Origins and meaning of -halgh name ending?

I’ve noticed a few surnames recently with -halgh, ie hesmondhalgh, Greenhalgh. What does it mean and what language/where does it originate from?

It seems to be northern English, and from the same origin as “haugh” according to this slightly unsatisfying entry in Google Books.

Thisis better:


A possible origin of Greenhalgh can be found here: