Single author papers against my advisor's will? I am a third year PhD student in an area of theoretical CS that would like advice for a difficult situation with my advisor.

My advisor is not involved in my research projects at all. In particular, I have come up with all of my paper ideas, and have executed the papers alone. However, she always insists on adding her name as a co-author. This has started to increasingly bother me, as I work very hard (alone) on my research and believe I should get credit for that. In addition, she is a bully and treats me quite badly, so it makes it even harder for me to benefit her in this way.

For my most recent paper, I brought up how I didn't believe she was meeting the IEEE 1 or ACM 2 guidelines for authorship, and told her that I believed I should be sole author on my paper. She agreed that she shouldn't be an author, although she was visibly angry. She said that I was a "weirdo" for doing this, and said that everybody already knows that advisors take credit for their student's work and that publishing with your advisor is the same as publishing alone. But most importantly, she told me that she would not approve my proposal/dissertation if I did not add her name to several more top-tier papers because then I "have no ties to the university" since I am not working with a professor, and therefore cannot receive my PhD.

Obviously, I need a new advisor. However, there is really no one in my department in my research area. Switching research areas or departments are not options. So the remaining options are the following:

(1) Add her name to several more papers. I do not like this idea because it is unethical, and there is no guarantee that anything is even gained in this option. She could simply refuse to recommend me in the end after I got her a bunch of papers.

(2) Ignore her threats, and force my way to finishing my PhD while publishing single author papers. I do not believe she could stop me from graduating since I already have a decent publication record, and presumably will continue getting my work out. I have a fellowship, so she can't control my funding. Clearly, I will not have a letter of recommendation in this case. On the other hand, I will have a bunch of single author papers.

(3) Try to convince a professor in an unrelated research area to be my advisor, emphasizing that I am independent and can do my work alone. There are a few theory professors in my dept, although they are totally different areas. I have no idea the chance of this working out.

(4) Go to the department chair and tell him the whole story, ask what to do.

What do you think I should do?
As a department chair, I can say you aren't alone. These situations come up all too often.

Please do reach out to your department chair, graduate program director or grad student ombudsperson if your institution has one. We want to know when our faculty are behaving badly and often we can help.