mass movement of turks into central anatolia is an unsourced statement from a wiki article so i am not sure if it's worth discussing the article i cited above disputes that if there was a massive wave of newcomers there should be genetic evidence also considering the byzantine empire of the comnens th century covered about half of anatolia i doubt the biggest areal turkish language spread happened from th to th in the anatolian area i don't think critical mass is a meaningful concept here as don ringe put it history shows that comparatively small groups of immigrants can induce their new neighbors to adopt their language gradually over several generations of course if they have enough economic or political power and they can offer some important advantage to those who are willing to adopt their language so it's not just a question of numbers of course there are some speakers someone has to speak the new language first