When is 的 needed to express "of"?
早晨的太阳为什么是红色的
中午太阳又变白了

中午的太阳又变白了 is a correct sentence. But, if you put that 的, you'd change the parsing:

[中午的太阳][又变白了] vs [中午][太阳又变白了]

The original sentence uses 中午 adverbially, which is for the effect of contrast: Why the sun in the morning is red, while at noon(when it comes to noon) it becomes white.(I'm curious how come).
中午的太阳又变白了 would reduce that effect dramatically.
So, the question here is not about grammar but the way people express their ideas.
P.S. I might think to add a comma after 中午 would probably be a little bit improvement? Maybe, not everyone would agree with that.

早晨的太阳为什么是红色的
中午, 太阳又变白了