Christian Shephard's third and most shocking appearance

Claire wakes up in the middle of the night to find Aaron in the arms of Christian Shephard. She says "dad?" Miles apparently sees Claire leave with Christian, but says nothing due to his "restraining order." This is the first time that Christian has appeared to someone on the island besides Jack, except when Hurley saw him briefly in Jacob's cabin.

The questions are endless. Why did Christian appear? Why did Claire go with him? Why did they leave Aaron behind?