGs, 103 Rank1’ and 31 Rank2') and 3 red supergiants (RSGs, all Rank1’). For M33, we identify 84 supergiant members (56 Rank1' and 28 Rank2’), which includes 28 BSGs (all Rank1'), 53 YSGs (25 Rank1’ and 28 Rank2') and 3 RSGs (all Rank1’). So far, this is one of the largest supergiant sample of M31/M33 with full optical wavelength coverage (3700 \textless $\lambda$ \textless 9100 Å). This sample is valuable for understanding the star formation and stellar evolution under different environments.