That's very strange! I checked it out and it seems like the barycenter is an invisible white main seq (or copy of the white mian seq in the binary system) and you can even SHIFT + G and go to its surface. and if you look down you see the space gets dimmer which means there is something there, or the engine thinks something is there. I have no idea what is going on other then that.
Good find. I'm sure SpaceEngineer will have some useful input on it.
Do you mean a "star" at the barycenter, that disappears as you get closer to it?
This is a star VBO particle. It's usually clipped by the near clipping plane, located at 0.1 parsecs for such stars. When you approach a star closer than 0.1 parsec, its particle disappears and gets replaced with a 3D model for that system with its own sun particle. But this binary system is very large, so its model gets generated and is seen from a much greater distance, greater than 0.1 parsec. So its VBO particle is rendered simultaneously with the two stars of the 3D model. I should disable this particle when the system is rendered with the model, but this may be a bit expensive - I should update the stars particles VBO. I will try this solution sometime.