Writing for the First Circuit in In re Bulger, Justice Souter's opinion provides a good discussion about recusal. You can view the opinion at THIS link. At issue was the defendant's petition for writ of mandamus seeking an order requiring the district court judge to recuse himself based upon allegations the judge had been invoked in the case (due to his role as an assistant US Attorney). Notably, the defendant was previously on the FBI's Ten Most Wanted list. After an analysis of what recusal is and isn't, and applying that analysis to the facts in this case, the opinion concluded:
In sum, despite our respect for Judge Stearns and our belief in his sincerity, we are nonetheless bound to conclude that it is clear that a reasonable person might question the judge’s ability to preserve impartiality through the course of this prosecution and the likely rulings made necessary by the immunity claim. The other mandamus conditions being satisfied, the petition is granted, and the case shall be reassigned to a judge whose curriculum vitae does not implicate the same level of institutional responsibility described here.