I believe it forms a connection between the two phrases but I’m not certain what its called. But if you wish to name it, consider “punctuated connector.”

I think linear asterism is actually a very nice definition; or otherwise asterism, because that’s where it obviously derives from. I don’t think it has an actual definition itself.
Perhaps it’s done in cases where the publisher (well, the printer) didn’t have the actual asterism, or simply didn’t like it. It’s certainly easier to type for most people (especially > 10 years ago think type writers), than looking it up (if they know it all).

The name of the function of that symbol, three asterisks, in poetry, is called a SECTION BREAK.

The name of the symbol, three asterisks, is an ASTERISM.

The asterism is frequently used instead of an INTERPUNCT or FLEURON or DINGBAT, or various other symbols which have been used to denote a SECTION BREAK.

And I think it is quite sad that I know this, but quite wonderful that you asked this question and I have, for the first time since learning this in copyediting class in 1985, used this bit of information.

excellent! Many, many thanks, hossman. Your deeply obscure knowledge is , in this case, a huge help.

No, thank you, as that class cost me hundreds of dollars and a semester of my time, and now, more than 2 decades later, it has finally paid off.

@soethe: what would cause a person to ask such a question, and with such sincerity?

@Trustinglife: I’m doing a PhD in English, and I’m about to write a short essay on the role of silence in a piece of criticism by Susan Sontag. One of the places where silence, um, occurs…if we can talk like that…is at the breaks in her argument, which are made with asterisms. I just wanted to know the actual word for it so that I didn’t have to say “those three asterisks” in the paper. This way I get to sound like a smarty-pants. Of course it’s not really possible to look up something like this in a conventional dictionary, and a Google search didn’t do much better. (I guess I could have looked for a typographical dictionary or copyeditor’s handbook…) And this is why Fluther is so excellent. (N.B. This’ll make me look smarter to the prof, but the essay is ungraded. And grades don’t really matter at this point so…I don’t feel like I’m being academically dishonest.)

I should add that, because I’ll be working professionally with literature and criticism for the rest of my life, it’ll be valuable to know this word for purposes above and beyond this short paper. I say that because, well, having this knowledge on a permanent basis is more the source of my enthusiasm than…just using a fancy word in an essay.

Wow! Well then hooray for asterisms!