A little more clarity from me and much thanks...
I probably should have clarified a bit that I was just trying to come close, but thank you so much for the direction you all gave me.
What I ended up doing, I did in Illy.  I took the original graphic and outlined a rough shape of the burst.  I then  put an outer glow effect on that shape and expanded the appearance separating the effect from the object.  I just pasted the resulting object (formally the effect) into the new Illustration and gave it a good helping of opacity.  Not exact, but pretty close.
Thanks again for all the responses.
Ben