The first thing you should think about is rafter thrust. That's what the 13' tie beam is doing. It's the most critical part of your design. The size of the beam is not as critical as the strenght of the joint where it meets the post. If the beam is bigger, the tenon is bigger, and thus stronger.
But perhaps you should consider modifying your design to change the tension joint into a compression joint. The easiest way to do that is to raise the tie beam so the rafter lands on it, rather than on the post top. CB.
