On the other hand, the relative contamination by MW stars in the MCs samples is more difficult to assess. We have to rely on the SH distance-based classification as an external comparison, with the caveat that this classification contains its own classification errors. These results point out to a possible contamination by MW stars in our samples around some tens of percentage.
However, we can do an additional check using the line-of-sight velocities in Gaia DR3, which are available only for a (small) subset of the total sample. These line-of-sight velocities are not used by any of our classification criteria and have different mean values for the MW and LMC/SMC (therefore providing an independent check).
In Fig. 4, we plot the histograms of line-of-sight velocities separately for stars classified as MW and LMC/SMC, and it is clear from these that the contamination of the MCs sample is reduced, likely to be significantly below the levels suggested above. We estimate the MW contamination to be around 5% (10%) if we take into account the LMC (SMC) NN complete sample and roughly separate the MW stars with a cut at 𝑉𝑙𝑜𝑠 < 125 (75) km s⁻¹. Also, this check is not entirely representative since only stars at the bright end of the sample (𝐺 ≲ 16) are included in the subset of Gaia DR3 stars having observed line-of-sight velocities.