The proper motion of Andromeda from Gaia eDR3: confirming a nearly radial orbit

We present an analysis of the proper motion of the Andromeda galaxy (M31), based on the Early Third Data Release of the {\it Gaia} mission. We use the {\it Gaia} photometry to select young blue main sequence stars, and apply several quality cuts to obtain clean samples of these tracers. After correcting the proper motion measurements for the internal rotation of the M31 disk motion, we derive an apparent motion of $53.6 \pm 7.7 \, \mu as/yr$ with respect to the {\it Gaia} reference frame, or $62.0 \pm 9.6 \, \mu as/yr$ after applying a zero-point correction determined from quasars within $20°$ from M31. Accounting for the Solar reflex motion we deduce a relative velocity between Andromeda and the Milky way (in a non-rotating frame at the current location of the Sun) of $46.7 \pm 40.8 \, {\rm km.s^{-1}}$, (along right ascension) and $-64.7 \pm 31.7 \, {\rm km.s^{-1}}$ (along declination), with a total transverse velocity of $V_{\rm trans} = 79.8 \pm 38.3 \, {\rm km.s^{-1}}$. These values are consistent with (but more accurate than) earlier Hubble Space Telescope measurements that predict future merger between the two galaxies. We also note a surprisingly large difference in the derived proper motion between the blue stars in M31 and samples of red stars that appear to lie in that galaxy. We suspect that this is due to contamination from a foreground stellar stream.