Style of inner line of 'circle split' shape

Hi,

I drawing state machines using the 'circle split' shapes (over the 'automata' library) and would
like to modify the style of the inner separation line, i.e. make its line width smaller than the style of the outer circle or sometimes remove it completely.
This line seems to be drawn by the 'beforebackground' code while the circle is drawn by the 'background' code of the shape.

Does anyone know if/how this is possible?

Best Regards,
Martin