hawk vs hunt down

hawk is a noun but hunt down is not a noun.

Word	Noun	Adjective	Verb	Adverb
hawk	Yes	No	Yes	No
hunt down	No	No	Yes	No

As verbs, hunt down is a hypernym of hawk; that is, hunt down is a word with a broader meaning than hawk:

Other hypernyms of hawk include hunt, run, track down.

hawk (noun)	hunt down (noun)
diurnal bird of prey typically having short rounded wings and a long tail
a square board with a handle underneath; used by masons to hold or carry mortar
an advocate of an aggressive policy on foreign relations

hawk (verb)	hunt down (verb)
clear mucus or food from one's throat	pursue for food or sport (as of wild animals)
hunt with hawks
sell or offer for sale from place to place