Hi All

Well I am impressed - they've measured the proper motion of M33 and because it and M31, Andromeda, are a bound system they could use the tidal evolution consistent with M33 remaining a spiral to constrain M31's proper motion...

Proper Motion of M31 Constrained

...so its motion is radially +113 km/s (towards us) and 0 +/- 100 km/s RA and 80 +/- 40 Dec. (Galactic co-ords.) Quite a range but sufficient to tell us that the Milky Way and Andromeda will mix their dark haloes in ~ 5 to 10 Gyr and they do form a bound system. Eventually the two will merge in a giant elliptical along with their various satellite galaxies.

Adam