the best way to pull this off is with the blend tool.
1. use the star tool to create a star with the number of points you want. if you click and drag and hold... you can use the arrow keys on the keyboard to adjust the number of points the star has. you can also access a dialog box but simply double clicking and empty space on the canvas with the star tool. to keep it from looking uniform i would then edit the path and create some different points. adjust this star color to dark blue and make it as large as the end of the light rays.
2. use the polygon tool and drag out a small shape... that will be the very center of the star. again use the up and down arrows on the keyboard to adjust the number of anchor points that make up the shape. you are roughly trying to get the number of anchor points the same.
3. once you have both shapes. select them and use the alignment panel to center them on each other.
4. make sure to turn off the stroke color for both shapes.
5. click on the blend tool. then click than anchor point of the center shape and then click the outer shape. this will create a blend from the inner color & shape to the outer color & shape.
P.S. if you run into any issues make sure that both shapes are in the same layer.
6. once you have this blend completed. simply make a new layer and make a large box with the same fill color as the outer star... this will hide the transition between the star and the background.