I'm planning on trapping him for eternity if possible.

I'll settle for Harkon as well, but I can't seem to find any info on either of the two regarding their soul.

Edit: Vrythur*

My iPhone saw fit to autocorrect.

In previous games you needed Azura's Star if you wanted to capture the soul of an important named enemy. If this was the case for Vyrthur you'd need to try it out on 2 characters, one who had the White Star, and one who had the Black.

Black, of course.

I think there's a bug in which the Black Star can collect both colors, so I decided to break my moral code and just get the black star. However I have a save file a little ways back I can try out the other as well.

I asked because I know some of the npcs involved in the dlc are unique in comparison to vanilla.

I think there is a very simple rule: if it is one of the nine playable races it is black. Vythur may be a "Snow Elf" on the outside, but in his gut (i.e. the code) he is a high elf.

Edit: Also, I find black soul gems to be a lot easier to find in Skyrim than Oblivion. In Oblivion I had to read the wiki to find out how to turn grand soul gems into black ones. In Skyrim I find quite a few and Falion always has one or two to sell.

I did an experiment and an ordinary Black Soul Gem caught Vyrthur. The Black Star will also catch him, but if you want to lock him away in a chest or something an ordinary gem would be better.

Edit: The experiment I did with Harkon didn't catch any soul. I tried with Azura's Star, an ordinary Black Soul gem and The Black Star. It may be that I would need a longer Soul Trap effect on him, since there is a bit of time before the last time you hit him and when he actually dies.

Thanks. Used the Black Star which will now go on display in the near future. Poor Vrythur.

In Morrowind I have Azura's Star sitting on a shelf with Almalexia trapped for all eternity. It's the only soul gem in the game that can trap her.
Edit: I love how in Morrowind the soul gem has the name of any NPC you trap.

A normal Black Soul Gem should work.
I have caught many a named man and mer NPCs with these, vampires and non vampires.
Generic NPCs of men or mer also work to fill them.

In Oblivion or Skyrim, if it is human or mer, it is a black soul.