Here's a paper that covers the matter: A deep Chandra observation of the Perseus cluster: shocks and ripples" Fig 5 gives a radius of 163kly. The shock/sound velocity is ~0.005-0.02c.
This discussion the two of you are having is above my pay grade. WAY above my pay grade. But the fact that you’re having this discussion at all has me more encouraged about the future of FR than anything I’ve read here for quite a while. Hope you don’t mind me peeking in the window from time to time just because I enjoy seeing IQ points flying around a room.