I'd like to say something like "Then, we have the question: why did this happen?" What is a proper way to say this using the phrase "The question then arises..."? Is it "The question then arises as to why this happened."? If this is correct usage, are there other continuations of this phrase (i.e. "The question then arises") that I could use?
The phrase means "this brings up the question", and sounds fine to a native English speaker. If you Google, the phrase the question then arises is usually used as follows (all of these are from Google results):
You can use the phrase the question then arises in the same way that you would use then we have the question. You could write:
The last example is a bit harder to understand, so I would recommend the first two over the third. You could use "the question then arises" with most questions that happen to arise--there aren't any exceptions which I can think of.
You have two options.
1. Put a colon ":" after the phrase, then state the question:
Sometimes a comma or dash is substituted for the colon; however, if you are a grammar stickler, you will not want to use these:
2. Temporarily move the "now arises" to the end of the sentence, form it that way, and put the "now arises" back in.
(Examples taken from the first page of a google search.)