  Motivated by recent theoretical work suggesting that a substantial fraction
of Population (Pop) III stars may have had masses low enough for them to
survive to the present day, we consider the role that the accretion of
metal-enriched gas may have had in altering their surface composition, thereby
disguising them as Pop II stars. We demonstrate that if weak, Solar-like winds
are launched from low-mass Pop III stars formed in the progenitors of the dark
matter halo of the Galaxy, then such stars are likely to avoid significant
enrichment via accretion of material from the interstellar medium. We find that
at early times accretion is easily prevented if the stars are ejected from the
central regions of the haloes in which they form, either by dynamical
interactions with more massive Pop III stars, or by violent relaxation during
halo mergers. While accretion may still take place during passage through
sufficiently dense molecular clouds at later times, we find that the
probability of such a passage is generally low (< 0.1), assuming that stars
have velocities of order the maximum circular velocity of their host haloes and
accounting for the orbital decay of merging haloes. In turn, due to the higher
gas density required for accretion onto stars with higher velocities, we find
an even lower probability of accretion (~ 0.01) for the subset of Pop III stars
formed at z > 10, which are more quickly incorporated into massive haloes than
stars formed at lower redshift. While there is no a priori reason to assume
that low-mass Pop III stars do not have Solar-like winds, without them surface
enrichment via accretion is likely to be inevitable. We briefly discuss the
implications that our results hold for stellar archaeology.
