We present a detailed analysis of two fields located 26 kpc ( \sim 5 radial scalelengths ) from the centre of M31 along the south-west semimajor axis of the disc .
One field samples the major axis populations – the Outer Disc field – while the other is offset by \sim 18 \arcmin and samples the warp in the stellar disc – the Warp field .
The color-magnitude diagrams ( CMDs ) based on Hubble Space Telescope Advanced Camera for Surveys imaging reach old main-sequence turn-offs ( \sim 12.5 Gyr ) .
We apply the CMD-fitting technique to the Warp field to reconstruct the star formation history ( SFH ) .
We find that after undergoing roughly constant star formation until about 4.5 Gyr ago , there was a rapid decline in activity and then a \sim 1.5 Gyr lull , followed by a strong burst lasting 1.5 Gyr and responsible for 25 % of the total stellar mass in this field .
This burst appears to be accompanied by a decline in global metallicity which could be a signature of the inflow of metal-poor gas .
The onset of the burst ( \sim 3 Gyr ago ) corresponds to the last close passage of M31 and M33 as predicted by detailed N-body modelling , and may have been triggered by this event .
We reprocess the deep M33 outer disc field data of Barker et al .
( 4 ) in order to compare consistently-derived SFHs .
This reveals a similar duration burst that is exactly coeval with that seen in the M31 Warp field , lending further support to the interaction hypothesis .
We reliably trace star formation as far back as 12-13 Gyr ago in the outer disc of M31 while the onset of star formation occured about 2 Gyr later in M33 , with median stellar ages of 7.5 Gyr and 4.5 Gyr , respectively .
The complex SFHs derived , as well as the smoothly-varying age-metallicity relations , suggest that the stellar populations observed in the far outer discs of both galaxies have largely formed in situ rather than migrated from smaller galactocentric radii .
The strong differential reddening affecting the CMD of the Outer Disc field prevents derivation of the SFH using the same method .
Instead , we quantify this reddening and find that the fine-scale distribution of dust precisely follows that of the H i gas .
This indicates that the outer H i disc of M31 contains a substantial amount of dust and therefore suggests significant metal enrichment in these parts , consistent with inferences from our CMD analysis .