At last Sigma recognized the telltale signs of fear for a loved one and for a moment, he stops struggling. The Doctor searches for some resemblance between the two of them and comes up short.

"I don't know where she is-" he begins honestly, immediately recognizing his mistake. That was not good enough. Now he had to come up with a reason for this man not to kill him, immediately.

"Wait. I am on your side. We're both trapped here. Ellie is a good kid - sweet, likes puns, tendency to experiment with curses, isn't that right?" He tries a small, genuinely sympathetic smile. "Please. I wish no harm on her. I can tell you what is going on and where she might be, but you have to let me go."