Well it seems that all she needs from you is your support.
Actually the best you can do is to NOT involve yourself in trying to get that guy arrested. As a third party person who didn't even witness anything, involving yourself may actually complicate things for the police.
I've been through a few things that are similar, and I can tell you that it's important to keep telling your friend you're on her side. Text or email her now and then and just say "hi" and "how are you" without talking about her issues. She'll bring it up if she wants to rant. Saying hi is just a good way to say "I'm free to listen if you want right now." and she'll get the message if she feels she wants to, but she wont be reminded if she isn't worrying about it at the time.
If it's mental abuse, you just need to keep your intimacy with her very open and secure.
It's hard with the distance, but that's why little efforts like that make a good impression.
Maybe send her a little gift, and if she asks why, just say you thought of getting it for her when you saw it. It'll also make her feel cared for without unsettling her about her situation.
Good luck to your friend, hang on too. Being strong means having a lot of support.